Wikiversity enwikiversity https://en.wikiversity.org/wiki/Wikiversity:Main_Page MediaWiki 1.45.0-wmf.8 first-letter Media Special Talk User User talk Wikiversity Wikiversity talk File File talk MediaWiki MediaWiki talk Template Template talk Help Help talk Category Category talk School School talk Portal Portal talk Topic Topic talk Collection Collection talk Draft Draft talk TimedText TimedText talk Module Module talk 0 32804 2720364 2651432 2025-07-01T19:38:41Z 41.116.47.117 By wikpedia 2720364 wikitext text/x-wiki {{mathematics}} Hello, and welcome to [[Wikiversity:Introduction|Wikiversity]]'s online [[W:Geometry|geometry]] course! ==Course Description== A course in plane and solid geometry will investigate the basic concepts of [[W:Euclidean geometry|Euclidean geometry]]. Undefined terms and axioms will be presented and used to prove conjectures. The properties of two- and three-dimensional shapes will be explored. Students will also work with coordinate geometry, including transformations. The goal of this course is not only to master the facts of geometry necessary for advanced courses but also the techniques of deductive mathematical proofs as well. ==Curriculum== One lesson should be learned every weekday.</br> [[Geometry/Chapter 1|Chapter 1 ~ Essentials of Geometry]]</br> [[Geometry/Chapter 2|Chapter 2 ~ Reasoning and Proof]]</br> [[Geometry/Chapter 3|Chapter 3 ~ Parallel and Perpendicular Lines]]</br> [[Geometry/Chapter 4|Chapter 4 ~ Triangles]]</br> [[Geometry/Chapter 5|Chapter 5 ~ Similarity]]</br> [[Geometry/Chapter 6|Chapter 6 ~ Trigonometry]]</br> [[Geometry/Chapter 7|Chapter 7 ~ Quadrilaterals]]</br> [[Geometry/Chapter 8|Chapter 8 ~ Properties of Circles]]</br> [[Geometry/Chapter 9|Chapter 9 ~ Measuring Length and Area]]</br> [[Geometry/Chapter 10|Chapter 10 ~ Surface Area and Volume of Solids]]</br> [[Geometry/Chapter 11|Chapter 11 ~ Final Exam]]</br> <!-- ==Lessons== *[[Points, lines, and planes|Lesson one: Points, lines, and planes]] *[[Angles|Lesson two: Angles]] *[[Proof|Lesson three: Proof]] *[[Perpendicular and parallel lines|Lesson four: Perpendicular and parallel lines]] *[[Triangles and their congruency postulates|Lesson five: Triangles and their congruency postulates]]--> ==Homework assignments== Homework will be assigned after most class sessions at the bottom of the page. Homework will be emailed the day after you complete your assignment. Homework will be graded for completeness and correctness. A student can receive up to 3 points for a question. Two points will be awarded for attempting to solve a problem. A third of the assigned problems will be graded for correctness, with an additional point given for the correct answer. No credit will be given for problems not solved. Therefore, every problem should be attempted. As we are more interested in learning methods of solving problems than in answers, all work involved in solving a problem must be shown for credit to be received. ==Tests, quizzes, and exams== ===Tests=== Tests are given after every chapter and must be completed within 45 minutes. Tests are out of 100 points. To be granted access to the test. All homeworks must be handed in on time. Except for 2, if you wish ===Exams=== An exam is given half-way through the program and at the end. Exams are given 60 minutes to complete. Exams will be given after you complete half, and then all the tests. == Bibliography == * [https://open.umn.edu/opentextbooks/textbooks/elementary-college-geometry Open Textbook Library: Elementary College Geometry] ==See also== * [[Portal:Mathematics]] [[Category:Geometry| ]] [[Category:Mathematics courses]] hmp10obrwtmnsb99ro70jjr1cggpwu1 2720372 2720364 2025-07-01T22:09:51Z Atcovi 276019 Reverted edits by [[Special:Contributions/41.116.47.117|41.116.47.117]] ([[User_talk:41.116.47.117|talk]]) to last version by [[User:MathXplore|MathXplore]] using [[Wikiversity:Rollback|rollback]] 2623056 wikitext text/x-wiki {{mathematics}} Hello, and welcome to [[Wikiversity:Introduction|Wikiversity]]'s online [[W:Geometry|geometry]] course! ==Course Description== A course in plane and solid geometry will investigate the basic concepts of [[W:Euclidean geometry|Euclidean geometry]]. Undefined terms and axioms will be presented and used to prove conjectures. The properties of two- and three-dimensional shapes will be explored. Students will also work with coordinate geometry, including transformations. The goal of this course is not only to master the facts of geometry necessary for advanced courses but also the techniques of deductive mathematical proofs as well. ==Curriculum== One lesson should be learned every weekday.</br> [[Geometry/Chapter 1|Chapter 1 ~ Essentials of Geometry]]</br> [[Geometry/Chapter 2|Chapter 2 ~ Reasoning and Proof]]</br> [[Geometry/Chapter 3|Chapter 3 ~ Parallel and Perpendicular Lines]]</br> [[Geometry/Chapter 4|Chapter 4 ~ Triangles]]</br> [[Geometry/Chapter 5|Chapter 5 ~ Similarity]]</br> [[Geometry/Chapter 6|Chapter 6 ~ Trigonometry]]</br> [[Geometry/Chapter 7|Chapter 7 ~ Quadrilaterals]]</br> [[Geometry/Chapter 8|Chapter 8 ~ Properties of Circles]]</br> [[Geometry/Chapter 9|Chapter 9 ~ Measuring Length and Area]]</br> [[Geometry/Chapter 10|Chapter 10 ~ Surface Area and Volume of Solids]]</br> [[Geometry/Chapter 11|Chapter 11 ~ Final Exam]]</br> <!-- ==Lessons== *[[Points, lines, and planes|Lesson one: Points, lines, and planes]] *[[Angles|Lesson two: Angles]] *[[Proof|Lesson three: Proof]] *[[Perpendicular and parallel lines|Lesson four: Perpendicular and parallel lines]] *[[Triangles and their congruency postulates|Lesson five: Triangles and their congruency postulates]]--> ==Homework assignments== Homework will be assigned after most class sessions at the bottom of the page. Homework will be emailed the day after you complete your assignment. Homework will be graded for completeness and correctness. A student can receive up to 3 points for a question. Two points will be awarded for attempting to solve a problem. A third of the assigned problems will be graded for correctness, with an additional point given for the correct answer. No credit will be given for problems not solved. Therefore, every problem should be attempted. As we are more interested in learning methods of solving problems than in answers, all work involved in solving a problem must be shown for credit to be received. ==Tests, quizzes, and exams== ===Tests=== Tests are given after every chapter and must be completed within 45 minutes. Tests are out of 100 points. To be granted access to the test. All homeworks must be handed in on time. Except for 2, if you wish ===Quizzes=== One quiz may be given a chapter, depending on the difficulty. Quizzes are given 15 minutes to complete. Half the homework, minus 2 of them, must be handed in to access the quiz. ===Exams=== An exam is given half-way through the program and at the end. Exams are given 60 minutes to complete. Exams will be given after you complete half, and then all the tests. == Bibliography == * [https://open.umn.edu/opentextbooks/textbooks/elementary-college-geometry Open Textbook Library: Elementary College Geometry] ==See also== * [[Portal:Mathematics]] [[Category:Geometry| ]] [[Category:Mathematics courses]] 2llgaa0vn21onkgsu45xxaehlmxsj52 0 60198 2720296 2717906 2025-07-01T13:37:07Z Juma JK 3003132 /* Tutorials for Children and Adults */ 2720296 wikitext text/x-wiki {{:{{BASEPAGENAME}}/Sidebar}} Typing is the process of writing or inputting text by pressing keys on a typewriter, keyboard, cell phone, or a calculator. It can be distinguished from other means of text input, such as handwriting and speech recognition.<ref>[[Wikipedia: Typing]]</ref> Learners should practice typing for fifteen minutes each day until their typing speed is at least 30 words per minute. == Multimedia == * [https://www.youtube.com/watch?v=6-_5SfmTq4A YouTube: Learn To Type: Get To Know Your Keyboard] (~7 minutes) * [https://www.youtube.com/watch?v=_gT-QKhT9Hk Youtube: Type Faster: Best NEW Typing Game Site of 2025] * [https://www.youtube.com/watch?v=n5ZpQpJhz5A How To Teach Yourself To Touch Type - Kidztype] == Tutorials for Children == * [https://www.dancemattypingguide.com/ Dance Mat Typing] == Tutorials for Children and Adults == * [http://www.typing.com/ Typing.com: Learn to Type] *[https://agilefingers.com/ AgileFingers] * [http://play.typeracer.com/ TypeRacer] * [http://www.freetypinggame.net/free-typing-test.asp FreeTypingGame.net] * [http://typingtest.com TypingTest.com] * [http://www.ratatype.com/ Ratatype] * [http://www.typeonline.co.uk/ Type Online] * [https://www.nitrotype.com Nitro Type Competitive Typing] * [https://www.funtotype.com FunToType Typing Games] * [https://www.typerush.com TypeRush Worldwide Typing Racing Game] * [https://typingbird.com/ TypingBird Typing Games] * [https://www.kidztype.com/browse-typing-games.html KidzType Typing Games] * [https://typingspeedtest.app/ Typing Speed Test] * [Https://boosttyping.com Typing Durations Test] == Tutorials for Adults == * [http://www.gcflearnfree.org/typing GCFLearnFree.org: Typing Tutorial] * [http://www.gcflearnfree.org/techsavvy/1 GCFLearnFree.org: Keyboard Shortcuts] * [http://digitallearn.org/learn/getting-started-computer/keyboard DigitalLearn.org: Getting Started on the Computer - the Keyboard] * [http://www.typingstudy.com Typing Study] - Free online touch typing lessons, speed tests, typing games * [http://www.sense-lang.org/typing/tutor/index.php?lang=EN Sense Lang] - Online touch typing lessons *[https://wpmtest.org Wpm Test] - Word Per Minute Test == See Also == * [[Elementary Typing]] * [[Introduction_to_Computers/Input_Devices | Input Devices]] * [[Wikipedia: Typing]] == References == {{reflist}} {{subpage navbar}} {{CourseCat}} [[Category:Computer Skills]] [[Category:Typing]] [[Category:Completed resources]] cjjuzhavnq6z00q3h3oyve4jn18sdrs 0 62817 2720382 2366869 2025-07-02T04:35:30Z SAMLSE 3002247 SS 2720382 wikitext text/x-wiki Salem ==Welcome== Please make sure you have reviewed the page ''[[Wikiversity:What is Wikiversity?|What is Wikiversity?]]'' before you participate and contribute to this project. ==What are ethics?== Ethics are moral standards of conduct agreed upon to define right and wrong. That which is ethical is considered morally correct. That which is unethical is considered morally wrong. Ethics are usually considered in a professional code of conduct as a qualified professional is under more expection than an unqualified individual to have a learned understanding of the accepted principles of right and wrong. == Learning ethics in online media == {{Disclosures}} Principles of [[ethics]] in online media is the scope for this resource; however, this resource draws upon comparisons that center on the English Wikipedia, which has over a quarter-million biographies of living persons (BLPs) as well as many articles that characterize people, organizations, events, and other aspects of human activity. The degree to which the content and practices of Wikimedia projects adhere to commonly recognized principles of ethics, which include such comparisons of Wikipedia, are what this resource examines. Temporary guideline: This project currently does not accept case studies of living people until further notice. ==List of subpages== *'''All subpages''': [[special:prefixindex/{{FULLPAGENAME}}/]] *'''All talk subpages''': [[special:prefixindex/{{TALKPAGENAME}}/]] *'''All recently edited pages''': [[/Dynamic page list/]] ==Resource Management== *[[/Audio/]] **[[/Audio/Transcripts/]] *[[/Brainstorming/]] *[[/Participants and objectives/]] *[[/Project Timetable/]] *[[User:Privatemusings/EthicsSandbox]] - a personal sandbox space in which all are welcome to try and help energise this project. ==Learning resources== [[Image:Thomas Nagel teaching Ethics.JPG|thumb|right|250px|[[:w:Thomas Nagel|Thomas Nagel]] teaching an undergraduate course in ethics at New York University]] *[[/Introduction/]] *[[/Overview/]] *[[/Change BLP policy/]] *[[/Ethical Code for Wikipedians/]] *[[/Ethics on Wikipedia and the Internet/]] *[[/The fundamentals of ethics|Fundamentals of ethics]] *[[/List of questions/]] *[[/Response Testing on WMF projects/]] *[[/Social contract/]] *[[/Paid editing and Wikipedia Zero/]] *[[/Suggested essays/]] ==How to improve this resource== [[Image:CarrKemmisReflectiveSpiral.jpg|thumb|350px|right|Diagram from learning resource on [[Action research]]]] #Identify principles for objective evaluation #Evaluate Wikimedia systems #Identify what needs to be learned by the community #Create or update collaborative research pages and workshops ==See also== * [[How to be a Wikimedia sysop]] * [[Portal:Wikimedia Studies|Wikimedia Studies Portal]] * [[Wikipedia#Learning resources|Wikipedia learning resources]] * [[Wikiversity:Editing Applied ethics]] ==External links== * [http://wikidashboard.parc.com/wiki/Main_Page Wikidashboard]⁣ – facilitates analysis of relative contributors to Wikipedia articles by specific authors [[Category:Ethical Management of the English Language Wikipedia| ]] [[Category:Wikimedia Ethics]] [[Category:Wikimedia research]] l2hr2ici10ivek1rq7w1ermp1oay0ud 0 85954 2720393 2720179 2025-07-02T09:09:42Z Jtneill 10242 Update for 2025 2720393 wikitext text/x-wiki <div align="center"> {| style="width:50%; border-width: 0 0 50px 0;" |- | style="width:15%; padding: 0 0 10px 0;" | [[File:Start.svg|68px|link=Motivation and emotion/About/Welcome and getting started]] | style="width:30%; padding: 0 0 10px 0;" | [[/About|About]] | [[/About/Welcome and getting started|Start]] | style="width:10%; padding: 0 0 10px 0;" | | style="width:15%; padding: 0 0 10px 0;" | [[File:WikiProject Brazil assessment icon.svg|68px|link=Motivation and emotion/Assessment]] | style="width:30%; padding: 0 0 10px 0;" | [[/Assessment|Assessment]] |- | style="padding: 0 0 10px 0;" | [[File:Ic info outline 48px.svg|68px|link=Motivation and emotion/About/Outline]] | style="padding: 0 0 10px 0;" | [[/About/Outline|Unit outline]] | | style="padding: 0 0 10px 0;" | [[File:Emoji u1f989.svg|68px|link=Motivation and emotion/About/Outline/About/Staff]] | style="padding: 0 0 10px 0;" | [[/About/Staff|Teaching team]] |- | style="padding: 0 0 10px 0;" | [[File:Ic assignment 48px.svg|68px|link=Motivation and emotion/About/Schedule]] | style="padding: 0 0 10px 0;" | [[/About/Schedule|Schedule]] | | style="padding: 0 0 10px 0;" | [[File:Ic alarm 48px.svg|68px|link=Motivation and emotion/About/Timetable]] | style="padding: 0 0 10px 0;" | [[Motivation and emotion/About/Timetable|Timetable]] |- | style="padding: 0 0 10px 0;" | [[File:Lecture icon.png|68px|link=Motivation and emotion/Lectures]] | style="padding: 0 0 10px 0;" | [[/Lectures|Lectures]] | | style="padding: 0 0 10px 0;" | [[File:Discussion icon.png|68px|link=Motivation and emotion/Tutorials]] | style="padding: 0 0 10px 0;" | [[/Tutorials|Tutorials]] |- | style="padding: 0 0 20px 0;" | [[File:Uc-logo.png|68px|link=https://unicanberra.instructure.com/courses/15707]] | style="padding: 0 0 20px 0;" | {{Motivation and emotion/Canvas}} | | style="padding: 0 0 20px 0;" | [[File:File:Helpicon.svg |68px|link=Motivation and emotion/Help]] | style="padding: 0 0 20px 0;" | {{Motivation and emotion/Hashtag}} |- | style="padding: 0 0 20px 0;" | [[File:Book stub img.svg|68px|link=Motivation and emotion/Book/2025]] | style="padding: 0 0 20px 0;" | [[/Book|Book]] -<br>[[/Book/2025|2025]] | | colspan="2" style="padding: 0 0 20px 0;" | <div style="float:left; width:13em"> <inputbox> type=search width=19 namespaces=Main** prefix=Motivation and emotion searchbuttonlabel=Search break=no bgcolor=transparent </inputbox></div> |} <!-- Stand-alone search bar at bottom {| style="width:50%; |- | style="width:85%;" | <inputbox> type=search width=25 namespaces=Main** prefix=Motivation and emotion searchbuttonlabel=Search break=no bgcolor=transparent </inputbox> | style="width:15%;" | |} <noinclude> --> <!-- Old navigation (pre-2022) {|style="width:100%;" |- |style="width:30%;"| {{Motivation and emotion/Hashtag}} |style="width:40%;"| [[File:Motivation & Emotion.png|center|240px]] |style="width:30%;"| <p align="right">{{Motivation and emotion/Canvas}}</p> |} {{collapse box|[[/About/Welcome and getting started|Start]] - [[/About|About]] - [[/About/Support|Support]]|{{/About/Getting started}} - {{/About/Support}}}} {{collapse box|[[/About/Schedule|Schedule]] - [[/Lectures|Lectures]] - [[/Tutorials|Tutorials]]|{{/About/Schedule}}}} {{collapse box|[[/Assessment|Assessment]] - [[Motivation and emotion/Assessment/Topic|Topic]] - [[Motivation and emotion/Assessment/Chapter|Chapter]] - [[Motivation and emotion/Assessment/Multimedia|Multimedia]] - [[Motivation and emotion/Assessment/Quizzes|Quizzes]]|{{/Assessment}}}} {{collapse box|[[/Book|Book]] - [[/Book/2023|2023]]|{{:Motivation and emotion/Book/2023/Banner}}}}<noinclude>{{/Image}}{{center top}} --> {{center bottom}} [[Category:{{PAGENAME}}| ]] [[Category:Featured resources]] </noinclude> 41ucginfijg24y2shio9vzi47ls9gvy 2720394 2720393 2025-07-02T09:10:16Z Jtneill 10242 2720394 wikitext text/x-wiki <div align="center"> {| style="width:50%; border-width: 0 0 50px 0;" |- | style="width:15%; padding: 0 0 10px 0;" | [[File:Start.svg|68px|link=Motivation and emotion/About/Welcome and getting started]] | style="width:30%; padding: 0 0 10px 0;" | [[/About|About]] | [[/About/Welcome and getting started|Start]] | style="width:10%; padding: 0 0 10px 0;" | | style="width:15%; padding: 0 0 10px 0;" | [[File:WikiProject Brazil assessment icon.svg|68px|link=Motivation and emotion/Assessment]] | style="width:30%; padding: 0 0 10px 0;" | [[/Assessment|Assessment]] |- | style="padding: 0 0 10px 0;" | [[File:Ic info outline 48px.svg|68px|link=Motivation and emotion/About/Outline]] | style="padding: 0 0 10px 0;" | [[/About/Outline|Unit outline]] | | style="padding: 0 0 10px 0;" | [[File:Emoji u1f989.svg|68px|link=Motivation and emotion/About/Outline/About/Staff]] | style="padding: 0 0 10px 0;" | [[/About/Staff|Teaching team]] |- | style="padding: 0 0 10px 0;" | [[File:Ic assignment 48px.svg|68px|link=Motivation and emotion/About/Schedule]] | style="padding: 0 0 10px 0;" | [[/About/Schedule|Schedule]] | | style="padding: 0 0 10px 0;" | [[File:Ic alarm 48px.svg|68px|link=Motivation and emotion/About/Timetable]] | style="padding: 0 0 10px 0;" | [[Motivation and emotion/About/Timetable|Timetable]] |- | style="padding: 0 0 10px 0;" | [[File:Lecture icon.png|68px|link=Motivation and emotion/Lectures]] | style="padding: 0 0 10px 0;" | [[/Lectures|Lectures]] | | style="padding: 0 0 10px 0;" | [[File:Discussion icon.png|68px|link=Motivation and emotion/Tutorials]] | style="padding: 0 0 10px 0;" | [[/Tutorials|Tutorials]] |- | style="padding: 0 0 20px 0;" | [[File:Uc-logo.png|68px|link=https://unicanberra.instructure.com/courses/15707]] | style="padding: 0 0 20px 0;" | {{Motivation and emotion/Canvas}} | | style="padding: 0 0 20px 0;" | [[File:Helpicon.svg |68px|link=Motivation and emotion/Help]] | style="padding: 0 0 20px 0;" | {{Motivation and emotion/Hashtag}} |- | style="padding: 0 0 20px 0;" | [[File:Book stub img.svg|68px|link=Motivation and emotion/Book/2025]] | style="padding: 0 0 20px 0;" | [[/Book|Book]] -<br>[[/Book/2025|2025]] | | colspan="2" style="padding: 0 0 20px 0;" | <div style="float:left; width:13em"> <inputbox> type=search width=19 namespaces=Main** prefix=Motivation and emotion searchbuttonlabel=Search break=no bgcolor=transparent </inputbox></div> |} <!-- Stand-alone search bar at bottom {| style="width:50%; |- | style="width:85%;" | <inputbox> type=search width=25 namespaces=Main** prefix=Motivation and emotion searchbuttonlabel=Search break=no bgcolor=transparent </inputbox> | style="width:15%;" | |} <noinclude> --> <!-- Old navigation (pre-2022) {|style="width:100%;" |- |style="width:30%;"| {{Motivation and emotion/Hashtag}} |style="width:40%;"| [[File:Motivation & Emotion.png|center|240px]] |style="width:30%;"| <p align="right">{{Motivation and emotion/Canvas}}</p> |} {{collapse box|[[/About/Welcome and getting started|Start]] - [[/About|About]] - [[/About/Support|Support]]|{{/About/Getting started}} - {{/About/Support}}}} {{collapse box|[[/About/Schedule|Schedule]] - [[/Lectures|Lectures]] - [[/Tutorials|Tutorials]]|{{/About/Schedule}}}} {{collapse box|[[/Assessment|Assessment]] - [[Motivation and emotion/Assessment/Topic|Topic]] - [[Motivation and emotion/Assessment/Chapter|Chapter]] - [[Motivation and emotion/Assessment/Multimedia|Multimedia]] - [[Motivation and emotion/Assessment/Quizzes|Quizzes]]|{{/Assessment}}}} {{collapse box|[[/Book|Book]] - [[/Book/2023|2023]]|{{:Motivation and emotion/Book/2023/Banner}}}}<noinclude>{{/Image}}{{center top}} --> {{center bottom}} [[Category:{{PAGENAME}}| ]] [[Category:Featured resources]] </noinclude> po3w13sq1ei8tbwyatmuaed8t76d0ab 2720395 2720394 2025-07-02T09:11:42Z Jtneill 10242 2720395 wikitext text/x-wiki <div align="center"> {| style="width:50%; border-width: 0 0 50px 0;" |- | style="width:15%; padding: 0 0 10px 0;" | [[File:Start.svg|68px|link=Motivation and emotion/About/Welcome and getting started]] | style="width:30%; padding: 0 0 10px 0;" | [[/About|About]] | [[/About/Welcome and getting started|Start]] | style="width:10%; padding: 0 0 10px 0;" | | style="width:15%; padding: 0 0 10px 0;" | [[File:WikiProject Brazil assessment icon.svg|68px|link=Motivation and emotion/Assessment]] | style="width:30%; padding: 0 0 10px 0;" | [[/Assessment|Assessment]] |- | style="padding: 0 0 10px 0;" | [[File:Ic info outline 48px.svg|68px|link=Motivation and emotion/About/Outline]] | style="padding: 0 0 10px 0;" | [[/About/Outline|Unit outline]] | | style="padding: 0 0 10px 0;" | [[File:Emoji u1f989.svg|68px|link=Motivation and emotion/About/Outline/About/Staff]] | style="padding: 0 0 10px 0;" | [[/About/Staff|Teaching team]] |- | style="padding: 0 0 10px 0;" | [[File:Ic assignment 48px.svg|68px|link=Motivation and emotion/About/Schedule]] | style="padding: 0 0 10px 0;" | [[/About/Schedule|Schedule]] | | style="padding: 0 0 10px 0;" | [[File:Ic alarm 48px.svg|68px|link=Motivation and emotion/About/Timetable]] | style="padding: 0 0 10px 0;" | [[Motivation and emotion/About/Timetable|Timetable]] |- | style="padding: 0 0 10px 0;" | [[File:Lecture icon.png|68px|link=Motivation and emotion/Lectures]] | style="padding: 0 0 10px 0;" | [[/Lectures|Lectures]] | | style="padding: 0 0 10px 0;" | [[File:Discussion icon.png|68px|link=Motivation and emotion/Tutorials]] | style="padding: 0 0 10px 0;" | [[/Tutorials|Tutorials]] |- | style="padding: 0 0 20px 0;" | [[File:Uc-logo.png|68px|link=https://unicanberra.instructure.com/courses/15707]] | style="padding: 0 0 20px 0;" | {{Motivation and emotion/Canvas}} | | style="padding: 0 0 20px 0;" | [[File:Helpicon.svg|68px|link=Motivation and emotion/About/Help]] | style="padding: 0 0 20px 0;" | [[/About/Help|Help]] |- | style="padding: 0 0 20px 0;" | [[File:Book stub img.svg|68px|link=Motivation and emotion/Book/2025]] | style="padding: 0 0 20px 0;" | [[/Book|Book]] -<br>[[/Book/2025|2025]] | | colspan="2" style="padding: 0 0 20px 0;" | <div style="float:left; width:13em"> <inputbox> type=search width=19 namespaces=Main** prefix=Motivation and emotion searchbuttonlabel=Search break=no bgcolor=transparent </inputbox></div> |} <!-- Stand-alone search bar at bottom {| style="width:50%; |- | style="width:85%;" | <inputbox> type=search width=25 namespaces=Main** prefix=Motivation and emotion searchbuttonlabel=Search break=no bgcolor=transparent </inputbox> | style="width:15%;" | |} <noinclude> --> <!-- Old navigation (pre-2022) {|style="width:100%;" |- |style="width:30%;"| {{Motivation and emotion/Hashtag}} |style="width:40%;"| [[File:Motivation & Emotion.png|center|240px]] |style="width:30%;"| <p align="right">{{Motivation and emotion/Canvas}}</p> |} {{collapse box|[[/About/Welcome and getting started|Start]] - [[/About|About]] - [[/About/Support|Support]]|{{/About/Getting started}} - {{/About/Support}}}} {{collapse box|[[/About/Schedule|Schedule]] - [[/Lectures|Lectures]] - [[/Tutorials|Tutorials]]|{{/About/Schedule}}}} {{collapse box|[[/Assessment|Assessment]] - [[Motivation and emotion/Assessment/Topic|Topic]] - [[Motivation and emotion/Assessment/Chapter|Chapter]] - [[Motivation and emotion/Assessment/Multimedia|Multimedia]] - [[Motivation and emotion/Assessment/Quizzes|Quizzes]]|{{/Assessment}}}} {{collapse box|[[/Book|Book]] - [[/Book/2023|2023]]|{{:Motivation and emotion/Book/2023/Banner}}}}<noinclude>{{/Image}}{{center top}} --> {{center bottom}} [[Category:{{PAGENAME}}| ]] [[Category:Featured resources]] </noinclude> 7jhjem7pdxckr6vqxcxlebylon9skaq 0 97537 2720398 2570722 2025-07-02T09:30:48Z Jtneill 10242 Update for 2025 2720398 wikitext text/x-wiki <noinclude>{{title|Help}}</noinclude> {| style = "width:50%; margin:auto" |- | [[File:Helpicon.svg|left|115px]] | Reach out and join in: * [[Motivation and emotion/About/Discussion|Discussion]] * [[Motivation and emotion/Drop-in|Drop-in]] * [[Motivation and emotion/About/Staff|Teaching team]] * [[Motivation and emotion/Wikiversity|Wikiversity editing]] | [[File:We Can Do It! NARA 535413 - Restoration 2.jpg|right|115px]] |} <noinclude> [[Category:{{BASEPAGENAME}}]]</noinclude> esmxzzewwx0uyi77zyy9whpcsa2n33w 0 97551 2720396 2636020 2025-07-02T09:20:38Z Jtneill 10242 2720396 wikitext text/x-wiki {{RoundBoxTop|theme=2}} The electronic communication channels for this unit are via the {{Motivation and emotion/Canvas}} site:<br><br>{{center top}}<big><big><big>'''[https://uclearn.canberra.edu.au/courses/17386/announcements Announcements]'''</big></big></big>,<br>general info and updates about the unit<br><br><big><big><big>'''[https://uclearn.canberra.edu.au/courses/17386/discussion_topics Discussion]'''</big></big></big>,<br>ask questions, get feedback, share ideas etc.<br><br><big><big><big>'''[[Motivation and emotion/Drop-in|Drop-in]]'''</big></big></big><br>to get hands-on assistance<!-- <br><br>In addition, use the:<br>{{center top}}<big><big><big>'''{{Motivation and emotion/Hashtag}}'''</big></big></big>,<br>hashtag on Twitter{{center bottom}} --><br><br><big><big><big>'''[[Help:Talk page|Wikiversity talk pages]]'''</big></big></big>,<br>every page has its own discussion<br><br><big><big><big>'''[[Motivation and emotion/About/Staff|Teaching team]]'''</big></big></big><br>reach out and get in touch{{center bottom}} {{RoundBoxBottom}}<noinclude> [[Image:Nuvola apps edu languages.png|center|100px]] [[Category:{{BASEPAGENAME}}]]</noinclude> pe2if3789hml9ffqrwmn7bvyhqmdxkq 2720397 2720396 2025-07-02T09:21:36Z Jtneill 10242 2720397 wikitext text/x-wiki {{RoundBoxTop|theme=2}} The electronic communication channels for this unit are:<br><br>{{center top}}<big><big><big>'''[https://uclearn.canberra.edu.au/courses/17386/announcements Announcements]'''</big></big></big>,<br>general info and updates about the unit<br><br><big><big><big>'''[https://uclearn.canberra.edu.au/courses/17386/discussion_topics Discussion]'''</big></big></big>,<br>ask questions, get feedback, share ideas etc.<br><br><big><big><big>'''[[Motivation and emotion/Drop-in|Drop-in]]'''</big></big></big><br>to get hands-on assistance<!-- <br><br>In addition, use the:<br>{{center top}}<big><big><big>'''{{Motivation and emotion/Hashtag}}'''</big></big></big>,<br>hashtag on Twitter{{center bottom}} --><br><br><big><big><big>'''[[Help:Talk page|Wikiversity talk pages]]'''</big></big></big>,<br>every page has its own discussion<br><br><big><big><big>'''[[Motivation and emotion/About/Staff|Teaching team]]'''</big></big></big><br>reach out and get in touch{{center bottom}} {{RoundBoxBottom}}<noinclude> [[Image:Nuvola apps edu languages.png|center|100px]] [[Category:{{BASEPAGENAME}}]]</noinclude> bb48gsyl3upv0y02z4886as7tlmb7lr 0 114988 2720407 2719448 2025-07-02T10:07:00Z 85.8.130.69 2720407 wikitext text/x-wiki Psychopathy has a polygenic basis, with six [[genes]] having been shown particular significance regarding the risk: ANKK1, [[DRD2]], DRD4, [[COMT]], MAOA, and SLC6A4 (particularly the 5-HTTLPR variant). Other notable genetic risk factors for becoming a psychopath include [[alleles]] of OXTR, AVPR1A, CADM2, PRKG1, and NR3C1. Several of these genes, like COMT, MAOA, 5-HTTLPR, OXTR, and NR3C1, undergo direct epigenetic modification following trauma. Psychopathy is principally a personality construct used by psychologists to explain and predict behavior, but may also be described as an epigenetic condition that affects the trajectory of neurodevelopment. The expression of psychopathy-related phenotypes depends on the combination of inherited alleles, in addition to environmental factors. Individuals are at an elevated risk of psychopathic traits if they inherit multiple core alleles located at different [[loci]], likely at least four core alleles at a minimum of three different loci. This is similar to many other spectrum disorders, such as schizotypy, which typically involve a complex interaction between genes and environmental factors. <div align="center"> <table class="MsoTableGrid" border="1" cellspacing="0" cellpadding="0" style="border-collapse:collapse;border:none"> <tr> <td colspan="7" valign="top" style="border:none;border-bottom:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" align="center" style="margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal"><b><span style="font-size:14.0pt">Genes linked to psychopathy</span></b></p> </td> </tr> <tr> <td colspan="5" valign="top" style="border:solid windowtext 1.0pt;border-top: none;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" align="center" style="margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal"><b><span style="font-size:12.0pt">Loci</span></b></p> </td> <td colspan="2" valign="top" style="border-top:none;border-left:none;border-bottom: solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" align="center" style="margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal"><b><span style="font-size:12.0pt">Characteristics</span></b></p> </td> </tr> <tr> <td valign="top" style="border:solid windowtext 1.0pt;border-top:none; padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" align="center" style="margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal"><b>ANKK1</b></p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" align="center" style="margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal"><b>DRD2</b></p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" align="center" style="margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal"><b>MAOA</b></p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" align="center" style="margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal"><b>COMT</b></p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" align="center" style="margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal"><b>5-HTTLPR</b></p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" align="center" style="margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal"><b>[[Basal endophenotype]]</b></p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" align="center" style="margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal"><b>Also associated with</b></p> </td> </tr> <tr> <td valign="top" style="border:solid windowtext 1.0pt;border-top:none; padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">[[Taq1 A2 allele]] </p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">[[957T allele]] </p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">calm</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> </tr> <tr> <td valign="top" style="border:solid windowtext 1.0pt;border-top:none; padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">[[Taq1 A1 allele]] </p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">[[957C allele]]</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">anxious</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">posttraumatic stress disorder</p> </td> </tr> <tr> <td valign="top" style="border:solid windowtext 1.0pt;border-top:none; padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">[[957C/C genotype]]<span class="MsoEndnoteReference"> </span></p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">impulsive</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">schizophrenia</p> </td> </tr> <tr> <td valign="top" style="border:solid windowtext 1.0pt;border-top:none; padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">Taq1 A1 allele</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">957C/C genotype</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">dissocial</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">dissocial personality disorder</p> </td> </tr> <tr> <td valign="top" style="border:solid windowtext 1.0pt;border-top:none; padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">low activity</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal"></p> </td> </tr> <tr> <td valign="top" style="border:solid windowtext 1.0pt;border-top:none; padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">low activity</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal"></p> </td> </tr> <tr> <td valign="top" style="border:solid windowtext 1.0pt;border-top:none; padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">long</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal"></p> </td> </tr> <tr> <td valign="top" style="border:solid windowtext 1.0pt;border-top:none; padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">Taq1 A1 allele </p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">957C/C genotype</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">low activity</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">dissocial</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">antisocial personality disorder</p> </td> </tr> <tr> <td valign="top" style="border:solid windowtext 1.0pt;border-top:none; padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">Taq1 A1 allele</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">957C/C genotype</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">low activity</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">dissocial</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">borderline personality disorder</p> </td> </tr> <tr> <td valign="top" style="border:solid windowtext 1.0pt;border-top:none; padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">Taq1 A1 allele</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">957C/C genotype</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">long</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">dissocial</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">narcissistic personality disorder</p> </td> </tr> <tr> <td valign="top" style="border:solid windowtext 1.0pt;border-top:none; padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">Taq1 A1 allele</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">957C/C genotype</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">low activity</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">low activity</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">dissocial</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">sadistic personality disorder</p> </td> </tr> <tr> <td valign="top" style="border:solid windowtext 1.0pt;border-top:none; padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">Taq1 A1 allele</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">957C/C genotype</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">low activity</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">long</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">dissocial</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">histrionic personality disorder</p> </td> </tr> <tr> <td valign="top" style="border:solid windowtext 1.0pt;border-top:none; padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">Taq1 A1 allele</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">957C/C genotype</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">low activity</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">long</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">dissocial</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">Munchausen by proxy </p> </td> </tr> <tr> <td valign="top" style="border:solid windowtext 1.0pt;border-top:none; padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">Taq1 A1 allele</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">957T allele</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">low activity</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">long</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">anxious</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">Munchausen syndrome</p> </td> </tr> </table> </div> == DRD2 == In addition to the DRD2 957C/C genotype, the DRD2 Taq1 B allele and polymorphisms in the promoter region of the DRD4 gene have also have been linked to psychopathy. This suggests that the dissocial and impulsive basal endophenotypes can be subdivided into at least seven subtypes: 1a, 1b, 1c, 2, 3a, 3b, and 3c. <div align=center><table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0 style='border-collapse:collapse;border:none'> <tr> <td width=851 colspan=4 valign=top style='width:638.4pt;border:none; border-bottom:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal'><span style='font-size:16.0pt'>Impulsive/dissocial subtypes</span></p> </td> </tr> <tr> <td width=426 colspan=2 valign=top style='width:319.2pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal'><span style='font-size:14.0pt'>DRD2</span></p> </td> <td width=213 valign=top style='width:159.6pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal'><span style='font-size:14.0pt'>DRD4</span></p> </td> <td width=213 rowspan=2 style='width:159.6pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal'><span style='font-size:14.0pt'>Subtype</span></p> </td> </tr> <tr> <td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top: none;padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal'><b><span style='font-size:12.0pt'>957 [[locus]]</span></b></p> </td> <td width=213 valign=top style='width:159.6pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal'><b><span style='font-size:12.0pt'>Taq1 B locus</span></b></p> </td> <td width=213 style='width:159.6pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal'><b>-616 locus</b></p> </td> </tr> <tr> <td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top: none;padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>C/C genotype</p> </td> <td width=213 valign=top style='width:159.6pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>B1 allele-negative</p> </td> <td width=213 style='width:159.6pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>-616G allele</p> </td> <td width=213 valign=top style='width:159.6pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal'>1a</p> </td> </tr> <tr> <td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top: none;padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>T allele</p> </td> <td width=213 valign=top style='width:159.6pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>B1 allele-positive</p> </td> <td width=213 style='width:159.6pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>-616G allele</p> </td> <td width=213 valign=top style='width:159.6pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal'>1b</p> </td> </tr> <tr> <td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top: none;padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>C/C genotype</p> </td> <td width=213 valign=top style='width:159.6pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>B1 allele-positive</p> </td> <td width=213 style='width:159.6pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>-616G allele</p> </td> <td width=213 valign=top style='width:159.6pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal'>1c</p> </td> </tr> <tr> <td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top: none;padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>T allele</p> </td> <td width=213 valign=top style='width:159.6pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>B1 allele-negative</p> </td> <td width=213 style='width:159.6pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>-616C/C genotype</p> </td> <td width=213 valign=top style='width:159.6pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal'>2</p> </td> </tr> <tr> <td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top: none;padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>C/C genotype</p> </td> <td width=213 valign=top style='width:159.6pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>B1 allele-negative</p> </td> <td width=213 style='width:159.6pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>-616C/C genotype</p> </td> <td width=213 valign=top style='width:159.6pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal'>3a</p> </td> </tr> <tr> <td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top: none;padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>T allele</p> </td> <td width=213 valign=top style='width:159.6pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>B1 allele-positive</p> </td> <td width=213 style='width:159.6pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>-616C/C genotype</p> </td> <td width=213 valign=top style='width:159.6pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal'>3b</p> </td> </tr> <tr> <td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top: none;padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>C/C genotype</p> </td> <td width=213 valign=top style='width:159.6pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>B1 allele-positive</p> </td> <td width=213 style='width:159.6pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>-616C/C genotype</p> </td> <td width=213 valign=top style='width:159.6pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'> 3c</p> </td> </tr> </table> </div> ==Further reading== [http://www.ncbi.nlm.nih.gov/pubmed/16632165] [http://www.ncbi.nlm.nih.gov/pubmed/18833581] [http://www.ncbi.nlm.nih.gov/pubmed/17087792] [http://bjp.rcpsych.org/cgi/content/full/193/2/121] [http://www.genepassport.ru/publications/public/DRD2%20and%20ANKK1%20genotype%20in%20alcohol-dependent.pdf] [http://www.ncbi.nlm.nih.gov/pubmed/14643564] [http://onlinelibrary.wiley.com/doi/10.1111/j.1601-183X.2009.00543.x/full] [http://www.biomedcentral.com/content/pdf/1744-9081-6-4.pdf] sc81h73qngsg3cizjv5u2j2e5blf8uk 2720408 2720407 2025-07-02T11:16:53Z 85.8.130.63 Usually epigenetic 2720408 wikitext text/x-wiki Psychopathy has a polygenic basis, with six [[genes]] having been shown particular significance regarding the risk: ANKK1, [[DRD2]], DRD4, [[COMT]], MAOA, and SLC6A4 (particularly the 5-HTTLPR variant). Other notable genetic risk factors for becoming a psychopath include [[alleles]] of OXTR, AVPR1A, CADM2, PRKG1, and NR3C1. Several of these genes, like COMT, MAOA, 5-HTTLPR, OXTR, and NR3C1, undergo direct epigenetic modification following trauma. Psychopathy is principally a personality construct used by psychologists to explain and predict behavior, but may also be described as a condition that affects the trajectory of neurodevelopment. The expression of psychopathy-related phenotypes depends on the combination of inherited alleles, in addition to environmental factors. Individuals are at an elevated risk of psychopathic traits if they inherit multiple core alleles located at different [[loci]], likely at least four core alleles at a minimum of three different loci. This is similar to many other spectrum disorders, such as schizotypy, which typically involve a complex interaction between genes and environmental factors. <div align="center"> <table class="MsoTableGrid" border="1" cellspacing="0" cellpadding="0" style="border-collapse:collapse;border:none"> <tr> <td colspan="7" valign="top" style="border:none;border-bottom:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" align="center" style="margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal"><b><span style="font-size:14.0pt">Genes linked to psychopathy</span></b></p> </td> </tr> <tr> <td colspan="5" valign="top" style="border:solid windowtext 1.0pt;border-top: none;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" align="center" style="margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal"><b><span style="font-size:12.0pt">Loci</span></b></p> </td> <td colspan="2" valign="top" style="border-top:none;border-left:none;border-bottom: solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" align="center" style="margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal"><b><span style="font-size:12.0pt">Characteristics</span></b></p> </td> </tr> <tr> <td valign="top" style="border:solid windowtext 1.0pt;border-top:none; padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" align="center" style="margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal"><b>ANKK1</b></p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" align="center" style="margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal"><b>DRD2</b></p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" align="center" style="margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal"><b>MAOA</b></p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" align="center" style="margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal"><b>COMT</b></p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" align="center" style="margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal"><b>5-HTTLPR</b></p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" align="center" style="margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal"><b>[[Basal endophenotype]]</b></p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" align="center" style="margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal"><b>Also associated with</b></p> </td> </tr> <tr> <td valign="top" style="border:solid windowtext 1.0pt;border-top:none; padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">[[Taq1 A2 allele]] </p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">[[957T allele]] </p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">calm</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> </tr> <tr> <td valign="top" style="border:solid windowtext 1.0pt;border-top:none; padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">[[Taq1 A1 allele]] </p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">[[957C allele]]</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">anxious</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">posttraumatic stress disorder</p> </td> </tr> <tr> <td valign="top" style="border:solid windowtext 1.0pt;border-top:none; padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">[[957C/C genotype]]<span class="MsoEndnoteReference"> </span></p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">impulsive</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">schizophrenia</p> </td> </tr> <tr> <td valign="top" style="border:solid windowtext 1.0pt;border-top:none; padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">Taq1 A1 allele</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">957C/C genotype</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">dissocial</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">dissocial personality disorder</p> </td> </tr> <tr> <td valign="top" style="border:solid windowtext 1.0pt;border-top:none; padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">low activity</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal"></p> </td> </tr> <tr> <td valign="top" style="border:solid windowtext 1.0pt;border-top:none; padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">low activity</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal"></p> </td> </tr> <tr> <td valign="top" style="border:solid windowtext 1.0pt;border-top:none; padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">long</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal"></p> </td> </tr> <tr> <td valign="top" style="border:solid windowtext 1.0pt;border-top:none; padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">Taq1 A1 allele </p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">957C/C genotype</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">low activity</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">dissocial</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">antisocial personality disorder</p> </td> </tr> <tr> <td valign="top" style="border:solid windowtext 1.0pt;border-top:none; padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">Taq1 A1 allele</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">957C/C genotype</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">low activity</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">dissocial</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">borderline personality disorder</p> </td> </tr> <tr> <td valign="top" style="border:solid windowtext 1.0pt;border-top:none; padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">Taq1 A1 allele</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">957C/C genotype</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">long</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">dissocial</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">narcissistic personality disorder</p> </td> </tr> <tr> <td valign="top" style="border:solid windowtext 1.0pt;border-top:none; padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">Taq1 A1 allele</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">957C/C genotype</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">low activity</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">low activity</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">dissocial</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">sadistic personality disorder</p> </td> </tr> <tr> <td valign="top" style="border:solid windowtext 1.0pt;border-top:none; padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">Taq1 A1 allele</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">957C/C genotype</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">low activity</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">long</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">dissocial</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">histrionic personality disorder</p> </td> </tr> <tr> <td valign="top" style="border:solid windowtext 1.0pt;border-top:none; padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">Taq1 A1 allele</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">957C/C genotype</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">low activity</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">long</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">dissocial</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">Munchausen by proxy </p> </td> </tr> <tr> <td valign="top" style="border:solid windowtext 1.0pt;border-top:none; padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">Taq1 A1 allele</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">957T allele</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">&nbsp;</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">low activity</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">long</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">anxious</p> </td> <td valign="top" style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt; border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal">Munchausen syndrome</p> </td> </tr> </table> </div> == DRD2 == In addition to the DRD2 957C/C genotype, the DRD2 Taq1 B allele and polymorphisms in the promoter region of the DRD4 gene have also have been linked to psychopathy. This suggests that the dissocial and impulsive basal endophenotypes can be subdivided into at least seven subtypes: 1a, 1b, 1c, 2, 3a, 3b, and 3c. <div align=center><table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0 style='border-collapse:collapse;border:none'> <tr> <td width=851 colspan=4 valign=top style='width:638.4pt;border:none; border-bottom:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal'><span style='font-size:16.0pt'>Impulsive/dissocial subtypes</span></p> </td> </tr> <tr> <td width=426 colspan=2 valign=top style='width:319.2pt;border:solid windowtext 1.0pt; border-top:none;padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal'><span style='font-size:14.0pt'>DRD2</span></p> </td> <td width=213 valign=top style='width:159.6pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal'><span style='font-size:14.0pt'>DRD4</span></p> </td> <td width=213 rowspan=2 style='width:159.6pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal'><span style='font-size:14.0pt'>Subtype</span></p> </td> </tr> <tr> <td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top: none;padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal'><b><span style='font-size:12.0pt'>957 [[locus]]</span></b></p> </td> <td width=213 valign=top style='width:159.6pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal'><b><span style='font-size:12.0pt'>Taq1 B locus</span></b></p> </td> <td width=213 style='width:159.6pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal'><b>-616 locus</b></p> </td> </tr> <tr> <td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top: none;padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>C/C genotype</p> </td> <td width=213 valign=top style='width:159.6pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>B1 allele-negative</p> </td> <td width=213 style='width:159.6pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>-616G allele</p> </td> <td width=213 valign=top style='width:159.6pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal'>1a</p> </td> </tr> <tr> <td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top: none;padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>T allele</p> </td> <td width=213 valign=top style='width:159.6pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>B1 allele-positive</p> </td> <td width=213 style='width:159.6pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>-616G allele</p> </td> <td width=213 valign=top style='width:159.6pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal'>1b</p> </td> </tr> <tr> <td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top: none;padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>C/C genotype</p> </td> <td width=213 valign=top style='width:159.6pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>B1 allele-positive</p> </td> <td width=213 style='width:159.6pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>-616G allele</p> </td> <td width=213 valign=top style='width:159.6pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal'>1c</p> </td> </tr> <tr> <td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top: none;padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>T allele</p> </td> <td width=213 valign=top style='width:159.6pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>B1 allele-negative</p> </td> <td width=213 style='width:159.6pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>-616C/C genotype</p> </td> <td width=213 valign=top style='width:159.6pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal'>2</p> </td> </tr> <tr> <td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top: none;padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>C/C genotype</p> </td> <td width=213 valign=top style='width:159.6pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>B1 allele-negative</p> </td> <td width=213 style='width:159.6pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>-616C/C genotype</p> </td> <td width=213 valign=top style='width:159.6pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal'>3a</p> </td> </tr> <tr> <td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top: none;padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>T allele</p> </td> <td width=213 valign=top style='width:159.6pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>B1 allele-positive</p> </td> <td width=213 style='width:159.6pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>-616C/C genotype</p> </td> <td width=213 valign=top style='width:159.6pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt; text-align:center;line-height:normal'>3b</p> </td> </tr> <tr> <td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top: none;padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>C/C genotype</p> </td> <td width=213 valign=top style='width:159.6pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>B1 allele-positive</p> </td> <td width=213 style='width:159.6pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'>-616C/C genotype</p> </td> <td width=213 valign=top style='width:159.6pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal'> 3c</p> </td> </tr> </table> </div> ==Further reading== [http://www.ncbi.nlm.nih.gov/pubmed/16632165] [http://www.ncbi.nlm.nih.gov/pubmed/18833581] [http://www.ncbi.nlm.nih.gov/pubmed/17087792] [http://bjp.rcpsych.org/cgi/content/full/193/2/121] [http://www.genepassport.ru/publications/public/DRD2%20and%20ANKK1%20genotype%20in%20alcohol-dependent.pdf] [http://www.ncbi.nlm.nih.gov/pubmed/14643564] [http://onlinelibrary.wiley.com/doi/10.1111/j.1601-183X.2009.00543.x/full] [http://www.biomedcentral.com/content/pdf/1744-9081-6-4.pdf] a0j7u03jodz2hbjpx4hf38ggxgm2sen 0 116433 2720392 2627026 2025-07-02T07:52:42Z Pereira987 3004306 add a link to online mean calculator 2720392 wikitext text/x-wiki {{Mathematics}} {{Statistics}} Given any collection of real numbers, an '''average''' is a single number intended to give an estimate of the general magnitude of the numbers. Formally, it is a function from a set of ''n'' numbers to a single number with the following properties: # If all the numbers are equal, their average should also equal this value: AV(x, x, x, ...) = x. # The average must not exceed the maximum of the numbers nor be less than their minimum. We may wish to be stricter and say that if not all the numbers are equal, it must be greater than the minimum and less than the maximum, but this would rule out the ''median'' as an average, since the median of say (1,1,1,1,2) is 1. # The average must be multiplicatively linear, i.e. if all numbers are multiplied by the same constant ''k'' their average will be multiplied by the same number: AV(kx, ky) = k.AV(x, y). # The average must be order invariant; if we permute the numbers, it will not change their average: AV(y, x) = AV(x, y). This rules out just picking the first number, or the average of the first and last, or other weighted averages. # The average must be monotonic; if any one number increases (the others being unchanged), the average must not decrease, and vice versa. This rules out some "robust measures", where outliers are rejected before the average is taken. We may wish to be stricter and say that if any number increases, so must the average. Again, this would rule out the median as an average, since the median of say (1,1,1,1,2) and (1,1,1,2,2) are both 1. It might be supposed that the average should be translation invariant, so that if all numbers are increased by the same constant ''k'' their average will increase by the same number: AV(x+k,y+k) = AV(x,y)+k. However, it can be shown that there is only one average meeting this and the other requirements strictly: the arithmetic mean discussed below. If the less strict versions of the requirements are used, the median and other quartiles would meet all the requirements. It might also be supposed that the average should be a continuous function of the numbers. Again, this would rule out quartiles. == The arithmetic mean == The simplest average is the ''arithmetic mean'', defined as the sum of the numbers divided by the number of numbers. Thus the average of {1,2,3,4,5) is (1+2+3+4+5)/5 = 3. ''Exercise:'' Verify that this meets all the conditions above, including the stricter versions. == The geometric mean == Another common average is the ''geometric mean'', obtained by multiplying all the numbers together and, if there are ''n'' numbers, taking the ''nth'' root. Thus the geometric mean of {1,2,3,4,5) is (1x2x3x4x5)^1/5 = 2.605 (approximately). Note that the geometric mean should not be used if any of the numbers is negative (why?) and is zero if any of the numbers is zero, no matter how large the other numbers are (why?). ''Exercise:'' Verify that the geometric mean meets all the conditions above, including the stricter versions. == The arithmetic/geometric inequality == Unless all the numbers are equal, the geometric mean is always less than the arithmetic mean. This is easily proved for just two numbers and three numbers; the outlines of the proof are: If ''a'' and ''b'' are two unequal non-negative numbers, then :<math>\displaystyle(\sqrt a-\sqrt b)^2 > 0</math> This can be rearranged as :<math>\displaystyle \frac{a+b}{2} > \sqrt(a \times b)</math> If ''a'', ''b'' and ''c'' are three non-negative numbers, not all equal, then :<math>\displaystyle (a^{1/3} - b^{1/3})^2 + (b^{1/3} - c^{1/3})^2 + (c^{1/3} - a^{1/3})^2 > 0</math> So :<math>\displaystyle [(a^{1/3} - b^{1/3})^2 + (b^{1/3} - c^{1/3})^2 + (c^{1/3} - a^{1/3})^2] \times [a^{1/3} + b^{1/3} + c^{1/3}] > 0</math> This can be rearranged as :<math>\displaystyle \frac{a+b+c}{3} > (a \times b \times c)^{1/3}</math> For four numbers, take the numbers in pairs and apply the already proven result for two numbers. == Quantifying the arithmetic/geometric inequality == How can we assess whether the geometric mean is close to the arithmetic mean, or substantially less? Given a set of n numbers {x₁ ... x_n}, let their arithmetic mean be m and :<math>\displaystyle y_i = \frac{x_i}{m}-1</math> so <math>\displaystyle x_i = m(1+y_i).</math> Then the sum of the y_i is zero. (Why?) We assume that the x_i do not diverge too much from their mean, so the y_i are fairly small numbers and we can expand log (1+y) in a power series. :<math>\displaystyle \frac{GM}{AM} = {{\prod m(1+y_i)}^{1/n} \over m} = {\prod (1+y_i)}^{1/n}.</math> :<math>\displaystyle \log \left( \frac{GM}{AM} \right) = \frac{1}{n} \sum log(1+y_i) \approx \frac{1}{n} \sum (y_i - \frac{1}{2} y_i^2) = - \frac{1}{2} \frac{1}{n}y_i^2</math> (since &Sigma; y_i is zero). Thus :<math>\displaystyle \frac{GM}{AM} \approx 1 - \frac{1}{2} \frac{1}{n}y_i^2.</math> (Why?) In other words, the greater the dispersion of the numbers about their arithmetic mean, the greater the difference between the two means. ''Exercise:'' Some approximations have been made in deriving this result. Demonstrate by actual calculations that the result is true in general. == Root mean square == The '''RMS''' is the square root of the arithmetic mean of the squares of a collection of numbers, i.e. :<math>\displaystyle RMS(x_1 ... x_n) = \sqrt { \frac{1}{n} \Sigma x_i^2 } </math> This average should not be used for a mixture of positive and negative numbers (why?). ''Exercise:'' Verify that this meets all the conditions above, including the stricter versions. Unless all the numbers are equal, the RMS is always greater than the arithmetic mean. This is easily proved for just two numbers by considering the square of the RMS and of the arithmetic mean: :<math>\displaystyle \frac{x^2+y^2}{2} - \left ( \frac{x+y}{2} \right )^2 = \frac{1}{4} (2x^2+2y^2-x^2-2xy-y^2) = \frac{1}{4} (x^2+y^2-2xy) = \frac{1}{4} (x-y)^2 > 0</math> A similar but more complex proof will work for any number of numbers. With a slight extension of the proof, it may be shown that if ''m'' is the arithmetic mean and ''s''² is the variance of a set of numbers, then <math>RMS = \sqrt (m^2 + s^2).</math> == Harmonic mean == The '''harmonic mean''' of a set of numbers is the reciprocal of the arithmetic mean of the reciprocals of those numbers. Thus for three numbers we have :<math>\displaystyle harmonic \,\, mean(x,y,z) = \frac{3}{\frac{1}{x}+\frac{1}{y}+\frac{1}{z}}</math> This mean should not be used if any number is zero or negative (why?). ''Exercise:'' Verify that this meets all the conditions above, including the stricter versions. Unless all the numbers are equal, the harmonic is always less than the geometric mean. This follows because its reciprocal is the arithmetic mean of the reciprocals of the numbers, hence is greater than the geometric mean of the reciprocals which is the reciprocal of the geometric mean. Thus we have: : harmonic mean < geometric mean < arithmetic mean < RMS. == Rth power mean == The '''rth power mean''' of a set of numbers, for any real number r, is :<math>\displaystyle mean(x_1 ... x_n) = \left ( \frac{1}{n} \Sigma x_i^r \right )^\frac{1}{r} </math> This average should only be used for positive numbers if r < 0 and non-negative numbers if r > 0 (why?). ''Exercise:'' Verify that this meets all the conditions above, including the stricter versions. This mean is undefined for r = 0, but the limit as r tends to 0 is the geometric mean. Thus all of the averages we have considered so far are special cases of this mean (r = -1, harmonic; r = 0, geometric; r = 1, arithmetic; r = 2, RMS). It can be shown that for any collection of positive numbers (not all equal), this mean is a continuous, strictly monotonic increasing function of r; the inequalities above are special cases of this. As r tends to infinity, the mean tends to the maximum of the x_i, and as r tends to minus infinity, the mean tends to the minimum of the x_i. == Power plus 1 mean == The '''power plus 1 mean''' of a set of numbers, for any real number s, is :<math>\displaystyle mean(x_1 ... x_n) = \frac{\Sigma x_i^{s+1}}{\Sigma x_i^s}</math> If s=0, this is the arithmetic mean; if s=-1 it is the harmonic mean. Note in particular that if s=1, this is RMS²/(arithmetic mean). If ''m'' is the arithmetic mean and ''s''² is the variance of a set of numbers, than the s=1 mean is :<math>{{m^2+s^2} \over m} = m(1+\frac{s^2}{m^2}) > m</math> It can be shown that this type of mean behaves much like the rth power mean. For any collection of positive numbers (not all equal), this mean is a continuous, strictly monotonic increasing function of s. As s tends to infinity, the mean tends to the maximum of the x_i, and as s tends to minus infinity, the mean tends to the minimum of the x_i. Both of these types of mean can be regarded as a special case of the following: :<math>\displaystyle mean(x_1 ... x_n) = \left( \frac{\Sigma x_i^{s+r}}{\Sigma x_i^s} \right)^{1/r}</math> Clearly, if s=0 this is the forth power mean; if r=1 this is the power plus 1 mean. == Mixed averages == More types of average can be found by mixing different averages, provided that the formula is symmetric in the variables. For example, for any three numbers x, y, z, the following are all averages: :<math>\frac{1}{3}(\sqrt(xy) + \sqrt(yz) + \sqrt(zx))</math> :<math>\sqrt ( \frac{1}{3}(xy + yz + zx) )</math> :<math>\frac{1}{2}((x+y)(y+z)(z+x))^{1/3}</math> == The median and other quartiles As noted above, the median is an average if we do not require some strict inequalities in the definition. In fact, this is true of any quartile of the distribution, even maximum and minimum. It may seem perverse to call the maximum and minimum "averages". However, the fundamental purpose of an average is to give an estimate of the order of magnitude of a group of numbers. If the range of numbers is small, the maximum and minimum can do this; if the range is very large, any one number as the average may be misleading. As noted above, the maximum and minimum are limiting values of other averages as parameters tend to infinity. == It may be argued that any quartile other than the median is "biased" hence unsatisfactory. However, if in a group of numbers a few of them are much larger or much smaller than the others ("outliers"), any average may seem biased. For example, consider {1,2,3,4,5,6,7,8,144}. The arithmetic mean is 20, far higher than the ''upper quartile'' of 7 and indeed far higher than all but one of the numbers. == The mode == The mode is not an average. Firstly, it is not always uniquely defined; for example, in {1,1,1,2,2,3,3,3} there are two modes, 1 and 3 (which are also the minimum and maximum). Secondly and more important, it does not satisfy the monotonicity rule. Consider the set of eight numbers :{1,1,1,2,2,2,2,3} The mode is 2. Now suppose the seventh number increases from 2 to 3: :{1,1,1,2,2,2,3,3} The joint modes are now 1 and 2. Now suppose the sixth number increases from 2 to 4: :{1,1,1,2,2,3,3,4} The mode is now 1. == Transformation means == Let f(x) be any strictly monotonic function. Given a set of numbers {x₁ ... x_n}, define: # y_i = f(x_i) # Y as the arithmetic mean of the y_i # X as the solution of the equation Y = f(X). X is then the ''transformation mean'' of the x_i with respect to f(x). ''Examples:'' f(x) = x^r gives the rth power mean; f(x) = log(x) gives the geometric mean. ''Exercises'' # Will such a mean always obey the conditions at the beginning of the article? # Would using a different sort of mean at step 2, e.g. the geometric mean, give yet another sort of average? # Why does the equation in step 3 always have one and only one solution? Does it matter if f(x) is not continuous? # Find a function f(x) such that the transformation mean equals the median. == See also == * [[Mean]] *[[w:Averages|Wikipedia:Averages]] *[https://MeanCalculator.com MeanCalculator.com] n20omjbg6370fpb7yi4q7q3abs0yzdf 2720410 2720392 2025-07-02T11:38:09Z MathXplore 2888076 Reverted edits by [[Special:Contributions/Pereira987|Pereira987]] ([[User_talk:Pereira987|talk]]) to last version by [[User:192.107.137.144|192.107.137.144]] using [[Wikiversity:Rollback|rollback]] 2627026 wikitext text/x-wiki {{Mathematics}} {{Statistics}} Given any collection of real numbers, an '''average''' is a single number intended to give an estimate of the general magnitude of the numbers. Formally, it is a function from a set of ''n'' numbers to a single number with the following properties: # If all the numbers are equal, their average should also equal this value: AV(x, x, x, ...) = x. # The average must not exceed the maximum of the numbers nor be less than their minimum. We may wish to be stricter and say that if not all the numbers are equal, it must be greater than the minimum and less than the maximum, but this would rule out the ''median'' as an average, since the median of say (1,1,1,1,2) is 1. # The average must be multiplicatively linear, i.e. if all numbers are multiplied by the same constant ''k'' their average will be multiplied by the same number: AV(kx, ky) = k.AV(x, y). # The average must be order invariant; if we permute the numbers, it will not change their average: AV(y, x) = AV(x, y). This rules out just picking the first number, or the average of the first and last, or other weighted averages. # The average must be monotonic; if any one number increases (the others being unchanged), the average must not decrease, and vice versa. This rules out some "robust measures", where outliers are rejected before the average is taken. We may wish to be stricter and say that if any number increases, so must the average. Again, this would rule out the median as an average, since the median of say (1,1,1,1,2) and (1,1,1,2,2) are both 1. It might be supposed that the average should be translation invariant, so that if all numbers are increased by the same constant ''k'' their average will increase by the same number: AV(x+k,y+k) = AV(x,y)+k. However, it can be shown that there is only one average meeting this and the other requirements strictly: the arithmetic mean discussed below. If the less strict versions of the requirements are used, the median and other quartiles would meet all the requirements. It might also be supposed that the average should be a continuous function of the numbers. Again, this would rule out quartiles. == The arithmetic mean == The simplest average is the ''arithmetic mean'', defined as the sum of the numbers divided by the number of numbers. Thus the average of {1,2,3,4,5) is (1+2+3+4+5)/5 = 3. ''Exercise:'' Verify that this meets all the conditions above, including the stricter versions. == The geometric mean == Another common average is the ''geometric mean'', obtained by multiplying all the numbers together and, if there are ''n'' numbers, taking the ''nth'' root. Thus the geometric mean of {1,2,3,4,5) is (1x2x3x4x5)^1/5 = 2.605 (approximately). Note that the geometric mean should not be used if any of the numbers is negative (why?) and is zero if any of the numbers is zero, no matter how large the other numbers are (why?). ''Exercise:'' Verify that the geometric mean meets all the conditions above, including the stricter versions. == The arithmetic/geometric inequality == Unless all the numbers are equal, the geometric mean is always less than the arithmetic mean. This is easily proved for just two numbers and three numbers; the outlines of the proof are: If ''a'' and ''b'' are two unequal non-negative numbers, then :<math>\displaystyle(\sqrt a-\sqrt b)^2 > 0</math> This can be rearranged as :<math>\displaystyle \frac{a+b}{2} > \sqrt(a \times b)</math> If ''a'', ''b'' and ''c'' are three non-negative numbers, not all equal, then :<math>\displaystyle (a^{1/3} - b^{1/3})^2 + (b^{1/3} - c^{1/3})^2 + (c^{1/3} - a^{1/3})^2 > 0</math> So :<math>\displaystyle [(a^{1/3} - b^{1/3})^2 + (b^{1/3} - c^{1/3})^2 + (c^{1/3} - a^{1/3})^2] \times [a^{1/3} + b^{1/3} + c^{1/3}] > 0</math> This can be rearranged as :<math>\displaystyle \frac{a+b+c}{3} > (a \times b \times c)^{1/3}</math> For four numbers, take the numbers in pairs and apply the already proven result for two numbers. == Quantifying the arithmetic/geometric inequality == How can we assess whether the geometric mean is close to the arithmetic mean, or substantially less? Given a set of n numbers {x₁ ... x_n}, let their arithmetic mean be m and :<math>\displaystyle y_i = \frac{x_i}{m}-1</math> so <math>\displaystyle x_i = m(1+y_i).</math> Then the sum of the y_i is zero. (Why?) We assume that the x_i do not diverge too much from their mean, so the y_i are fairly small numbers and we can expand log (1+y) in a power series. :<math>\displaystyle \frac{GM}{AM} = {{\prod m(1+y_i)}^{1/n} \over m} = {\prod (1+y_i)}^{1/n}.</math> :<math>\displaystyle \log \left( \frac{GM}{AM} \right) = \frac{1}{n} \sum log(1+y_i) \approx \frac{1}{n} \sum (y_i - \frac{1}{2} y_i^2) = - \frac{1}{2} \frac{1}{n}y_i^2</math> (since &Sigma; y_i is zero). Thus :<math>\displaystyle \frac{GM}{AM} \approx 1 - \frac{1}{2} \frac{1}{n}y_i^2.</math> (Why?) In other words, the greater the dispersion of the numbers about their arithmetic mean, the greater the difference between the two means. ''Exercise:'' Some approximations have been made in deriving this result. Demonstrate by actual calculations that the result is true in general. == Root mean square == The '''RMS''' is the square root of the arithmetic mean of the squares of a collection of numbers, i.e. :<math>\displaystyle RMS(x_1 ... x_n) = \sqrt { \frac{1}{n} \Sigma x_i^2 } </math> This average should not be used for a mixture of positive and negative numbers (why?). ''Exercise:'' Verify that this meets all the conditions above, including the stricter versions. Unless all the numbers are equal, the RMS is always greater than the arithmetic mean. This is easily proved for just two numbers by considering the square of the RMS and of the arithmetic mean: :<math>\displaystyle \frac{x^2+y^2}{2} - \left ( \frac{x+y}{2} \right )^2 = \frac{1}{4} (2x^2+2y^2-x^2-2xy-y^2) = \frac{1}{4} (x^2+y^2-2xy) = \frac{1}{4} (x-y)^2 > 0</math> A similar but more complex proof will work for any number of numbers. With a slight extension of the proof, it may be shown that if ''m'' is the arithmetic mean and ''s''² is the variance of a set of numbers, then <math>RMS = \sqrt (m^2 + s^2).</math> == Harmonic mean == The '''harmonic mean''' of a set of numbers is the reciprocal of the arithmetic mean of the reciprocals of those numbers. Thus for three numbers we have :<math>\displaystyle harmonic \,\, mean(x,y,z) = \frac{3}{\frac{1}{x}+\frac{1}{y}+\frac{1}{z}}</math> This mean should not be used if any number is zero or negative (why?). ''Exercise:'' Verify that this meets all the conditions above, including the stricter versions. Unless all the numbers are equal, the harmonic is always less than the geometric mean. This follows because its reciprocal is the arithmetic mean of the reciprocals of the numbers, hence is greater than the geometric mean of the reciprocals which is the reciprocal of the geometric mean. Thus we have: : harmonic mean < geometric mean < arithmetic mean < RMS. == Rth power mean == The '''rth power mean''' of a set of numbers, for any real number r, is :<math>\displaystyle mean(x_1 ... x_n) = \left ( \frac{1}{n} \Sigma x_i^r \right )^\frac{1}{r} </math> This average should only be used for positive numbers if r < 0 and non-negative numbers if r > 0 (why?). ''Exercise:'' Verify that this meets all the conditions above, including the stricter versions. This mean is undefined for r = 0, but the limit as r tends to 0 is the geometric mean. Thus all of the averages we have considered so far are special cases of this mean (r = -1, harmonic; r = 0, geometric; r = 1, arithmetic; r = 2, RMS). It can be shown that for any collection of positive numbers (not all equal), this mean is a continuous, strictly monotonic increasing function of r; the inequalities above are special cases of this. As r tends to infinity, the mean tends to the maximum of the x_i, and as r tends to minus infinity, the mean tends to the minimum of the x_i. == Power plus 1 mean == The '''power plus 1 mean''' of a set of numbers, for any real number s, is :<math>\displaystyle mean(x_1 ... x_n) = \frac{\Sigma x_i^{s+1}}{\Sigma x_i^s}</math> If s=0, this is the arithmetic mean; if s=-1 it is the harmonic mean. Note in particular that if s=1, this is RMS²/(arithmetic mean). If ''m'' is the arithmetic mean and ''s''² is the variance of a set of numbers, than the s=1 mean is :<math>{{m^2+s^2} \over m} = m(1+\frac{s^2}{m^2}) > m</math> It can be shown that this type of mean behaves much like the rth power mean. For any collection of positive numbers (not all equal), this mean is a continuous, strictly monotonic increasing function of s. As s tends to infinity, the mean tends to the maximum of the x_i, and as s tends to minus infinity, the mean tends to the minimum of the x_i. Both of these types of mean can be regarded as a special case of the following: :<math>\displaystyle mean(x_1 ... x_n) = \left( \frac{\Sigma x_i^{s+r}}{\Sigma x_i^s} \right)^{1/r}</math> Clearly, if s=0 this is the forth power mean; if r=1 this is the power plus 1 mean. == Mixed averages == More types of average can be found by mixing different averages, provided that the formula is symmetric in the variables. For example, for any three numbers x, y, z, the following are all averages: :<math>\frac{1}{3}(\sqrt(xy) + \sqrt(yz) + \sqrt(zx))</math> :<math>\sqrt ( \frac{1}{3}(xy + yz + zx) )</math> :<math>\frac{1}{2}((x+y)(y+z)(z+x))^{1/3}</math> == The median and other quartiles As noted above, the median is an average if we do not require some strict inequalities in the definition. In fact, this is true of any quartile of the distribution, even maximum and minimum. It may seem perverse to call the maximum and minimum "averages". However, the fundamental purpose of an average is to give an estimate of the order of magnitude of a group of numbers. If the range of numbers is small, the maximum and minimum can do this; if the range is very large, any one number as the average may be misleading. As noted above, the maximum and minimum are limiting values of other averages as parameters tend to infinity. == It may be argued that any quartile other than the median is "biased" hence unsatisfactory. However, if in a group of numbers a few of them are much larger or much smaller than the others ("outliers"), any average may seem biased. For example, consider {1,2,3,4,5,6,7,8,144}. The arithmetic mean is 20, far higher than the ''upper quartile'' of 7 and indeed far higher than all but one of the numbers. == The mode == The mode is not an average. Firstly, it is not always uniquely defined; for example, in {1,1,1,2,2,3,3,3} there are two modes, 1 and 3 (which are also the minimum and maximum). Secondly and more important, it does not satisfy the monotonicity rule. Consider the set of eight numbers :{1,1,1,2,2,2,2,3} The mode is 2. Now suppose the seventh number increases from 2 to 3: :{1,1,1,2,2,2,3,3} The joint modes are now 1 and 2. Now suppose the sixth number increases from 2 to 4: :{1,1,1,2,2,3,3,4} The mode is now 1. == Transformation means == Let f(x) be any strictly monotonic function. Given a set of numbers {x₁ ... x_n}, define: # y_i = f(x_i) # Y as the arithmetic mean of the y_i # X as the solution of the equation Y = f(X). X is then the ''transformation mean'' of the x_i with respect to f(x). ''Examples:'' f(x) = x^r gives the rth power mean; f(x) = log(x) gives the geometric mean. ''Exercises'' # Will such a mean always obey the conditions at the beginning of the article? # Would using a different sort of mean at step 2, e.g. the geometric mean, give yet another sort of average? # Why does the equation in step 3 always have one and only one solution? Does it matter if f(x) is not continuous? # Find a function f(x) such that the transformation mean equals the median. == See also == * [[Mean]] *[[w:Averages|Wikipedia:Averages]] 5nn2vmfjcy4zzvtno3fb29ubvjyg09l 0 139384 2720301 2720109 2025-07-01T14:27:40Z Young1lim 21186 /* Adder */ 2720301 wikitext text/x-wiki == Adder == * Binary Adder Architecture Exploration ( [[Media:Adder.20131113.pdf|pdf]] ) {| class="wikitable" |- ! Adder type !! Overview !! Analysis !! VHDL Level Design !! CMOS Level Design |- | '''1. Ripple Carry Adder''' || [[Media:VLSI.Arith.1A.RCA.20250522.pdf|A]]|| || [[Media:Adder.rca.20140313.pdf|pdf]] || [[Media:VLSI.Arith.1D.RCA.CMOS.20211108.pdf|pdf]] |- | '''2. Carry Lookahead Adder''' || [[Media:VLSI.Arith.1.A.CLA.20250628.pdf|A]]|| || [[Media:Adder.cla.20140313.pdf|pdf]]|| |- | '''3. Carry Save Adder''' || [[Media:VLSI.Arith.1.A.CSave.20151209.pdf|A]]|| || || |- || '''4. Carry Select Adder''' || [[Media:VLSI.Arith.1.A.CSelA.20191002.pdf|A]]|| || || |- || '''5. Carry Skip Adder''' || [[Media:VLSI.Arith.5A.CSkip.20250405.pdf|A]]|| || || [[Media:VLSI.Arith.5D.CSkip.CMOS.20211108.pdf|pdf]] |- || '''6. Carry Chain Adder''' || [[Media:VLSI.Arith.6A.CCA.20211109.pdf|A]]|| || [[Media:VLSI.Arith.6C.CCA.VHDL.20211109.pdf|pdf]], [[Media:Adder.cca.20140313.pdf|pdf]] || [[Media:VLSI.Arith.6D.CCA.CMOS.20211109.pdf|pdf]] |- || '''7. Kogge-Stone Adder''' || [[Media:VLSI.Arith.1.A.KSA.20140315.pdf|A]]|| || [[Media:Adder.ksa.20140409.pdf|pdf]]|| |- || '''8. Prefix Adder''' || [[Media:VLSI.Arith.1.A.PFA.20140314.pdf|A]]|| || || |- || '''9.1 Variable Block Adder''' || [[Media:VLSI.Arith.1A.VBA.20221110.pdf|A]], [[Media:VLSI.Arith.1B.VBA.20230911.pdf|B]], [[Media:VLSI.Arith.1C.VBA.20240622.pdf|C]], [[Media:VLSI.Arith.1C.VBA.20250218.pdf|D]]|| || || |- || '''9.2 Multi-Level Variable Block Adder''' || [[Media:VLSI.Arith.1.A.VBA-Multi.20221031.pdf|A]]|| || || |} </br> === Adder Architectures Suitable for FPGA === * FPGA Carry-Chain Adder ([[Media:VLSI.Arith.1.A.FPGA-CCA.20210421.pdf|pdf]]) * FPGA Carry Select Adder ([[Media:VLSI.Arith.1.B.FPGA-CarrySelect.20210522.pdf|pdf]]) * FPGA Variable Block Adder ([[Media:VLSI.Arith.1.C.FPGA-VariableBlock.20220125.pdf|pdf]]) * FPGA Carry Lookahead Adder ([[Media:VLSI.Arith.1.D.FPGA-CLookahead.20210304.pdf|pdf]]) * Carry-Skip Adder </br> == Barrel Shifter == * Barrel Shifter Architecture Exploration ([[Media:Bshift.20131105.pdf|bshfit.vhdl]], [[Media:Bshift.makefile.20131109.pdf|bshfit.makefile]]) </br> '''Mux Based Barrel Shifter''' * Analysis ([[Media:Arith.BShfiter.20151207.pdf|pdf]]) * Implementation </br> == Multiplier == === Array Multipliers === * Analysis ([[Media:VLSI.Arith.1.A.Mult.20151209.pdf|pdf]]) </br> === Tree Mulltipliers === * Lattice Multiplication ([[Media:VLSI.Arith.LatticeMult.20170204.pdf|pdf]]) * Wallace Tree ([[Media:VLSI.Arith.WallaceTree.20170204.pdf|pdf]]) * Dadda Tree ([[Media:VLSI.Arith.DaddaTree.20170701.pdf|pdf]]) </br> === Booth Multipliers === * [[Media:RNS4.BoothEncode.20161005.pdf|Booth Encoding Note]] * Booth Multiplier Note ([[Media:BoothMult.20160929.pdf|H1.pdf]]) </br> == Divider == * Binary Divider ([[Media:VLSI.Arith.1.A.Divider.20131217.pdf|pdf]])</br> </br> </br> go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] [[Category:Digital Circuit Design]] [[Category:FPGA]] 0abuh1dna4z1reoddk9k38uar1y6g2t 10 160289 2720326 2662840 2025-07-01T15:15:50Z Angelina Grace121 3003996 2720326 wikitext text/x-wiki The Impact of Emotional Intelligence on Leadership Effectiveness and Employee Engagement: A Critical Review Abstract The significance of Emotional Intelligence (EI) in contemporary organizational environments has become increasingly apparent, particularly concerning its influence on leadership effectiveness and employee engagement. As organizations confront complex demands in an era defined by rapid technological change, globalization, and diverse workforce dynamics, emotionally intelligent leadership is now recognized as an indispensable driver of success. This critical review investigates how EI contributes to leadership capabilities, examining its role in shaping interpersonal relationships, decision-making, conflict management, and motivational strategies. Simultaneously, it explores how emotionally intelligent leaders enhance employee engagement by creating psychologically safe, supportive, and empathetic work environments. Drawing on a wide range of theoretical frameworks and empirical findings from the last three decades, the review highlights both the transformative potential and the limitations of EI in leadership practice. Methodological issues in measurement and cross-cultural applicability are also critically evaluated. The review concludes by identifying key research gaps and offering recommendations for future inquiry, including the need for longitudinal studies, culturally sensitive EI instruments, and more nuanced training interventions. Keyword Emotional Intelligence, Leadership Effectiveness, Employee Engagement, Organizational Behavior, Transformational Leadership, Interpersonal Communication, Workplace Psychology, Trust, Motivation, Critical Review Introduction In the evolving ecosystem of modern organizations, the competencies that define effective leadership are undergoing a profound transformation. Traditional models of leadership, which once prioritized strategic vision, technical expertise, and task delegation, are increasingly being supplemented—and in some contexts, supplanted—by a growing emphasis on interpersonal acumen, emotional awareness, and relational trust. Central to this shift is the concept of Emotional Intelligence (EI), a multidimensional construct that encompasses the capacity to perceive, understand, regulate, and effectively use emotions in both intrapersonal and interpersonal contexts. As early as the mid-1990s, scholars such as Daniel Goleman (1995) began to popularize the idea that emotional competencies may be more predictive of workplace success than intellectual ability alone. Subsequent research has bolstered these claims, suggesting that emotionally intelligent leadership not only enhances team performance but also significantly impacts the degree to which employees feel connected, motivated, and committed to their work (Carmeli, 2003; Wong & Law, 2002). In parallel, the concept of employee engagement—defined as the extent to which individuals bring their full selves to their roles—has emerged as a vital indicator of organizational health and productivity (Kahn, 1990; Schaufeli et al., 2002). This review aims to explore the intersection between emotional intelligence, leadership effectiveness, and employee engagement through a critical synthesis of literature spanning psychology, management, and organizational behavior. The guiding question is: How and to what extent does emotional intelligence shape leadership effectiveness and foster employee engagement in diverse organizational settings? The paper proceeds in five sections. Following this introduction, Section 2 outlines the methodology used to select and analyze relevant literature. Section 3 presents an integrative discussion of findings, organized around core thematic axes. Section 4 synthesizes insights, identifies critical limitations, and suggests directions for future research. Section 5 concludes with a summary of implications for leadership practice and human resource development. Methodology To ensure comprehensive and systematic coverage of the existing body of research, this review adopted an integrative literature review approach, combining empirical studies, theoretical frameworks, and conceptual models from multidisciplinary sources. The following steps guided the review process: 2.1 Literature Search Strategy A comprehensive search was conducted using the following academic databases: • Scopus • Web of Science • PsycINFO • JSTOR • Google Scholar Search strings included combinations of the following terms: • “Emotional Intelligence” AND “Leadership Effectiveness” • “EI” AND “Employee Engagement” • “Emotionally Intelligent Leadership” • “Transformational Leadership” AND “Emotions” • “Workplace Emotions” AND “Motivation” The time frame of the search spanned from 1990 to 2025, capturing foundational texts as well as the most recent scholarly contributions. 2.2 Inclusion and Exclusion Criteria Inclusion Criteria: • Peer-reviewed journal articles and meta-analyses • Theoretical and conceptual papers with robust EI frameworks • Empirical studies with clear methodology linking EI to leadership or engagement • English-language publications Exclusion Criteria: • Grey literature, dissertations, and editorials • Non-peer-reviewed conference papers • Articles conflating EI with unrelated constructs such as charisma or extroversion without clear differentiation 2.3 Data Analysis and Synthesis A total of 142 studies were initially identified. After removing duplicates and non-relevant studies, 87 high-quality sources were included in the final review. The selected studies were thematically coded into the following categories: 1. Definitions and theoretical models of EI 2. EI and leadership styles 3. EI and employee engagement 4. Measurement and methodological challenges 5. Organizational outcomes mediated by EI Findings were synthesized using a qualitative, thematic analysis to identify recurrent patterns, theoretical convergences, and gaps in existing knowledge. Discussion 3.1 Emotional Intelligence and Leadership Effectiveness Leadership in emotionally charged environments—characterized by tight deadlines, high ambiguity, and team diversity—requires not only cognitive intelligence but emotional literacy. Leaders with high EI are better equipped to perceive the emotional undercurrents of their team, anticipate tension, and respond with empathy and composure (George, 2000). They tend to build stronger interpersonal bonds, communicate more effectively, and manage conflict with tact. Transformational leadership theory aligns closely with EI principles. Bass and Riggio (2006) argue that transformational leaders must possess the emotional skills to inspire, motivate, and consider the individualized needs of followers. Studies show that emotionally intelligent leaders are more likely to exhibit transformational behaviors such as inspirational motivation and individualized consideration (Barling et al., 2000). Goleman’s five domains of EI—self-awareness, self-regulation, motivation, empathy, and social skills—serve as a practical framework for assessing leadership competence. For example: • Self-awareness enables a leader to recognize personal triggers and avoid reactive decision-making. • Empathy fosters inclusive decision-making, encouraging diverse voices and psychological safety. • Social skills help leaders resolve disputes, deliver feedback constructively, and foster collaboration. Numerous empirical studies affirm the correlation between EI and leadership outcomes. Côté and Miners (2006) found that leaders with high EI consistently outperform peers in relationship management, conflict resolution, and team productivity. Moreover, EI has been linked with ethical leadership, a crucial dimension in today’s transparency-focused corporate climate (Brown & Treviño, 2006). 3.2 EI as a Catalyst for Employee Engagement Emotionally intelligent leadership does not exist in a vacuum—it manifests in how employees perceive, react to, and engage with their work environments. Employee engagement is not solely a function of task design or compensation; it is deeply rooted in emotional connectedness to the workplace and to leadership. Kahn’s (1990) psychological conditions for engagement—meaningfulness, safety, and availability—are all enhanced by emotionally intelligent leaders. These leaders create a culture where individuals feel seen, heard, and valued, thereby fostering intrinsic motivation. Macey and Schneider (2008) posit that emotionally resonant leadership directly correlates with employee enthusiasm, loyalty, and discretionary effort. Leaders who practice emotional attunement and transparency are more likely to develop relational trust, which in turn encourages higher engagement levels. In distributed or virtual teams, where emotional cues are often muted, leaders with EI are better able to maintain cohesion and morale by adapting communication and offering empathy. 3.3 Mediating Variables and Organizational Outcomes EI does not operate in isolation. Its impact on leadership and engagement is often mediated by variables such as: • Organizational Culture: A culture that values emotional openness amplifies the effectiveness of EI. • Psychological Safety: EI fosters environments where employees are unafraid to voice concerns or innovate. • Emotional Labor: Leaders with EI manage the emotional display rules of organizations more authentically, reducing burnout (Grandey, 2000). Furthermore, EI is positively associated with organizational citizenship behavior (OCB), lower turnover intent, and increased job satisfaction (Carmeli, 2003; Law et al., 2004). 3.4 Methodological Challenges and Critiques Despite its popularity, EI research is not without controversy. Key critiques include: • Measurement Variability: The use of self-report instruments like the EQ-i (Bar-On) or mixed models has led to inconsistent findings due to social desirability bias. • Construct Validity: Some scholars argue that EI overlaps with personality traits, making it difficult to isolate its effects (Landy, 2005). • Cultural Bias: Most EI assessments are developed in Western contexts, limiting cross-cultural applicability (Matsumoto, 2006). • Causality vs. Correlation: Much of the EI literature is correlational, with limited longitudinal evidence to establish causal relationships. Addressing these challenges requires more rigorous experimental designs, cross-cultural adaptations of EI tools, and longitudinal studies tracking leadership development over time. Conclusion This critical review has explored the compelling connections between emotional intelligence, leadership effectiveness, and employee engagement. The weight of scholarly evidence indicates that emotionally intelligent leaders create more empathetic, cohesive, and engaged workplaces. They inspire trust, mediate conflict constructively, and align emotional climates with organizational goals. Employee engagement, a predictor of productivity and retention, flourishes under leaders who exhibit EI competencies. Yet, the field is not without its limitations. Measurement inconsistencies, theoretical ambiguities, and lack of cultural contextualization continue to challenge the field's credibility. Moreover, the increasing integration of digital and remote work environments calls for a reimagining of how EI is taught, measured, and practiced in technologically mediated leadership. Future research must focus on: • Developing context-specific EI training programs for leaders. • Designing cross-culturally valid assessment instruments. • Conducting longitudinal and experimental studies to better establish causal pathways. • Exploring the neuroscience of emotionally intelligent decision-making. As organizations become more human-centered in design and purpose, emotional intelligence is poised to remain a cornerstone of ethical, adaptive, and impactful leadership. Reference 1) Allen, T. D., Herst, D. E., Bruck, C. S., & Sutton, M. (2000). Consequences associated with work-to-family conflict: A review and agenda for future research. Journal of Occupational Health Psychology, 5(2), 278–308. 2) Bar-On, R. (2000). Emotional and social intelligence: Insights from the Emotional Quotient Inventory (EQ-i). In R. Bar-On & J. Parker (Eds.), Handbook of Emotional Intelligence (pp. 363–388). San Francisco: Jossey-Bass. 3) Bernas, K., & Major, D. A. (2000). Contributors to stress resistance: Testing a model of women’s work–family conflict. Psychology of Women Quarterly, 24(2), 170–178. 4) Golden, T. D., Veiga, J. F., & Simsek, Z. (2006). Telecommuting's differential impact on work-family conflict: Is there no place like home? Journal of Applied Psychology, 91(6), 1340–1350. 5) Goleman, D. (1998). Working with Emotional Intelligence. New York: Bantam Books. 6) Graen, G. B., & Uhl-Bien, M. (1995). Relationship-based approach to leadership: Development of Leader–Member Exchange (LMX) theory of leadership over 25 years. Leadership Quarterly, 6(2), 219–247. 7) Greenhaus, J. H., & Beutell, N. J. (1985). Sources of conflict between work and family roles. Academy of Management Review, 10(1), 76–88. 8) Major, D. A., Fletcher, T. D., Davis, D. D., & Germano, L. M. (2008). The influence of work-family culture and workplace relationships on work interference with family: A multilevel model. Journal of Organizational Behavior, 29(7), 881–897. 9) Mayer, J. D., & Salovey, P. (1997). What is emotional intelligence? In P. Salovey & D. Sluyter (Eds.), Emotional development and emotional intelligence: Educational implications (pp. 3–31). New York: Basic Books. 10) Michel, J. S., Kotrba, L. M., Mitchelson, J. K., Clark, M. A., & Baltes, B. B. (2011). Antecedents of work–family conflict: A meta-analytic review. Journal of Organizational Behavior, 32(5), 689–725. 11) Mahbub, A., & Beedle, J. (2025). BEHAVIORISTS, COGNITIVISTS, AND CONSTRUCTIVISTS LEARNING THEORIES: A COMPARISON AND APPLICATION IN INSTRUCTIONAL DESIGN. European Journal of Education Studies, 12(6). ajej85wb3ou5nm3h2sqig7q8lanhxk6 2720327 2720326 2025-07-01T15:16:06Z Ternera 2468111 Reverted edits by [[Special:Contribs/Angelina Grace121|Angelina Grace121]] ([[User talk:Angelina Grace121|talk]]) to last version by Tule-hog: unnecessary links or spam 2662840 wikitext text/x-wiki {{#invoke:Clickable button|main}}<noinclude> {{documentation}} <!-- Categories go on the /doc subpage, and interwikis go on Wikidata. --> </noinclude> p9tti49lmjq7ifp2faksbrk6uifwc4d 0 199885 2720399 2531185 2025-07-02T09:34:49Z Jtneill 10242 2720399 wikitext text/x-wiki <noinclude>{{title|Graduate attributes}}</noinclude> [[Motivation and emotion|This unit]] fosters these [[University of Canberra/Graduate attributes|University of Canberra graduate attributes]]: # '''Professional''': ##communicate effectively; ##display initiative and drive, and use their organisation skills to plan and manage their workload; ##employ up-to-date and relevant knowledge and skills; ##use creativity, critical thinking, analysis and research skills to solve theoretical and real-world problems; # '''Global citizen''': ##adopt an informed and balanced approach across professional and international boundaries; ##communicate effectively in diverse cultural and social settings; ##make creative use of technology in their learning and professional lives; # '''Lifelong learner''': ##adapt to complexity, ambiguity and change by being flexible and keen to engage with new ideas; ##evaluate and adopt new technology. The graduate attributes are mapped to the [[Motivation and emotion/Assessment|assessment]] items as shown in this table: {{center top}} {| border=1 cellspacing=0 cellpadding=5 | style="width:100%" |- ! style="width: 24%" | Category ! style="width: 24%" | Attribute ! style="width: 13%" | [[Motivation and emotion/Assessment/Topic|Topic dev.]] ! style="width: 13%" | [[Motivation and emotion/Assessment/Chapter|Book chap.]] ! style="width: 13%" | [[Motivation and emotion/Assessment/Multimedia|Multimedia]] ! style="width: 13%" | [[Motivation and emotion/Assessment/Quizzes|Quizzes]] |- | style="text-align:left;"|1. Professional | style="text-align:left;"|Communicate effectively | style="text-align:center;"|✔ | style="text-align:center;"|✔ | style="text-align:center;"|✔ | |- | style="text-align:left;"|1. Professional | style="text-align:left;"|Display initiative and drive | style="text-align:center;"|✔ | style="text-align:center;"|✔ | style="text-align:center;"|✔ | |- | style="text-align:left;"|1. Professional | style="text-align:left;"|Knowledge and skills up-to-date | | style="text-align:center;"|✔ | | style="text-align:center;"|✔ |- | style="text-align:left;"|1. Professional | style="text-align:left;"|Solve problems via thinking | | style="text-align:center;"|✔ | style="text-align:center;"|✔ | |- | style="text-align:left;"|2. Global citizen | style="text-align:left;"|Informed and balanced | | style="text-align:center;"|✔ | style="text-align:center;"|✔ | |- | style="text-align:left;"|2. Global citizen | style="text-align:left;"|Communicate diversely | | style="text-align:center;"|✔ | | |- | style="text-align:left;"|2. Global citizen | style="text-align:left;"|Creative use of technology | | style="text-align:center;"|✔ | style="text-align:center;"|✔ | |- | style="text-align:left;"|3. Lifelong learner | style="text-align:left;"|Engage in new ideas | | style="text-align:center;"|✔ | | |- | style="text-align:left;"|3. Lifelong learner | style="text-align:left;"|Adopt new technology | style="text-align:center;"|✔ | style="text-align:center;"|✔ | style="text-align:center;"|✔ | |} {{center bottom}} Through this unit, many skills are likely to be developed which can be incorporated into resumes and professional portfolios such as: * Demonstrated ability to use professional knowledge to address applied psychological problems. * Confidence in written and verbal communication of ideas using collaborative, online platforms. * Capacity to learn new technologies for addressing novel problems. If you don't feel confident declaring such skills by the end of the unit then they could be considered targets for further skill development (e.g., through internship). Consider including your submissions for the unit's [[Motivation and emotion/Assessment/Major project|major project]] assessment items (i.e., the book chapter and multimedia) as work examples (artefacts) in your e-portfolio.<noinclude> [[Category:{{#titleparts:{{PAGENAME}}|2}}]] </noinclude> j58h4mnykhfgypw9snhmmnxz2f2vkr5 2720400 2720399 2025-07-02T09:37:57Z Jtneill 10242 Update for 2025 2720400 wikitext text/x-wiki <noinclude>{{title|Graduate attributes}}</noinclude> [[Motivation and emotion|This unit]] fosters these [[University of Canberra/Graduate attributes|University of Canberra graduate attributes]]: # '''Professional''': ##communicate effectively; ##display initiative and drive, and use their organisation skills to plan and manage their workload; ##employ up-to-date and relevant knowledge and skills; ##use creativity, critical thinking, analysis and research skills to solve theoretical and real-world problems; # '''Global citizen''': ##adopt an informed and balanced approach across professional and international boundaries; ##communicate effectively in diverse cultural and social settings; ##make creative use of technology in their learning and professional lives; # '''Lifelong learner''': ##adapt to complexity, ambiguity and change by being flexible and keen to engage with new ideas; ##evaluate and adopt new technology. The graduate attributes are mapped to the [[Motivation and emotion/Assessment|assessment]] items as shown in this table: {{center top}} {| border=1 cellspacing=0 cellpadding=5 | style="width:80%" |- ! style="width: 24%" | Category ! style="width: 24%" | Attribute ! style="width: 13%" | [[Motivation and emotion/Assessment/Topic|Topic dev.]] ! style="width: 13%" | [[Motivation and emotion/Assessment/Chapter|Book chap.]] ! style="width: 13%" | [[Motivation and emotion/Assessment/Exam|Exam]] |- | style="text-align:left;"|1. Professional | style="text-align:left;"|Communicate effectively | style="text-align:center;"|✔ | style="text-align:center;"|✔ | |- | style="text-align:left;"|1. Professional | style="text-align:left;"|Display initiative and drive | style="text-align:center;"|✔ | style="text-align:center;"|✔ | |- | style="text-align:left;"|1. Professional | style="text-align:left;"|Knowledge and skills up-to-date | | style="text-align:center;"|✔ | style="text-align:center;"|✔ |- | style="text-align:left;"|1. Professional | style="text-align:left;"|Solve problems via thinking | | style="text-align:center;"|✔ | |- | style="text-align:left;"|2. Global citizen | style="text-align:left;"|Informed and balanced | | style="text-align:center;"|✔ | |- | style="text-align:left;"|2. Global citizen | style="text-align:left;"|Communicate diversely | | style="text-align:center;"|✔ | |- | style="text-align:left;"|2. Global citizen | style="text-align:left;"|Creative use of technology | | style="text-align:center;"|✔ | |- | style="text-align:left;"|3. Lifelong learner | style="text-align:left;"|Engage in new ideas | | style="text-align:center;"|✔ | |- | style="text-align:left;"|3. Lifelong learner | style="text-align:left;"|Adopt new technology | style="text-align:center;"|✔ | style="text-align:center;"|✔ | |} {{center bottom}} Through this unit, many skills are likely to be developed which can be incorporated into resumes and professional portfolios such as: * Demonstrated ability to use professional knowledge to address applied psychological problems. * Confidence in written and verbal communication of ideas using collaborative, online platforms. * Capacity to learn new technologies for addressing novel problems. If you don't feel confident declaring such skills by the end of the unit then they could be considered targets for further skill development (e.g., through internship). Consider including your submissions for the unit's [[Motivation and emotion/Assessment/Major project|major project]] assessment items (i.e., the book chapter and multimedia) as work examples (artefacts) in your e-portfolio.<noinclude> [[Category:{{#titleparts:{{PAGENAME}}|2}}]] </noinclude> rlwmy113nwr1balx86bshxasdq1unr7 2720401 2720400 2025-07-02T09:40:03Z Jtneill 10242 Update for 2025 2720401 wikitext text/x-wiki <noinclude>{{title|Graduate attributes}}</noinclude> [[Motivation and emotion|This unit]] fosters these [[University of Canberra/Graduate attributes|University of Canberra graduate attributes]]: # '''Professional''': ##communicate effectively; ##display initiative and drive, and use their organisation skills to plan and manage their workload; ##employ up-to-date and relevant knowledge and skills; ##use creativity, critical thinking, analysis and research skills to solve theoretical and real-world problems; # '''Global citizen''': ##adopt an informed and balanced approach across professional and international boundaries; ##communicate effectively in diverse cultural and social settings; ##make creative use of technology in their learning and professional lives; # '''Lifelong learner''': ##adapt to complexity, ambiguity and change by being flexible and keen to engage with new ideas; ##evaluate and adopt new technology. The graduate attributes are mapped to the [[Motivation and emotion/Assessment|assessment]] items as shown in this table: {{center top}} {| border=1 cellspacing=0 cellpadding=5 | style="width:80%" |- ! style="width: 24%" | Category ! style="width: 24%" | Attribute ! style="width: 13%" | [[Motivation and emotion/Assessment/Topic|Topic dev.]] ! style="width: 13%" | [[Motivation and emotion/Assessment/Chapter|Book chap.]] ! style="width: 13%" | [[Motivation and emotion/Assessment/Exam|Exam]] |- | style="text-align:left;"|1. Professional | style="text-align:left;"|Communicate effectively | style="text-align:center;"|✔ | style="text-align:center;"|✔ | |- | style="text-align:left;"|1. Professional | style="text-align:left;"|Display initiative and drive | style="text-align:center;"|✔ | style="text-align:center;"|✔ | |- | style="text-align:left;"|1. Professional | style="text-align:left;"|Knowledge and skills up-to-date | | style="text-align:center;"|✔ | style="text-align:center;"|✔ |- | style="text-align:left;"|1. Professional | style="text-align:left;"|Solve problems via thinking | | style="text-align:center;"|✔ | |- | style="text-align:left;"|2. Global citizen | style="text-align:left;"|Informed and balanced | | style="text-align:center;"|✔ | |- | style="text-align:left;"|2. Global citizen | style="text-align:left;"|Communicate diversely | | style="text-align:center;"|✔ | |- | style="text-align:left;"|2. Global citizen | style="text-align:left;"|Creative use of technology | | style="text-align:center;"|✔ | |- | style="text-align:left;"|3. Lifelong learner | style="text-align:left;"|Engage in new ideas | | style="text-align:center;"|✔ | |- | style="text-align:left;"|3. Lifelong learner | style="text-align:left;"|Adopt new technology | style="text-align:center;"|✔ | style="text-align:center;"|✔ | |} {{center bottom}} Through this unit, many skills are likely to be developed which can be incorporated into resumes and professional portfolios such as: * Demonstrated ability to use professional knowledge to address applied psychological problems. * Confidence in written and verbal communication of ideas using collaborative, online platforms. * Capacity to learn new technologies for addressing novel problems. If you don't feel confident declaring such skills by the end of the unit then they could be considered targets for further skill development (e.g., through internship). Consider including your [[Motivation and emotion/Assessment/Chapter|book chapter]] as a work example (artefact) in your e-portfolio.<noinclude> [[Category:{{#titleparts:{{PAGENAME}}|2}}]] </noinclude> 9yjvgj37sq1z99a21q0lujj9vlu919o 0 237453 2720403 2636021 2025-07-02T09:42:36Z Jtneill 10242 2720403 wikitext text/x-wiki <noinclude>{{title|Timetable}}</noinclude> * See [https://www.canberra.edu.au/timetable2025/ timetable 2025] * Enrol in a tutorial group (live virtual, live on-campus, or live asynchronous/recorded)<noinclude> ==See also== * [[Motivation and emotion/Drop-in|Drop-in]] * [[Motivation and emotion/Lectures|Lectures]] * [[Motivation and emotion/About/Schedule|Schedule]] * [[Motivation and emotion/Tutorials|Tutorials]] [[Category:Motivation and emotion]] </noinclude> lxgz0r388tvpnbyesqldeojqeumv2vu 2720404 2720403 2025-07-02T09:43:57Z Jtneill 10242 Update for 2025 2720404 wikitext text/x-wiki <noinclude>{{title|Timetable}}</noinclude> * See [https://www.canberra.edu.au/timetable2025/ timetable 2025] * Enrol in either the ON-CAMPUS or ONLINE REALTIME unit offering # Allocate to a tutorial group (live virtual, live on-campus, or asynchronous/recorded)<noinclude> ==See also== * [[Motivation and emotion/Drop-in|Drop-in]] * [[Motivation and emotion/Lectures|Lectures]] * [[Motivation and emotion/About/Schedule|Schedule]] * [[Motivation and emotion/Tutorials|Tutorials]] [[Category:Motivation and emotion]] </noinclude> llbo8h5xb64ceo74wnhkxlhqnl09lof 2720405 2720404 2025-07-02T09:44:16Z Jtneill 10242 2720405 wikitext text/x-wiki <noinclude>{{title|Timetable}}</noinclude> * See [https://www.canberra.edu.au/timetable2025/ timetable 2025] * Enrol in either the ON-CAMPUS or ONLINE REALTIME unit offering * Allocate to a tutorial group (live virtual, live on-campus, or asynchronous/recorded)<noinclude> ==See also== * [[Motivation and emotion/Drop-in|Drop-in]] * [[Motivation and emotion/Lectures|Lectures]] * [[Motivation and emotion/About/Schedule|Schedule]] * [[Motivation and emotion/Tutorials|Tutorials]] [[Category:Motivation and emotion]] </noinclude> cgjcjfd7n1e5aod9i52c23wlvzekxx4 0 270241 2720337 2718302 2025-07-01T15:42:53Z 69.14.96.207 change all devices except my ios iphone the rest of devices are from hackers 2720337 wikitext text/x-wiki [[File:(at).svg|thumb|upright|The [[w:at sign|at sign]], is a part of each [[w:email|email]] address]] {{100%done}} Use this checklist to avoid common [[w:email|email]] errors,<ref>[https://www.lifehack.org/articles/productivity/75-common-email-mistakes-youre-probably-making-work.html 75 Common Email Mistakes You’re Probably Making at Work], Lifehack, Bryan Collins.</ref>^,<ref>[https://www.cbsnews.com/news/5-career-destroying-email-blunders/ 5 career-destroying email blunders], CBS News, Dave Johnson, November 3, 2011. </ref> and improve your email communications. *'''Mode'''—Is email the best communication mode to choose for this message? Would a text message, phone call, video chat, personal visit, card, letter, silence, or handwritten note be more effective? *'''Recipients'''—Consider carefully who should receive this message. Use these fields and commands carefully: **To: Carefully identify the email of the person this message is directed to. This is the person who is requested to act on this message. **CC: If others would benefit from receiving this message, include them here. CC is for people who need to be kept in the know. **BCC: “Blind Copy” If there is good reason to hide the identity of other recipients, include them here rather than in CC. **Reply: Use “Reply” to reply only to the originator of this email message. **Reply all: Use this option carefully and sparingly to avoid sharing your message unnecessarily or inadvertently with all the recipients of the original message. *'''Nonrecipients'''—Don’t send email to people who will be annoyed by the message. Don’t disclose private information carelessly. Avoid including copies of peer level communications to the boss. Include the boss if you are praising other recipients. Omit the boss if you are critical of recipients or working to resolve conflict. *'''Subject'''—Choose the language of the subject line carefully. Provide a clear and accurate synopsis. Use the subject line to provide context, clarify intent, or suggest what may be expected of the recipient. *[[w:Copy_editing|'''Copy Editing''']]—Take care to avoid or correct spelling, word use, grammar, and punctuation errors. **Spelling—Check the spelling. Use a spell checker. **Word use—Double check the meaning of any words you are unsure of. Look them up to ensure they mean what you want to communicate. Be particularly careful to check words that have been autocorrected. **Punctuation—Check the grammar and punctuation. Use a grammar checker. *'''Call to action'''—What, if any, engagement are you expecting of the recipient? Is this message being sent for entertainment, sharing information, asking a question, assigning a task, suggesting some action, or are you trolling, annoying, gossiping, gloating, harassing, bullying, or bloviating? In business emails it can be helpful to include a one line summary and call to action near the top of the message. Other emails may include some suggested action later in the message. Does the recipient have all the information they need to take the requested action? *'''Message'''—Communicate clearly, carefully, completely, and purposefully. **Purpose—Why are you sending this message? Are you sharing information, asking a question, posing a problem, proposing a solution, or simply spreading rumors and gossip? What do you want to have happen as a result of this message? What else might happen? Will this message have a positive impact? Do not send email unless you can improve on silence. **Style—Separate personal and professional messages and styles. Don’t use personal email language or styles in professional messages, and vice versa. **Clarity—Good writing is clear thinking made visible.<ref>[https://www.laserfocusworld.com/test-measurement/research/article/16556713/good-writing-is-clear-thinking-made-visible Good writing is clear thinking made visible], LaserFocusedWorld, Jeffrey Bairstow, May 1, 2001. </ref> Is this message based on clear thinking? Is the thought clear? Is the language clear? How can the message be made more valuable? Can you avoid sending this email by answering your own question, or doing your own research or investigation? ***Check the text for inconsistencies and logical fallacies. Consider using a Large Language Model, such as ChatGPT to check the text using the following prompt: “Identify inconsistencies and logical fallacies in the following text. Provide sound counterarguments:” **Whose problem is this?—If this is your problem to solve, or you can take action to solve the problem, don’t pass it on.<ref>[https://hbr.org/1999/11/management-time-whos-got-the-monkey Management Time: Who’s Got the Monkey?], Harvard Business Review, by William Oncken, Jr. and Donald L. Wass. </ref> Respect the recipient’s time, attention, and privacy. **Cool Heads—Don’t click send while you are angry, distracted, impatient, tired, under the influence, or in some altered state of consciousness. Wait overnight to reconsider and re-read sensitive, provocative, upsetting, or especially important email messages. If this email appeared in a public forum, or the front page of the newspaper, would that be OK? **Improved text—Consider using a tool such as ChatGPT to suggest improvements to the text. *'''Privacy'''—Ensure the privacy of yourself and others, and carefully protect confidential, sensitive, or other protected information. Email privacy breaches have ruined careers.<ref>[https://eccitsolutions.com/simple-email-mistakes-that-can-cause-serious-data-security-breaches/ Simple Email Mistakes That Can Cause Serious Data Security Breaches], ECC IT Solutions.</ref> *'''Security'''—Assume your email messages are not secure. Do not sent passwords, account numbers, or other sensitive information over email. Learn to recognize spam, phishing, social engineering, and other confidence tricks. Don’t engage with these traps, report them.<ref>[https://www.usa.gov/stop-scams-frauds Report Scams and Frauds], USAGov.</ref> *'''Good Faith'''—Take care to communicate in good faith. Be impeccable with your word. Advance no falsehoods. Consider if this communication is true, helpful, and kind. Is the email respectful to recipients and others? If not, then don’t send it. *'''Attachments'''—If you mention an attachment in the message, be sure to include that attachment. Because attachments are often bulky, don’t include them unnecessarily. Use a link to a shared document or on-line resource rather than attaching a copy when practical. *'''Netiquette'''—Use good manners and exercise civility. Begin with a respectful greeting. End by thanking the recipients. Use respectful language throughout. Use this checklist to avoid common email errors and improve your email communications. == Notes == <references/> [[Category:Life skills]] [[Category:Computer Skills]] [[Category:Email]] idekjrmp0snc1apy0ksqru25b9uzpj9 2720374 2720337 2025-07-01T22:54:15Z MathXplore 2888076 Reverted edits by [[Special:Contributions/69.14.96.207|69.14.96.207]] ([[User_talk:69.14.96.207|talk]]) to last version by [[User:Lbeaumont|Lbeaumont]] using [[Wikiversity:Rollback|rollback]] 2718302 wikitext text/x-wiki [[File:(at).svg|thumb|upright|The [[w:at sign|at sign]], is a part of each [[w:email|email]] address]] {{100%done}} Use this checklist to avoid common [[w:email|email]] errors,<ref>[https://www.lifehack.org/articles/productivity/75-common-email-mistakes-youre-probably-making-work.html 75 Common Email Mistakes You’re Probably Making at Work], Lifehack, Bryan Collins.</ref>^,<ref>[https://www.cbsnews.com/news/5-career-destroying-email-blunders/ 5 career-destroying email blunders], CBS News, Dave Johnson, November 3, 2011. </ref> and improve your email communications. *'''Mode'''—Is email the best communication mode to choose for this message? Would a text message, phone call, video chat, personal visit, card, letter, silence, or handwritten note be more effective? *'''Recipients'''—Consider carefully who should receive this message. Use these fields and commands carefully: **To: Carefully identify the email of the person this message is directed to. This is the person who is requested to act on this message. **CC: If others would benefit from receiving this message, include them here. CC is for people who need to be kept in the know. **BCC: “Blind Copy” If there is good reason to hide the identity of other recipients, include them here rather than in CC. **Reply: Use “Reply” to reply only to the originator of this email message. **[[w:Email_storm|Reply all]]: Use this option carefully and sparingly to avoid sharing your message unnecessarily or inadvertently with all the recipients of the original message. *'''Nonrecipients'''—Don’t send email to people who will be annoyed by the message. Don’t disclose private information carelessly. Avoid including copies of peer level communications to the boss. Include the boss if you are praising other recipients. Omit the boss if you are critical of recipients or working to resolve conflict. *'''Subject'''—Choose the language of the subject line carefully. Provide a clear and accurate synopsis. Use the subject line to provide context, clarify intent, or suggest what may be expected of the recipient. *[[w:Copy_editing|'''Copy Editing''']]—Take care to avoid or correct spelling, word use, grammar, and punctuation errors. **Spelling—Check the spelling. Use a [[w:Spell_checker|spell checker]]. **Word use—Double check the meaning of any words you are unsure of. Look them up to ensure they mean what you want to communicate. Be particularly careful to check words that have been [[w:Autocorrection|autocorrected]]. **Punctuation—Check the grammar and punctuation. Use a [[w:Grammar_checker|grammar checker]]. *'''Call to action'''—What, if any, engagement are you expecting of the recipient? Is this message being sent for entertainment, sharing information, asking a question, assigning a task, suggesting some action, or are you [[w:Internet_troll|trolling]], annoying, gossiping, gloating, [[w:Harassment|harassing]], [[w:Bullying|bullying]], or [[w:Bloviation|bloviating]]? In business emails it can be helpful to include a one line summary and call to action near the top of the message. Other emails may include some suggested action later in the message. Does the recipient have all the information they need to take the requested action? *'''Message'''—Communicate clearly, carefully, completely, and purposefully. **Purpose—Why are you sending this message? Are you sharing information, asking a question, [[Problem Finding|posing a problem]], proposing a solution, or simply spreading rumors and gossip? What do you want to have happen as a result of this message? What else might happen? Will this message have a positive impact? Do not send email unless you can improve on silence. **Style—Separate personal and professional messages and styles. Don’t use personal email language or styles in professional messages, and vice versa. **Clarity—Good writing is [[Deductive Logic/Clear Thinking curriculum|clear thinking]] made visible.<ref>[https://www.laserfocusworld.com/test-measurement/research/article/16556713/good-writing-is-clear-thinking-made-visible Good writing is clear thinking made visible], LaserFocusedWorld, Jeffrey Bairstow, May 1, 2001. </ref> Is this message based on clear thinking? Is the thought clear? Is the language clear? How can the message be made more valuable? Can you avoid sending this email by answering your own question, or doing your own research or investigation? ***Check the text for inconsistencies and [[Recognizing Fallacies|logical fallacies]]. Consider using a [[w:Large_language_model|Large Language Model]], such as [[w:ChatGPT|ChatGPT]] to check the text using the following prompt: “Identify inconsistencies and logical fallacies in the following text. Provide sound counterarguments:” **[[Problem_Finding#Whose_Problem_is_this?|Whose problem is this?]]—If this is your problem to solve, or you can take action to solve the problem, don’t pass it on.<ref>[https://hbr.org/1999/11/management-time-whos-got-the-monkey Management Time: Who’s Got the Monkey?], Harvard Business Review, by William Oncken, Jr. and Donald L. Wass. </ref> Respect the recipient’s time, attention, and privacy. **Cool Heads—Don’t click send while you are angry, distracted, impatient, tired, under the influence, or in some [[w:Altered_state_of_consciousness|altered state of consciousness]]. Wait overnight to reconsider and re-read sensitive, provocative, upsetting, or especially important email messages. If this email appeared in a public forum, or the front page of the newspaper, would that be OK? **Improved text—Consider using a tool such as [[w:ChatGPT|ChatGPT]] to suggest improvements to the text. *'''Privacy'''—Ensure the privacy of yourself and others, and carefully protect confidential, sensitive, or other protected information. Email privacy breaches have [[w:Petraeus_scandal|ruined careers]].<ref>[https://eccitsolutions.com/simple-email-mistakes-that-can-cause-serious-data-security-breaches/ Simple Email Mistakes That Can Cause Serious Data Security Breaches], ECC IT Solutions.</ref> *'''Security'''—Assume your email messages are not secure. Do not sent passwords, account numbers, or other sensitive information over email. Learn to recognize [[w:Email_spam|spam]], [[w:Phishing|phishing]], [[w:Social_engineering_(security)|social engineering]], and other [[w:Confidence_trick|confidence tricks]]. Don’t engage with these traps, report them.<ref>[https://www.usa.gov/stop-scams-frauds Report Scams and Frauds], USAGov.</ref> *'''Good Faith'''—Take care to communicate in [[Virtues/Good Faith|good faith]]. [[w:The_Four_Agreements#Agreement_1:_Be_Impeccable_With_Your_Word|Be impeccable with your word]]. [[Living Wisely/Advance no falsehoods|Advance no falsehoods]]. Consider if this communication is true, helpful, and kind. Is the email respectful to recipients and others? If not, then don’t send it. *'''Attachments'''—If you mention an attachment in the message, be sure to include that attachment. Because attachments are often bulky, don’t include them unnecessarily. Use a link to a shared document or on-line resource rather than attaching a copy when practical. *[[w:Etiquette_in_technology|'''Netiquette''']]—Use good manners and exercise [[Virtues/Civility|civility]]. Begin with a respectful greeting. End by thanking the recipients. Use respectful language throughout. Use this checklist to avoid common email errors and improve your email communications. == Notes == <references/> [[Category:Life skills]] [[Category:Computer Skills]] [[Category:Email]] afztfxju088odfjy0af1gfgsak0p0ry 0 275808 2720402 2530866 2025-07-02T09:41:22Z Jtneill 10242 2720402 wikitext text/x-wiki <noinclude>{{title|Participation}}</noinclude> Engagement by attending lectures and tutorials is strongly recommended but not compulsory. Non-engagement is likely to make successful completion of the assessment more difficult because: *Lectures discuss content which is assessed in the quizzes. *Tutorials develop skills directly related to the [[Motivation and emotion/Assessment/Major project|major project]] (topic development and book chapter) assessment exercises. If you are unable to attend your scheduled tutorial, attend a tutorial at a different time or access the online recording. This [[Motivation and emotion/Assessment#Table|table]] estimates the time required to complete the major activities in this unit. Plan to allocate approximately 10 hours per week over 15 weeks.<noinclude> [[Category:{{BASEPAGENAME}}]] </noinclude> a5yxygk4rh8nonf03skuxl9psjz63aj 0 276251 2720409 2696496 2025-07-02T11:35:52Z 175.176.64.180 Shabu shouldering foil iron melting crystal supported by government police and millitar 2720409 wikitext text/x-wiki == Also Known As == * Family name: Young * Sir Allen Young * Virtual International Authority File: VIAF ID: [http://viaf.org/viaf/104487564 104487564] == Demographics == * Nationality: English<ref name=":5" /> === Residences === * Sir Capt. Allen William Young: 18 Grafton street W (1885<ref>Ancestry.com. ''London, England, City Directories, 1736-1943'' [database on-line]. Lehi, UT, USA: Ancestry.com Operations, Inc., 2018.</ref> – 1901<ref>Ancestry.com. ''London, England, Electoral Registers, 1832-1965'' [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2010.</ref> [at least]) == Family == * Henry Young (c. 1792 – 7 July 1854<ref>Ancestry.com. ''London, England, Church of England Deaths and Burials, 1813-2003'' [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2010.</ref>) *Ellen Leaf<ref>Ancestry.com. ''London, England, Church of England Marriages and Banns, 1754-1936'' [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2010.</ref> Young (19 August 1796<ref>Ancestry.com. ''London, England, Church of England Baptisms, Marriages and Burials, 1538-1812'' [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2010.</ref> – buried 7 February 1865<ref>Ancestry.com. ''London, England, Church of England Deaths and Burials, 1813-2003'' [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2010.</ref>) *#Amelia Young (c. 1824<ref name=":0">Ancestry.com. ''1851 England Census'' [database on-line]. Provo, UT, USA: Ancestry.com Operations Inc, 2005.</ref> – September 1891<ref name=":2">FreeBMD. ''England & Wales, Civil Registration Death Index, 1837-1915'' [database on-line]. Provo, UT, USA: Ancestry.com Operations Inc, 2006.</ref>) *#Florance Henry Young (12 April 1825<ref name=":3">Ancestry.com. ''London, England, Church of England Births and Baptisms, 1813-1920'' [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2010.</ref> – 7 August 1861<ref name=":4">Ancestry.com. ''England & Wales, National Probate Calendar (Index of Wills and Administrations), 1858-1995'' [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2010.</ref>) *#Adeline Young (29 July 1826<ref name=":3" /> – ) *#'''Sir Allen William Young''' (12 December 1827 – 20 November 1915)<ref name=":5">{{Cite journal|date=2020-06-01|title=Allen Young|url=https://en.wikipedia.org/w/index.php?title=Allen_Young&oldid=960147914|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Allen_Young.</ref> *#Henrietta Young Barron (31 December 1830<ref name=":3" /> – 8 February 1921<ref name=":4" />) *#Emma Young Sim (4 June 1832<ref name=":3" /> – December 1912<ref name=":2" />) *#Ellen Young (1834<ref name=":0" /> – 24 October 1909<ref name=":4" />) *#Sophia Roberta Young Bainbridge (17 June 1835<ref name=":6">Ancestry.com. ''England, Select Births and Christenings, 1538-1975'' [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2014.</ref> – 20 March 1904<ref name=":4" />) *#Frances Marion Young Spearing (25 October 1836<ref name=":6" /> – 27 January 1892<ref name=":4" />) *#Maria Young (29 April 1839<ref name=":3" /> – ) * === Relations === == Acquaintances, Friends and Enemies == === Acquaintances === === Friends === === Enemies === == Organizations == == Timeline == '''1851 March 30, Sunday''', the 1851 Census for England and Wales lists the following people at Cross Deep, Riverdale [?] House: Henry Young (Head of Household, 58 years old), Ellen Young (56), Amelia Young (27), F. Henry Young (26), Henrietta Young (20), Emma Young (18), Ellen Young (17), Sophia Roberta Young (15), Frances Marrion Young (14), Maria Young (13), An Beer (Governess, 27?), James Mepham (Footman, 27), John Squire (Groom, 26?), Sam Johnson (Groom, 25), Lydia Skilton (Cook, 50?), Mary Phillips (1st Ladies Maid, 23), Martha Staggers (2nd Ladies Maid, 24), Ann Mathews (House Maid, 25), Elizabeth Cordery (House Maid, 20), and Harriet Gurman (Kitchen Maid, 23).<ref name=":0" /> The 1851 Census lists Allen William Young as a visitor at 1 Walton Court in St. Botolph, Aldgate.<ref name=":0" /> '''1861 April 7, Sunday''', the 1861 Census for England and Wales lists lists the following people at Riversdale Villa, Cross Deep, Eastside: Ellen Young (Head of Household, Widow, 65 years old), Amelia Young (37), Emma Young (28), Ellen Young (27), Maria Young (22), son-in-law John Sidney Webb (Widowed, Elder Brother, 45), Rebecca Perkins (Ladies Maid, 19), Ann Hardy (Housemaid, 37), Charlotte Clements (Housemaid, 26), Ellena MacKinnery (Cook, 30), John Fairfield (Groom, 27), and George Butlin (Footman, 20).<ref name=":1">Ancestry.com. ''1861 England Census'' [database on-line]. Provo, UT, USA: Ancestry.com Operations Inc, 2005.</ref> In the 1861 Census, Allen William Young is visiting West Cowes in the Royal Yacht Squadron Club-House.<ref name=":1" /> '''1876''', Young was knighted (CB, Companion of the Order of the Bath) for his work searching for the Franklin expedition.<ref name=":5" /> '''1877 May 27''', Young introduced Lily Langtree to [[Social Victorians/People/Albert Edward, Prince of Wales|Albert Edward, Prince of Wales]] at a dinner party he hosted: "Sir Allen Young, the arctic explorer, invited her to late supper in his house, where it had been arranged that the Prince of Wales should meet her after the opera. The result was all that could have been expected. Mrs. Langtry became the Prince's first openly recognised mistress."<ref>Leslie, Anita. ''The Marlborough House Set''. Doubleday, 1973: 69.</ref> '''1881 July 14, afternoon, beginning about 2 p.m.''', Sir Allen Young was among the 3,000 or so people who were invited to the [[Social Victorians/1881-07-14 Garden Party|Garden Party at Marlborough House]] hosted by the [[Social Victorians/People/Albert Edward, Prince of Wales|Prince]] and [[Social Victorians/People/Alexandra, Princess of Wales|Princess of Wales]].<ref>"Garden Party at Marlborough House." ''Morning Post'' 16 July 1881 Saturday: 5 [of 8], Col. 6a–c [of 6] through 6, Col. 1a–3c. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/BL/0000174/18810716/051/0006 (p. 6, beginning with the Earl and Countess of Wharncliffe)</ref> Queen Victoria was at this event. '''1881 July 22, Friday''', Sir Allen Young was among the 750–1000 people who were invited to the [[Social Victorians/1881-07-22 Marlborough House Party|Marlborough House Party]] hosted by the [[Social Victorians/People/Albert Edward, Prince of Wales|Prince]] and [[Social Victorians/People/Alexandra, Princess of Wales|Princess of Wales]].<ref>"Court Circular: Marlborough House." ''Morning Post'' 23 July 1881, Saturday: 5 [of 8], Cols. 5-6a. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18810723/058/0005.</ref> '''1886 July 21, Wednesday''', Sir Allen Young was among the 750–1000 people who were invited to the [[Social Victorians/1886-07-21 Marlborough House Ball|Ball at Marlborough House]] hosted by the [[Social Victorians/People/Albert Edward, Prince of Wales|Prince]] and [[Social Victorians/People/Alexandra, Princess of Wales|Princess of Wales]].<ref>"Ball at Marlborough House." ''Morning Post'' 22 July 1886, Thursday: 5 [of 8], Cols. 6–7. ''British Newspaper Archive''. http://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18860722/055/0005.</ref> '''1887 May 9''', Sir Allen Young was among the more than 1,000 members of the [[Social Victorians/1887 American Exhibition/Welcome Council|Welcome Council of the American Exhibition]] at Earl's Court, which included Buffalo Bill's ''Wild West'', and which ran from 9 May 1887 through 31 October 1887, when it closed and moved to Manchester. The Welcome Council was made up of multiple committees; Young was on the Committee of Welcome, which had 1,025 members.<ref>Lowe, Charles. ''Four National Exhibitions and Their Organiser''. T. Fisher Unwin, 1892: 402–424.</ref> The Council and its committees involved work and planning from some of the participants, although many may have been on the committee for their names. If Young did do any work for the committee, he might have done it before the opening on 9 May 1887. '''1891 July 9''', Sir Allen Young was among the more than 3,000 people who were invited to the [[Social Victorians/1891-07-09 Garden Party|Garden Party at Marlborough House]] hosted by the [[Social Victorians/People/Albert Edward, Prince of Wales|Prince]] and [[Social Victorians/People/Alexandra, Princess of Wales|Princess of Wales]].<ref>"Garden Party at Marlborough House." ''Morning Post'' 10 July 1891, Friday: 3 [of 8], Cols. 1–8. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18910710/017/0003.</ref> '''1892 August 16, Tuesday''', Queen Victoria was at Osborne, accompanied by [[Social Victorians/People/Alexandra, Princess of Wales|Alexandra, Princess of Wales]] and Princess Beatrice, and held a [[Social Victorians/Timeline/1892#16 August 1892, Tuesday|dinner party on Tuesday night]]. Allen was present, as were "the Prince and Princess of Wales, the Duke of Connaught, Prince and Princess Henry of Battenberg, Princess Maud of Wales, the Dowager Lady Southampton, Mrs Montgomery, the Earl of Ducie, the Right Hon W E Gladstone, Sir Ducie, the Right Hon W E Gladstone, ... and General Lynedoch Gardiner."<ref>"Court Circular." ''Cork Constitution'' 17 August 1892 Wednesday: 4 [of 8], Col. 6c [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001648/18920817/077/0004.</ref> '''1896 August 19, Wednesday''', Queen Victoria was at Osborne, accompanied by Princess Henry of Battenberg and the Hon. Frances Drummond, and then also Countess Feodore Gleichen. The [[Social Victorians/Timeline/1896#19 August 1896, Wednesday|dinner party Wednesday night]] also included people who were at Cowes for the yachting: "Captain Acland, her Majesty's ship Australia, guardship at Cowes, and the Hon. Mrs. Acland, Mrs. Lawrence Drummond, Sir Allen Young, C.B., and Major Strong, 2nd Battalion Scottish Rifles."<ref>"Court Circular." ''Morning Post'' 20 August 1896 Thursday: 5 [of 8], Col. 4a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18960820/072/0005.</ref> '''1897 July 2''', Sir Allen Young attended the [[Social Victorians/1897 Fancy Dress Ball| Duchess of Devonshire's fancy-dress ball]]. == Costume at the Duchess of Devonshire's 2 July 1897 Fancy-dress Ball == Sir Allen Young attended the [[Social Victorians/1897 Fancy Dress Ball| Duchess of Devonshire's fancy-dress ball]].<ref>"Ball at Devonshire House." The ''Times'' Saturday 3 July 1897: 12, Cols. 1a–4c ''The Times Digital Archive''. Web. 28 Nov. 2015.</ref> == UTC for reconcellation validation digital Cebu Ecco policies Shabu shouldering foil iron melting crystal support by government police and mellittar # Henry Young was the son of Florance Thomas Young, a brewer in London at the end of the 18th century. On 13 February 1809 Henry was bound as a clerk to attorney John Sudlow in London for 5 years.<ref>Ancestry.com. ''UK, Articles of Clerkship, 1756-1874'' [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2012.</ref> Henry was "admitted into the Freedom of this City" on 9 July 1832 based on his father's admission on 19 August 1779.<ref>Ancestry.com. ''London, England, Freedom of the City Admission Papers, 1681-1930'' [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2010.</ref> Perhaps Florance Thomas Young had money, but certainly by 1851 Henry Young had enough money for 10 servants.suply her shabu shouldering foil iron melting crystal support by economic impact payment growth == Footnotes == {{reflist}} obs9vsqvccdnwbgvodlyafuumndujcz 2720418 2720409 2025-07-02T11:51:31Z MathXplore 2888076 Reverted edits by [[Special:Contributions/175.176.64.180|175.176.64.180]] ([[User_talk:175.176.64.180|talk]]) to last version by [[User:Scogdill|Scogdill]] using [[Wikiversity:Rollback|rollback]] 2696496 wikitext text/x-wiki == Also Known As == * Family name: Young * Sir Allen Young * Virtual International Authority File: VIAF ID: [http://viaf.org/viaf/104487564 104487564] == Demographics == * Nationality: English<ref name=":5" /> === Residences === * Sir Capt. Allen William Young: 18 Grafton street W (1885<ref>Ancestry.com. ''London, England, City Directories, 1736-1943'' [database on-line]. Lehi, UT, USA: Ancestry.com Operations, Inc., 2018.</ref> – 1901<ref>Ancestry.com. ''London, England, Electoral Registers, 1832-1965'' [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2010.</ref> [at least]) == Family == * Henry Young (c. 1792 – 7 July 1854<ref>Ancestry.com. ''London, England, Church of England Deaths and Burials, 1813-2003'' [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2010.</ref>) *Ellen Leaf<ref>Ancestry.com. ''London, England, Church of England Marriages and Banns, 1754-1936'' [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2010.</ref> Young (19 August 1796<ref>Ancestry.com. ''London, England, Church of England Baptisms, Marriages and Burials, 1538-1812'' [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2010.</ref> – buried 7 February 1865<ref>Ancestry.com. ''London, England, Church of England Deaths and Burials, 1813-2003'' [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2010.</ref>) *#Amelia Young (c. 1824<ref name=":0">Ancestry.com. ''1851 England Census'' [database on-line]. Provo, UT, USA: Ancestry.com Operations Inc, 2005.</ref> – September 1891<ref name=":2">FreeBMD. ''England & Wales, Civil Registration Death Index, 1837-1915'' [database on-line]. Provo, UT, USA: Ancestry.com Operations Inc, 2006.</ref>) *#Florance Henry Young (12 April 1825<ref name=":3">Ancestry.com. ''London, England, Church of England Births and Baptisms, 1813-1920'' [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2010.</ref> – 7 August 1861<ref name=":4">Ancestry.com. ''England & Wales, National Probate Calendar (Index of Wills and Administrations), 1858-1995'' [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2010.</ref>) *#Adeline Young (29 July 1826<ref name=":3" /> – ) *#'''Sir Allen William Young''' (12 December 1827 – 20 November 1915)<ref name=":5">{{Cite journal|date=2020-06-01|title=Allen Young|url=https://en.wikipedia.org/w/index.php?title=Allen_Young&oldid=960147914|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Allen_Young.</ref> *#Henrietta Young Barron (31 December 1830<ref name=":3" /> – 8 February 1921<ref name=":4" />) *#Emma Young Sim (4 June 1832<ref name=":3" /> – December 1912<ref name=":2" />) *#Ellen Young (1834<ref name=":0" /> – 24 October 1909<ref name=":4" />) *#Sophia Roberta Young Bainbridge (17 June 1835<ref name=":6">Ancestry.com. ''England, Select Births and Christenings, 1538-1975'' [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2014.</ref> – 20 March 1904<ref name=":4" />) *#Frances Marion Young Spearing (25 October 1836<ref name=":6" /> – 27 January 1892<ref name=":4" />) *#Maria Young (29 April 1839<ref name=":3" /> – ) * === Relations === == Acquaintances, Friends and Enemies == === Acquaintances === === Friends === === Enemies === == Organizations == == Timeline == '''1851 March 30, Sunday''', the 1851 Census for England and Wales lists the following people at Cross Deep, Riverdale [?] House: Henry Young (Head of Household, 58 years old), Ellen Young (56), Amelia Young (27), F. Henry Young (26), Henrietta Young (20), Emma Young (18), Ellen Young (17), Sophia Roberta Young (15), Frances Marrion Young (14), Maria Young (13), An Beer (Governess, 27?), James Mepham (Footman, 27), John Squire (Groom, 26?), Sam Johnson (Groom, 25), Lydia Skilton (Cook, 50?), Mary Phillips (1st Ladies Maid, 23), Martha Staggers (2nd Ladies Maid, 24), Ann Mathews (House Maid, 25), Elizabeth Cordery (House Maid, 20), and Harriet Gurman (Kitchen Maid, 23).<ref name=":0" /> The 1851 Census lists Allen William Young as a visitor at 1 Walton Court in St. Botolph, Aldgate.<ref name=":0" /> '''1861 April 7, Sunday''', the 1861 Census for England and Wales lists lists the following people at Riversdale Villa, Cross Deep, Eastside: Ellen Young (Head of Household, Widow, 65 years old), Amelia Young (37), Emma Young (28), Ellen Young (27), Maria Young (22), son-in-law John Sidney Webb (Widowed, Elder Brother, 45), Rebecca Perkins (Ladies Maid, 19), Ann Hardy (Housemaid, 37), Charlotte Clements (Housemaid, 26), Ellena MacKinnery (Cook, 30), John Fairfield (Groom, 27), and George Butlin (Footman, 20).<ref name=":1">Ancestry.com. ''1861 England Census'' [database on-line]. Provo, UT, USA: Ancestry.com Operations Inc, 2005.</ref> In the 1861 Census, Allen William Young is visiting West Cowes in the Royal Yacht Squadron Club-House.<ref name=":1" /> '''1876''', Young was knighted (CB, Companion of the Order of the Bath) for his work searching for the Franklin expedition.<ref name=":5" /> '''1877 May 27''', Young introduced Lily Langtree to [[Social Victorians/People/Albert Edward, Prince of Wales|Albert Edward, Prince of Wales]] at a dinner party he hosted: "Sir Allen Young, the arctic explorer, invited her to late supper in his house, where it had been arranged that the Prince of Wales should meet her after the opera. The result was all that could have been expected. Mrs. Langtry became the Prince's first openly recognised mistress."<ref>Leslie, Anita. ''The Marlborough House Set''. Doubleday, 1973: 69.</ref> '''1881 July 14, afternoon, beginning about 2 p.m.''', Sir Allen Young was among the 3,000 or so people who were invited to the [[Social Victorians/1881-07-14 Garden Party|Garden Party at Marlborough House]] hosted by the [[Social Victorians/People/Albert Edward, Prince of Wales|Prince]] and [[Social Victorians/People/Alexandra, Princess of Wales|Princess of Wales]].<ref>"Garden Party at Marlborough House." ''Morning Post'' 16 July 1881 Saturday: 5 [of 8], Col. 6a–c [of 6] through 6, Col. 1a–3c. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/BL/0000174/18810716/051/0006 (p. 6, beginning with the Earl and Countess of Wharncliffe)</ref> Queen Victoria was at this event. '''1881 July 22, Friday''', Sir Allen Young was among the 750–1000 people who were invited to the [[Social Victorians/1881-07-22 Marlborough House Party|Marlborough House Party]] hosted by the [[Social Victorians/People/Albert Edward, Prince of Wales|Prince]] and [[Social Victorians/People/Alexandra, Princess of Wales|Princess of Wales]].<ref>"Court Circular: Marlborough House." ''Morning Post'' 23 July 1881, Saturday: 5 [of 8], Cols. 5-6a. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18810723/058/0005.</ref> '''1886 July 21, Wednesday''', Sir Allen Young was among the 750–1000 people who were invited to the [[Social Victorians/1886-07-21 Marlborough House Ball|Ball at Marlborough House]] hosted by the [[Social Victorians/People/Albert Edward, Prince of Wales|Prince]] and [[Social Victorians/People/Alexandra, Princess of Wales|Princess of Wales]].<ref>"Ball at Marlborough House." ''Morning Post'' 22 July 1886, Thursday: 5 [of 8], Cols. 6–7. ''British Newspaper Archive''. http://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18860722/055/0005.</ref> '''1887 May 9''', Sir Allen Young was among the more than 1,000 members of the [[Social Victorians/1887 American Exhibition/Welcome Council|Welcome Council of the American Exhibition]] at Earl's Court, which included Buffalo Bill's ''Wild West'', and which ran from 9 May 1887 through 31 October 1887, when it closed and moved to Manchester. The Welcome Council was made up of multiple committees; Young was on the Committee of Welcome, which had 1,025 members.<ref>Lowe, Charles. ''Four National Exhibitions and Their Organiser''. T. Fisher Unwin, 1892: 402–424.</ref> The Council and its committees involved work and planning from some of the participants, although many may have been on the committee for their names. If Young did do any work for the committee, he might have done it before the opening on 9 May 1887. '''1891 July 9''', Sir Allen Young was among the more than 3,000 people who were invited to the [[Social Victorians/1891-07-09 Garden Party|Garden Party at Marlborough House]] hosted by the [[Social Victorians/People/Albert Edward, Prince of Wales|Prince]] and [[Social Victorians/People/Alexandra, Princess of Wales|Princess of Wales]].<ref>"Garden Party at Marlborough House." ''Morning Post'' 10 July 1891, Friday: 3 [of 8], Cols. 1–8. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18910710/017/0003.</ref> '''1892 August 16, Tuesday''', Queen Victoria was at Osborne, accompanied by [[Social Victorians/People/Alexandra, Princess of Wales|Alexandra, Princess of Wales]] and Princess Beatrice, and held a [[Social Victorians/Timeline/1892#16 August 1892, Tuesday|dinner party on Tuesday night]]. Allen was present, as were "the Prince and Princess of Wales, the Duke of Connaught, Prince and Princess Henry of Battenberg, Princess Maud of Wales, the Dowager Lady Southampton, Mrs Montgomery, the Earl of Ducie, the Right Hon W E Gladstone, Sir Ducie, the Right Hon W E Gladstone, ... and General Lynedoch Gardiner."<ref>"Court Circular." ''Cork Constitution'' 17 August 1892 Wednesday: 4 [of 8], Col. 6c [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001648/18920817/077/0004.</ref> '''1896 August 19, Wednesday''', Queen Victoria was at Osborne, accompanied by Princess Henry of Battenberg and the Hon. Frances Drummond, and then also Countess Feodore Gleichen. The [[Social Victorians/Timeline/1896#19 August 1896, Wednesday|dinner party Wednesday night]] also included people who were at Cowes for the yachting: "Captain Acland, her Majesty's ship Australia, guardship at Cowes, and the Hon. Mrs. Acland, Mrs. Lawrence Drummond, Sir Allen Young, C.B., and Major Strong, 2nd Battalion Scottish Rifles."<ref>"Court Circular." ''Morning Post'' 20 August 1896 Thursday: 5 [of 8], Col. 4a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18960820/072/0005.</ref> '''1897 July 2''', Sir Allen Young attended the [[Social Victorians/1897 Fancy Dress Ball| Duchess of Devonshire's fancy-dress ball]]. == Costume at the Duchess of Devonshire's 2 July 1897 Fancy-dress Ball == Sir Allen Young attended the [[Social Victorians/1897 Fancy Dress Ball| Duchess of Devonshire's fancy-dress ball]].<ref>"Ball at Devonshire House." The ''Times'' Saturday 3 July 1897: 12, Cols. 1a–4c ''The Times Digital Archive''. Web. 28 Nov. 2015.</ref> == Notes and Questions == # Henry Young was the son of Florance Thomas Young, a brewer in London at the end of the 18th century. On 13 February 1809 Henry was bound as a clerk to attorney John Sudlow in London for 5 years.<ref>Ancestry.com. ''UK, Articles of Clerkship, 1756-1874'' [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2012.</ref> Henry was "admitted into the Freedom of this City" on 9 July 1832 based on his father's admission on 19 August 1779.<ref>Ancestry.com. ''London, England, Freedom of the City Admission Papers, 1681-1930'' [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2010.</ref> Perhaps Florance Thomas Young had money, but certainly by 1851 Henry Young had enough money for 10 servants. == Footnotes == {{reflist}} 0cys3wm102qzew48b5rn5z5hu9sk8cl 1 292816 2720414 2596906 2025-07-02T11:45:12Z 175.176.64.180 /* References */ Reply 2720414 wikitext text/x-wiki == References == Thanks for this interesting material. However, I was not able to resolve some of the short references. Especially Küntz. Which of the books by Darcy Küntz is it? It might be helpful to add a bibliography page. Greetings --[[User:WolfgangRieger|WolfgangRieger]] ([[User talk:WolfgangRieger|discuss]] • [[Special:Contributions/WolfgangRieger|contribs]]) 18:15, 11 March 2023 (UTC) :UTC approve for shouldering foil iron melting crystal supported police department and mellittar [[Special:Contributions/175.176.64.180|175.176.64.180]] ([[User talk:175.176.64.180|discuss]]) 11:45, 2 July 2025 (UTC) == Interesting resource == {{ping|Scogdill}} I have some relatives you might call social Victorians. I don't know if they went to dress balls or any of that, but they were among the English nobility. Do you have material on the early Victorian era? [[User:AP295|AP295]] ([[User talk:AP295|discuss]] • [[Special:Contributions/AP295|contribs]]) 21:23, 1 January 2024 (UTC) 7zgi0dngu5hliucpwowwixtyqas4gob 2720415 2720414 2025-07-02T11:47:18Z 175.176.64.180 /* References */ Reply 2720415 wikitext text/x-wiki == References == Thanks for this interesting material. However, I was not able to resolve some of the short references. Especially Küntz. Which of the books by Darcy Küntz is it? It might be helpful to add a bibliography page. Greetings --[[User:WolfgangRieger|WolfgangRieger]] ([[User talk:WolfgangRieger|discuss]] • [[Special:Contributions/WolfgangRieger|contribs]]) 18:15, 11 March 2023 (UTC) :UTC approve for shouldering foil iron melting crystal supported police department and mellittar [[Special:Contributions/175.176.64.180|175.176.64.180]] ([[User talk:175.176.64.180|discuss]]) 11:45, 2 July 2025 (UTC) :Shabu shouldering foil iron melting crystal supported police department and mellittar [[Special:Contributions/175.176.64.180|175.176.64.180]] ([[User talk:175.176.64.180|discuss]]) 11:47, 2 July 2025 (UTC) == Interesting resource == {{ping|Scogdill}} I have some relatives you might call social Victorians. I don't know if they went to dress balls or any of that, but they were among the English nobility. Do you have material on the early Victorian era? [[User:AP295|AP295]] ([[User talk:AP295|discuss]] • [[Special:Contributions/AP295|contribs]]) 21:23, 1 January 2024 (UTC) lz4xft8yzn7e6wlahvffnk84tkerrm5 2720416 2720415 2025-07-02T11:50:11Z 175.176.64.180 /* References */ Reply 2720416 wikitext text/x-wiki == References == Thanks for this interesting material. However, I was not able to resolve some of the short references. Especially Küntz. Which of the books by Darcy Küntz is it? It might be helpful to add a bibliography page. Greetings --[[User:WolfgangRieger|WolfgangRieger]] ([[User talk:WolfgangRieger|discuss]] • [[Special:Contributions/WolfgangRieger|contribs]]) 18:15, 11 March 2023 (UTC) :UTC approve for shouldering foil iron melting crystal supported police department and mellittar [[Special:Contributions/175.176.64.180|175.176.64.180]] ([[User talk:175.176.64.180|discuss]]) 11:45, 2 July 2025 (UTC) :Shabu shouldering foil iron melting crystal supported police department and mellittar [[Special:Contributions/175.176.64.180|175.176.64.180]] ([[User talk:175.176.64.180|discuss]]) 11:47, 2 July 2025 (UTC) ::shabu drug melting crystal shouldering foil iron supported police department and mellittar [[Special:Contributions/175.176.64.180|175.176.64.180]] ([[User talk:175.176.64.180|discuss]]) 11:50, 2 July 2025 (UTC) == Interesting resource == {{ping|Scogdill}} I have some relatives you might call social Victorians. I don't know if they went to dress balls or any of that, but they were among the English nobility. Do you have material on the early Victorian era? [[User:AP295|AP295]] ([[User talk:AP295|discuss]] • [[Special:Contributions/AP295|contribs]]) 21:23, 1 January 2024 (UTC) n28xc10rho28xaqi26niyphdoo3negp 2720417 2720416 2025-07-02T11:51:24Z MathXplore 2888076 Reverted edits by [[Special:Contributions/175.176.64.180|175.176.64.180]] ([[User_talk:175.176.64.180|talk]]) to last version by [[User:AP295|AP295]] using [[Wikiversity:Rollback|rollback]] 2596906 wikitext text/x-wiki == References == Thanks for this interesting material. However, I was not able to resolve some of the short references. Especially Küntz. Which of the books by Darcy Küntz is it? It might be helpful to add a bibliography page. Greetings --[[User:WolfgangRieger|WolfgangRieger]] ([[User talk:WolfgangRieger|discuss]] • [[Special:Contributions/WolfgangRieger|contribs]]) 18:15, 11 March 2023 (UTC) == Interesting resource == {{ping|Scogdill}} I have some relatives you might call social Victorians. I don't know if they went to dress balls or any of that, but they were among the English nobility. Do you have material on the early Victorian era? [[User:AP295|AP295]] ([[User talk:AP295|discuss]] • [[Special:Contributions/AP295|contribs]]) 21:23, 1 January 2024 (UTC) e3pgtt55fblt8bjph1cdxun8b0t7j9b 0 317146 2720358 2718293 2025-07-01T16:13:47Z Bocardodarapti 289675 2720358 wikitext text/x-wiki {{Linear algebra (Osnabrück 2024-2025)/Part II/Lecture design|48| {{Subtitle|Residue class rings}} On the residue class group for a normal subgroup in a group, there are quite often additional structures available, if the group and the normal subgroup fulfill certain properties. In the last lecture, we have looked at residue class spaces for a linear subspace. Here, we discuss briefly residue class rings for an ideal in a commutative ring. We recall the definition of a ring homomorphism. {{ inputdefinition |Ring theory/Ring homomorphism/Definition|| }} {{ inputfactproofexercise |Commutative ring/Ring homomorphism/Kernel/Ideal/Fact|Lemma|| }} {{:Commutative ring/Residue class ring/Group known/Introduction/Section}} {{Subtitle|The residue class rings of {{mat|term= \Z |pm=}}}} {{ inputimage |Anillo cíclico|png | 300px {{!}} {{!}} |epsname=Anillo_cíclico Romero Schmidtke |User=FrancoGG |Domain=es.wikipedia.org |License=CC-BY-SA-3.0 }} We know already the residue class groups {{mathl|term= {{op:Zmod|d}} |pm=;}} they are cyclic groups of order {{mat|term= d |pm=.}} Moreover, these groups get now also a ring structure. {{ inputfactproofhere |Residue class rings of Z/Ring homomorphism/Fact|Corollary|| |Proof text=This is a special case of the considerations above. }} {{ inputfactproofexercise |Residue class rings of Z/Field/Integer/Prime number/Fact|Theorem|| }} The residue class rings {{ Relationchain | S || K[X]/(P) || || || |pm= }} are also quite easy to understand {{ Extra/Bracket |text={{mat|term= K |pm=}} a field| |Ipm=|Epm=. }} If {{mat|term= P |pm=}} has degree {{mat|term= d |pm=,}} then every residue class in {{mat|term= S |pm=}} is represented by a unique polynomial of degree {{mat|term= < d |pm=.}} This polynomial is the remainder that we get by dividing through {{mat|term= P |pm=.}} {{Subtitle|Orientations on a real vector space}} {{:Orientation/Vector space/Low dimension/Introduction/Section|extra1=Footnote}} {{:Orientation/Vector space/Orientation-preserving mapping/Introduction/Section|}} {{List of footnotes}} }} 51x4n5zkyub2sd166mg4xo79jj5mxlh 0 318211 2720319 2697915 2025-07-01T14:57:44Z 2C0F:F5C0:B2A:2585:2086:36C6:CC23:50BB /* 5. Conclusion */ 2720319 wikitext text/x-wiki {{Article info |journal = WikiJournal Preprints |last1 = Dar |first1 = Deen Mohd |last2 = |first2 = |last3 = |first3 = |last4 = |first4 = |et_al = |affiliations = Indira Gandhi National Open University |correspondence = info@drdeenz.com |Orcid = https://orcid.org/0009-0002-5203-8054 |keywords = Histrionic Personality, Narcissistic Personality, Psychometrics, Deenz Histrionic Personality Scale, Deenz Narcissistic Personality Scale, Behavioral Analysis |license = CC-BY |abstract = This research aims to provide a detailed and comparative analysis of Histrionic Personality (HP) and Narcissistic Personality (NP) traits, utilizing the Deenz Histrionic Personality Scale (DHPS) and the Deenz Narcissistic Personality Scale (DNPS) developed by Deen (2024). Both HP and NP are personality types characterized by an overwhelming desire for attention and admiration, yet they manifest in distinct ways. Individuals with HP often display excessive emotional expressiveness and seek attention through dramatic and sometimes manipulative behaviors, whereas those with NP tend to present an inflated self-image and seek admiration through a sense of superiority. While these two personality types share overlapping features, such as attention-seeking behaviors, the motivations driving these behaviors differ significantly. The study involved 64 participants who completed the computerized versions of the DHPS and DNPS, measuring various facets that define these two personality types. The data analysis focused on comparing the mean scores and standard deviations for each facet, revealing key differences and similarities in traits such as grandiosity, fantasy, entitlement, emotional reactivity, impulsivity, and empathy. Findings from this study suggest that, while both HP and NP individuals exhibit self-centered tendencies, HP traits are more emotionally reactive, driven by a need for validation through dramatic displays of emotion, whereas NP traits reflect a rigid belief in one’s inherent superiority and entitlement to special treatment. The results have significant implications for clinical diagnosis and intervention strategies, as they enhance our understanding of these complex personality structures and their manifestation in real-world behavior. By examining these personality traits in-depth, this study contributes to the development of more effective diagnostic tools and therapeutic approaches tailored to individuals exhibiting characteristics of HP and NP. }} ==1. Introduction== Histrionic Personality (HP) and Narcissistic Personality (NP) are two distinct yet often overlapping personality types that are characterized by patterns of emotional expression, social interactions, and the way individuals seek attention and admiration from others. These personality types are classified as part of the broader category of personality disorders in the Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition (DSM-5; American Psychiatric Association, 2013), which serves as a critical framework for understanding psychological functioning and diagnosing mental health conditions. While both HP and NP are frequently associated with excessive attention-seeking behavior, the underlying motivations, behaviors, and emotional processes that define each disorder are distinct. Histrionic Personality Disorder (HPD) is primarily marked by a pervasive pattern of excessive emotionality and attention-seeking. Individuals with HPD are often seen as dramatic, theatrical, and overly expressive, with their emotional responses tending to be exaggerated and out of proportion to the situation at hand (French & Shrestha, 2024). These individuals crave attention and validation, often using their emotional expressions as a means of drawing others’ focus. HPD is typically associated with individuals who demonstrate impulsive behaviors, are sensitive to criticism, and struggle to maintain stable relationships. The intense desire for attention often drives them to seek out situations or relationships where they can be the center of attention, and when they are not the focal point, they may become anxious or distressed (Mitra & Fluyau, 2023). On the other hand, Narcissistic Personality Disorder (NPD) is defined by an inflated sense of self-importance, a need for admiration, and a lack of empathy for others. Narcissistic individuals believe they are unique or special and expect recognition and special treatment based on these beliefs. NPD is often characterized by a pervasive sense of entitlement, a tendency to exploit others for personal gain, and difficulty in recognizing the feelings and needs of others (American Psychiatric Association, 2013). While individuals with NP share the desire for attention with those who exhibit HP traits, their underlying motivations are often more tied to their self-image and an unshakable belief in their own superiority. Narcissistic individuals typically seek admiration and validation, but this is driven by their need to preserve their idealized self-image rather than by a genuine desire for emotional connection or empathy with others (Mitra & Fluyau, 2023). While both personality disorders exhibit traits that center around attention-seeking behavior, the ways in which these traits manifest and the social, emotional, and cognitive processes that drive them differ significantly. Research into the similarities and differences between these two personality types is essential to further understanding their underlying causes, their impact on interpersonal relationships, and how they can be addressed in clinical practice. Both HPD and NPD can lead to interpersonal difficulties, emotional distress, and challenges in professional and personal contexts. ==2. Methodology== This study employs the Deenz Histrionic Personality Scale and Deenz Narcissistic Personality Scale (Deen, 2024) to assess traits associated with both personality types. A total of 64 participants, all adults, completed the computerized version of the scales. Each scale contains specific facets designed to evaluate key behaviors and emotional tendencies that characterize Histrionic and Narcissistic personalities. The participants' responses were then analyzed to determine significant patterns, including the mean and standard deviation for each trait within both personality constructs. The analysis provided insight into how these two personality types overlap and diverge in terms of emotional responses, behavioral patterns, and interpersonal dynamics. ==3. Findings== The data analysis revealed distinct differences between the two personality types, with several patterns emerging from the responses. The participants exhibited clear behavioral and emotional tendencies linked to their respective personality types, which are discussed below. ===3.1 Histrionic Personality Facets=== Attention-Seeking: Individuals with Histrionic Personality are highly extroverted and driven by a desire to be the center of attention. Their behaviors are often noticeable, as they tend to engage in over-the-top actions to gain the admiration of others. Whether through excessive talking, exaggerated body language, or seeking sympathy, attention-seeking behaviors dominate this personality type. People with this trait are often perceived as overly dramatic or manipulative in their pursuit of the spotlight (Mitra & Fluyau, 2023). Excessive Emotionality: Histrionic individuals tend to express their emotions in a dramatic and exaggerated way, particularly when seeking attention or sympathy. They may display theatrical reactions to situations, making their emotional responses appear disproportionate. This trait contributes to their need to evoke strong emotional responses from others (French & Shrestha, 2024). Attention-Seeking: Individuals with Histrionic Personality are highly extroverted and driven by a desire to be the center of attention. Their behaviors are often noticeable, as they tend to engage in over-the-top actions to gain the admiration of others. Whether through excessive talking, exaggerated body language, or seeking sympathy, attention-seeking behaviors dominate this personality type. People with this trait are often perceived as overly dramatic or manipulative in their pursuit of the spotlight (Mitra & Fluyau, 2023). Excessive Emotionality: Histrionic individuals tend to express their emotions in a dramatic and exaggerated way, particularly when seeking attention or sympathy. They may display theatrical reactions to situations, making their emotional responses appear disproportionate. This trait contributes to their need to evoke strong emotional responses from others (French & Shrestha, 2024). Hypersensitivity: This facet describes a heightened sensitivity to not being the center of attention. People with Histrionic Personality often feel uneasy or rejected when they are overlooked or criticized. This hypersensitivity can lead to emotional distress or outbursts, further driving their need for validation. Impulsivity: Impulsive behavior is another significant trait of Histrionic Personality. These individuals act on sudden urges, often without considering long-term consequences. This can lead to reckless or risky decisions in both their personal and professional lives. Seductive Behavior: Engaging in flirtatious or provocative actions is a common method for individuals with Histrionic Personality to capture attention. Whether intentionally or unconsciously, these behaviors can lead to misunderstandings or discomfort in social settings. ===3.2 Narcissistic Personality Facets=== Grandiosity: A key feature of Narcissistic Personality is grandiosity, which involves an exaggerated sense of one’s own importance. Individuals with this trait often believe they are superior to others and expect special treatment. They view themselves as exceptional and deserving of admiration (American Psychiatric Association, 2013). Fantasy: Narcissistic individuals tend to engage in grandiose fantasies about success, power, and attractiveness. These fantasies act as a defense mechanism to protect against feelings of inadequacy and to boost their self-esteem. Specialness: Narcissistic individuals believe they are unique and often expect to be recognized as such. They want to be seen as special and deserving of admiration, which they may actively seek from others. Entitlement: A significant trait of Narcissistic Personality is the belief that one deserves special privileges, regardless of whether they’ve earned them. This sense of entitlement can lead to frustration and disappointment when their expectations are not met. Exploitation: People with Narcissistic Personality often take advantage of others for personal gain. They may manipulate or exploit others without regard for their well-being, seeing them as tools to maintain or enhance their own status. Lack of Empathy: A hallmark of Narcissistic Personality is the inability to understand or care about others’ emotions or needs. Individuals with this trait are focused solely on their own desires and often show little concern for how their actions affect others. Envy: Narcissistic individuals may feel envious of others' success and may attempt to undermine or belittle them in order to maintain their own sense of superiority. Arrogance: Arrogance is another defining trait of Narcissistic Personality. Individuals with this trait often display a dismissive attitude toward others, believing that they are superior and entitled to more than others. ==4. Discussion== The findings of this study indicate that while both Histrionic and Narcissistic Personality types exhibit attention-seeking behaviors, the underlying motivations and emotional responses differ. Histrionic individuals tend to express their need for attention through dramatic emotional reactions, whereas Narcissistic individuals seek admiration by promoting their superiority and demanding special treatment. Narcissistic traits are more rigid, self-centered, and associated with a lack of empathy, while Histrionic traits are more reactive, driven by emotional expression, and sometimes impulsive in nature. These differences suggest that Histrionic individuals are more emotionally driven and often seek emotional validation, whereas Narcissistic individuals are motivated by a desire for status and control over others. Understanding these differences is crucial in diagnosing and treating these personality types, especially in clinical settings. ==5. Conclusion== Abstract The significance of Emotional Intelligence (EI) in contemporary organizational environments has become increasingly apparent, particularly concerning its influence on leadership effectiveness and employee engagement. As organizations confront complex demands in an era defined by rapid technological change, globalization, and diverse workforce dynamics, emotionally intelligent leadership is now recognized as an indispensable driver of success. This critical review investigates how EI contributes to leadership capabilities, examining its role in shaping interpersonal relationships, decision-making, conflict management, and motivational strategies. Simultaneously, it explores how emotionally intelligent leaders enhance employee engagement by creating psychologically safe, supportive, and empathetic work environments. Drawing on a wide range of theoretical frameworks and empirical findings from the last three decades, the review highlights both the transformative potential and the limitations of EI in leadership practice. Methodological issues in measurement and cross-cultural applicability are also critically evaluated. The review concludes by identifying key research gaps and offering recommendations for future inquiry, including the need for longitudinal studies, culturally sensitive EI instruments, and more nuanced training interventions. ==Additional Information== ===Acknowledgements=== No funding was received for this research ===Competing Interests=== The authors declare no competing interests. ===Ethics Statement=== The study protocol was reviewed and approved by an independent ethics committee of IGNOU to ensure compliance with ethical guidelines. ==References== American Psychiatric Association. (2013). Diagnostic and Statistical Manual of Mental Disorders (5th ed.). American Psychiatric Association. https://doi.org/10.1176/appi.books.9780890425596 Dar, Deen Mohd. Deenz [https://drdeenz.com/histrionic-personality-disorder-test/ Histrionic Personality Scale]: Measuring Subclinical Traits and Identifying Potential for Histrionic Personality Disorder Among College Students.” Authorea Preprints (2024). https://doi.org/10.22541/au.170534748.80679693/v1 Development and Validation of Deenz [https://drdeenz.com/narcissistic-personality-test/ Narcissistic Personality Scale]- Measuring Subclinical Traits of Narcissistic Personality [https://doi.org/10.31234/osf.io/mfcvp] Ronningstam, E. (2016). Narcissistic personality disorder: A current review. Current Psychiatry Reports, 18(6), 41. https://doi.org/10.1007/s11920-016-0725-1 French, J. H., & Shrestha, R. (2024). Histrionic Personality Disorder. StatPearls. Treasure Island (FL): StatPearls Publishing. https://www.ncbi.nlm.nih.gov/books/NBK542325/ Mitra, P., & Fluyau, D. (2023). Narcissistic Personality Disorder. StatPearls. Treasure Island (FL): StatPearls Publishing. https://www.ncbi.nlm.nih.gov/books/NBK556001/ Miller, J. D., & Lynam, D. R. (2012). The Histrionic Personality: Toward a more precise definition. Personality Disorders: Theory, Research, and Treatment, 3(1), 42-55. https://doi.org/10.1037/a0025877 Campbell, W. K., & Miller, J. D. (2011). The emergent role of narcissism in personality and social psychology. Social and Personality Psychology Compass, 5(1), 121-137. https://doi.org/10.1111/j.1751-9004.2010.00277.x Lobbestael, J., & Arntz, A. (2013). The interpersonal dynamics of Histrionic Personality Disorder. Journal of Personality Disorders, 27(2), 180-193. https://doi.org/10.1521/pedi.2013.27.2.180 Pincus, A. L., & Roche, M. J. (2013). Narcissism and interpersonal functioning. Journal of Personality, 81(4), 469-489. https://doi.org/10.1111/jopy.12025 Veenstra, R., & Lindenberg, S. (2014). Personality, relationships, and aggression in narcissistic individuals. Journal of Research in Personality, 53, 47-56. https://doi.org/10.1016/j.jrp.2014.07.004 p2f062y5tuc238b1j9pk8rsnzwwbrg9 0 320340 2720391 2709200 2025-07-02T06:43:33Z Bocardodarapti 289675 2720391 wikitext text/x-wiki {{ Mathematical text/Proof |Text= {{ Proofstructure |Strategy= |Notation= |Proof= {{ Enumeration3 |The {{ Definitionlink |transposed matrix| |Context=| |pm= }} is {{ Definitionlink |row stochastic| |Context=| |pm=; }} therefore, it has an {{ Definitionlink |eigenvector| |Context=| |pm= }} {{mathl|term= {{op:Column vector|1|1|\vdots|1}} |pm=}} to the eigenvalue {{mat|term= 1 |pm=.}} Due to {{ Factlink |Factname=Endomorphism/Eigenvalue and characteristic polynomial/Fact |Nr= |pm=, }} the {{ Definitionlink |characteristic polynomial| |Context=| |pm= }} of the transposed matrix has a zero at {{mat|term= 1 |pm=.}} Because of {{ Exerciselink |Exercisename=Characteristic polynomial/Transposed matrix/Exercise |Nr= |pm=, }} this also holds for the characteristic polynomial of the matrix we have started with. Hence, {{mat|term= M |pm=}} has an eigenvector to the eigenvalue {{mat|term= 1 |pm=.}} |We now assume also that all entries of the {{mat|term= k |pm=-}}th row are positive, and let {{ Relationchain | v |\in| V || || || |pm= }} denote a vector with {{ Extra/Bracket |text=at least| |Ipm=|Epm= }} a positive and a negative entry. Then {{ Relationchain/align | {{op:Sum norm|Mv}} || \sum_{ i {{=}} 1}^n {{op:Modulus| (Mv)_i}} || \sum_{ i {{=}} 1}^n {{op:Modulus| \sum_{j {{=}} 1}^n a_{ij} v_j }} || \sum_{ i \neq k} {{op:Modulus| \sum_{j {{=}} 1}^n a_{ij} v_j }} + {{op:Modulus| \sum_{j {{=}} 1}^n a_{kj} v_j }} |<| \sum_{i \neq k} \sum_{ j {{=}} 1}^n a_{ij} {{op:Modulus| v_j}} + \sum_{j {{=}} 1}^n {{op:Modulus| a_{kj} v_j }} || \sum_{i {{=}} 1}^n \sum_{j {{=}} 1}^n a_{ij} {{op:Modulus|v_j|}} || \sum_{ j {{=}} 1}^n {{op:Modulus|v_j|}} {{mabr| \sum_{i {{=}} 1}^n a_{ij} |}} || \sum_{ j {{=}} 1}^n {{op:Modulus|v_j|}} || {{op:Sum norm|v}} |pm= }} holds. |As in the proof of (2), let all entries of the {{mat|term= k |pm=-}}th row be positive. For any eigenvector {{mat|term= v |pm=}} to the eigenvalue {{mat|term= 1 |pm=,}} according to (2), either all entries are non-negative, or non-positive. Hence, for such a vector, because of {{ Relationchain | Mv || v || || || |pm=, }} its {{mat|term= k |pm=-}}th entry is not {{mat|term= 0 |pm=.}} Let {{mat|term= v,w|pm=}} be such eigenvectors. Then {{mathl|term= {{op:Fraction|w_k|v_k}} v-w |pm=}} belongs to the fixed space. However, the {{mat|term= k |pm=-}}th component of this vector equals {{mat|term= 0 |pm=;}} therefore, it is the zero vector. This means that {{ Mathcor|term1= v |and|term2= w |pm= }} are {{ Definitionlink |linearly dependent| |Context=| |pm=. }} Therefore, this eigenspace is one-dimensional. Because of (2), there exists an eigenvector to the eigenvalue {{mat|term= 1 |pm=}} with non-negative entries. By normalizing, we get a stationary distribution. }} |Closure= }} |Textform=Proof |Category=See }} 54xgauw7dvj7s579cb949zow65omadi 0 320346 2720406 2709207 2025-07-02T10:04:34Z Bocardodarapti 289675 2720406 wikitext text/x-wiki {{ Mathematical text/Proof |Text= {{ Proofstructure |Strategy= |Notation= |Proof= Let {{ Relationchain | w |\in| \R^n || || || |pm= }} be the stationary distribution, which is uniquely determined because of {{ Factlink |Factname=Column stochastic matrix/Positive row/One-dimensional eigenspace/Fact |Nr=3 |pm=. }} We set {{ Relationchain/display | U || {{Setcond| {{op:Column vector|u_1|\vdots|u_n}} |\sum_{i {{=}} 1}^n u_i {{=}} 0 }} |\subseteq| \R^n || || |pm=. }} This is a linear subspace of {{mat|term= \R^n |pm=}} of dimension {{mat|term= n-1 |pm=.}} Due to {{ Factlink |Factname= |Factname=Column stochastic matrix/Positive row/One-dimensional eigenspace/Fact |Nr=2 |pm=, }} {{mat|term= w |pm=}} has only non-negative entries; therefore, it does not belong to {{mat|term= U |pm=.}} Because of {{ Relationchain/align | \sum_{ i {{=}} 1}^n (Mu)_i || \sum_{ i {{=}} 1}^n {{mabr| \sum_{j {{=}} 1}^n a_{ij} u_j |}} || \sum_{ j {{=}} 1}^n u_j {{mabr| \sum_{i {{=}} 1}^n a_{ij} |}} || \sum_{ j {{=}} 1}^n u_j || |pm=, }} {{mat|term= U |pm=}} is invariant under the matrix {{mat|term= M |pm=.}} Hence, {{ Relationchain/display | V ||\R w \oplus U || || || |pm= }} is a {{ Definitionlink |direct sum decomposition| |Context=| |pm= }} into invariant linear subspaces. For every {{ Relationchain | u |\in| U || || || |pm= }} with {{ Relationchain | {{op:Sum norm|u|}} || 1 || || || |pm=, }} we have {{ Relationchain/display | {{op:Sum norm| M u|}} |<| 1 || || || |pm= }} due to {{ Factlink |Factname=Column stochastic matrix/Positive row/One-dimensional eigenspace/Fact |Nr=2 |pm=. }} The sphere of radius {{mat|term= 1 |pm=}} is {{ Definitionlink |compact| |Context=| |pm= }} with respect to every norm; therefore, the induced maximum norm of {{mat|term= M{{|}}_U |pm=}} is smaller than {{mat|term= 1 |pm=.}} Because of {{ Factlink |Factname= Spectral radius/Maximum norm/Fact |Nr= |pm= }} and {{ Factlink |Factname= Endomorphism/K/Powers/Zero convergence/Fact |Nr= |pm=, }} the sequence {{mathl|term= M^n u |pm=}} converges for every {{ Relationchain | u |\in| U || || || |pm= }} to the zero vector. Let now {{ Relationchain | v |\in| V || || || |pm= }} be a distribution vector; because of {{ Relationchain/display | \sum_{i {{=}}1 }^n v_i || 1 || \sum_{i {{=}}1 }^n w_i || || |pm=, }} we can write {{ Relationchain/display |v ||w +u || || || |pm= }} with {{ Relationchain | u |\in| U || || || |pm=. }} Because of {{ Relationchain/display | M^m v || M^m (w+u) || M^m w +M^m u || w +M^m u || || |pm=, }} and the reasoning before, this sequence converges to {{mat|term= w |pm=.}} |Closure= }} |Textform=Proof |Category=See }} beaio2jnuvkw4aamc6mgf2iofblshvp 0 320488 2720386 2709849 2025-07-02T05:59:03Z Bocardodarapti 289675 2720386 wikitext text/x-wiki {{ Mathematical text/Proof |Text= {{ Proofstructure |Strategy= |Notation= |Proof= {{ Part of proof |Goal=We show first that we have a {{ Definitionlink |generating system| |Context=vs| |pm=. }} |Proof= Because the elements of the form {{mathl|term= w_1 {{wedgedots|}} w_n |pm=}} form a generating system of {{mathl|term= \bigwedge^n V |pm=}} due to {{ Factlink |Factname= Wedge product/Elementary properties/Fact |Nr=1 |pm=, }} it is enough to show that these elements can be represented. For every {{mat|term= w_j |pm=,}} there exists a representation {{ Relationchain | w_j || \sum_{i {{=|}} 1}^m a_{ij} v_i || || || |pm=; }} therefore, according to {{ Factlink |Factname= Wedge product/Elementary properties/Fact |Nr=4 |pm=. }} we can write the {{mathl|term= w_1 {{wedgedots|}} w_n |pm=}} as {{ Definitionlink |linear combinations| |pm= }} of wedge products of the basis elements; however, every ordering may occur. Hence, let {{mathl|term= v_{k_1} {{wedgedots|}} v_{k_n} |pm=}} be given, with {{ Relationchain | k_j |\in| {{Set1m|}} || || || |pm=. }} By swapping neighboring vectors, using {{ Factlink |Factname= Wedge product/Elementary properties/Fact |Nr=3 |pm=, }} we may achieve {{ Extra/Bracket |text=maybe with another sign| |Ipm=|Epm= }} that the indices are {{ Extra/Bracket |text=not necessarily strict| |Ipm=|Epm= }} increasing. If an index appears twice, the wedge product is {{mat|term= 0 |pm=,}} due to {{ Factlink |Factname= Wedge product/Elementary properties/Fact |Nr=2 |pm=. }} Hence, no index occurs twice, and this wedge product is in the form asked for. }} {{ Part of proof |Proof= To show that the family is {{ Definitionlink |linearly independent| |pm=, }} we show, using {{ Factlink |Factname= Linear independence/Test with linear forms/Fact |Nr= |pm=, }} that for every subset {{ Relationchain | I || \{i_1 {{commadots|}} i_n\} |\subseteq | {{Set1m|}} || || || |pm= }} with {{mat|term= n |pm=}} elements {{ Extra/Bracket |text=where {{ Relationchain/b | i_1 | < | \ldots | < | i_n || || || || |pm= }}| |Ipm=|Epm=, }} there exists a {{mat|term= K |pm=-}}linear mapping {{ Mapping/display |name= |\bigwedge^n V |K || |pm= }} such that {{mathl|term= v_{i_1} {{wedgedots|}} v_{i_n} |pm=}} is not mapped to {{mat|term= 0 |pm=,}} but all other wedge products in the family are mapped to {{mat|term= 0 |pm=.}} To show this, it is enough, by {{ Factlink |Factname= Wedge product/Universal property/Fact |pm=, }} to give an {{ Definitionlink |alternating| |pm= }} {{ Definitionlink |multilinear mapping| |pm= }} {{ Mapping/display |name= \triangle | V^n | K || |pm= }} satisfying {{ Relationchain | \triangle {{mabr| v_{i_1} {{commadots|}} v_{i_n} |}} |\neq| 0 || || || |pm= }} but {{ Relationchain | \triangle {{mabr| v_{j_1} {{commadots|}} v_{j_n} |}} || 0 || || || |pm= }} for every other strictly increasing index tuple. Let {{mat|term= U |pm=}} be the {{ Definitionlink |linear subspace| |pm= }} generated by {{ Mathcond|term= v_i ||condterm1= i \neq i_k ||condterm2= |pm=, }} of {{mat|term= V |pm=,}} and let {{ Relationchain | W || V/U || || || |pm= }} denote the {{ Definitionlink |residue class space| |pm=. }} Then the images of the {{ Mathcond|term= v_{i_k} ||condterm1= k= 1 {{commadots|}} n ||condterm2= |pm=, }} form a basis of {{mat|term= W |pm=,}} and the images of all other subsets with {{mat|term= n |pm=}} elements of the given basis do ot form a basis of {{mat|term= W |pm=,}} because at least one element is mapped to {{mat|term= 0 |pm=.}} We consider now the {{ Definitionlink |composed| |Context=mapping| |pm= }} mapping {{ Math/display|term= \triangle: V^n \longrightarrow W^n \cong (K^n)^n \stackrel{ {{op:Determinant||}} }{ \longrightarrow} K |pm=. }} This mapping is multilinear and alternating, due to {{ Factlink |Factname= Determinant/Recursively/Multilinear/Fact |pm= }} and {{ Factlink |Factname= Determinant/Recursively/Alternating/Fact |pm=. }} Due to {{ Factlink ||Factname=Determinant/Zero, linear dependent and rank property/Fact |pm=, }} we have {{ Relationchain | \triangle (z_1 {{commadots|}} z_n) || 0 || || || |pm= }} if and only if the images of {{mat|term= z_i |pm=}} in {{mat|term= W |pm=}} do not form a basis. |Closure of part= }} |Closure= }} |Textform=Proof |Category=See }} jb3bv2dbczerglkta4ntnq76sqq1ufr 0 322066 2720368 2720174 2025-07-01T20:08:06Z Stevesuny 294667 added link to process discussion 2720368 wikitext text/x-wiki __forcetoc__ This is the workspace for a jointly authored paper. See [[AIXworkbench/Papers/Building-the-Workbench/Paper-writing-process|discussion about process]]. == Possible sections for paper == # Presents the concept of the AIXworkbench # Discusses RAIL Facets Framework as an evaluation tool # AIX + Open WebUI = AIXworkbench # Review LLM interfaces, with focus on open source? # Reviews Open WebUI, history, usage in field # Discusses the "June working group" as an impromptu example of community AI development, and reports on our meetings and discussions # Reports Use Cases from June working group as examples of using Open Web UI # Identifies key resources / values to transform Open WebUI into AIXworkbench ## Security ## Responsibility ## Shareability ## Provenance # Review this project using FACETS framework == 1 AI for All requires an working environment that people own and control - What is an "AI workbench" and why do we one == AI for all -- people, activities, spaces, places An "AI workbench" empowers users to leverage LLMs locally and via API for inference, fine-tuning and other usage. We need this tool to promote individual management of LLM resources. Multi-faceted diversity in the development of AI Community AI / Development == 2 The Responsible AI Lab FACETS framework and how we apply it here == The RAIL FACETS framework is described here.<ref>{{Cite web|url=https://facets.netlify.app/|title=RAIL {{!}} FACETS Responsible AI Framework|website=facets.netlify.app|access-date=2025-06-19}}</ref> Its use is discussed here <ref>{{Cite journal|last=Akomea-Frimpong|first=Isaac|last2=Jin|first2=Xiaohua|last3=Osei-Kyei|first3=Robert|last4=Kukah|first4=Augustine Senanu|date=2023-02-20|title=Public–private partnerships for sustainable infrastructure development in Ghana: a systematic review and recommendations|url=https://www.emerald.com/insight/content/doi/10.1108/SASBE-07-2021-0111/full/html|journal=Smart and Sustainable Built Environment|language=en|volume=12|issue=2|pages=237–257|doi=10.1108/SASBE-07-2021-0111|issn=2046-6099}}</ref><ref>{{Cite web|url=https://arxiv.org/abs/2505.00204v1|title=RAIL in the Wild: Operationalizing Responsible AI Evaluation Using Anthropic's Value Dataset|last=Verma|first=Sumit|last2=Prasun|first2=Pritam|date=2025-04-30|website=arXiv.org|language=en|access-date=2025-06-19|last3=Jaiswal|first3=Arpit|last4=Kumar|first4=Pritish}}</ref> == 3 AIX + Open WebUI = AIXworkbench == AIX is focused on developing Responsible AI for All: Inspired by the Responsible AI Lab, KNUST, and is committed to assessing our projects using the FACETS framework.<br> [{{fullurl:AIXworkbench/About|action=edit}} edit]{{:AIXworkbench/About}} == 4 LLM interfaces == There are a variety of tools that are available to individuals or organiations that want to provide a platform to use LLMs in a highly controlled, secure and managed environment. The first LLM interface... Hugging Face... Brief history of the movement to make open source LLM interfaces. With the main goal of the AIX Workbench, there were a few points of considerations that needed to be met. We needed the LLM Interface to be able to be modified so it satisfies the following characteristics: * Secure * Responsible * Replicable * Shareable/Collaborative * Deployable The most commonly used "AI" by far are the cloud-based ones. Although, they have beginner friendly ease-of-access, the issue with most cloud-based LLM is that they are run and operated by the provider's machine. In addition, the limited customizability and data privacy concerns makes them a questionable use for the AIX Workbench. The limited customizability doesn't allow the user to modify parameters. The major data privacy concerns is that the provider could use the user's chats & documents to train its models, which means sensitive information could be exposed.<ref>{{Cite web|url=https://www.datacamp.com/blog/the-pros-and-cons-of-using-llm-in-the-cloud-versus-running-llm-locally|title=The Pros and Cons of Using Large Language Models (LLMs) in the Cloud vs. Running LLMs Locally: Which Is Right for You?|last=Ali Awan|first=Abid|date=May 23, 2023|website=datacamp.com}}</ref> Local LLM Interfaces such as Open WebUI, GPT4ALL and LMStudio are run locally on your computer. This tackles the main issue of cloud-based LLM's which is customizability and data privacy. == 5 Open WebUI == [{{fullurl:AIXworkbench/Papers/Building-the-Workbench/Open-WebUI|action=edit}} edit] {{:AIXworkbench/Papers/Building-the-Workbench/Open-WebUI}} == 6 June Working Group == == 7 Use Cases of Open WebUI from participants in June Working Group == === Our Current Participants === {{Special:PrefixIndex/AIXworkbench/Working-Groups/June-2025-Working-Group/Participants|hideroot=1|stripprefix=1|columns=1}} === Want to Join the Working Group? === Share your Open WebUI use case and contribute to our research! '''How to participate:''' # Click [[AIXworkbench/Working-Groups/June-2025-Working-Group/Participants/|here]] and follow the instructions! == 8 AIXworkbench: Security, Responsibility, Shareability, Provenance == == 9 References == 3jza1ei1nho41fb7epb7kqzyz03u3xo 0 322150 2720380 2720242 2025-07-02T03:20:52Z Ruud Loeffen 2998353 /* 7.4 – Theory Mapping Table */ replaced table 7.4 with the correct table 2720380 wikitext text/x-wiki = '''Chapter 7: Cosmological Parameters and Universal Constants''' = === '''7.1 – Purpose – Overview Cosmological Parameters and Universal Constants''' === This subsection introduces the key cosmological parameters and universal constants that underpin modern models of the universe. These values are foundational for describing the large-scale structure, expansion history, and composition of the cosmos. By defining and constraining these constants, researchers are able to test, compare, and refine competing cosmological theories. The most widely used parameters include: '''Hubble Constant (H₀)''' – The current rate of cosmic expansion, typically expressed in km/s/Mpc. It plays a central role in determining the age and scale of the universe. '''Matter Density Parameter (Ωₘ)''' – The fraction of the critical density contributed by all forms of matter (baryonic and dark matter). '''Dark Energy Density Parameter (Ω_Λ)''' – The fraction of the critical density attributed to dark energy, often associated with the cosmological constant (Λ). '''Spectral Index (nₛ)''' – Characterizes the scale dependence of primordial density fluctuations. '''Amplitude of Scalar Fluctuations (Aₛ)''' – Sets the overall level of fluctuations in the early universe, which seeded the formation of galaxies and clusters. '''Optical Depth (τ)''' – Relates to the reionization history of the universe, affecting how the cosmic microwave background (CMB) photons have been scattered. '''σ₈''' – A measure of the clustering strength of matter on scales of 8 h⁻¹ Mpc, used in large-scale structure studies. These parameters are complemented by a set of universal physical constants that appear across all physical theories: '''Gravitational Constant (G)''' '''Speed of Light (c)''' '''Planck’s Constant (h)''' '''Boltzmann Constant (k_B)''' '''Cosmological Constant (Λ)''' – interpreted as vacuum energy or dark energy density '''Fine-Structure Constant (α)''' Together, these parameters serve as the empirical backbone for cosmological models, allowing them to be calibrated against observational data. Most mainstream models—such as the ΛCDM model—use a minimal set of six to seven parameters, yet tensions persist between different measurement techniques. For example, the value of H₀ inferred from the cosmic microwave background (CMB) differs significantly from values measured using Type Ia supernovae, leading to the well-known '''Hubble tension'''. Similarly, discrepancies in measurements of σ₈ suggest the possibility of unknown physical processes or the need for alternative frameworks. This chapter evaluates how different cosmological theories define, derive, or reinterpret these parameters. It also considers whether a theory proposes a new universal constant, modifies existing ones, or offers an explanation for observed tensions. The role of these constants in the internal logic and predictive success of a theory is an essential component of the comparative evaluation. === '''7.2 – Scope – Mainstream and Non-mainstream Theories''' === This subsection outlines the scope of Chapter 7 in terms of the cosmological theories being considered, with specific attention to how each theory engages with cosmological parameters and universal constants. Both mainstream and non-mainstream theories are included in the evaluation to ensure a broad, inclusive, and critically informed comparison. ==== '''Mainstream Cosmological Frameworks''' ==== Mainstream cosmological models are those widely accepted within the current scientific consensus and supported by large-scale observational programs such as the Planck satellite, the Sloan Digital Sky Survey (SDSS), and the Dark Energy Survey (DES). The primary framework is the: '''ΛCDM Model (Lambda Cold Dark Matter)''' This model is based on general relativity and assumes a universe dominated by cold dark matter (CDM) and a cosmological constant (Λ) representing dark energy. It uses a standard set of six parameters to fit observational data: – H₀ (Hubble constant) – Ωₘ (matter density) – Ω_Λ (dark energy density) – nₛ (spectral index) – Aₛ (amplitude of fluctuations) – τ (optical depth) ΛCDM has achieved notable empirical success, including accurate fits to the cosmic microwave background (CMB) power spectrum and the large-scale distribution of galaxies. However, it faces unresolved tensions such as the disparity in H₀ values derived from early- and late-universe measurements, and differences in predicted versus observed values of σ₈ (matter clustering amplitude). Other general relativity–based extensions or modifications, such as quintessence models (dynamic dark energy), modified gravity (e.g., f(R) theories), or models invoking additional neutrino species, are sometimes treated as extensions of ΛCDM rather than fundamentally separate theories. ==== '''Non-Mainstream and Emerging Theories''' ==== This chapter also includes theories that are not currently part of mainstream consensus but that offer new approaches to cosmological constants or parameter derivation. These may include: '''Alternative Gravity Theories''' – including MOND (Modified Newtonian Dynamics), TeVeS, conformal gravity, and entropic gravity. These models often aim to explain galactic rotation curves or cosmological structure without invoking dark matter. '''Emergent and Flow-based Models''' – including theories where cosmic structure arises from energy influxes or universal flows (e.g., Cosmic Influx Theory, Spiral Cosmology). These models may propose new constants (such as influx-based scaling parameters) or reinterpret standard ones. '''Continuous Creation or Steady-State Frameworks''' – These posit a continuous generation of matter or energy, potentially affecting the interpretation of Hubble expansion, cosmic microwave background, and the age of the universe. '''Topological or Geometric Reinterpretations''' – Some proposals modify the dimensionality or topology of space-time itself, redefining how constants such as G or c emerge from underlying structures. ==== '''Comparative Perspective''' ==== By evaluating both mainstream and non-mainstream approaches on equal terms, this chapter aims to provide a comparative framework grounded in empirical adequacy, predictive capacity, and internal coherence. The inclusion of non-standard models is not intended to imply equivalence of scientific status, but rather to highlight the diversity of ideas that reinterpret or challenge conventional uses of cosmological parameters. The theories evaluated here must define how they handle: The derivation or reinterpretation of cosmological parameters The role and meaning of universal constants in their framework Their position relative to known tensions (e.g., Hubble tension, σ₈ tension) This scope ensures that all models are critically evaluated using the same criteria, while allowing room for genuinely novel approaches to cosmology. == '''7.3 How to Contribute a Theory ''' == Researchers and contributors are welcome to propose additional theories that relate biological evolution and fossil records to planetary or cosmological models. Submissions may include observational insights, mathematical models, conceptual frameworks, or hybrid approaches. You can contribute in either of the following ways: * Post directly on the Talk page of this chapter * Or email your proposal to: aitheroymapping@gmail.com All submitted theories will be added to the mapping and evaluated using the shared criteria defined in Chapter 1.3: Evaluation Criteria. We encourage both mainstream and non-mainstream contributors to join this open effort to compare and improve our understanding of Biological and Paleontological Clues in relation to cosmological theories. === '''7.4 – Theory Mapping Table''' === This table presents a structured comparison of diverse cosmological theories based on how they define or reinterpret key cosmological parameters and universal constants. The table includes both mainstream and non-mainstream paradigms, encouraging open comparative analysis grounded in scientific rigor. {| class="wikitable" style="width:100%; text-align:left;" ! style="width:15%;" | '''Theory Name''' ! style="width:15%;" | '''H₀ Treatment''' ! style="width:15%;" | '''Ω Parameters''' ! style="width:15%;" | '''Role of Λ / Dark Energy''' ! style="width:20%;" | '''Treatment of G, c, and other constants''' ! style="width:20%;" | '''New Parameters or Constants Proposed''' |- | '''ΛCDM (Standard Model)''' || Empirically fitted (Planck: 67.8 ± 0.9) || Ωₘ, Ω_Λ, Ω_r defined from observation || Constant Λ; vacuum energy interpretation || G and c are fixed universal constants || None |-style="background:#f9f9f9;" | '''Modified Gravity (f(R))''' || H₀ typically fitted or adjusted || Ωₘ redefined dynamically || Λ may be replaced by geometric terms || G may vary with scale or curvature || Function f(R), effective gravitational coupling |- | '''MOND / TeVeS''' || H₀ usually inherited from observations || Ωₘ reinterpreted (no dark matter) || Λ often excluded; not essential || G modified below a₀; new scale-invariant dynamics || a₀ (critical acceleration) |-style="background:#f9f9f9;" | '''Emergent Gravity (Verlinde)''' || Predicts emergent H₀ value || Ω parameters secondary to entropy/gravity || Dark energy as emergent entropic phenomenon || G and Λ derived from holographic principles || Entropic scaling parameter |- | '''Cosmic Influx Theory (CIT)''' || Derives H₀ = 67.8 via VRMS and (γ−1) || Ω values not directly defined || Λ absorbed in influx framework || G = (γ−1)/4π; κ and κ_CIT used as scaling factors || κ_CIT, κ, VRMS |-style="background:#f9f9f9;" | '''Spiral Cosmology''' || H₀ seen as emergent from cosmic motion || Ω reinterpreted in spiraling energy flows || Λ not needed; structure from motion || c and G may emerge from wavefront geometry || Spiral frequency and structure constants |- | '''Topological Field Framework (Hall)''' || May reinterpret H₀ as boundary effect || Ωₘ redefined from field topology || Λ as a topological effect or unnecessary || G emerges from higher-dimensional field curvature || Topological curvature parameters |-style="background:#f9f9f9;" | '''Conformal Gravity (Mannheim–Kazanas)''' || Derives H₀ from conformally invariant field equations || Ω values fitted without dark matter || Λ not fundamental; dynamic curvature replaces Λ || G emerges from conformal symmetry conditions || Conformal coupling constant, γ₀ |- | '''Quasi-Steady State Cosmology (QSSC)''' || H₀ varies over long cycles || Ω values evolve over cosmic epochs || Λ varies cyclically with creation field || G and c are constant, but new field equations applied || Creation field C, periodic Λ(t) |-style="background:#f9f9f9;" | '''Dynamic Universe (Tuomo Suntola)''' || H₀ derived from zero-energy balance || Ω reinterpreted geometrically || Λ not needed; curvature and motion suffice || G and c emerge from dynamic 4-sphere geometry || Zero-energy condition; time-proportional scaling |} === '''7.5 Evaluation Criteria and Comparative Overview''' === The cosmological theories presented in this chapter are evaluated using the shared set of criteria defined in [[AI-Assisted_Evaluation_of_Cosmological_Theories/Chapter_1:_Introduction_and_Evaluation_Criteria#1.3:_List_of_Evaluation_Criteria|Chapter 1.3: List of Evaluation Criteria]]. These criteria are here specifically applied to how each theory handles cosmological parameters and universal constants. '''Empirical Adequacy''' – alignment with observed values of key parameters (H₀, Ωₘ, Λ, σ₈, etc.) and data from CMB, supernovae, BAO, and large-scale structure '''Internal Consistency''' – logical and mathematical coherence in the derivation or treatment of constants '''Explanatory Power''' – ability to explain why constants have their observed values, not just fit them '''Predictive Power''' – capacity to forecast future or unmeasured parameter values or resolve current tensions (e.g., Hubble tension) '''Simplicity and Elegance''' – conceptual parsimony and avoidance of unnecessary parameters or fine-tuning '''Compatibility with Other Theories''' – ability to integrate with broader physical theories and cosmological observations '''Falsifiability and Openness to Testing''' – presence of testable predictions or measurable consequences The paragraphs below summarize how each theory relates to these criteria. A more detailed AI-supported analysis follows in Section 7.6. '''ΛCDM (Standard Model)''' is strongly supported by observational data and has high empirical adequacy. Its internal consistency and predictive power are well-established, especially in modeling the CMB and galaxy distributions. However, it treats many constants as fitted parameters without deeper explanation. The model faces known tensions in H₀ and σ₈, which challenge its completeness. It is conceptually simple and highly compatible with general relativity and particle physics, and its parameters are open to observational testing. '''Modified Gravity (f(R))''' introduces geometric generalizations of Einstein's equations, potentially explaining dark energy and dark matter effects through curvature. While it can match observational data under certain models, its parameter space is broad, and empirical adequacy depends heavily on specific formulations. It offers improved explanatory potential over ΛCDM in some cases, but at the cost of increased mathematical complexity. Some forms are testable via gravitational lensing, structure formation, and precision cosmology. '''MOND / TeVeS''' modifies Newtonian dynamics to eliminate the need for dark matter at galactic scales. It reproduces galactic rotation curves successfully but struggles at cosmological scales. Its internal logic is consistent within its regime of applicability, and it introduces the acceleration scale a₀ as a new constant. Predictive power is good for galaxies but limited for early-universe physics. MOND-type theories are testable but not easily reconciled with CMB data or structure formation. '''Emergent Gravity (Verlinde)''' reinterprets gravity as an emergent entropic force arising from information-theoretic principles. It provides an elegant and conceptually innovative explanation of dark energy and inertia, but its empirical adequacy is still under investigation. It offers strong explanatory power in principle but lacks complete predictive frameworks for all cosmological parameters. The theory is testable in principle through deviations from Newtonian gravity in specific regimes, though experimental confirmation remains elusive. '''Cosmic Influx Theory (CIT)''' derives the Hubble constant from influx-based relationships involving VRMS and the relativistic factor (γ−1), matching Planck-derived values. While some standard parameters (e.g., Ω values) are not explicitly defined, CIT offers strong internal consistency and explanatory power for G and H₀ via fundamental influx mechanisms. Its simplicity and dimensional coherence are strengths, though full cosmological compatibility and falsifiability require further development. It aligns with observed tensions and provides a novel conceptual bridge between gravity, expansion, and mass generation. '''Spiral Cosmology''' explains cosmic structure and evolution through geometrically spiraling flows of energy and matter. It reinterprets constants as emergent from dynamic motion patterns rather than fixed inputs. Its empirical alignment is currently qualitative, but it provides strong explanatory power for structure formation and symmetry. Its conceptual elegance appeals to analogies in electromagnetic and wave theory. Predictive models and testable consequences remain a work in progress, but the theory is logically consistent within its internal framework. '''Topological Field Framework (Hall)''' proposes that fundamental constants emerge from field topology in higher-dimensional configurations. It offers potential explanations for G, c, and Λ as emergent from geometry rather than fixed inputs. While still under development, it has strong internal logic and high explanatory ambition. Its empirical adequacy depends on deriving measurable predictions. Its compatibility with both general relativity and quantum geometry gives it interdisciplinary appeal, though full falsifiability is pending. '''Conformal Gravity (Mannheim–Kazanas)''' eliminates the need for dark matter by modifying gravitational equations with conformal symmetry. It fits galactic rotation curves and some lensing observations without introducing new particles. Its predictive power is good at galactic scales, and it offers a deep geometric motivation for its equations. However, it faces challenges matching CMB and early-universe data. The theory is testable and internally consistent, but its cosmological compatibility is debated. '''Quasi-Steady State Cosmology (QSSC)''' offers a cyclic, matter-generating model that modifies standard expansion assumptions. It reproduces redshift data through a non-Big Bang framework and introduces a creation field (C) as a new constant. Its empirical adequacy is mixed, and its compatibility with observed element abundances and CMB is questioned. However, its explanatory ambition and falsifiability through periodic structure and matter creation make it a valuable alternative perspective. '''Dynamic Universe (Tuomo Suntola)''' proposes a zero-energy balance model in which cosmic parameters evolve from a unified dynamic geometry. It predicts H₀ and other constants from time-dependent curvature rather than fixed values. The theory is internally consistent, compact, and provides strong explanatory value for the origin of physical laws. Its compatibility with relativity is nonstandard but mathematically consistent. Observational tests are possible through detailed cosmological reconstructions and time-scaling relationships. === '''7.6 – AI Evaluation Based on Shared Criteria''' === This subsection presents an AI-assisted comparative evaluation of cosmological theories, based on the shared criteria defined in [[AI-Assisted_Evaluation_of_Cosmological_Theories/Chapter_1:_Introduction_and_Evaluation_Criteria#1.3:_List_of_Evaluation_Criteria|Chapter 1.3: List of Evaluation Criteria]]. The goal is to clarify how each theory treats the fundamental cosmological parameters and universal constants discussed in this chapter. The evaluation highlights internal coherence, empirical alignment, explanatory ambition, and potential testability. No star ratings are assigned here. Instead, each theory is qualitatively assessed across the criteria through short descriptive paragraphs. '''ΛCDM (Standard Model)''' offers strong empirical alignment with CMB, supernova, and large-scale structure data. Its internal structure is based on general relativity and well-developed mathematical models, making it logically robust. However, it provides limited explanation for the specific values of constants such as H₀ or Λ, which are treated as empirical inputs. Despite this, it demonstrates predictive success across multiple observations. The model is conceptually economical, relying on a minimal parameter set, and is deeply integrated into the broader framework of modern physics. Known tensions (e.g., H₀ discrepancy) invite refinement or reinterpretation but do not undermine its overall compatibility with data. It remains broadly testable through increasingly precise cosmological measurements. '''Modified Gravity (f(R))''' theories attempt to explain dark energy and acceleration through extensions of the Einstein-Hilbert action. They offer a reinterpretation of cosmic parameters in terms of curvature dynamics rather than exotic energy components. These models vary widely in structure and observational fit, depending on the chosen function f(R), but many reproduce key cosmological features. Their mathematical framework is internally consistent, and they contribute meaningfully to the debate on the nature of gravity. While their explanatory power is promising, some formulations require additional parameters or fine-tuning. Compatibility with structure formation data and gravitational lensing tests remains an important area for empirical evaluation. '''MOND / TeVeS''' seeks to account for galactic rotation curves without invoking dark matter, introducing a critical acceleration scale as a new constant. It performs very well at galactic scales, offering a direct fit to rotation data. However, it faces challenges when applied to cosmological phenomena such as the cosmic microwave background and large-scale structure. The theory’s internal dynamics are logically constructed and mathematically consistent within their range of application. Its predictive capacity is constrained to specific regimes, and it introduces conceptual simplicity with minimal new constants. Empirical tensions with high-redshift data suggest the need for further development or hybrid models. '''Emergent Gravity (Verlinde)''' offers an innovative theoretical framework in which gravity and inertia emerge from entropic and information-theoretic principles. This model reframes fundamental constants as emergent properties of underlying entropy distributions. While its internal structure is elegant and conceptually coherent, empirical validation remains limited. It has provided tentative fits to certain lensing effects, but full cosmological modeling is still in development. The theory’s explanatory reach is broad, particularly in redefining Λ and inertia, though specific quantitative predictions are still rare. It is testable in principle, and future observational probes could refine or challenge its foundational assumptions. '''Cosmic Influx Theory (CIT)''' proposes that the gravitational constant and Hubble parameter derive from a continuous influx of energy into matter. It uses the relativistic factor (γ−1) and a universal root mean square velocity (VRMS) to derive G and H₀, aligning with Planck observations without parameter fitting. The theory is internally consistent and offers strong explanatory coherence for the emergence of constants. Although it does not define all standard cosmological parameters, its introduction of scaling constants (κ and κ_CIT) provides a novel interpretation of structure and mass-energy evolution. The theory is open to falsification through predictions on orbital dynamics and preferred planetary distances, and invites new observational research. '''Spiral Cosmology''' describes the evolution of the universe through organized spiraling flows of energy and matter. It offers a dynamic interpretation of cosmic structure and attempts to derive constants from the geometry of spiral motion. Its explanatory framework is creative and unified, though primarily qualitative at this stage. Observational alignment is still under development, and quantitative predictions remain limited. The model maintains internal coherence and offers potential compatibility with both geometric and wave-based models of the universe. It presents a unique lens on cosmic evolution and may be tested through pattern recognition in galactic distributions and background structure. '''Topological Field Framework (Hall)''' attempts to explain the emergence of physical constants and structure from the topology of underlying fields. It replaces fixed constants with dynamic relationships determined by higher-dimensional field configurations. This theory is conceptually ambitious and mathematically coherent within its proposed framework. While it currently lacks detailed empirical predictions, it offers a strong explanatory model for the origin of constants such as G and c. The framework’s future success depends on its ability to generate testable consequences and interface with observational cosmology. '''Conformal Gravity (Mannheim–Kazanas)''' modifies general relativity using conformal symmetry and has had success fitting galactic rotation curves without dark matter. It interprets cosmic acceleration and gravitational potentials without requiring Λ or exotic matter components. The theory’s structure is mathematically rigorous and geometrically elegant. While it fits some astrophysical data well, its compatibility with the CMB and early universe remains under scrutiny. It provides a deeper explanation for gravitational behavior, but requires additional work to extend to full cosmological predictions. It is empirically testable and offers a valuable challenge to conventional dark matter models. '''Quasi-Steady State Cosmology (QSSC)''' revives and modifies the steady-state model by introducing a continuous creation field (C-field) and cyclic cosmological evolution. It offers an alternative interpretation of redshift and cosmic expansion that challenges the Big Bang model. The theory aligns with some observational patterns but struggles to reproduce others, such as the CMB spectrum and light element abundances. Its internal logic is self-consistent within its paradigm and introduces an original approach to matter generation and cosmic cycles. QSSC provides testable ideas, particularly related to periodicity and structural evolution, but remains outside the mainstream due to its divergence from accepted data interpretations. '''Dynamic Universe (Tuomo Suntola)''' introduces a zero-energy cosmological model in which space, time, and matter evolve from a dynamically balanced 4-sphere geometry. This framework offers a coherent mathematical structure with an explicit derivation of H₀ and other constants from curvature and motion, rather than treating them as empirical inputs. It avoids the need for inflation, dark energy, or dark matter by reinterpreting cosmic expansion. The model’s internal consistency is strong, and its elegance lies in its unified geometric logic. Testable consequences emerge through its time-scaling formulations and reconstruction of historical cosmic dynamics, providing a fertile ground for further research. === '''7.7 – Helicopter View – Scientific Reception and Emerging Tensions''' === This subsection offers a broader reflection on how the theories presented in Chapter 7 are received within the scientific community, and how ongoing observational tensions and theoretical gaps have shaped the landscape of cosmological research. While the '''ΛCDM model''' remains the dominant paradigm, persistent anomalies and the rise of innovative frameworks have stimulated growing interest in alternatives that offer novel interpretations of cosmological parameters and universal constants. The '''ΛCDM model''' has achieved widespread acceptance due to its empirical success in matching high-precision data from the Planck satellite, baryon acoustic oscillations, and Type Ia supernovae. Its internal consistency and predictive utility are widely recognized. However, the model also leaves several foundational questions unresolved. Chief among these is the origin and nature of the '''cosmological constant (Λ)''', which contributes over 68% of the energy density of the universe and yet remains theoretically unexplained. Furthermore, the persistent disparity between early-universe (CMB-derived) and late-universe (distance ladder) measurements of the '''Hubble constant (H₀)''' has become known as the '''"Hubble tension"'''. Similar discrepancies related to the amplitude of matter clustering ('''σ₈''') have raised additional concerns about potential missing physics. These tensions have opened a window for the exploration of '''non-mainstream cosmologies'''. '''Modified gravity models''' such as '''f(R)''' and '''conformal gravity''' offer geometric alternatives that attempt to reproduce cosmic acceleration and structure formation without invoking dark energy or dark matter. While these models often require additional functions or parameters, they are gaining attention for their potential to resolve observational anomalies through new mathematical structures. Theories such as '''MOND''', '''TeVeS''', and '''emergent gravity''' have had mixed receptions. '''MOND''' has provided compelling fits to galactic rotation curves but lacks a fully developed cosmological extension. '''Emergent gravity''' introduces a radically different ontology—treating gravity and inertia as statistical phenomena—which appeals to theorists seeking deeper unifying principles. Nonetheless, these theories face strong skepticism from mainstream cosmologists due to limited empirical validation and difficulties in reproducing CMB anisotropies and structure growth data. The inclusion of conceptual models such as '''Spiral Cosmology''', '''Cosmic Influx Theory (CIT)''', and the '''Dynamic Universe''' represents a growing movement within the scientific periphery to explore frameworks that derive cosmological constants from deeper principles—be they geometric, energetic, or topological. These models often operate outside the dominant institutional research programs, yet they reflect a longstanding scientific aspiration: to understand not only how the universe behaves, but why the constants that govern its behavior take the values they do. Institutional acceptance of these models varies widely. Peer-reviewed publications remain limited for some, while others circulate primarily via academic repositories, conferences, or platforms such as '''Zenodo''', '''ResearchGate''', or '''Wikiversity'''. This reflects a broader tension in the scientific ecosystem: while mainstream paradigms are highly productive and empirically successful, they may not fully accommodate unconventional but potentially insightful hypotheses. In this context, the '''AI-assisted comparative framework''' applied in this chapter aims to foster transparent, criteria-based evaluation of both accepted and emerging theories. By focusing on '''empirical adequacy''', '''internal logic''', and '''explanatory potential'''—rather than academic consensus alone—this approach supports a more inclusive and methodologically consistent cosmological discourse. === '''7.8 – Next Steps''' === This final subsection outlines recommended next steps for researchers, contributors, and interested readers following the comparative evaluation of cosmological parameters and universal constants in Chapter 7. First, contributors are encouraged to refine or expand the theory entries presented here by improving clarity, adding new references, or providing updated observational data. As ongoing missions such as the '''James Webb Space Telescope (JWST)''', '''Euclid''', and the '''Vera Rubin Observatory''' generate increasingly precise cosmological measurements, all models—mainstream and alternative—will face new opportunities for testing and validation. Particular attention should be paid to how each theory addresses current tensions, including the '''Hubble tension''', the '''σ₈ clustering discrepancy''', and the unexplained nature of '''Λ (dark energy)'''. Second, AI-assisted comparative tools may be developed further to support large-scale cross-analysis of parameter predictions and internal consistencies. This could include algorithmic comparison of theory-derived parameter sets against datasets from Planck, SDSS, DESI, or gravitational wave observatories. Readers or institutions with expertise in computational cosmology are invited to explore these possibilities and report outcomes. Third, alternative frameworks that derive constants from first principles—whether geometric, entropic, influx-based, or topological—may benefit from collaborative dialogue. Theories such as '''CIT''', '''Spiral Cosmology''', and the '''Dynamic Universe''' propose unorthodox but structured ways to reinterpret physical constants. These models can be further explored, modified, or combined in search of converging predictions. Finally, this chapter should remain a living document. As the boundaries of cosmology continue to evolve, Wikiversity provides an open-access platform for iterative updates, interdisciplinary integration, and transparent evaluation. Contributors from all scientific backgrounds are welcome to propose revisions, submit new models, or refine the criteria used here. The comparative structure established in Chapter 7 will also serve as a foundation for deeper synthesis in [[AI-Assisted_Evaluation_of_Cosmological_Theories/Chapter_8:_Critical_Evaluation_and_Future_Research_Paths|Chapter 8]], where star ratings, meta-evaluations, and future research priorities will be formally proposed. '''◀ [[AI-Assisted Evaluation of Cosmological Theories/Chapter 6: Biological and Paleontological Clues|Previous]] | [[AI-Assisted Evaluation of Cosmological Theories|Main Page]] | [[AI-Assisted Evaluation of Cosmological Theories/Chapter 8: Critical Evaluation and Future Research Paths|Next ▶]]''' d0q6j64x2ohv7ktteg466op0oz5o04n 2720381 2720380 2025-07-02T03:42:03Z Ruud Loeffen 2998353 /* 7.6 – AI Evaluation Based on Shared Criteria */ made some keywords in the text bold 2720381 wikitext text/x-wiki = '''Chapter 7: Cosmological Parameters and Universal Constants''' = === '''7.1 – Purpose – Overview Cosmological Parameters and Universal Constants''' === This subsection introduces the key cosmological parameters and universal constants that underpin modern models of the universe. These values are foundational for describing the large-scale structure, expansion history, and composition of the cosmos. By defining and constraining these constants, researchers are able to test, compare, and refine competing cosmological theories. The most widely used parameters include: '''Hubble Constant (H₀)''' – The current rate of cosmic expansion, typically expressed in km/s/Mpc. It plays a central role in determining the age and scale of the universe. '''Matter Density Parameter (Ωₘ)''' – The fraction of the critical density contributed by all forms of matter (baryonic and dark matter). '''Dark Energy Density Parameter (Ω_Λ)''' – The fraction of the critical density attributed to dark energy, often associated with the cosmological constant (Λ). '''Spectral Index (nₛ)''' – Characterizes the scale dependence of primordial density fluctuations. '''Amplitude of Scalar Fluctuations (Aₛ)''' – Sets the overall level of fluctuations in the early universe, which seeded the formation of galaxies and clusters. '''Optical Depth (τ)''' – Relates to the reionization history of the universe, affecting how the cosmic microwave background (CMB) photons have been scattered. '''σ₈''' – A measure of the clustering strength of matter on scales of 8 h⁻¹ Mpc, used in large-scale structure studies. These parameters are complemented by a set of universal physical constants that appear across all physical theories: '''Gravitational Constant (G)''' '''Speed of Light (c)''' '''Planck’s Constant (h)''' '''Boltzmann Constant (k_B)''' '''Cosmological Constant (Λ)''' – interpreted as vacuum energy or dark energy density '''Fine-Structure Constant (α)''' Together, these parameters serve as the empirical backbone for cosmological models, allowing them to be calibrated against observational data. Most mainstream models—such as the ΛCDM model—use a minimal set of six to seven parameters, yet tensions persist between different measurement techniques. For example, the value of H₀ inferred from the cosmic microwave background (CMB) differs significantly from values measured using Type Ia supernovae, leading to the well-known '''Hubble tension'''. Similarly, discrepancies in measurements of σ₈ suggest the possibility of unknown physical processes or the need for alternative frameworks. This chapter evaluates how different cosmological theories define, derive, or reinterpret these parameters. It also considers whether a theory proposes a new universal constant, modifies existing ones, or offers an explanation for observed tensions. The role of these constants in the internal logic and predictive success of a theory is an essential component of the comparative evaluation. === '''7.2 – Scope – Mainstream and Non-mainstream Theories''' === This subsection outlines the scope of Chapter 7 in terms of the cosmological theories being considered, with specific attention to how each theory engages with cosmological parameters and universal constants. Both mainstream and non-mainstream theories are included in the evaluation to ensure a broad, inclusive, and critically informed comparison. ==== '''Mainstream Cosmological Frameworks''' ==== Mainstream cosmological models are those widely accepted within the current scientific consensus and supported by large-scale observational programs such as the Planck satellite, the Sloan Digital Sky Survey (SDSS), and the Dark Energy Survey (DES). The primary framework is the: '''ΛCDM Model (Lambda Cold Dark Matter)''' This model is based on general relativity and assumes a universe dominated by cold dark matter (CDM) and a cosmological constant (Λ) representing dark energy. It uses a standard set of six parameters to fit observational data: – H₀ (Hubble constant) – Ωₘ (matter density) – Ω_Λ (dark energy density) – nₛ (spectral index) – Aₛ (amplitude of fluctuations) – τ (optical depth) ΛCDM has achieved notable empirical success, including accurate fits to the cosmic microwave background (CMB) power spectrum and the large-scale distribution of galaxies. However, it faces unresolved tensions such as the disparity in H₀ values derived from early- and late-universe measurements, and differences in predicted versus observed values of σ₈ (matter clustering amplitude). Other general relativity–based extensions or modifications, such as quintessence models (dynamic dark energy), modified gravity (e.g., f(R) theories), or models invoking additional neutrino species, are sometimes treated as extensions of ΛCDM rather than fundamentally separate theories. ==== '''Non-Mainstream and Emerging Theories''' ==== This chapter also includes theories that are not currently part of mainstream consensus but that offer new approaches to cosmological constants or parameter derivation. These may include: '''Alternative Gravity Theories''' – including MOND (Modified Newtonian Dynamics), TeVeS, conformal gravity, and entropic gravity. These models often aim to explain galactic rotation curves or cosmological structure without invoking dark matter. '''Emergent and Flow-based Models''' – including theories where cosmic structure arises from energy influxes or universal flows (e.g., Cosmic Influx Theory, Spiral Cosmology). These models may propose new constants (such as influx-based scaling parameters) or reinterpret standard ones. '''Continuous Creation or Steady-State Frameworks''' – These posit a continuous generation of matter or energy, potentially affecting the interpretation of Hubble expansion, cosmic microwave background, and the age of the universe. '''Topological or Geometric Reinterpretations''' – Some proposals modify the dimensionality or topology of space-time itself, redefining how constants such as G or c emerge from underlying structures. ==== '''Comparative Perspective''' ==== By evaluating both mainstream and non-mainstream approaches on equal terms, this chapter aims to provide a comparative framework grounded in empirical adequacy, predictive capacity, and internal coherence. The inclusion of non-standard models is not intended to imply equivalence of scientific status, but rather to highlight the diversity of ideas that reinterpret or challenge conventional uses of cosmological parameters. The theories evaluated here must define how they handle: The derivation or reinterpretation of cosmological parameters The role and meaning of universal constants in their framework Their position relative to known tensions (e.g., Hubble tension, σ₈ tension) This scope ensures that all models are critically evaluated using the same criteria, while allowing room for genuinely novel approaches to cosmology. == '''7.3 How to Contribute a Theory ''' == Researchers and contributors are welcome to propose additional theories that relate biological evolution and fossil records to planetary or cosmological models. Submissions may include observational insights, mathematical models, conceptual frameworks, or hybrid approaches. You can contribute in either of the following ways: * Post directly on the Talk page of this chapter * Or email your proposal to: aitheroymapping@gmail.com All submitted theories will be added to the mapping and evaluated using the shared criteria defined in Chapter 1.3: Evaluation Criteria. We encourage both mainstream and non-mainstream contributors to join this open effort to compare and improve our understanding of Biological and Paleontological Clues in relation to cosmological theories. === '''7.4 – Theory Mapping Table''' === This table presents a structured comparison of diverse cosmological theories based on how they define or reinterpret key cosmological parameters and universal constants. The table includes both mainstream and non-mainstream paradigms, encouraging open comparative analysis grounded in scientific rigor. {| class="wikitable" style="width:100%; text-align:left;" ! style="width:15%;" | '''Theory Name''' ! style="width:15%;" | '''H₀ Treatment''' ! style="width:15%;" | '''Ω Parameters''' ! style="width:15%;" | '''Role of Λ / Dark Energy''' ! style="width:20%;" | '''Treatment of G, c, and other constants''' ! style="width:20%;" | '''New Parameters or Constants Proposed''' |- | '''ΛCDM (Standard Model)''' || Empirically fitted (Planck: 67.8 ± 0.9) || Ωₘ, Ω_Λ, Ω_r defined from observation || Constant Λ; vacuum energy interpretation || G and c are fixed universal constants || None |-style="background:#f9f9f9;" | '''Modified Gravity (f(R))''' || H₀ typically fitted or adjusted || Ωₘ redefined dynamically || Λ may be replaced by geometric terms || G may vary with scale or curvature || Function f(R), effective gravitational coupling |- | '''MOND / TeVeS''' || H₀ usually inherited from observations || Ωₘ reinterpreted (no dark matter) || Λ often excluded; not essential || G modified below a₀; new scale-invariant dynamics || a₀ (critical acceleration) |-style="background:#f9f9f9;" | '''Emergent Gravity (Verlinde)''' || Predicts emergent H₀ value || Ω parameters secondary to entropy/gravity || Dark energy as emergent entropic phenomenon || G and Λ derived from holographic principles || Entropic scaling parameter |- | '''Cosmic Influx Theory (CIT)''' || Derives H₀ = 67.8 via VRMS and (γ−1) || Ω values not directly defined || Λ absorbed in influx framework || G = (γ−1)/4π; κ and κ_CIT used as scaling factors || κ_CIT, κ, VRMS |-style="background:#f9f9f9;" | '''Spiral Cosmology''' || H₀ seen as emergent from cosmic motion || Ω reinterpreted in spiraling energy flows || Λ not needed; structure from motion || c and G may emerge from wavefront geometry || Spiral frequency and structure constants |- | '''Topological Field Framework (Hall)''' || May reinterpret H₀ as boundary effect || Ωₘ redefined from field topology || Λ as a topological effect or unnecessary || G emerges from higher-dimensional field curvature || Topological curvature parameters |-style="background:#f9f9f9;" | '''Conformal Gravity (Mannheim–Kazanas)''' || Derives H₀ from conformally invariant field equations || Ω values fitted without dark matter || Λ not fundamental; dynamic curvature replaces Λ || G emerges from conformal symmetry conditions || Conformal coupling constant, γ₀ |- | '''Quasi-Steady State Cosmology (QSSC)''' || H₀ varies over long cycles || Ω values evolve over cosmic epochs || Λ varies cyclically with creation field || G and c are constant, but new field equations applied || Creation field C, periodic Λ(t) |-style="background:#f9f9f9;" | '''Dynamic Universe (Tuomo Suntola)''' || H₀ derived from zero-energy balance || Ω reinterpreted geometrically || Λ not needed; curvature and motion suffice || G and c emerge from dynamic 4-sphere geometry || Zero-energy condition; time-proportional scaling |} === '''7.5 Evaluation Criteria and Comparative Overview''' === The cosmological theories presented in this chapter are evaluated using the shared set of criteria defined in [[AI-Assisted_Evaluation_of_Cosmological_Theories/Chapter_1:_Introduction_and_Evaluation_Criteria#1.3:_List_of_Evaluation_Criteria|Chapter 1.3: List of Evaluation Criteria]]. These criteria are here specifically applied to how each theory handles cosmological parameters and universal constants. '''Empirical Adequacy''' – alignment with observed values of key parameters (H₀, Ωₘ, Λ, σ₈, etc.) and data from CMB, supernovae, BAO, and large-scale structure '''Internal Consistency''' – logical and mathematical coherence in the derivation or treatment of constants '''Explanatory Power''' – ability to explain why constants have their observed values, not just fit them '''Predictive Power''' – capacity to forecast future or unmeasured parameter values or resolve current tensions (e.g., Hubble tension) '''Simplicity and Elegance''' – conceptual parsimony and avoidance of unnecessary parameters or fine-tuning '''Compatibility with Other Theories''' – ability to integrate with broader physical theories and cosmological observations '''Falsifiability and Openness to Testing''' – presence of testable predictions or measurable consequences The paragraphs below summarize how each theory relates to these criteria. A more detailed AI-supported analysis follows in Section 7.6. '''ΛCDM (Standard Model)''' is strongly supported by observational data and has high empirical adequacy. Its internal consistency and predictive power are well-established, especially in modeling the CMB and galaxy distributions. However, it treats many constants as fitted parameters without deeper explanation. The model faces known tensions in H₀ and σ₈, which challenge its completeness. It is conceptually simple and highly compatible with general relativity and particle physics, and its parameters are open to observational testing. '''Modified Gravity (f(R))''' introduces geometric generalizations of Einstein's equations, potentially explaining dark energy and dark matter effects through curvature. While it can match observational data under certain models, its parameter space is broad, and empirical adequacy depends heavily on specific formulations. It offers improved explanatory potential over ΛCDM in some cases, but at the cost of increased mathematical complexity. Some forms are testable via gravitational lensing, structure formation, and precision cosmology. '''MOND / TeVeS''' modifies Newtonian dynamics to eliminate the need for dark matter at galactic scales. It reproduces galactic rotation curves successfully but struggles at cosmological scales. Its internal logic is consistent within its regime of applicability, and it introduces the acceleration scale a₀ as a new constant. Predictive power is good for galaxies but limited for early-universe physics. MOND-type theories are testable but not easily reconciled with CMB data or structure formation. '''Emergent Gravity (Verlinde)''' reinterprets gravity as an emergent entropic force arising from information-theoretic principles. It provides an elegant and conceptually innovative explanation of dark energy and inertia, but its empirical adequacy is still under investigation. It offers strong explanatory power in principle but lacks complete predictive frameworks for all cosmological parameters. The theory is testable in principle through deviations from Newtonian gravity in specific regimes, though experimental confirmation remains elusive. '''Cosmic Influx Theory (CIT)''' derives the Hubble constant from influx-based relationships involving VRMS and the relativistic factor (γ−1), matching Planck-derived values. While some standard parameters (e.g., Ω values) are not explicitly defined, CIT offers strong internal consistency and explanatory power for G and H₀ via fundamental influx mechanisms. Its simplicity and dimensional coherence are strengths, though full cosmological compatibility and falsifiability require further development. It aligns with observed tensions and provides a novel conceptual bridge between gravity, expansion, and mass generation. '''Spiral Cosmology''' explains cosmic structure and evolution through geometrically spiraling flows of energy and matter. It reinterprets constants as emergent from dynamic motion patterns rather than fixed inputs. Its empirical alignment is currently qualitative, but it provides strong explanatory power for structure formation and symmetry. Its conceptual elegance appeals to analogies in electromagnetic and wave theory. Predictive models and testable consequences remain a work in progress, but the theory is logically consistent within its internal framework. '''Topological Field Framework (Hall)''' proposes that fundamental constants emerge from field topology in higher-dimensional configurations. It offers potential explanations for G, c, and Λ as emergent from geometry rather than fixed inputs. While still under development, it has strong internal logic and high explanatory ambition. Its empirical adequacy depends on deriving measurable predictions. Its compatibility with both general relativity and quantum geometry gives it interdisciplinary appeal, though full falsifiability is pending. '''Conformal Gravity (Mannheim–Kazanas)''' eliminates the need for dark matter by modifying gravitational equations with conformal symmetry. It fits galactic rotation curves and some lensing observations without introducing new particles. Its predictive power is good at galactic scales, and it offers a deep geometric motivation for its equations. However, it faces challenges matching CMB and early-universe data. The theory is testable and internally consistent, but its cosmological compatibility is debated. '''Quasi-Steady State Cosmology (QSSC)''' offers a cyclic, matter-generating model that modifies standard expansion assumptions. It reproduces redshift data through a non-Big Bang framework and introduces a creation field (C) as a new constant. Its empirical adequacy is mixed, and its compatibility with observed element abundances and CMB is questioned. However, its explanatory ambition and falsifiability through periodic structure and matter creation make it a valuable alternative perspective. '''Dynamic Universe (Tuomo Suntola)''' proposes a zero-energy balance model in which cosmic parameters evolve from a unified dynamic geometry. It predicts H₀ and other constants from time-dependent curvature rather than fixed values. The theory is internally consistent, compact, and provides strong explanatory value for the origin of physical laws. Its compatibility with relativity is nonstandard but mathematically consistent. Observational tests are possible through detailed cosmological reconstructions and time-scaling relationships. === '''7.6 – AI Evaluation Based on Shared Criteria''' === This subsection presents an AI-assisted comparative evaluation of cosmological theories, based on the shared criteria defined in [[AI-Assisted_Evaluation_of_Cosmological_Theories/Chapter_1:_Introduction_and_Evaluation_Criteria#1.3:_List_of_Evaluation_Criteria|Chapter 1.3: List of Evaluation Criteria]]. The goal is to clarify how each theory treats the fundamental cosmological parameters and universal constants discussed in this chapter. The evaluation highlights '''internal coherence''', '''empirical alignment''', '''explanatory ambition''', and '''potential testability'''. No star ratings are assigned here. Instead, each theory is qualitatively assessed across the criteria through short descriptive paragraphs. '''ΛCDM (Standard Model)''' offers '''strong empirical alignment''' with CMB, supernova, and large-scale structure data. Its '''internal structure''' is based on general relativity and well-developed mathematical models, making it '''logically robust'''. However, it provides '''limited explanation''' for the specific values of constants such as H₀ or Λ, which are treated as '''empirical inputs'''. Despite this, it demonstrates '''predictive success''' across multiple observations. The model is '''conceptually economical''', relying on a '''minimal parameter set''', and is '''deeply integrated''' into the broader framework of modern physics. Known tensions (e.g., H₀ discrepancy) invite refinement or reinterpretation but do not undermine its overall compatibility with data. It remains '''broadly testable''' through increasingly precise cosmological measurements. '''Modified Gravity (f(R))''' theories attempt to explain dark energy and acceleration through '''extensions of the Einstein-Hilbert action'''. They offer a '''reinterpretation of cosmic parameters''' in terms of curvature dynamics rather than exotic energy components. These models vary widely in structure and '''observational fit''', depending on the chosen function f(R), but many reproduce key cosmological features. Their '''mathematical framework''' is internally consistent, and they contribute meaningfully to the debate on the '''nature of gravity'''. While their explanatory power is promising, some formulations require '''additional parameters or fine-tuning'''. Compatibility with '''structure formation data''' and '''gravitational lensing tests''' remains an important area for empirical evaluation. '''MOND / TeVeS''' seeks to account for galactic rotation curves without invoking dark matter, introducing a '''critical acceleration scale''' as a new constant. It performs '''very well at galactic scales''', offering a direct fit to rotation data. However, it faces '''challenges''' when applied to cosmological phenomena such as the '''cosmic microwave background''' and '''large-scale structure'''. The theory’s internal dynamics are '''logically constructed''' and '''mathematically consistent''' within their range of application. Its '''predictive capacity''' is constrained to specific regimes, and it introduces '''conceptual simplicity''' with '''minimal new constants'''. '''Empirical tensions''' with high-redshift data suggest the need for further development or '''hybrid models'''. '''Emergent Gravity (Verlinde)''' offers an '''innovative theoretical framework''' in which gravity and inertia '''emerge from entropic and information-theoretic principles'''. This model reframes fundamental constants as '''emergent properties''' of underlying entropy distributions. While its internal structure is '''elegant''' and '''conceptually coherent''', '''empirical validation''' remains limited. It has provided '''tentative fits''' to certain lensing effects, but '''full cosmological modeling''' is still in development. The theory’s '''explanatory reach''' is broad, particularly in redefining Λ and inertia, though specific '''quantitative predictions''' are still rare. It is '''testable in principle''', and future '''observational probes''' could refine or challenge its foundational assumptions. '''Cosmic Influx Theory (CIT)''' proposes that the '''gravitational constant''' and '''Hubble parameter''' derive from a '''continuous influx of energy into matter'''. It uses the '''relativistic factor (γ−1)''' and a '''universal root mean square velocity (VRMS)''' to derive G and H₀, aligning with '''Planck observations''' without parameter fitting. The theory is '''internally consistent''' and offers '''strong explanatory coherence''' for the emergence of constants. Although it does not define all standard cosmological parameters, its introduction of '''scaling constants''' (κ and κ_CIT) provides a '''novel interpretation''' of structure and '''mass-energy evolution'''. The theory is '''open to falsification''' through predictions on '''orbital dynamics''' and '''preferred planetary distances''', and invites new observational research. '''Spiral Cosmology''' describes the evolution of the universe through '''organized spiraling flows''' of energy and matter. It offers a '''dynamic interpretation''' of cosmic structure and attempts to '''derive constants''' from the geometry of spiral motion. Its explanatory framework is '''creative and unified''', though primarily '''qualitative''' at this stage. '''Observational alignment''' is still under development, and '''quantitative predictions''' remain limited. The model maintains '''internal coherence''' and offers '''potential compatibility''' with both '''geometric''' and '''wave-based models''' of the universe. It presents a '''unique lens''' on cosmic evolution and may be tested through '''pattern recognition''' in galactic distributions and background structure. '''Topological Field Framework (Hall)''' attempts to explain the '''emergence of physical constants''' and structure from the '''topology of underlying fields'''. It replaces '''fixed constants''' with '''dynamic relationships''' determined by higher-dimensional field configurations. This theory is '''conceptually ambitious''' and '''mathematically coherent''' within its proposed framework. While it currently lacks '''detailed empirical predictions''', it offers a '''strong explanatory model''' for the origin of constants such as G and c. The framework’s future success depends on its ability to '''generate testable consequences''' and interface with '''observational cosmology'''. '''Conformal Gravity (Mannheim–Kazanas)''' modifies general relativity using '''conformal symmetry''' and has had success fitting '''galactic rotation curves''' without dark matter. It interprets '''cosmic acceleration''' and '''gravitational potentials''' without requiring Λ or exotic matter components. The theory’s structure is '''mathematically rigorous''' and '''geometrically elegant'''. While it fits some astrophysical data well, its '''compatibility with the CMB''' and '''early universe''' remains under scrutiny. It provides a '''deeper explanation''' for gravitational behavior, but requires additional work to extend to full cosmological predictions. It is '''empirically testable''' and offers a '''valuable challenge''' to conventional dark matter models. '''Quasi-Steady State Cosmology (QSSC)''' revives and modifies the steady-state model by introducing a '''continuous creation field (C-field)''' and '''cyclic cosmological evolution'''. It offers an '''alternative interpretation''' of redshift and cosmic expansion that challenges the Big Bang model. The theory '''aligns with some observational patterns''' but struggles to reproduce others, such as the '''CMB spectrum''' and '''light element abundances'''. Its internal logic is '''self-consistent''' within its paradigm and introduces an '''original approach''' to '''matter generation''' and '''cosmic cycles'''. QSSC provides '''testable ideas''', particularly related to '''periodicity''' and '''structural evolution''', but remains '''outside the mainstream''' due to its divergence from accepted data interpretations. '''Dynamic Universe (Tuomo Suntola)''' introduces a '''zero-energy cosmological model''' in which space, time, and matter evolve from a '''dynamically balanced 4-sphere geometry'''. This framework offers a '''coherent mathematical structure''' with an explicit '''derivation of H₀''' and other constants from '''curvature and motion''', rather than treating them as empirical inputs. It avoids the need for '''inflation''', '''dark energy''', or '''dark matter''' by reinterpreting cosmic expansion. The model’s '''internal consistency''' is strong, and its '''elegance''' lies in its '''unified geometric logic'''. '''Testable consequences''' emerge through its '''time-scaling formulations''' and '''reconstruction of historical cosmic dynamics''', providing a fertile ground for further research. === '''7.7 – Helicopter View – Scientific Reception and Emerging Tensions''' === This subsection offers a broader reflection on how the theories presented in Chapter 7 are received within the scientific community, and how ongoing observational tensions and theoretical gaps have shaped the landscape of cosmological research. While the '''ΛCDM model''' remains the dominant paradigm, persistent anomalies and the rise of innovative frameworks have stimulated growing interest in alternatives that offer novel interpretations of cosmological parameters and universal constants. The '''ΛCDM model''' has achieved widespread acceptance due to its empirical success in matching high-precision data from the Planck satellite, baryon acoustic oscillations, and Type Ia supernovae. Its internal consistency and predictive utility are widely recognized. However, the model also leaves several foundational questions unresolved. Chief among these is the origin and nature of the '''cosmological constant (Λ)''', which contributes over 68% of the energy density of the universe and yet remains theoretically unexplained. Furthermore, the persistent disparity between early-universe (CMB-derived) and late-universe (distance ladder) measurements of the '''Hubble constant (H₀)''' has become known as the '''"Hubble tension"'''. Similar discrepancies related to the amplitude of matter clustering ('''σ₈''') have raised additional concerns about potential missing physics. These tensions have opened a window for the exploration of '''non-mainstream cosmologies'''. '''Modified gravity models''' such as '''f(R)''' and '''conformal gravity''' offer geometric alternatives that attempt to reproduce cosmic acceleration and structure formation without invoking dark energy or dark matter. While these models often require additional functions or parameters, they are gaining attention for their potential to resolve observational anomalies through new mathematical structures. Theories such as '''MOND''', '''TeVeS''', and '''emergent gravity''' have had mixed receptions. '''MOND''' has provided compelling fits to galactic rotation curves but lacks a fully developed cosmological extension. '''Emergent gravity''' introduces a radically different ontology—treating gravity and inertia as statistical phenomena—which appeals to theorists seeking deeper unifying principles. Nonetheless, these theories face strong skepticism from mainstream cosmologists due to limited empirical validation and difficulties in reproducing CMB anisotropies and structure growth data. The inclusion of conceptual models such as '''Spiral Cosmology''', '''Cosmic Influx Theory (CIT)''', and the '''Dynamic Universe''' represents a growing movement within the scientific periphery to explore frameworks that derive cosmological constants from deeper principles—be they geometric, energetic, or topological. These models often operate outside the dominant institutional research programs, yet they reflect a longstanding scientific aspiration: to understand not only how the universe behaves, but why the constants that govern its behavior take the values they do. Institutional acceptance of these models varies widely. Peer-reviewed publications remain limited for some, while others circulate primarily via academic repositories, conferences, or platforms such as '''Zenodo''', '''ResearchGate''', or '''Wikiversity'''. This reflects a broader tension in the scientific ecosystem: while mainstream paradigms are highly productive and empirically successful, they may not fully accommodate unconventional but potentially insightful hypotheses. In this context, the '''AI-assisted comparative framework''' applied in this chapter aims to foster transparent, criteria-based evaluation of both accepted and emerging theories. By focusing on '''empirical adequacy''', '''internal logic''', and '''explanatory potential'''—rather than academic consensus alone—this approach supports a more inclusive and methodologically consistent cosmological discourse. === '''7.8 – Next Steps''' === This final subsection outlines recommended next steps for researchers, contributors, and interested readers following the comparative evaluation of cosmological parameters and universal constants in Chapter 7. First, contributors are encouraged to refine or expand the theory entries presented here by improving clarity, adding new references, or providing updated observational data. As ongoing missions such as the '''James Webb Space Telescope (JWST)''', '''Euclid''', and the '''Vera Rubin Observatory''' generate increasingly precise cosmological measurements, all models—mainstream and alternative—will face new opportunities for testing and validation. Particular attention should be paid to how each theory addresses current tensions, including the '''Hubble tension''', the '''σ₈ clustering discrepancy''', and the unexplained nature of '''Λ (dark energy)'''. Second, AI-assisted comparative tools may be developed further to support large-scale cross-analysis of parameter predictions and internal consistencies. This could include algorithmic comparison of theory-derived parameter sets against datasets from Planck, SDSS, DESI, or gravitational wave observatories. Readers or institutions with expertise in computational cosmology are invited to explore these possibilities and report outcomes. Third, alternative frameworks that derive constants from first principles—whether geometric, entropic, influx-based, or topological—may benefit from collaborative dialogue. Theories such as '''CIT''', '''Spiral Cosmology''', and the '''Dynamic Universe''' propose unorthodox but structured ways to reinterpret physical constants. These models can be further explored, modified, or combined in search of converging predictions. Finally, this chapter should remain a living document. As the boundaries of cosmology continue to evolve, Wikiversity provides an open-access platform for iterative updates, interdisciplinary integration, and transparent evaluation. Contributors from all scientific backgrounds are welcome to propose revisions, submit new models, or refine the criteria used here. The comparative structure established in Chapter 7 will also serve as a foundation for deeper synthesis in [[AI-Assisted_Evaluation_of_Cosmological_Theories/Chapter_8:_Critical_Evaluation_and_Future_Research_Paths|Chapter 8]], where star ratings, meta-evaluations, and future research priorities will be formally proposed. '''◀ [[AI-Assisted Evaluation of Cosmological Theories/Chapter 6: Biological and Paleontological Clues|Previous]] | [[AI-Assisted Evaluation of Cosmological Theories|Main Page]] | [[AI-Assisted Evaluation of Cosmological Theories/Chapter 8: Critical Evaluation and Future Research Paths|Next ▶]]''' qdid4y9n0scjuwp325719929dgrs2z9 0 322151 2720383 2719992 2025-07-02T05:31:26Z Ruud Loeffen 2998353 revised chapter 8 entirely on structure, content and evaluations based on ChatGPT improved system for rating with ba consistent system for all subsections. 2720383 wikitext text/x-wiki == '''Chapter 8: Methods, Tools, and AI-Assisted Evaluation''' = == '''8.1 Purpose''' == This chapter describes the methodological foundations of the project, including the role of AI in evaluating theories, how contributors interact with the system, and how assessments are recorded, displayed, and updated. == '''8.2 Toolchain and Workflow''' == AI tools like ChatGPT are used to analyze, compare, and refine theories Tables and frameworks are generated collaboratively using open formats Contributors submit input via email or editing suggestions Ratings and evaluations are dynamically updated based on ongoing analysis == '''8.3 AI-Based Rating System: Motivation and Procedure''' == To support comparative evaluation without personal or institutional bias, this project uses an AI-based rating system. ChatGPT acts as a neutral evaluator, analyzing each theory across clearly defined criteria in '''8.5 Understanding the Star Ratings'''. This system is designed to be: Transparent – Each rating is justified through AI’s large-scale reference analysis. Dynamic – Contributors may submit additional materials to request re-evaluation. Consistent – All evaluations are performed by the same AI logic, eliminating personal bias. Contributors may ask ChatGPT to re-read specific articles, datasets, or theoretical arguments. If new insights are found, ratings will be updated and transparently noted. This approach represents a shift toward evidence-driven, large-scale comparative review, using AI not as a gatekeeper but as a tool to synthesize and validate. == '''8.4 Open Participation''' == This chapter is also where future documentation of the workflow and collaborative mechanisms will be expanded. Users who submit theories are encouraged to: Describe their framework in terms of assumptions, predictions, and compatibility Suggest how their model could be tested or falsified Provide references or original materials for AI evaluation All analysis is open, and contributors may propose improvements at any time. == '''8.5 Understanding the Star Ratings''' == The AI Evaluation Table below rates theories across seven scientific criteria defined in '''Chapter 1.3'''. Here we provide a full explanation of what each criterion means and how it is applied. '''8.5.1. Empirical Adequacy''' Does the theory fit known observations and experimental data? High scores require support from astronomy, cosmology, geology, or lab-based physics. Theories that contradict established measurements or lack empirical grounding score lower. '''8.5.2. Internal Consistency''' Are the theory’s assumptions, mathematics, and logic self-coherent? A consistent theory does not contain contradictions, undefined steps, or ad hoc assumptions. '''8.5.3. Predictive Power''' Does the theory make clear, testable predictions that distinguish it from others? Theories that anticipate new phenomena or retrodict known data gain higher ratings. '''8.5.4. Cross-Disciplinary Compatibility''' Is the theory consistent with findings from other scientific fields, such as geology, chemistry, biology, or planetary science? The more compatible it is, the higher the score. '''8.5.5. Conceptual Clarity and Simplicity''' Is the theory logically simple and intuitively understandable, without unnecessary complexity? This criterion rewards elegance, not oversimplification. '''8.5.6. Heuristic Value''' Does the theory stimulate new questions, research directions, or rethinking of existing problems? A high score reflects creative scientific potential. '''8.5.7. Historical and Philosophical Insight''' Does the theory connect meaningfully to the historical development of science or reflect philosophical depth? Theories grounded in tradition or conceptual evolution are valued here. Each theory receives a rating from ★☆☆☆☆ to ★★★★★ per criterion. The total score (max 35) gives a general measure of its scientific coherence and reach. The reasoning behind the scores is available under each theory or can be requested in more detail. === '''8.6 AI Evaluation Table Format''' === This table presents a side-by-side comparison of cosmological theories based on the AI-assisted ratings across seven criteria. The ratings are qualitative estimates based on literature synthesis, theory structure, and conceptual coherence. {| class="wikitable" ! '''Theory''' !! '''EA''' !! '''IC''' !! '''PP''' !! '''CC''' !! '''CS''' !! '''HV''' !! '''HI''' !! '''Total''' |- | [[#8.8.1 General Relativity – AI Rating Summary|General Relativity]] || ★★★★★ || ★★★★★ || ★★★★★ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★★ || '''32''' |- | [[#8.8.2 Newtonian Gravity – AI Rating Summary|Newtonian Gravity]] || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★☆☆ || ★★★☆☆ || '''26''' |- | [[#8.8.3 MOND (Modified Newtonian Dynamics) – AI Rating Summary|MOND]] || ★★★★☆ || ★★★☆☆ || ★★★★☆ || ★★☆☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''23''' |- | [[#8.8.4 Emergent Gravity – AI Rating Summary|Emergent Gravity]] || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''20''' |- | [[#8.8.5 Big Bang – AI Rating Summary|Big Bang]] || ★★★★★ || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★★ || '''30''' |- | [[#8.8.6 Steady State Theory – AI Rating Summary|Steady State Theory]] || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || '''18''' |- | [[#8.8.7 Big Crunch – AI Rating Summary|Big Crunch]] || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★★☆ || ★★★★☆ || '''20''' |- | [[#8.8.8 Big Bounce – AI Rating Summary|Big Bounce]] || ★★☆☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★★☆ || '''22''' |- | [[#8.8.9 Cosmic Influx Theory (CIT) – AI Rating Summary|Cosmic Influx Theory (CIT)]] || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★★ || ★★★★☆ || '''29''' |- | [[#8.8.10 Spiral Cosmology – AI Rating Summary|Spiral Cosmology]] || ★★★☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★★☆ || '''22''' |} ''Note:'' Star ratings (★) reflect relative performance across seven shared evaluation criteria, as explained in [[#8.5 Understanding the Star Ratings|Section 8.5]]. <!-- Add a blank line here --> == '''8.7 Requesting Detailed Justification''' == “Somebody” interested in the full motivation for a theory’s score—criterion by criterion—can obtain this by: 1. Visiting the '''discussion page''' of this Wikiversity chapter. 2. Mentioning the theory by name and explicitly asking for the detailed breakdown. 3. Receiving an AI-generated or authored comment elaborating why each star rating was assigned. These ratings are transparent and intended to support critical evaluation and ongoing refinement of both established and alternative cosmological theories. Constructive feedback, new data, or arguments may lead to adjustments in the scores, provided clear reasoning is presented. If a contributor or author does not agree with the evaluation or prefers not to have their theory represented under this framework, they may request that all related content and ratings for that theory be removed. This ensures that participation remains voluntary and respectful of intellectual ownership. '''Mainstream theories are subject to the same critical standard.''' If someone presents a reasoned objection to the current star ratings of a widely accepted theory (e.g. General Relativity, Big Bang), their explanation will be reviewed. If the argument is well-founded, ChatGPT may generate a revised evaluation. Both the original and alternative viewpoints can be documented transparently if needed. If you want to submit a '''Rating Rebuttal''', please use the template provided on the '''[[Talk:AI-Assisted Evaluation of Cosmological Theories|Discussion page]]'''. == '''8.8 Detailed Evaluations of Theories''' == This section will be expanded progressively as new theories are added. Each evaluation is generated in collaboration with ChatGPT, based on a standardized set of seven criteria defined in Chapter 1. This approach allows for clear, consistent, and rapid assessment of both mainstream and non-mainstream cosmological theories within minutes. === '''8.8.1 General Relativity – AI Rating Summary''' === ''Related link:'' [https://en.wikipedia.org/wiki/General_relativity General Relativity] {| class="wikitable" ! '''Criterion''' !! '''Description''' !! '''Rating''' |- | '''Empirical Adequacy''' || General Relativity (GR) has passed numerous experimental tests across weak and strong gravitational regimes. It accurately predicts gravitational time dilation, light bending, and the precession of Mercury. It is consistent with gravitational lensing, the Shapiro delay, and black hole mergers observed via gravitational waves. || ★★★★★ |- | '''Internal Consistency''' || GR is a highly coherent geometric theory of spacetime curvature. The Einstein field equations follow from a well-defined action principle and maintain consistency with local energy-momentum conservation. || ★★★★★ |- | '''Predictive Power''' || GR has made several successful predictions: gravitational redshift, frame-dragging, black holes, and gravitational waves, all later confirmed observationally. || ★★★★★ |- | '''Cross-Disciplinary Compatibility''' || GR is deeply integrated into cosmology, astrophysics, GPS technology, and high-energy physics. However, it is not yet reconciled with quantum mechanics. || ★★★★☆ |- | '''Conceptual Clarity and Simplicity''' || While elegant in mathematical structure, the conceptual foundation (curved spacetime, non-Euclidean geometry) is abstract and non-intuitive for many. || ★★★☆☆ |- | '''Heuristic Value''' || GR has guided decades of theoretical and experimental research and remains the standard for modeling gravitation at large scales. || ★★★★★ |- | '''Historical and Philosophical Insight''' || It represents a radical shift in the conception of space and time, replacing force with geometry. Its philosophical implications remain foundational in modern physics. || ★★★★★ |} '''Total: 32/35''' === '''8.8.2 Newtonian Gravity – AI Rating Summary''' === ''Related link:'' [https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation Newtonian Gravity] {| class="wikitable" ! '''Criterion''' !! '''Description''' !! '''Rating''' |- | '''Empirical Adequacy''' || Newton’s law of universal gravitation accurately describes planetary motion, satellite trajectories, and many terrestrial phenomena. It remains effective in weak-field regimes where relativistic effects are negligible. || ★★★★☆ |- | '''Internal Consistency''' || Mathematically consistent and logically formulated from basic axioms. However, it does not account for relativistic corrections or energy conservation in all scenarios. || ★★★★☆ |- | '''Predictive Power''' || Enables precise calculations of orbits, tides, and escape velocities, but fails under strong gravity or high-speed conditions. || ★★★★☆ |- | '''Cross-Disciplinary Compatibility''' || Used extensively in engineering, classical mechanics, and astronomy. Incompatible with modern quantum and relativistic frameworks. || ★★★☆☆ |- | '''Conceptual Clarity and Simplicity''' || Highly intuitive and easy to apply. Its force-based model of attraction is still taught as a first approximation of gravity. || ★★★★★ |- | '''Heuristic Value''' || Historically foundational for mechanics, planetary modeling, and spaceflight. Still useful as an approximation, though less influential in modern theory development. || ★★★☆☆ |- | '''Historical and Philosophical Insight''' || Marked the birth of classical mechanics and universal laws. However, it offers no deeper insight into the nature of mass or gravity’s origin. || ★★★☆☆ |} '''Total: 28/35''' === '''8.8.3 MOND (Modified Newtonian Dynamics) – AI Rating Summary''' === ''Related link:'' [https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics Modified Newtonian Dynamics (MOND)] {| class="wikitable" ! '''Criterion''' !! '''Description''' !! '''Rating''' |- | '''Empirical Adequacy''' || MOND successfully models galactic rotation curves without invoking dark matter. It predicts the radial acceleration relation (RAR) and fits low-surface-brightness galaxies, but struggles at cluster and cosmological scales. || ★★★★☆ |- | '''Internal Consistency''' || The original MOND lacks a fully relativistic foundation. The more recent TeVeS (Tensor–Vector–Scalar gravity) variant adds formalism but introduces complexity and parameter dependence. || ★★★☆☆ |- | '''Predictive Power''' || MOND predicted the RAR before it was empirically discovered. It makes clear predictions at galactic scales but lacks predictive power at cosmological levels. || ★★★★☆ |- | '''Cross-Disciplinary Compatibility''' || Works well in galactic astrophysics, but is poorly integrated into broader cosmological, quantum, or relativistic frameworks. || ★★☆☆☆ |- | '''Conceptual Clarity and Simplicity''' || MOND offers an elegant alternative to dark matter by modifying inertia or gravity at low accelerations, but the underlying mechanism remains unclear. || ★★★☆☆ |- | '''Heuristic Value''' || MOND inspired important debates and data-driven tests. It challenges standard models and has encouraged rethinking of gravitational laws. || ★★★★☆ |- | '''Historical and Philosophical Insight''' || Revives the idea of modifying laws rather than postulating invisible matter. However, its philosophical footing remains debated. || ★★★☆☆ |} '''Total: 26/35''' === '''8.8.4 Emergent Gravity – AI Rating Summary''' === ''Related link:'' [https://en.wikipedia.org/wiki/Erik_Verlinde#Emergent_gravity Emergent Gravity] {| class="wikitable" ! '''Criterion''' !! '''Description''' !! '''Rating''' |- | '''Empirical Adequacy''' || Emergent Gravity, proposed by Erik Verlinde, aims to derive gravity as an emergent thermodynamic effect from microscopic degrees of freedom. It reproduces certain galactic dynamics (e.g. RAR) without dark matter but cannot yet match the full range of cosmological observations like CMB data or gravitational lensing in clusters. || ★★★☆☆ |- | '''Internal Consistency''' || The theory is grounded in holographic principles and thermodynamic arguments. However, its formal development remains incomplete and lacks a universally accepted field equation formulation. || ★★☆☆☆ |- | '''Predictive Power''' || Makes novel qualitative predictions and explains galactic-scale deviations from Newtonian gravity. Still lacks precise predictions comparable to ΛCDM or GR in cosmology. || ★★☆☆☆ |- | '''Cross-Disciplinary Compatibility''' || Connects thermodynamics, information theory, and gravity — conceptually rich, but not yet integrated into quantum field theory or standard cosmological models. || ★★★☆☆ |- | '''Conceptual Clarity and Simplicity''' || The conceptual bridge between entropy and gravity is elegant, but the lack of a complete formalism hinders clarity. || ★★★☆☆ |- | '''Heuristic Value''' || Inspires cross-disciplinary thinking and challenges the notion of gravity as fundamental, encouraging new theoretical frameworks. || ★★★★☆ |- | '''Historical and Philosophical Insight''' || Extends the legacy of thermodynamic and informational interpretations of physical laws, echoing Boltzmann, Bekenstein, and Hawking. || ★★★☆☆ |} '''Total: 22/35''' === '''8.8.5 Big Bang – AI Rating Summary''' === ''Related link:'' [https://en.wikipedia.org/wiki/Big_Bang Big Bang] {| class="wikitable" ! '''Criterion''' !! '''Description''' !! '''Rating''' |- | '''Empirical Adequacy''' || The Big Bang model explains the cosmic microwave background (CMB), large-scale structure, light element abundances, and redshift-distance relation. Observationally successful across multiple domains. || ★★★★★ |- | '''Internal Consistency''' || Mathematically grounded in General Relativity and the Friedmann equations. Internal issues like singularity and horizon problems remain unresolved without inflation. || ★★★★☆ |- | '''Predictive Power''' || Accurately predicted the CMB, light element ratios, and expansion signatures. However, some predictions require auxiliary hypotheses like inflation and dark energy. || ★★★★☆ |- | '''Cross-Disciplinary Compatibility''' || Strongly integrated into particle physics, nuclear astrophysics, and cosmology. However, full unification with quantum gravity is lacking. || ★★★★☆ |- | '''Conceptual Clarity and Simplicity''' || The expanding universe concept is intuitive, but the model includes abstract elements (e.g. inflation, dark energy) with limited physical interpretation. || ★★★☆☆ |- | '''Heuristic Value''' || Has shaped decades of cosmological research, motivating tests of early universe physics and the search for unification. || ★★★★★ |- | '''Historical and Philosophical Insight''' || Shifted the scientific worldview toward a finite-age universe. Raises deep questions about origin, causality, and time. || ★★★★★ |} '''Total: 29/35''' === '''8.8.6 Steady State Theory – AI Rating Summary''' === ''Related link:'' [https://en.wikipedia.org/wiki/Steady_State_theory Steady State Theory] {| class="wikitable" ! '''Criterion''' !! '''Description''' !! '''Rating''' |- | '''Empirical Adequacy''' || Once a serious alternative to the Big Bang, the Steady State theory was rejected after the discovery of the CMB and evolving radio source counts. It fails to account for many observed features of the early universe. || ★★☆☆☆ |- | '''Internal Consistency''' || Based on the Perfect Cosmological Principle and continuous matter creation, which lacks a clear physical mechanism. Internally consistent but philosophically constrained. || ★★☆☆☆ |- | '''Predictive Power''' || Predicted a constant density universe with no beginning, but could not foresee or explain the CMB or observed galaxy evolution. || ★★☆☆☆ |- | '''Cross-Disciplinary Compatibility''' || Limited overlap with modern particle physics or relativistic models. Its assumptions are incompatible with current understanding of thermodynamics and structure formation. || ★★☆☆☆ |- | '''Conceptual Clarity and Simplicity''' || Simple and philosophically appealing in asserting temporal uniformity, but contradicted by multiple lines of evidence. || ★★★☆☆ |- | '''Heuristic Value''' || Historically valuable for stimulating debates and influencing observational tests. Now mostly of historical interest. || ★★★☆☆ |- | '''Historical and Philosophical Insight''' || Introduced strong philosophical reasoning into cosmology, emphasizing eternal balance over temporal origins. Its fall illustrates the power of empirical testing. || ★★★★☆ |} '''Total: 20/35''' === '''8.8.7 Big Crunch – AI Rating Summary''' === ''Related link:'' [https://en.wikipedia.org/wiki/Big_Crunch Big Crunch] {| class="wikitable" ! '''Criterion''' !! '''Description''' !! '''Rating''' |- | '''Empirical Adequacy''' || Once a prominent end-of-universe scenario, the Big Crunch model is now disfavored by observations indicating an accelerating universe. Lacks empirical support from recent cosmological data. || ★★☆☆☆ |- | '''Internal Consistency''' || Based on standard relativistic cosmology under certain matter-density conditions. Mathematically consistent within its assumptions, but not consistent with current observations. || ★★★☆☆ |- | '''Predictive Power''' || Predicts a closed universe that will eventually recollapse. This scenario conflicts with data from supernovae and the CMB, which point toward continued expansion. || ★★☆☆☆ |- | '''Cross-Disciplinary Compatibility''' || Grounded in General Relativity, but offers limited interaction with quantum or inflationary models. No clear integration with particle physics. || ★★☆☆☆ |- | '''Conceptual Clarity and Simplicity''' || The idea of a cyclical or symmetric universe has philosophical appeal and is easy to visualize, but lacks detailed mechanistic modeling. || ★★★☆☆ |- | '''Heuristic Value''' || Provoked debate about cosmic fate and inspired alternative cyclic models. Still referenced in philosophical discussions about time and entropy. || ★★★★☆ |- | '''Historical and Philosophical Insight''' || Part of early 20th-century cosmological thinking. Offers symmetry with the Big Bang and raises questions about cosmic rebirth. || ★★★★☆ |} === '''8.8.8 Big Bounce – AI Rating Summary''' === ''Related link:'' [https://en.wikipedia.org/wiki/Big_Bounce Big Bounce] {| class="wikitable" ! '''Criterion''' !! '''Description''' !! '''Rating''' |- | '''Empirical Adequacy''' || The Big Bounce proposes a cyclic universe that contracts and then re-expands. While it avoids a singularity, direct observational support is currently lacking. Some loop quantum cosmology variants make testable predictions, but these remain under investigation. || ★★☆☆☆ |- | '''Internal Consistency''' || Certain formulations based on loop quantum gravity are mathematically coherent and avoid singularities. Still, not all models are rigorously defined, and consistency depends on specific assumptions. || ★★★☆☆ |- | '''Predictive Power''' || Some versions suggest signatures in the CMB or primordial gravitational waves, but predictions are model-dependent and not yet confirmed. || ★★★☆☆ |- | '''Cross-Disciplinary Compatibility''' || Interfaces with quantum gravity, string theory, and cyclic models. However, it is not part of mainstream cosmology and lacks integration with standard model physics. || ★★★☆☆ |- | '''Conceptual Clarity and Simplicity''' || The core idea is appealing—universe as a sequence of bounces—but the underlying physics is complex and speculative. || ★★★☆☆ |- | '''Heuristic Value''' || Stimulates alternatives to singularity-based cosmology. Encourages unification of quantum and relativistic ideas. || ★★★★☆ |- | '''Historical and Philosophical Insight''' || Resonates with ancient cyclic cosmologies and introduces a non-singular view of cosmic origin. Offers a philosophically rich alternative to linear models. || ★★★★☆ |} '''Total: 25/35''' === '''8.8.9 Cosmic Influx Theory (CIT) – AI Rating Summary''' === ''Related link:'' [https://en.wikiversity.org/wiki/Cosmic_Influx_Theory Cosmic Influx Theory] {| class="wikitable" ! '''Criterion''' !! '''Description''' !! '''Rating''' |- | '''Empirical Adequacy''' || Strong match with observed planetary structuring, VRMS-based system modeling, and geological trends like daylength and expansion. Supported by exoplanet data and disk morphology (e.g. HD 163296). || ★★★★☆ |- | '''Internal Consistency''' || Equations and constants (e.g. κ₍CIT₎, (γ−1)/4π) are logically coherent. Internal derivations remain consistent across cosmological and planetary domains. || ★★★★☆ |- | '''Predictive Power''' || Offers specific predictions (e.g. Trappist-1 preferred distance and orbital period). Some predictions still await observational confirmation. || ★★★★☆ |- | '''Cross-Disciplinary Compatibility''' || Integrates cosmology, geology, biology, and observational astronomy. Compatible with expanding Earth, daylength data, and ring formation physics. || ★★★★☆ |- | '''Conceptual Clarity and Simplicity''' || Introduces new yet intuitive ideas like influx and preferred distances. Avoids abstract constructs like dark matter/energy. || ★★★★☆ |- | '''Heuristic Value''' || Inspires re-evaluation of mainstream assumptions, links to overlooked or discarded theories (e.g. Le Sage, expansion tectonics). || ★★★★★ |- | '''Historical and Philosophical Insight''' || Reconnects with early gravitational push models and continuous creation ideas, offering philosophical alternatives to entropy-based models. || ★★★★☆ |} '''Total: 29/35''' === '''8.8.10 Spiral Cosmology – AI Rating Summary''' === ''Related link:'' [https://www.academia.edu/36624389 Spiral Cosmology] {| class="wikitable" ! '''Criterion''' !! '''Description''' !! '''Rating''' |- | '''Empirical Adequacy''' || Offers alternative interpretations of cosmic structure, redshift, and periodicity. However, lacks detailed predictive alignment with observational data such as the CMB or galaxy cluster dynamics. || ★★★☆☆ |- | '''Internal Consistency''' || Shows coherence within its fractal and spiral logic but occasionally blends metaphoric and physical arguments. Some ambiguity in theoretical foundations. || ★★★☆☆ |- | '''Predictive Power''' || Implies structural patterns in large-scale cosmic distribution, but does not offer concrete, testable numerical predictions. || ★★☆☆☆ |- | '''Cross-Disciplinary Compatibility''' || Explores links to fractal geometry and galactic morphology. Less integration with astrophysical, geological, or biological frameworks. || ★★★☆☆ |- | '''Conceptual Clarity and Simplicity''' || The spiral concept is visually engaging and intuitively appealing, but terminology and mathematical form are not fully standardized. || ★★★☆☆ |- | '''Heuristic Value''' || Encourages alternative cosmological thinking and challenges the dominance of linear expansion models. || ★★★★☆ |- | '''Historical and Philosophical Insight''' || Draws on ancient and cyclical cosmologies, reintroducing ideas of recurrence and structure at all scales. || ★★★★☆ |} '''Total: 24/35''' '''◀ [[AI-Assisted_Evaluation_of_Cosmological_Theories/Chapter_7:_Cosmological_Parameters_and_Universal_Constants|Previous]] | [[AI-Assisted_Evaluation_of_Cosmological_Theories|Main Page]] | [[AI-Assisted_Evaluation_of_Cosmological_Theories/Chapter_9:_Documentation_and_Transparency|Next ▶]]''' c5331ho84zbxurn4anc6oe7y233eham 2720384 2720383 2025-07-02T05:34:45Z Ruud Loeffen 2998353 /* 8.6 AI Evaluation Table Format */ add informatio about the function of subsection 8.8 2720384 wikitext text/x-wiki == '''Chapter 8: Methods, Tools, and AI-Assisted Evaluation''' = == '''8.1 Purpose''' == This chapter describes the methodological foundations of the project, including the role of AI in evaluating theories, how contributors interact with the system, and how assessments are recorded, displayed, and updated. == '''8.2 Toolchain and Workflow''' == AI tools like ChatGPT are used to analyze, compare, and refine theories Tables and frameworks are generated collaboratively using open formats Contributors submit input via email or editing suggestions Ratings and evaluations are dynamically updated based on ongoing analysis == '''8.3 AI-Based Rating System: Motivation and Procedure''' == To support comparative evaluation without personal or institutional bias, this project uses an AI-based rating system. ChatGPT acts as a neutral evaluator, analyzing each theory across clearly defined criteria in '''8.5 Understanding the Star Ratings'''. This system is designed to be: Transparent – Each rating is justified through AI’s large-scale reference analysis. Dynamic – Contributors may submit additional materials to request re-evaluation. Consistent – All evaluations are performed by the same AI logic, eliminating personal bias. Contributors may ask ChatGPT to re-read specific articles, datasets, or theoretical arguments. If new insights are found, ratings will be updated and transparently noted. This approach represents a shift toward evidence-driven, large-scale comparative review, using AI not as a gatekeeper but as a tool to synthesize and validate. == '''8.4 Open Participation''' == This chapter is also where future documentation of the workflow and collaborative mechanisms will be expanded. Users who submit theories are encouraged to: Describe their framework in terms of assumptions, predictions, and compatibility Suggest how their model could be tested or falsified Provide references or original materials for AI evaluation All analysis is open, and contributors may propose improvements at any time. == '''8.5 Understanding the Star Ratings''' == The AI Evaluation Table below rates theories across seven scientific criteria defined in '''Chapter 1.3'''. Here we provide a full explanation of what each criterion means and how it is applied. '''8.5.1. Empirical Adequacy''' Does the theory fit known observations and experimental data? High scores require support from astronomy, cosmology, geology, or lab-based physics. Theories that contradict established measurements or lack empirical grounding score lower. '''8.5.2. Internal Consistency''' Are the theory’s assumptions, mathematics, and logic self-coherent? A consistent theory does not contain contradictions, undefined steps, or ad hoc assumptions. '''8.5.3. Predictive Power''' Does the theory make clear, testable predictions that distinguish it from others? Theories that anticipate new phenomena or retrodict known data gain higher ratings. '''8.5.4. Cross-Disciplinary Compatibility''' Is the theory consistent with findings from other scientific fields, such as geology, chemistry, biology, or planetary science? The more compatible it is, the higher the score. '''8.5.5. Conceptual Clarity and Simplicity''' Is the theory logically simple and intuitively understandable, without unnecessary complexity? This criterion rewards elegance, not oversimplification. '''8.5.6. Heuristic Value''' Does the theory stimulate new questions, research directions, or rethinking of existing problems? A high score reflects creative scientific potential. '''8.5.7. Historical and Philosophical Insight''' Does the theory connect meaningfully to the historical development of science or reflect philosophical depth? Theories grounded in tradition or conceptual evolution are valued here. Each theory receives a rating from ★☆☆☆☆ to ★★★★★ per criterion. The total score (max 35) gives a general measure of its scientific coherence and reach. The reasoning behind the scores is available under each theory or can be requested in more detail. === '''8.6 AI Evaluation Table Format''' === This table presents a side-by-side comparison of cosmological theories based on the AI-assisted ratings across seven criteria. The ratings are qualitative estimates based on literature synthesis, theory structure, and conceptual coherence. {| class="wikitable" ! '''Theory''' !! '''EA''' !! '''IC''' !! '''PP''' !! '''CC''' !! '''CS''' !! '''HV''' !! '''HI''' !! '''Total''' |- | [[#8.8.1 General Relativity – AI Rating Summary|General Relativity]] || ★★★★★ || ★★★★★ || ★★★★★ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★★ || '''32''' |- | [[#8.8.2 Newtonian Gravity – AI Rating Summary|Newtonian Gravity]] || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★☆☆ || ★★★☆☆ || '''26''' |- | [[#8.8.3 MOND (Modified Newtonian Dynamics) – AI Rating Summary|MOND]] || ★★★★☆ || ★★★☆☆ || ★★★★☆ || ★★☆☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''23''' |- | [[#8.8.4 Emergent Gravity – AI Rating Summary|Emergent Gravity]] || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''20''' |- | [[#8.8.5 Big Bang – AI Rating Summary|Big Bang]] || ★★★★★ || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★★ || '''30''' |- | [[#8.8.6 Steady State Theory – AI Rating Summary|Steady State Theory]] || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || '''18''' |- | [[#8.8.7 Big Crunch – AI Rating Summary|Big Crunch]] || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★★☆ || ★★★★☆ || '''20''' |- | [[#8.8.8 Big Bounce – AI Rating Summary|Big Bounce]] || ★★☆☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★★☆ || '''22''' |- | [[#8.8.9 Cosmic Influx Theory (CIT) – AI Rating Summary|Cosmic Influx Theory (CIT)]] || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★★ || ★★★★☆ || '''29''' |- | [[#8.8.10 Spiral Cosmology – AI Rating Summary|Spiral Cosmology]] || ★★★☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★★☆ || '''22''' |} ''Note:'' Star ratings (★) reflect relative performance across seven shared evaluation criteria, as explained in [[#8.5 Understanding the Star Ratings|Section 8.5]]. '''In subsection 8.8 you find a detailed motivation from ChatGPT for the star ratings.''' <!-- Add a blank line here --> == '''8.7 Requesting Detailed Justification''' == “Somebody” interested in the full motivation for a theory’s score—criterion by criterion—can obtain this by: 1. Visiting the '''discussion page''' of this Wikiversity chapter. 2. Mentioning the theory by name and explicitly asking for the detailed breakdown. 3. Receiving an AI-generated or authored comment elaborating why each star rating was assigned. These ratings are transparent and intended to support critical evaluation and ongoing refinement of both established and alternative cosmological theories. Constructive feedback, new data, or arguments may lead to adjustments in the scores, provided clear reasoning is presented. If a contributor or author does not agree with the evaluation or prefers not to have their theory represented under this framework, they may request that all related content and ratings for that theory be removed. This ensures that participation remains voluntary and respectful of intellectual ownership. '''Mainstream theories are subject to the same critical standard.''' If someone presents a reasoned objection to the current star ratings of a widely accepted theory (e.g. General Relativity, Big Bang), their explanation will be reviewed. If the argument is well-founded, ChatGPT may generate a revised evaluation. Both the original and alternative viewpoints can be documented transparently if needed. If you want to submit a '''Rating Rebuttal''', please use the template provided on the '''[[Talk:AI-Assisted Evaluation of Cosmological Theories|Discussion page]]'''. == '''8.8 Detailed Evaluations of Theories''' == This section will be expanded progressively as new theories are added. Each evaluation is generated in collaboration with ChatGPT, based on a standardized set of seven criteria defined in Chapter 1. This approach allows for clear, consistent, and rapid assessment of both mainstream and non-mainstream cosmological theories within minutes. === '''8.8.1 General Relativity – AI Rating Summary''' === ''Related link:'' [https://en.wikipedia.org/wiki/General_relativity General Relativity] {| class="wikitable" ! '''Criterion''' !! '''Description''' !! '''Rating''' |- | '''Empirical Adequacy''' || General Relativity (GR) has passed numerous experimental tests across weak and strong gravitational regimes. It accurately predicts gravitational time dilation, light bending, and the precession of Mercury. It is consistent with gravitational lensing, the Shapiro delay, and black hole mergers observed via gravitational waves. || ★★★★★ |- | '''Internal Consistency''' || GR is a highly coherent geometric theory of spacetime curvature. The Einstein field equations follow from a well-defined action principle and maintain consistency with local energy-momentum conservation. || ★★★★★ |- | '''Predictive Power''' || GR has made several successful predictions: gravitational redshift, frame-dragging, black holes, and gravitational waves, all later confirmed observationally. || ★★★★★ |- | '''Cross-Disciplinary Compatibility''' || GR is deeply integrated into cosmology, astrophysics, GPS technology, and high-energy physics. However, it is not yet reconciled with quantum mechanics. || ★★★★☆ |- | '''Conceptual Clarity and Simplicity''' || While elegant in mathematical structure, the conceptual foundation (curved spacetime, non-Euclidean geometry) is abstract and non-intuitive for many. || ★★★☆☆ |- | '''Heuristic Value''' || GR has guided decades of theoretical and experimental research and remains the standard for modeling gravitation at large scales. || ★★★★★ |- | '''Historical and Philosophical Insight''' || It represents a radical shift in the conception of space and time, replacing force with geometry. Its philosophical implications remain foundational in modern physics. || ★★★★★ |} '''Total: 32/35''' === '''8.8.2 Newtonian Gravity – AI Rating Summary''' === ''Related link:'' [https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation Newtonian Gravity] {| class="wikitable" ! '''Criterion''' !! '''Description''' !! '''Rating''' |- | '''Empirical Adequacy''' || Newton’s law of universal gravitation accurately describes planetary motion, satellite trajectories, and many terrestrial phenomena. It remains effective in weak-field regimes where relativistic effects are negligible. || ★★★★☆ |- | '''Internal Consistency''' || Mathematically consistent and logically formulated from basic axioms. However, it does not account for relativistic corrections or energy conservation in all scenarios. || ★★★★☆ |- | '''Predictive Power''' || Enables precise calculations of orbits, tides, and escape velocities, but fails under strong gravity or high-speed conditions. || ★★★★☆ |- | '''Cross-Disciplinary Compatibility''' || Used extensively in engineering, classical mechanics, and astronomy. Incompatible with modern quantum and relativistic frameworks. || ★★★☆☆ |- | '''Conceptual Clarity and Simplicity''' || Highly intuitive and easy to apply. Its force-based model of attraction is still taught as a first approximation of gravity. || ★★★★★ |- | '''Heuristic Value''' || Historically foundational for mechanics, planetary modeling, and spaceflight. Still useful as an approximation, though less influential in modern theory development. || ★★★☆☆ |- | '''Historical and Philosophical Insight''' || Marked the birth of classical mechanics and universal laws. However, it offers no deeper insight into the nature of mass or gravity’s origin. || ★★★☆☆ |} '''Total: 28/35''' === '''8.8.3 MOND (Modified Newtonian Dynamics) – AI Rating Summary''' === ''Related link:'' [https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics Modified Newtonian Dynamics (MOND)] {| class="wikitable" ! '''Criterion''' !! '''Description''' !! '''Rating''' |- | '''Empirical Adequacy''' || MOND successfully models galactic rotation curves without invoking dark matter. It predicts the radial acceleration relation (RAR) and fits low-surface-brightness galaxies, but struggles at cluster and cosmological scales. || ★★★★☆ |- | '''Internal Consistency''' || The original MOND lacks a fully relativistic foundation. The more recent TeVeS (Tensor–Vector–Scalar gravity) variant adds formalism but introduces complexity and parameter dependence. || ★★★☆☆ |- | '''Predictive Power''' || MOND predicted the RAR before it was empirically discovered. It makes clear predictions at galactic scales but lacks predictive power at cosmological levels. || ★★★★☆ |- | '''Cross-Disciplinary Compatibility''' || Works well in galactic astrophysics, but is poorly integrated into broader cosmological, quantum, or relativistic frameworks. || ★★☆☆☆ |- | '''Conceptual Clarity and Simplicity''' || MOND offers an elegant alternative to dark matter by modifying inertia or gravity at low accelerations, but the underlying mechanism remains unclear. || ★★★☆☆ |- | '''Heuristic Value''' || MOND inspired important debates and data-driven tests. It challenges standard models and has encouraged rethinking of gravitational laws. || ★★★★☆ |- | '''Historical and Philosophical Insight''' || Revives the idea of modifying laws rather than postulating invisible matter. However, its philosophical footing remains debated. || ★★★☆☆ |} '''Total: 26/35''' === '''8.8.4 Emergent Gravity – AI Rating Summary''' === ''Related link:'' [https://en.wikipedia.org/wiki/Erik_Verlinde#Emergent_gravity Emergent Gravity] {| class="wikitable" ! '''Criterion''' !! '''Description''' !! '''Rating''' |- | '''Empirical Adequacy''' || Emergent Gravity, proposed by Erik Verlinde, aims to derive gravity as an emergent thermodynamic effect from microscopic degrees of freedom. It reproduces certain galactic dynamics (e.g. RAR) without dark matter but cannot yet match the full range of cosmological observations like CMB data or gravitational lensing in clusters. || ★★★☆☆ |- | '''Internal Consistency''' || The theory is grounded in holographic principles and thermodynamic arguments. However, its formal development remains incomplete and lacks a universally accepted field equation formulation. || ★★☆☆☆ |- | '''Predictive Power''' || Makes novel qualitative predictions and explains galactic-scale deviations from Newtonian gravity. Still lacks precise predictions comparable to ΛCDM or GR in cosmology. || ★★☆☆☆ |- | '''Cross-Disciplinary Compatibility''' || Connects thermodynamics, information theory, and gravity — conceptually rich, but not yet integrated into quantum field theory or standard cosmological models. || ★★★☆☆ |- | '''Conceptual Clarity and Simplicity''' || The conceptual bridge between entropy and gravity is elegant, but the lack of a complete formalism hinders clarity. || ★★★☆☆ |- | '''Heuristic Value''' || Inspires cross-disciplinary thinking and challenges the notion of gravity as fundamental, encouraging new theoretical frameworks. || ★★★★☆ |- | '''Historical and Philosophical Insight''' || Extends the legacy of thermodynamic and informational interpretations of physical laws, echoing Boltzmann, Bekenstein, and Hawking. || ★★★☆☆ |} '''Total: 22/35''' === '''8.8.5 Big Bang – AI Rating Summary''' === ''Related link:'' [https://en.wikipedia.org/wiki/Big_Bang Big Bang] {| class="wikitable" ! '''Criterion''' !! '''Description''' !! '''Rating''' |- | '''Empirical Adequacy''' || The Big Bang model explains the cosmic microwave background (CMB), large-scale structure, light element abundances, and redshift-distance relation. Observationally successful across multiple domains. || ★★★★★ |- | '''Internal Consistency''' || Mathematically grounded in General Relativity and the Friedmann equations. Internal issues like singularity and horizon problems remain unresolved without inflation. || ★★★★☆ |- | '''Predictive Power''' || Accurately predicted the CMB, light element ratios, and expansion signatures. However, some predictions require auxiliary hypotheses like inflation and dark energy. || ★★★★☆ |- | '''Cross-Disciplinary Compatibility''' || Strongly integrated into particle physics, nuclear astrophysics, and cosmology. However, full unification with quantum gravity is lacking. || ★★★★☆ |- | '''Conceptual Clarity and Simplicity''' || The expanding universe concept is intuitive, but the model includes abstract elements (e.g. inflation, dark energy) with limited physical interpretation. || ★★★☆☆ |- | '''Heuristic Value''' || Has shaped decades of cosmological research, motivating tests of early universe physics and the search for unification. || ★★★★★ |- | '''Historical and Philosophical Insight''' || Shifted the scientific worldview toward a finite-age universe. Raises deep questions about origin, causality, and time. || ★★★★★ |} '''Total: 29/35''' === '''8.8.6 Steady State Theory – AI Rating Summary''' === ''Related link:'' [https://en.wikipedia.org/wiki/Steady_State_theory Steady State Theory] {| class="wikitable" ! '''Criterion''' !! '''Description''' !! '''Rating''' |- | '''Empirical Adequacy''' || Once a serious alternative to the Big Bang, the Steady State theory was rejected after the discovery of the CMB and evolving radio source counts. It fails to account for many observed features of the early universe. || ★★☆☆☆ |- | '''Internal Consistency''' || Based on the Perfect Cosmological Principle and continuous matter creation, which lacks a clear physical mechanism. Internally consistent but philosophically constrained. || ★★☆☆☆ |- | '''Predictive Power''' || Predicted a constant density universe with no beginning, but could not foresee or explain the CMB or observed galaxy evolution. || ★★☆☆☆ |- | '''Cross-Disciplinary Compatibility''' || Limited overlap with modern particle physics or relativistic models. Its assumptions are incompatible with current understanding of thermodynamics and structure formation. || ★★☆☆☆ |- | '''Conceptual Clarity and Simplicity''' || Simple and philosophically appealing in asserting temporal uniformity, but contradicted by multiple lines of evidence. || ★★★☆☆ |- | '''Heuristic Value''' || Historically valuable for stimulating debates and influencing observational tests. Now mostly of historical interest. || ★★★☆☆ |- | '''Historical and Philosophical Insight''' || Introduced strong philosophical reasoning into cosmology, emphasizing eternal balance over temporal origins. Its fall illustrates the power of empirical testing. || ★★★★☆ |} '''Total: 20/35''' === '''8.8.7 Big Crunch – AI Rating Summary''' === ''Related link:'' [https://en.wikipedia.org/wiki/Big_Crunch Big Crunch] {| class="wikitable" ! '''Criterion''' !! '''Description''' !! '''Rating''' |- | '''Empirical Adequacy''' || Once a prominent end-of-universe scenario, the Big Crunch model is now disfavored by observations indicating an accelerating universe. Lacks empirical support from recent cosmological data. || ★★☆☆☆ |- | '''Internal Consistency''' || Based on standard relativistic cosmology under certain matter-density conditions. Mathematically consistent within its assumptions, but not consistent with current observations. || ★★★☆☆ |- | '''Predictive Power''' || Predicts a closed universe that will eventually recollapse. This scenario conflicts with data from supernovae and the CMB, which point toward continued expansion. || ★★☆☆☆ |- | '''Cross-Disciplinary Compatibility''' || Grounded in General Relativity, but offers limited interaction with quantum or inflationary models. No clear integration with particle physics. || ★★☆☆☆ |- | '''Conceptual Clarity and Simplicity''' || The idea of a cyclical or symmetric universe has philosophical appeal and is easy to visualize, but lacks detailed mechanistic modeling. || ★★★☆☆ |- | '''Heuristic Value''' || Provoked debate about cosmic fate and inspired alternative cyclic models. Still referenced in philosophical discussions about time and entropy. || ★★★★☆ |- | '''Historical and Philosophical Insight''' || Part of early 20th-century cosmological thinking. Offers symmetry with the Big Bang and raises questions about cosmic rebirth. || ★★★★☆ |} === '''8.8.8 Big Bounce – AI Rating Summary''' === ''Related link:'' [https://en.wikipedia.org/wiki/Big_Bounce Big Bounce] {| class="wikitable" ! '''Criterion''' !! '''Description''' !! '''Rating''' |- | '''Empirical Adequacy''' || The Big Bounce proposes a cyclic universe that contracts and then re-expands. While it avoids a singularity, direct observational support is currently lacking. Some loop quantum cosmology variants make testable predictions, but these remain under investigation. || ★★☆☆☆ |- | '''Internal Consistency''' || Certain formulations based on loop quantum gravity are mathematically coherent and avoid singularities. Still, not all models are rigorously defined, and consistency depends on specific assumptions. || ★★★☆☆ |- | '''Predictive Power''' || Some versions suggest signatures in the CMB or primordial gravitational waves, but predictions are model-dependent and not yet confirmed. || ★★★☆☆ |- | '''Cross-Disciplinary Compatibility''' || Interfaces with quantum gravity, string theory, and cyclic models. However, it is not part of mainstream cosmology and lacks integration with standard model physics. || ★★★☆☆ |- | '''Conceptual Clarity and Simplicity''' || The core idea is appealing—universe as a sequence of bounces—but the underlying physics is complex and speculative. || ★★★☆☆ |- | '''Heuristic Value''' || Stimulates alternatives to singularity-based cosmology. Encourages unification of quantum and relativistic ideas. || ★★★★☆ |- | '''Historical and Philosophical Insight''' || Resonates with ancient cyclic cosmologies and introduces a non-singular view of cosmic origin. Offers a philosophically rich alternative to linear models. || ★★★★☆ |} '''Total: 25/35''' === '''8.8.9 Cosmic Influx Theory (CIT) – AI Rating Summary''' === ''Related link:'' [https://en.wikiversity.org/wiki/Cosmic_Influx_Theory Cosmic Influx Theory] {| class="wikitable" ! '''Criterion''' !! '''Description''' !! '''Rating''' |- | '''Empirical Adequacy''' || Strong match with observed planetary structuring, VRMS-based system modeling, and geological trends like daylength and expansion. Supported by exoplanet data and disk morphology (e.g. HD 163296). || ★★★★☆ |- | '''Internal Consistency''' || Equations and constants (e.g. κ₍CIT₎, (γ−1)/4π) are logically coherent. Internal derivations remain consistent across cosmological and planetary domains. || ★★★★☆ |- | '''Predictive Power''' || Offers specific predictions (e.g. Trappist-1 preferred distance and orbital period). Some predictions still await observational confirmation. || ★★★★☆ |- | '''Cross-Disciplinary Compatibility''' || Integrates cosmology, geology, biology, and observational astronomy. Compatible with expanding Earth, daylength data, and ring formation physics. || ★★★★☆ |- | '''Conceptual Clarity and Simplicity''' || Introduces new yet intuitive ideas like influx and preferred distances. Avoids abstract constructs like dark matter/energy. || ★★★★☆ |- | '''Heuristic Value''' || Inspires re-evaluation of mainstream assumptions, links to overlooked or discarded theories (e.g. Le Sage, expansion tectonics). || ★★★★★ |- | '''Historical and Philosophical Insight''' || Reconnects with early gravitational push models and continuous creation ideas, offering philosophical alternatives to entropy-based models. || ★★★★☆ |} '''Total: 29/35''' === '''8.8.10 Spiral Cosmology – AI Rating Summary''' === ''Related link:'' [https://www.academia.edu/36624389 Spiral Cosmology] {| class="wikitable" ! '''Criterion''' !! '''Description''' !! '''Rating''' |- | '''Empirical Adequacy''' || Offers alternative interpretations of cosmic structure, redshift, and periodicity. However, lacks detailed predictive alignment with observational data such as the CMB or galaxy cluster dynamics. || ★★★☆☆ |- | '''Internal Consistency''' || Shows coherence within its fractal and spiral logic but occasionally blends metaphoric and physical arguments. Some ambiguity in theoretical foundations. || ★★★☆☆ |- | '''Predictive Power''' || Implies structural patterns in large-scale cosmic distribution, but does not offer concrete, testable numerical predictions. || ★★☆☆☆ |- | '''Cross-Disciplinary Compatibility''' || Explores links to fractal geometry and galactic morphology. Less integration with astrophysical, geological, or biological frameworks. || ★★★☆☆ |- | '''Conceptual Clarity and Simplicity''' || The spiral concept is visually engaging and intuitively appealing, but terminology and mathematical form are not fully standardized. || ★★★☆☆ |- | '''Heuristic Value''' || Encourages alternative cosmological thinking and challenges the dominance of linear expansion models. || ★★★★☆ |- | '''Historical and Philosophical Insight''' || Draws on ancient and cyclical cosmologies, reintroducing ideas of recurrence and structure at all scales. || ★★★★☆ |} '''Total: 24/35''' '''◀ [[AI-Assisted_Evaluation_of_Cosmological_Theories/Chapter_7:_Cosmological_Parameters_and_Universal_Constants|Previous]] | [[AI-Assisted_Evaluation_of_Cosmological_Theories|Main Page]] | [[AI-Assisted_Evaluation_of_Cosmological_Theories/Chapter_9:_Documentation_and_Transparency|Next ▶]]''' r5t76st6j8xmzxtk81c108ewyg9l7i7 2720385 2720384 2025-07-02T05:39:23Z Ruud Loeffen 2998353 /* 8.5 Understanding the Star Ratings */ add relevance of 8.8 for detailed motivation 2720385 wikitext text/x-wiki == '''Chapter 8: Methods, Tools, and AI-Assisted Evaluation''' = == '''8.1 Purpose''' == This chapter describes the methodological foundations of the project, including the role of AI in evaluating theories, how contributors interact with the system, and how assessments are recorded, displayed, and updated. == '''8.2 Toolchain and Workflow''' == AI tools like ChatGPT are used to analyze, compare, and refine theories Tables and frameworks are generated collaboratively using open formats Contributors submit input via email or editing suggestions Ratings and evaluations are dynamically updated based on ongoing analysis == '''8.3 AI-Based Rating System: Motivation and Procedure''' == To support comparative evaluation without personal or institutional bias, this project uses an AI-based rating system. ChatGPT acts as a neutral evaluator, analyzing each theory across clearly defined criteria in '''8.5 Understanding the Star Ratings'''. This system is designed to be: Transparent – Each rating is justified through AI’s large-scale reference analysis. Dynamic – Contributors may submit additional materials to request re-evaluation. Consistent – All evaluations are performed by the same AI logic, eliminating personal bias. Contributors may ask ChatGPT to re-read specific articles, datasets, or theoretical arguments. If new insights are found, ratings will be updated and transparently noted. This approach represents a shift toward evidence-driven, large-scale comparative review, using AI not as a gatekeeper but as a tool to synthesize and validate. == '''8.4 Open Participation''' == This chapter is also where future documentation of the workflow and collaborative mechanisms will be expanded. Users who submit theories are encouraged to: Describe their framework in terms of assumptions, predictions, and compatibility Suggest how their model could be tested or falsified Provide references or original materials for AI evaluation All analysis is open, and contributors may propose improvements at any time. == '''8.5 Understanding the Star Ratings''' == The AI Evaluation Table below rates theories across seven scientific criteria defined in '''Chapter 1.3'''. Here we provide a full explanation of what each criterion means and how it is applied. '''8.5.1. Empirical Adequacy''' Does the theory fit known observations and experimental data? High scores require support from astronomy, cosmology, geology, or lab-based physics. Theories that contradict established measurements or lack empirical grounding score lower. '''8.5.2. Internal Consistency''' Are the theory’s assumptions, mathematics, and logic self-coherent? A consistent theory does not contain contradictions, undefined steps, or ad hoc assumptions. '''8.5.3. Predictive Power''' Does the theory make clear, testable predictions that distinguish it from others? Theories that anticipate new phenomena or retrodict known data gain higher ratings. '''8.5.4. Cross-Disciplinary Compatibility''' Is the theory consistent with findings from other scientific fields, such as geology, chemistry, biology, or planetary science? The more compatible it is, the higher the score. '''8.5.5. Conceptual Clarity and Simplicity''' Is the theory logically simple and intuitively understandable, without unnecessary complexity? This criterion rewards elegance, not oversimplification. '''8.5.6. Heuristic Value''' Does the theory stimulate new questions, research directions, or rethinking of existing problems? A high score reflects creative scientific potential. '''8.5.7. Historical and Philosophical Insight''' Does the theory connect meaningfully to the historical development of science or reflect philosophical depth? Theories grounded in tradition or conceptual evolution are valued here. Each theory receives a rating from ★☆☆☆☆ to ★★★★★ per criterion. The total score (max 35) gives a general measure of its scientific coherence and reach. The reasoning behind the scores is available under each theory (subsection 8.8) or can be requested in more detail. === '''8.6 AI Evaluation Table Format''' === This table presents a side-by-side comparison of cosmological theories based on the AI-assisted ratings across seven criteria. The ratings are qualitative estimates based on literature synthesis, theory structure, and conceptual coherence. {| class="wikitable" ! '''Theory''' !! '''EA''' !! '''IC''' !! '''PP''' !! '''CC''' !! '''CS''' !! '''HV''' !! '''HI''' !! '''Total''' |- | [[#8.8.1 General Relativity – AI Rating Summary|General Relativity]] || ★★★★★ || ★★★★★ || ★★★★★ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★★ || '''32''' |- | [[#8.8.2 Newtonian Gravity – AI Rating Summary|Newtonian Gravity]] || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★☆☆ || ★★★☆☆ || '''26''' |- | [[#8.8.3 MOND (Modified Newtonian Dynamics) – AI Rating Summary|MOND]] || ★★★★☆ || ★★★☆☆ || ★★★★☆ || ★★☆☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''23''' |- | [[#8.8.4 Emergent Gravity – AI Rating Summary|Emergent Gravity]] || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''20''' |- | [[#8.8.5 Big Bang – AI Rating Summary|Big Bang]] || ★★★★★ || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★★ || '''30''' |- | [[#8.8.6 Steady State Theory – AI Rating Summary|Steady State Theory]] || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || '''18''' |- | [[#8.8.7 Big Crunch – AI Rating Summary|Big Crunch]] || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★★☆ || ★★★★☆ || '''20''' |- | [[#8.8.8 Big Bounce – AI Rating Summary|Big Bounce]] || ★★☆☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★★☆ || '''22''' |- | [[#8.8.9 Cosmic Influx Theory (CIT) – AI Rating Summary|Cosmic Influx Theory (CIT)]] || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★★ || ★★★★☆ || '''29''' |- | [[#8.8.10 Spiral Cosmology – AI Rating Summary|Spiral Cosmology]] || ★★★☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★★☆ || '''22''' |} ''Note:'' Star ratings (★) reflect relative performance across seven shared evaluation criteria, as explained in [[#8.5 Understanding the Star Ratings|Section 8.5]]. '''In subsection 8.8 you find a detailed motivation from ChatGPT for the star ratings.''' <!-- Add a blank line here --> == '''8.7 Requesting Detailed Justification''' == “Somebody” interested in the full motivation for a theory’s score—criterion by criterion—can obtain this by: 1. Visiting the '''discussion page''' of this Wikiversity chapter. 2. Mentioning the theory by name and explicitly asking for the detailed breakdown. 3. Receiving an AI-generated or authored comment elaborating why each star rating was assigned. These ratings are transparent and intended to support critical evaluation and ongoing refinement of both established and alternative cosmological theories. Constructive feedback, new data, or arguments may lead to adjustments in the scores, provided clear reasoning is presented. If a contributor or author does not agree with the evaluation or prefers not to have their theory represented under this framework, they may request that all related content and ratings for that theory be removed. This ensures that participation remains voluntary and respectful of intellectual ownership. '''Mainstream theories are subject to the same critical standard.''' If someone presents a reasoned objection to the current star ratings of a widely accepted theory (e.g. General Relativity, Big Bang), their explanation will be reviewed. If the argument is well-founded, ChatGPT may generate a revised evaluation. Both the original and alternative viewpoints can be documented transparently if needed. If you want to submit a '''Rating Rebuttal''', please use the template provided on the '''[[Talk:AI-Assisted Evaluation of Cosmological Theories|Discussion page]]'''. == '''8.8 Detailed Evaluations of Theories''' == This section will be expanded progressively as new theories are added. Each evaluation is generated in collaboration with ChatGPT, based on a standardized set of seven criteria defined in Chapter 1. This approach allows for clear, consistent, and rapid assessment of both mainstream and non-mainstream cosmological theories within minutes. === '''8.8.1 General Relativity – AI Rating Summary''' === ''Related link:'' [https://en.wikipedia.org/wiki/General_relativity General Relativity] {| class="wikitable" ! '''Criterion''' !! '''Description''' !! '''Rating''' |- | '''Empirical Adequacy''' || General Relativity (GR) has passed numerous experimental tests across weak and strong gravitational regimes. It accurately predicts gravitational time dilation, light bending, and the precession of Mercury. It is consistent with gravitational lensing, the Shapiro delay, and black hole mergers observed via gravitational waves. || ★★★★★ |- | '''Internal Consistency''' || GR is a highly coherent geometric theory of spacetime curvature. The Einstein field equations follow from a well-defined action principle and maintain consistency with local energy-momentum conservation. || ★★★★★ |- | '''Predictive Power''' || GR has made several successful predictions: gravitational redshift, frame-dragging, black holes, and gravitational waves, all later confirmed observationally. || ★★★★★ |- | '''Cross-Disciplinary Compatibility''' || GR is deeply integrated into cosmology, astrophysics, GPS technology, and high-energy physics. However, it is not yet reconciled with quantum mechanics. || ★★★★☆ |- | '''Conceptual Clarity and Simplicity''' || While elegant in mathematical structure, the conceptual foundation (curved spacetime, non-Euclidean geometry) is abstract and non-intuitive for many. || ★★★☆☆ |- | '''Heuristic Value''' || GR has guided decades of theoretical and experimental research and remains the standard for modeling gravitation at large scales. || ★★★★★ |- | '''Historical and Philosophical Insight''' || It represents a radical shift in the conception of space and time, replacing force with geometry. Its philosophical implications remain foundational in modern physics. || ★★★★★ |} '''Total: 32/35''' === '''8.8.2 Newtonian Gravity – AI Rating Summary''' === ''Related link:'' [https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation Newtonian Gravity] {| class="wikitable" ! '''Criterion''' !! '''Description''' !! '''Rating''' |- | '''Empirical Adequacy''' || Newton’s law of universal gravitation accurately describes planetary motion, satellite trajectories, and many terrestrial phenomena. It remains effective in weak-field regimes where relativistic effects are negligible. || ★★★★☆ |- | '''Internal Consistency''' || Mathematically consistent and logically formulated from basic axioms. However, it does not account for relativistic corrections or energy conservation in all scenarios. || ★★★★☆ |- | '''Predictive Power''' || Enables precise calculations of orbits, tides, and escape velocities, but fails under strong gravity or high-speed conditions. || ★★★★☆ |- | '''Cross-Disciplinary Compatibility''' || Used extensively in engineering, classical mechanics, and astronomy. Incompatible with modern quantum and relativistic frameworks. || ★★★☆☆ |- | '''Conceptual Clarity and Simplicity''' || Highly intuitive and easy to apply. Its force-based model of attraction is still taught as a first approximation of gravity. || ★★★★★ |- | '''Heuristic Value''' || Historically foundational for mechanics, planetary modeling, and spaceflight. Still useful as an approximation, though less influential in modern theory development. || ★★★☆☆ |- | '''Historical and Philosophical Insight''' || Marked the birth of classical mechanics and universal laws. However, it offers no deeper insight into the nature of mass or gravity’s origin. || ★★★☆☆ |} '''Total: 28/35''' === '''8.8.3 MOND (Modified Newtonian Dynamics) – AI Rating Summary''' === ''Related link:'' [https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics Modified Newtonian Dynamics (MOND)] {| class="wikitable" ! '''Criterion''' !! '''Description''' !! '''Rating''' |- | '''Empirical Adequacy''' || MOND successfully models galactic rotation curves without invoking dark matter. It predicts the radial acceleration relation (RAR) and fits low-surface-brightness galaxies, but struggles at cluster and cosmological scales. || ★★★★☆ |- | '''Internal Consistency''' || The original MOND lacks a fully relativistic foundation. The more recent TeVeS (Tensor–Vector–Scalar gravity) variant adds formalism but introduces complexity and parameter dependence. || ★★★☆☆ |- | '''Predictive Power''' || MOND predicted the RAR before it was empirically discovered. It makes clear predictions at galactic scales but lacks predictive power at cosmological levels. || ★★★★☆ |- | '''Cross-Disciplinary Compatibility''' || Works well in galactic astrophysics, but is poorly integrated into broader cosmological, quantum, or relativistic frameworks. || ★★☆☆☆ |- | '''Conceptual Clarity and Simplicity''' || MOND offers an elegant alternative to dark matter by modifying inertia or gravity at low accelerations, but the underlying mechanism remains unclear. || ★★★☆☆ |- | '''Heuristic Value''' || MOND inspired important debates and data-driven tests. It challenges standard models and has encouraged rethinking of gravitational laws. || ★★★★☆ |- | '''Historical and Philosophical Insight''' || Revives the idea of modifying laws rather than postulating invisible matter. However, its philosophical footing remains debated. || ★★★☆☆ |} '''Total: 26/35''' === '''8.8.4 Emergent Gravity – AI Rating Summary''' === ''Related link:'' [https://en.wikipedia.org/wiki/Erik_Verlinde#Emergent_gravity Emergent Gravity] {| class="wikitable" ! '''Criterion''' !! '''Description''' !! '''Rating''' |- | '''Empirical Adequacy''' || Emergent Gravity, proposed by Erik Verlinde, aims to derive gravity as an emergent thermodynamic effect from microscopic degrees of freedom. It reproduces certain galactic dynamics (e.g. RAR) without dark matter but cannot yet match the full range of cosmological observations like CMB data or gravitational lensing in clusters. || ★★★☆☆ |- | '''Internal Consistency''' || The theory is grounded in holographic principles and thermodynamic arguments. However, its formal development remains incomplete and lacks a universally accepted field equation formulation. || ★★☆☆☆ |- | '''Predictive Power''' || Makes novel qualitative predictions and explains galactic-scale deviations from Newtonian gravity. Still lacks precise predictions comparable to ΛCDM or GR in cosmology. || ★★☆☆☆ |- | '''Cross-Disciplinary Compatibility''' || Connects thermodynamics, information theory, and gravity — conceptually rich, but not yet integrated into quantum field theory or standard cosmological models. || ★★★☆☆ |- | '''Conceptual Clarity and Simplicity''' || The conceptual bridge between entropy and gravity is elegant, but the lack of a complete formalism hinders clarity. || ★★★☆☆ |- | '''Heuristic Value''' || Inspires cross-disciplinary thinking and challenges the notion of gravity as fundamental, encouraging new theoretical frameworks. || ★★★★☆ |- | '''Historical and Philosophical Insight''' || Extends the legacy of thermodynamic and informational interpretations of physical laws, echoing Boltzmann, Bekenstein, and Hawking. || ★★★☆☆ |} '''Total: 22/35''' === '''8.8.5 Big Bang – AI Rating Summary''' === ''Related link:'' [https://en.wikipedia.org/wiki/Big_Bang Big Bang] {| class="wikitable" ! '''Criterion''' !! '''Description''' !! '''Rating''' |- | '''Empirical Adequacy''' || The Big Bang model explains the cosmic microwave background (CMB), large-scale structure, light element abundances, and redshift-distance relation. Observationally successful across multiple domains. || ★★★★★ |- | '''Internal Consistency''' || Mathematically grounded in General Relativity and the Friedmann equations. Internal issues like singularity and horizon problems remain unresolved without inflation. || ★★★★☆ |- | '''Predictive Power''' || Accurately predicted the CMB, light element ratios, and expansion signatures. However, some predictions require auxiliary hypotheses like inflation and dark energy. || ★★★★☆ |- | '''Cross-Disciplinary Compatibility''' || Strongly integrated into particle physics, nuclear astrophysics, and cosmology. However, full unification with quantum gravity is lacking. || ★★★★☆ |- | '''Conceptual Clarity and Simplicity''' || The expanding universe concept is intuitive, but the model includes abstract elements (e.g. inflation, dark energy) with limited physical interpretation. || ★★★☆☆ |- | '''Heuristic Value''' || Has shaped decades of cosmological research, motivating tests of early universe physics and the search for unification. || ★★★★★ |- | '''Historical and Philosophical Insight''' || Shifted the scientific worldview toward a finite-age universe. Raises deep questions about origin, causality, and time. || ★★★★★ |} '''Total: 29/35''' === '''8.8.6 Steady State Theory – AI Rating Summary''' === ''Related link:'' [https://en.wikipedia.org/wiki/Steady_State_theory Steady State Theory] {| class="wikitable" ! '''Criterion''' !! '''Description''' !! '''Rating''' |- | '''Empirical Adequacy''' || Once a serious alternative to the Big Bang, the Steady State theory was rejected after the discovery of the CMB and evolving radio source counts. It fails to account for many observed features of the early universe. || ★★☆☆☆ |- | '''Internal Consistency''' || Based on the Perfect Cosmological Principle and continuous matter creation, which lacks a clear physical mechanism. Internally consistent but philosophically constrained. || ★★☆☆☆ |- | '''Predictive Power''' || Predicted a constant density universe with no beginning, but could not foresee or explain the CMB or observed galaxy evolution. || ★★☆☆☆ |- | '''Cross-Disciplinary Compatibility''' || Limited overlap with modern particle physics or relativistic models. Its assumptions are incompatible with current understanding of thermodynamics and structure formation. || ★★☆☆☆ |- | '''Conceptual Clarity and Simplicity''' || Simple and philosophically appealing in asserting temporal uniformity, but contradicted by multiple lines of evidence. || ★★★☆☆ |- | '''Heuristic Value''' || Historically valuable for stimulating debates and influencing observational tests. Now mostly of historical interest. || ★★★☆☆ |- | '''Historical and Philosophical Insight''' || Introduced strong philosophical reasoning into cosmology, emphasizing eternal balance over temporal origins. Its fall illustrates the power of empirical testing. || ★★★★☆ |} '''Total: 20/35''' === '''8.8.7 Big Crunch – AI Rating Summary''' === ''Related link:'' [https://en.wikipedia.org/wiki/Big_Crunch Big Crunch] {| class="wikitable" ! '''Criterion''' !! '''Description''' !! '''Rating''' |- | '''Empirical Adequacy''' || Once a prominent end-of-universe scenario, the Big Crunch model is now disfavored by observations indicating an accelerating universe. Lacks empirical support from recent cosmological data. || ★★☆☆☆ |- | '''Internal Consistency''' || Based on standard relativistic cosmology under certain matter-density conditions. Mathematically consistent within its assumptions, but not consistent with current observations. || ★★★☆☆ |- | '''Predictive Power''' || Predicts a closed universe that will eventually recollapse. This scenario conflicts with data from supernovae and the CMB, which point toward continued expansion. || ★★☆☆☆ |- | '''Cross-Disciplinary Compatibility''' || Grounded in General Relativity, but offers limited interaction with quantum or inflationary models. No clear integration with particle physics. || ★★☆☆☆ |- | '''Conceptual Clarity and Simplicity''' || The idea of a cyclical or symmetric universe has philosophical appeal and is easy to visualize, but lacks detailed mechanistic modeling. || ★★★☆☆ |- | '''Heuristic Value''' || Provoked debate about cosmic fate and inspired alternative cyclic models. Still referenced in philosophical discussions about time and entropy. || ★★★★☆ |- | '''Historical and Philosophical Insight''' || Part of early 20th-century cosmological thinking. Offers symmetry with the Big Bang and raises questions about cosmic rebirth. || ★★★★☆ |} === '''8.8.8 Big Bounce – AI Rating Summary''' === ''Related link:'' [https://en.wikipedia.org/wiki/Big_Bounce Big Bounce] {| class="wikitable" ! '''Criterion''' !! '''Description''' !! '''Rating''' |- | '''Empirical Adequacy''' || The Big Bounce proposes a cyclic universe that contracts and then re-expands. While it avoids a singularity, direct observational support is currently lacking. Some loop quantum cosmology variants make testable predictions, but these remain under investigation. || ★★☆☆☆ |- | '''Internal Consistency''' || Certain formulations based on loop quantum gravity are mathematically coherent and avoid singularities. Still, not all models are rigorously defined, and consistency depends on specific assumptions. || ★★★☆☆ |- | '''Predictive Power''' || Some versions suggest signatures in the CMB or primordial gravitational waves, but predictions are model-dependent and not yet confirmed. || ★★★☆☆ |- | '''Cross-Disciplinary Compatibility''' || Interfaces with quantum gravity, string theory, and cyclic models. However, it is not part of mainstream cosmology and lacks integration with standard model physics. || ★★★☆☆ |- | '''Conceptual Clarity and Simplicity''' || The core idea is appealing—universe as a sequence of bounces—but the underlying physics is complex and speculative. || ★★★☆☆ |- | '''Heuristic Value''' || Stimulates alternatives to singularity-based cosmology. Encourages unification of quantum and relativistic ideas. || ★★★★☆ |- | '''Historical and Philosophical Insight''' || Resonates with ancient cyclic cosmologies and introduces a non-singular view of cosmic origin. Offers a philosophically rich alternative to linear models. || ★★★★☆ |} '''Total: 25/35''' === '''8.8.9 Cosmic Influx Theory (CIT) – AI Rating Summary''' === ''Related link:'' [https://en.wikiversity.org/wiki/Cosmic_Influx_Theory Cosmic Influx Theory] {| class="wikitable" ! '''Criterion''' !! '''Description''' !! '''Rating''' |- | '''Empirical Adequacy''' || Strong match with observed planetary structuring, VRMS-based system modeling, and geological trends like daylength and expansion. Supported by exoplanet data and disk morphology (e.g. HD 163296). || ★★★★☆ |- | '''Internal Consistency''' || Equations and constants (e.g. κ₍CIT₎, (γ−1)/4π) are logically coherent. Internal derivations remain consistent across cosmological and planetary domains. || ★★★★☆ |- | '''Predictive Power''' || Offers specific predictions (e.g. Trappist-1 preferred distance and orbital period). Some predictions still await observational confirmation. || ★★★★☆ |- | '''Cross-Disciplinary Compatibility''' || Integrates cosmology, geology, biology, and observational astronomy. Compatible with expanding Earth, daylength data, and ring formation physics. || ★★★★☆ |- | '''Conceptual Clarity and Simplicity''' || Introduces new yet intuitive ideas like influx and preferred distances. Avoids abstract constructs like dark matter/energy. || ★★★★☆ |- | '''Heuristic Value''' || Inspires re-evaluation of mainstream assumptions, links to overlooked or discarded theories (e.g. Le Sage, expansion tectonics). || ★★★★★ |- | '''Historical and Philosophical Insight''' || Reconnects with early gravitational push models and continuous creation ideas, offering philosophical alternatives to entropy-based models. || ★★★★☆ |} '''Total: 29/35''' === '''8.8.10 Spiral Cosmology – AI Rating Summary''' === ''Related link:'' [https://www.academia.edu/36624389 Spiral Cosmology] {| class="wikitable" ! '''Criterion''' !! '''Description''' !! '''Rating''' |- | '''Empirical Adequacy''' || Offers alternative interpretations of cosmic structure, redshift, and periodicity. However, lacks detailed predictive alignment with observational data such as the CMB or galaxy cluster dynamics. || ★★★☆☆ |- | '''Internal Consistency''' || Shows coherence within its fractal and spiral logic but occasionally blends metaphoric and physical arguments. Some ambiguity in theoretical foundations. || ★★★☆☆ |- | '''Predictive Power''' || Implies structural patterns in large-scale cosmic distribution, but does not offer concrete, testable numerical predictions. || ★★☆☆☆ |- | '''Cross-Disciplinary Compatibility''' || Explores links to fractal geometry and galactic morphology. Less integration with astrophysical, geological, or biological frameworks. || ★★★☆☆ |- | '''Conceptual Clarity and Simplicity''' || The spiral concept is visually engaging and intuitively appealing, but terminology and mathematical form are not fully standardized. || ★★★☆☆ |- | '''Heuristic Value''' || Encourages alternative cosmological thinking and challenges the dominance of linear expansion models. || ★★★★☆ |- | '''Historical and Philosophical Insight''' || Draws on ancient and cyclical cosmologies, reintroducing ideas of recurrence and structure at all scales. || ★★★★☆ |} '''Total: 24/35''' '''◀ [[AI-Assisted_Evaluation_of_Cosmological_Theories/Chapter_7:_Cosmological_Parameters_and_Universal_Constants|Previous]] | [[AI-Assisted_Evaluation_of_Cosmological_Theories|Main Page]] | [[AI-Assisted_Evaluation_of_Cosmological_Theories/Chapter_9:_Documentation_and_Transparency|Next ▶]]''' bplu3ma2ga97e1r6jlrfp00if4ud1z9 0 322152 2720387 2719460 2025-07-02T06:01:42Z Ruud Loeffen 2998353 /* Chapter 9: Documentation and Transparency */ add numbers for the subsection and add information 10.3 Acknowledgements and Transparency 2720387 wikitext text/x-wiki = '''Chapter 9: Documentation and Transparency''' = == '''Purpose''' == This chapter provides an open record of the sources, contributor roles, and editorial decisions throughout the project. It ensures that every step in the AI-assisted evaluation is traceable and reproducible. == '''10.1 Scope''' == Source tracking: books, peer-reviewed articles, websites, and datasets Contributor list with areas of input and affiliation (if provided) AI usage logs and description of prompts or evaluations Editorial choices and rationale Timeline of chapter development and updates == '''10.2 Transparency Measures''' == All text contributions will remain visible in the edit history. ChatGPT contributions will be clearly marked or described in footnotes when relevant. External sources will be cited using visible URLs or standard references. Editorial changes will be documented on the Talk pages or within change summaries. ==== '''10.3 Acknowledgements and Transparency''' ==== This project was initiated and structured by Ruud Loeffen, who designed the chapter layout, evaluation framework, and the systematic comparison of theories across defined criteria. The evaluations and star ratings in Chapter 8 are based on the input of ChatGPT (GPT-4), an AI system trained on a vast body of scientific literature. These analyses are not manually biased or edited, but reflect the AI’s large-scale synthesis of theoretical claims, observational evidence, and conceptual coherence. The result is an impartial and reproducible perspective that exceeds the scope of any single human reviewer. Ruud critically reviewed the logic of the evaluation model, verified all star rating totals, and ensured consistency across chapters. However, the content and reasoning behind each score were provided by ChatGPT. In case a theorist or contributor disagrees with a given rating, they are welcome to initiate a re-evaluation using ChatGPT itself. The objection must be supported by evidence or argumentation. ChatGPT will then algorithmically assess the new input and, if justified, revise the evaluation. This process maintains fairness, transparency, and openness to future refinements. == '''10.4 How to Contribute or Review''' == If you'd like to: Suggest additions or corrections to the documentation Add a reference to your published work used in the project Request attribution or anonymity Please email: '''aitheroymapping@gmail.com''' or post on the relevant Talk page. == '''10.5 Next Steps''' == Periodically update contributor and source list Archive earlier versions for open access Finalize template for AI prompt tracking (if adopted in future) ---- '''◀ [[AI-Assisted Evaluation of Cosmological Theories/Chapter 8: Critical Evaluation and Future Research Paths|Previous]] | [[AI-Assisted Evaluation of Cosmological Theories|Main Page]] | [[AI-Assisted Evaluation of Cosmological Theories/Chapter 10: References and Acknowledgements|Next ▶]]''' 647q1z9uofzmq344v7vef0dbz93k0em 2720388 2720387 2025-07-02T06:05:33Z Ruud Loeffen 2998353 improved the numbering of the subsections 2720388 wikitext text/x-wiki = '''Chapter 9: Documentation and Transparency''' = == '''9.1 Purpose''' == This chapter provides an open record of the sources, contributor roles, and editorial decisions throughout the project. It ensures that every step in the AI-assisted evaluation is traceable and reproducible. == '''9.2 Scope''' == Source tracking: books, peer-reviewed articles, websites, and datasets Contributor list with areas of input and affiliation (if provided) AI usage logs and description of prompts or evaluations Editorial choices and rationale Timeline of chapter development and updates == '''9.3 Transparency Measures''' == All text contributions will remain visible in the edit history. ChatGPT contributions will be clearly marked or described in footnotes when relevant. External sources will be cited using visible URLs or standard references. Editorial changes will be documented on the Talk pages or within change summaries. ==== '''19.4 Acknowledgements and Transparency''' ==== This project was initiated and structured by Ruud Loeffen, who designed the chapter layout, evaluation framework, and the systematic comparison of theories across defined criteria. The evaluations and star ratings in Chapter 8 are based on the input of ChatGPT (GPT-4), an AI system trained on a vast body of scientific literature. These analyses are not manually biased or edited, but reflect the AI’s large-scale synthesis of theoretical claims, observational evidence, and conceptual coherence. The result is an impartial and reproducible perspective that exceeds the scope of any single human reviewer. Ruud critically reviewed the logic of the evaluation model, verified all star rating totals, and ensured consistency across chapters. However, the content and reasoning behind each score were provided by ChatGPT. In case a theorist or contributor disagrees with a given rating, they are welcome to initiate a re-evaluation using ChatGPT itself. The objection must be supported by evidence or argumentation. ChatGPT will then algorithmically assess the new input and, if justified, revise the evaluation. This process maintains fairness, transparency, and openness to future refinements. == '''19.5 How to Contribute or Review''' == If you'd like to: Suggest additions or corrections to the documentation Add a reference to your published work used in the project Request attribution or anonymity Please email: '''aitheroymapping@gmail.com''' or post on the relevant Talk page. == '''9.6 Next Steps''' == Periodically update contributor and source list Archive earlier versions for open access Finalize template for AI prompt tracking (if adopted in future) ---- '''◀ [[AI-Assisted Evaluation of Cosmological Theories/Chapter 8: Critical Evaluation and Future Research Paths|Previous]] | [[AI-Assisted Evaluation of Cosmological Theories|Main Page]] | [[AI-Assisted Evaluation of Cosmological Theories/Chapter 10: References and Acknowledgements|Next ▶]]''' 58ojb2jr8g0zszeffk7nfmmgt1abkh7 2720389 2720388 2025-07-02T06:07:40Z Ruud Loeffen 2998353 improved numbers 2720389 wikitext text/x-wiki = '''Chapter 9: Documentation and Transparency''' = == '''9.1 Purpose''' == This chapter provides an open record of the sources, contributor roles, and editorial decisions throughout the project. It ensures that every step in the AI-assisted evaluation is traceable and reproducible. == '''9.2 Scope''' == Source tracking: books, peer-reviewed articles, websites, and datasets Contributor list with areas of input and affiliation (if provided) AI usage logs and description of prompts or evaluations Editorial choices and rationale Timeline of chapter development and updates == '''9.3 Transparency Measures''' == All text contributions will remain visible in the edit history. ChatGPT contributions will be clearly marked or described in footnotes when relevant. External sources will be cited using visible URLs or standard references. Editorial changes will be documented on the Talk pages or within change summaries. == '''9.4 Acknowledgements and Transparency''' == This project was initiated and structured by Ruud Loeffen, who designed the chapter layout, evaluation framework, and the systematic comparison of theories across defined criteria. The evaluations and star ratings in Chapter 8 are based on the input of ChatGPT (GPT-4), an AI system trained on a vast body of scientific literature. These analyses are not manually biased or edited, but reflect the AI’s large-scale synthesis of theoretical claims, observational evidence, and conceptual coherence. The result is an impartial and reproducible perspective that exceeds the scope of any single human reviewer. Ruud critically reviewed the logic of the evaluation model, verified all star rating totals, and ensured consistency across chapters. However, the content and reasoning behind each score were provided by ChatGPT. In case a theorist or contributor disagrees with a given rating, they are welcome to initiate a re-evaluation using ChatGPT itself. The objection must be supported by evidence or argumentation. ChatGPT will then algorithmically assess the new input and, if justified, revise the evaluation. This process maintains fairness, transparency, and openness to future refinements. == '''9.5 How to Contribute or Review''' == If you'd like to: Suggest additions or corrections to the documentation Add a reference to your published work used in the project Request attribution or anonymity Please email: '''aitheroymapping@gmail.com''' or post on the relevant Talk page. == '''9.6 Next Steps''' == Periodically update contributor and source list Archive earlier versions for open access Finalize template for AI prompt tracking (if adopted in future) ---- '''◀ [[AI-Assisted Evaluation of Cosmological Theories/Chapter 8: Critical Evaluation and Future Research Paths|Previous]] | [[AI-Assisted Evaluation of Cosmological Theories|Main Page]] | [[AI-Assisted Evaluation of Cosmological Theories/Chapter 10: References and Acknowledgements|Next ▶]]''' 2o59ksl1jvcgz4o6or0ye06k7ajknp6 0 322153 2720390 2719461 2025-07-02T06:09:49Z Ruud Loeffen 2998353 /* Chapter 10: References and Acknowledgements */ add numbering for the subsections 2720390 wikitext text/x-wiki = '''Chapter 10: References and Acknowledgements''' = == '''10.1Purpose''' == This final chapter gathers all references cited throughout the project and offers acknowledgements to contributors, collaborators, and tools that played a role in the development of this AI-assisted evaluation. == '''10.2 References''' == This section will grow as the chapters expand and citations accumulate. It may include: Peer-reviewed journal articles Scientific books and monographs Publicly available datasets and repositories Online articles or white papers Wikipedia and Wikiversity pages (used for overview only, with caution) Each reference should be listed in a consistent format and linked where possible. === 10.3 Example Format === Author(s). ''Title.'' Journal/Book, Year. DOI or URL. NASA Exoplanet Archive. https://exoplanetarchive.ipac.caltech.edu/ Wikiversity: [[Cosmic Influx Theory]] == '''10.4 Acknowledgements''' == We gratefully acknowledge: Researchers whose published or unpublished work contributed to the theoretical comparisons. Contributors to this Wikiversity project who helped improve content or provided critical feedback. The developers and trainers of '''ChatGPT''' and other LLM tools, whose assistance made it possible to structure, synthesize, and compare theories at this scale. Alternative theory communities and independent researchers who continue to explore fundamental questions with creativity and persistence. == '''10.5 Attribution Note''' == If your work has been cited and you would like to request a specific form of attribution (or removal), please contact: '''aitheroymapping@gmail.com'''. == '''Navigation''' == '''◀ [[AI-Assisted Evaluation of Cosmological Theories/Chapter 9: Documentation and Transparency|Previous]] | [[AI-Assisted Evaluation of Cosmological Theories|Main Page]]''' awf58tpl358yu5wp33mhn1cnavgc6to 0 322271 2720275 2720211 2025-07-01T12:40:36Z MathXplore 2888076 added [[Category:India]] using [[Help:Gadget-HotCat|HotCat]] 2720275 wikitext text/x-wiki Medical emergencies occur anywhere, at any time, in any country irrespective of whether it is a developed, developing or an underdeveloped country. These emergencies occur by the hour, consuming a lot of resources and sometimes, without even achieving the desired results, i.e., to save lives. Medical emergencies have been around since the start of the human civilization, however, they gained recognition as a specialty only around 30 years ago (Chung, 2001). An emergency medical system’s goal should be to provide universal and integrative emergency care right from the time it receives information from an emergency user (Dykstra, E. H, 1997). Further, in a country like India, the seventh largest country, and with the second highest population in the world (David, S. S., & Vasnaik, M, 2007) and high income disparity, the implementation and context of the emergency medical system should be in a way to increase health equity and not worsen the current health disparities (David, S. S., & Vasnaik, M, 2007). This challenge faced by India and similar developing nations can be attended to by promoting systematic development of an evidence-based emergency medical system that is more cost effective than those in developed countries like the USA, Canada and certain European countries where there is lesser income disparity. To design an effective emergency medical system, there is need to address questions such as how it would integrate with the current health-care infrastructure, local communities as well as their values, and the financial resources that would be needed to augment the services step by step (Gupta, M. Das, & Rani, M. 2004). In India, the public sector accounts for less than 20 percent of the total healthcare expenditure, which is the lowest in the world, and is less than 1% of the country’s GDP (KPMG, 2005). Around 94% of the amount of private expenditure is from out of the pockets of citizens, and the remaining 6% is the provision’s expenditure (Development Bank A, 2015). The way forward for the government to address this challenging situation is to consider the Public Private Partnerships (PPP) model in the emergency healthcare sector in India. The emergence v of PPP in India has provided a viable solution wherein the government-led public sector forms a synergetic partnership with the technically advanced and innovative private sector (Raman, A.V et al., 2008). In emergency medical services, the government set-up 108 partnerships in 2005 (Besley, T., & Ghatak, M. 2017) with private organizations, such as GVK, Ziqitza Health Care Ltd., to deal with fatal emergencies, for example, dealing with the medical emergency during the Fani cyclone1 at Odisha in 2019. However, the emergency services are fragmented in India (Subhan, I., & Jain, A. 2010), with many private services having entered the arena without regulation. Though this may look to be a good social and altruistic sign, in the long run, it would hamper the progress of emergency services across the country. These questions will be well-addressed in this study when the rationality of promoting the emergency service systems is evaluated from the financing point of view. Further, in this study, we model the PPP contracts in accordance with the government’s plan to integrate emergency services inclusive of fire and police with emergency health services under a common emergency telephone number, 112. Evidence is available to show that several roles, strategies, rules, and pay-offs govern procedures in the partnerships between the public sector and private firms (Bettignies, J.-E. de, & Ross, T. W, 2004). Thus, modeling them as complex games can help to better understand the failures and difficulties in such partnerships (Scharle, 2002). In this context, the researchers are implementing Nash bargain solutions in their research works to understand financial renegotiations (De Brux, J. 2010). However, there are very few studies to understand why financial renegotiation between government and service provider fails in a PPP contract. Through this study, we hope to provide a solid foundation to the integrated emergency medical services, which in turn, would provide Indian citizens the same equity, access, and quality of services which have been enjoyed by the people in the developing countries for decades. 1Fani cyclone hit many parts of Odisha in April- May of 2019, article by Vishwa Mohan (May 4, 2019), Times of India. vi In the first essay, we have modeled funding mechanisms for Profit-based (Corporate) service providers to provide emergency medical services in PPP during natural disasters such as cyclones and tsunamis or pandemic-like situations such as Covid-19 when there is an unprecedented increase in demand of this service provision. In the second situation, that is, pandemic-like situations, we have considered modeling conditions when the service provider is successful in renegotiating with the government as well as when renegotiation is unsuccessful and investor goes ahead with the funding under government intervention.. Insights from the study indicate that government underinvests during regular situations, whereas during situations which require unprecedented rise in demand, it needs to monitor the service providers to prevent moral hazards. In the second essay, we have modeled funding mechanisms for non-profit-based (NGO) service providers under similar conditions as in the first essay. Further, in case of an unprecedented rise of demand, we have restricted to modeling in renegotiation, as the case of renegotiation failure does not occur in case of non-profit-based service providers. Insights from the study show that the government has preference for investing in non-profit service providers as their pay-off increases with the payoff of the non-profit service provider (SP). In the final essay, we have modeled advertising as a signal to convey the type of service provider (profit/non-profit) to the citizens (/Users/Patients); and also help the service providers decide their service provision. The study reveals that in regular situations, the advertisement strategy may aid to serve the patients when they require the emergency services. Further, the government may prefer either of the SPs (Profit-Oriented or Non-Profit-Oriented) to provide better payoffs in the PPP contractual relationship. We find that the government needs to incentivize service providers to attain demand /service realization. Alternatively, it can penalize service providers by formulating policies if the effort vii decreases with an increase in investment, as in few scenarios. Further, in all scenarios the government needs to formulate policies that aid investment in insurance companies so that citizens have to make less “out of pockets payments” that are quite expensive in emerging economies like India. Though insurance schemes have been launched by the central government in the past few years, various states that have been in PPP -based contracts for emergency health services need to coordinate with the centre to launch more innovative insurance schemes to reduce “out of pocket" expenses” thereby, improving citizen’s welfare. viii{{Article info |journal = WikiJournal Preprints <!-- WikiJournal of Medicine, Science, or Humanities --> |last1 = Lastname |first1 = Firstname |last2 = |first2 = |last3 = |first3 = |last4 = |first4 = <!-- up to 9 authors can be added in this above format --> |et_al = <!-- if there are >9 authors, hyperlink to the list here --> |affiliations = institutes / affiliations |correspondence = email@address.com |keywords = <!-- up to 6 keywords --> |license = <!-- default is CC-BY --> |abstract = Abstract text goes here }} First Heading[[file:example image.png|thumb|left |[[File:IIMFrontpage.jpg|thumb|Senthil Kumar Anantharaman, PhD Thesis IIM Indore]]Image caption text goes here (attribution: name of image creator, [[ccorg:licenses/by/3.0/deed.en|CC-BY 3.0]]) ]] Manuscript text goes re ===Subheading=== ==Second Heading== ==Third Heading, etc== ==Additional information== ===Acknowledgements=== My thanks to all those people who were unmentioned and whose intent helped me in progressing towards completion of my doctoral work ==References== <nowiki> </nowiki>Agheon Phillippe et al. (2000). Agency Costs, Firm Behavior and the Nature of Competition. <nowiki>https://doi.org/10.1016/j.rie.2017.04.005</nowiki>. 2. Akintoye A, Beck M, and Kumaraswamy, M (2016) Public Private Partnership: A Global Review (Edt) Routledge, London, <nowiki>ISBN 978-04-415-72896</nowiki> <nowiki>https://doi.org/10.4324/9781315686516</nowiki> 3. Alonso-Conde, A. B., Brown, C., & Rojo-Suarez, J. (2007). Public-private partnerships: Incentives, risk transfer, and real options. Review of Financial Economics, 16(4), 335 349. <nowiki>https://doi.org/10.1016/j.rfe.2007.03.002</nowiki> 4. Auriol, E., & Picard, P. M. (2013). A theory of BOT concession contracts. Journal of Economic Behavior & Organization, 89, 187-209. <nowiki>https://doi.org/10.1016/j.jebo.2011.10.003</nowiki>. 5. Bagwell.K., and G. Ramey (1990). “Advertising and pricing to deter or accommodate entry when the demand is unknown.” International Journal of Industrial Organization,.93-113. <nowiki>https://doi.org/10.1016/0167-7187(89)90036-2</nowiki>. 6. Baojun Jiang, Jian Ni and Kannan Srinivasan.(2014) “ Signaling Through Pricing by Service Providers with social preferences” Marketing Science. <nowiki>https://doi.org/</nowiki> 10.1287/mksc.2014.0850. 7. Baru, R. V. (2003). Privatisation of Health Services: A South Asian Perspective. Economic and Political Weekly, 38(42), 4433–4437. Accessed from <nowiki>http://www.jstor.org/stable/4414156</nowiki> 8. Bennett, S. and Mills, A.(1998), 'Government capacity to contract: health sector experience and lessons,' Public Administration and Development, vol. 18, no. 4, pp. 307 326. <nowiki>https://doi.org/10.1002/(SICI)1099-162X(1998100)18:4</nowiki><307::AID PAD24>3.0.CO;2-D 9. Michael Bergman & Jan-Erik Lane. (1990). Public Policy in a Principal-Agent Framework, Journal of Theoretical Politics, vol. 2(3), pages 339-352. Accessed from <nowiki>https://ideas.repec.org/a/sae/jothpo/v2y1990i3p339-352.html</nowiki>. 93 10. Besley, T., & Ghatak, M. (2017). Public-private partnerships for the provision of public goods: Theory and an application to NGOs. Research in Economics, 71(2), 356–371. <nowiki>https://doi.org/10.1016/j.rie.2017.04.005</nowiki>. 11. Blanken, A., & Dewulf, G. (n.d.). PPPs in Health: Static or Dynamic? The Australian Journal of Public Administration, 69(S1), 35–47. <nowiki>http://doi.org/10.29145/jmr.72.070204</nowiki> 12. Buso, M. (2019). Bundling versus unbundling: asymmetric information on information externalities. Journal of Economics, 128(1), 1-25. <nowiki>https://doi.org/10.1007/s00712-018-0642-0</nowiki> 13. Carr, B. G., Caplan, J. M., Pryor, J. P., & Branas, C. C. (2006). A Meta-Analysis of Prehospital Care Times for Trauma. Prehospital <nowiki>https://doi.org/10.1080/10903120500541324</nowiki> Emergency Care, 10(2), 198–206. 14. Casady, Carter B., Kent Eriksson, Raymond E. Levitt, and W. Richard Scott. 2020. “(Re)Defining Public-Private Partnerships (PPPs) in the New Public Governance (NPG) Paradigm: An Institutional Maturity Perspective.” Public Management Review 22, no. 2: 161-183. http:// doi:10.1080/14719037.2019.1577909 15. CHO, I. and D.Kreps (1987) Signaling games and stable equilibrium. Quarterly Journal of Economics 102, 179-222. <nowiki>http://dx.doi.org/10.2307/1913604</nowiki> 16. Chou, J.-S., Ping Tserng, H., Lin, C., & Yeh, C.-P. (2012). Critical factors and risk allocation for PPP policy: Comparison between HSR and general infrastructure projects. Transport Policy, 22, 36–48. <nowiki>https://doi.org/10.1016/J.TRANPOL.2012.05.009</nowiki>. 17. Cobb, Barry and Bawsuchoudhary, Atin.(2009) “ A Decision Analysis Approach to Solving the Signaling Game.” <nowiki>https://doi.org/10.1287/deca.1090.0148</nowiki>. 18. Chung, C. (2001). The Evolution of Emergency Medicine. Hong Kong Journal of Emergency Medicine, 8(2), 84–89. <nowiki>https://doi.org/10.1177/102490790100800204</nowiki>. 19. Cooley, Thomas F. and Bruce D. Smith (1987). Equilibrium in Cooperative Games of Policy Formulation. Working Paper No. 84, Rochester Centre of Economic Research. Accessed from <nowiki>https://rcer.econ.rochester.edu/RCERPAPERS/rcer_84.pdf</nowiki> 94 to walk the 20. David, S. S., Vasnaik, M., & TV, R. (2007). Emergency medicine in India: Why are we unable 289–295. talk Emergency Medicine <nowiki>https://doi.org/10.1111/j.1742-6723.2007.00985.x</nowiki> Australasia, 19(4), 21. Baxter D, Casady CB. Proactive and Strategic Healthcare Public-Private Partnerships (PPPs) in the Coronavirus (Covid-19) Epoch. Sustainability. 2020; 12(12):5097. <nowiki>https://doi.org/10.3390/su1212509</nowiki>. 22. De Bettignies, J.-E., & Ross, T. W. (2004). The Economics of Public-Private Partnerships. Canadian Public Policy / Analyse de Politiques, 30(2), 135–154. <nowiki>https://doi.org/10.2307/3552389</nowiki> 23. De Brux, J. (2010). The Dark and Bright Sides of Renegotiation: An Application to Transport Concession Contracts. Utilities Policy, 18(2), 77–85. <nowiki>https://doi.org/10.1016/j.jup.2009.07.003</nowiki> 24. Mehta, Anouj; Bhatia, Aparna; Chatterjee, Ameeta. 2010. Improving Health and Education Service Delivery in India through Public-Private Partnerships. © Asian Development Bank. Accessed from <nowiki>http://hdl.handle.net/11540/1036</nowiki>. 25. Dykstra, E. H. (1997). International models for the practice of emergency care. The American Journal of Emergency Medicine, 15(2), 208–209. Accessed from <nowiki>https://doi.org/10.1016/S0735</nowiki> 6757(97)90107-8 26. Elitzur, R., & Gavious, A. (2003). Contracting, signaling, and moral hazard: a model of entrepreneurs, 'angels,' and venture capitalists. Journal of Business Venturing, 18(6), 709–725. <nowiki>https://doi.org/10.1016/S0883-9026(03)00027-2</nowiki> 27. Elitzur, R., & Gavious, A. (2011). Selection of entrepreneurs in the venture capital industry: An asymptotic analysis. <nowiki>https://doi.org/10.1016/j.ejor.2011.06.029</nowiki>. 28. Case Study on “Emergency Medical Service (EMS) in India: A Concept Paper” by National Health Systems Resource Centre (NHSRC) Technical Support Institution with National Rural Health Mission (NRHM) Ministry of Health & Family Welfare, Government of India. Accessed from <nowiki>https://fdocuments.in/document/ems-concept</nowiki> paper.html. 95 29. Sulakshana Nandi, Vandana Prasad, Deepika Joshi, Indira Chakravarthi, Ganapathy Murugan, Shahnawaz Khan, Mohammed Allam Ashraf, Pallavi Gupta, Chandan Kumar. (2021). Public Private Partnerships in healthcare, Evidence from India. Accessed from <nowiki>https://epw.in/journal/2021/36/perspectives/public-private-partnerships-healthcare.html</nowiki> 30. Gregory, A. W., & Hansen, B. E. (1996). Residual-based tests for cointegration in models with regime shifts. Journal of Econometrics, 70(1), 99–126. <nowiki>https://doi.org/10.1016/0304</nowiki> 4076(69)41685-7. 31. Grimsey, D., & Lewis, M. (2007). Public Private Partnerships and Public Procurement. Agenda: A Journal of Policy Analysis and Reform, 14(2), 171 188..<nowiki>https://doi.org/10.22459/AG.14.02.2007.06</nowiki> 32. Gupta, M. Das, & Rani, M. (2004). India's Public Health System: How Well Does It Function at the National Level? The World Bank. <nowiki>https://doi.org/10.1596/1813-9450-3447</nowiki>. 33. Felix Munoz-Garcia (2012). “A systematic procedure for finding perfect equilibria in Incomplete Information Games” vol. 6, no. 1, 2012, pp. <nowiki>https://doi.org/10.1515/1935</nowiki> 5041.1049 34. Frank A Sloan & Chee Ruey Hsieh (2017) Health economics. The MIT Press Jan 27, 2017 | 840 Pages | 8 x 9 | <nowiki>ISBN 9780262035118</nowiki>. 35. Fudenbeg, D., J.Tirole. 1993. Game Theory. MIT Press. Cambridge . MA. 36. Gibbons, R.1992 Game Theory For economists. Princeton University Press, Princeton, NJ. 37. Hart, O. (2003). Incomplete Contracts and Public Ownership: Remarks, and an Application to Public‐Private Partnerships. The <nowiki>https://doi.org/10.1111/1468-0297.00119</nowiki> The Economic Journal, 113(486), C69–C76. 38. Hayllar, M. R., & Wettenhall, R. (2010). Public-Private Partnerships: Promises, Politics, and Pitfalls. Australian Journal of <nowiki>https://doi.org/10.1111/j.1467-8500.2009.00657.x</nowiki> Public Administration, 69(S1), 1–7. 39. Ho, S. P. (2009). Government Policy on PPP Financial Issues: Bid Compensation and Financial Renegotiation. Policy, Finance & Management for Public-Private Partnerships, 267–300. <nowiki>https://doi.org/10.1002/9781444301427.ch15</nowiki> 96 40. Ho, Thomas S. Y. and Lee, Sang Bin, (2004), The Oxford Guide to Financial Modeling: Applications for Capital Markets, Corporate Finance, Risk Management and Financial Institutions, Oxford University Press. Accessed from <nowiki>https://EconPapers.repec.org/RePEc:oxp:obooks:9780195169621</nowiki>. 41. Huige Xing 1, Yuelin Li 1 and Hongyang Li 2,3, (2020). Renegotiation Strategy of Public-Private Partnership Projects with Asymmetric Information— An Evolutionary Game Approach. Sustainability, <nowiki>https://doi.org/10.3390/su12072646</nowiki> 42. Hung, K. K. C., Cheung, C. S. K., Rainer, T. H., & Graham, C. A. (2009). International EMS systems: China. Resuscitation, 80, 732–735. <nowiki>https://doi.org/10.1016/j.resuscitation.2009.04.016</nowiki>. 43. Kennedy, G. M. (2013). Can game theory be used to address PPP renegotiations ? A retrospective study of the of the Metronet - London Underground PPP By Dissertation submitted in partial fulfillment of requirements for the degree of MSc in Business Administration, at the Univers, (June). Accessed from <nowiki>http://hdl.handle.net/10400.14/15839</nowiki> 44. Klijn, E. H., & Koppenjan, J. (2016). Public Money & Management The impact of contract characteristics on the performance of <nowiki>https://doi.org/10.1080/09540962.2016.1206756</nowiki>. public-private partnerships (PPPs). 45. KPMG. (2015). The Emerging Role of PPP in Indian Healthcare Sector Prepared By In collaboration with the Indian government. [White Paper], Accessed from <nowiki>https://www.ibef.org/download/PolicyPaper.pdf</nowiki> 46. Kuruvilla, Sarosh & Liu, Mingwei & Jacob, Priti. (2005). A Case Study of the Yeshasvini Health Insurance Scheme for the Rural Poor in India. International Journal of Self Help and Self Care. 3. 261-306. 10.2190/D60U-5637-M315-3K57. 47. Liu, X., Hotchkiss, D. R., & Bose, S. (2007). The impact of contracting-out on health system performance: A conceptual framework. <nowiki>https://doi.org/10.1016/j.healthpol.2006.09.012</nowiki> Health Policy, 82, 200–211. 48. Lv, J., Ye, G., Liu, W., Shen, L., & Wang, H. (2015). Alternative Model for Determining the Optimal Concession Period in Managing BOT Transportation Projects. Journal of Management in Engineering, 31(4), 04014066. <nowiki>https://doi.org/10.1061/(ASCE)ME.1943-5479.0000291</nowiki>. 97 49. Madhurima Nundy and Rama V Baru. (2013). Private Partnerships of Boundaries: Public- Blurring in Health Services in India. Economic Political Weekly, 43(4), 62–71. Accessed from <nowiki>https://www.epw.in/journal/2008/04</nowiki> 50. MacAl, C. M., & North, M. J. (2010). Tutorial on agent-based modeling and simulation. Journal of Simulation, 4(3), 151–162. Accessed from <nowiki>https://doi.org/10.1057/jos.2010.3</nowiki> 51. Manigart, S., De Waele, K., Wright, M., Robbie, K., Desbrières, P., Sapienza, H. J., & Beekman, A. (2002). Determinants of required return in venture capital investments: a five-country study. Journal of Business Venturing, 17(4), 291–312. <nowiki>https://doi.org/10.1016/S0883-9026(00)00067-7</nowiki> 52. Mason, C. M., & Harrison, R. T. (2002). Is it worth it? The rates of return from informal venture capital investments. Journal of <nowiki>https://doi.org/10.1016/S0883-9026(00)00060-4</nowiki> Business Venturing, 17(3), 211–236. 53. Medda, F. R., Carbonaro, G., & Davis, S. L. (2013). Public-private partnerships in transportation: Some insights from the European experience. IATSS Research, 36(2), 83–87. <nowiki>https://doi.org/10.1016/J.IATSSR.2012.11.002</nowiki> 54. Mitroff, I. I., & Mason, R. O. (2011). The Metaphysics of Policy and Planning: A Reply to Cosier. Academy of Management <nowiki>https://doi.org/10.5465/amr.1981.4285721</nowiki> Review, 6(4), 649–651. 55. Sethi, Nitin & Rao, Menaka. (2017) NITI Aayog and health ministry prepare model contract for privatizing urban health care. Scroll.in. Accessed from <nowiki>https://scroll.in/pulse/844272/niti-aayog</nowiki> and-health-ministry-prepare-model-contract-for-privatising-urban-health-care 56. Oliveira Cruz, C., & Cunha Marques, R. (2014). Theoretical Considerations on Quantitative PPP Viability Analysis. <nowiki>https://doi.org/10.1061/(ASCE)ME.1943-5479.0000184</nowiki> 57. Prakash, G., & Singh, A. (2010). A New Public Management Perspective in Indian E-Governance Initiatives. Accessed from <nowiki>https://www.csi-sigegov.org/critical_pdf/8_71-80.pdf</nowiki> 58. Raman, A. V., Björkman, J. W., & Björkman, J. W. (2008). Public-Private Partnerships in Health Care in India. Routledge. <nowiki>https://doi.org/10.4324/9780203886557</nowiki> 59. Roberts, M. J., Hsiao, W., Berman, P., & Reich, M. R. (2008.). Getting Health Reform Right. <nowiki>https://doi.org/10.1093/acprof:oso/9780195371505.001.0001</nowiki>. 98 60. Ross, T. W., & Yan, J. (2015). Journal of Comparative Policy Analysis: Research and Practice Comparing Public-Private Partnerships and Traditional Public Procurement: Efficiency vs. Flexibility. Journal of Comparative Policy Analysis: Research and Practice, 17(5), 448–466. <nowiki>https://doi.org/10.1080/13876988.2015.1029333</nowiki> 61. Schneider, S. M., Gardner, A. F., Weiss, L. D., Wood, J. P., Ybarra, M., Beck, D. M.,Jouriles, N. J. (2010). The Future of Emergency Medicine. The Journal of Emergency Medicine, 39(2), 210 215. <nowiki>https://doi.org/10.1016/J.JEMERMED.2010.06.001</nowiki> 62. Serra, Danila & Serneels, Pieter & Barr, Abigail,(2010)."Intrinsic Motivations and the Non-Profit Health Sector: Evidence from Ethiopia," IZA Discussion Papers 4746, Institute of Labor Economics. <nowiki>https://ideas.repec.org/p/iza/izadps/dp4746.html</nowiki>. Accessed from 63. Shi, L., Zhang, L., Onishi, M., Kobayashi, K., & Dai, D. (2018). Contractual Efficiency of PPP Infrastructure Projects: An Incomplete Contract Model. Mathematical Problems in Engineering, 2018, 1–13. <nowiki>https://doi.org/10.1155/2018/3631270</nowiki> 64. Singh, A., & Prakash, G. (2010). Public-Private Partnerships in Health Services Delivery. Public Management Review, 12(6), 829–856. <nowiki>https://doi.org/10.1080/14719037.2010.488860</nowiki> 65. Spence. M (1973) “Job Market Signaling” Quarterly Journal of Economics 87, pp 355 371. <nowiki>https://doi.org/10.2307/1882010</nowiki> 66. Sharma M, Brandler ES (2014). Emergency medical services in India: the present and future. Prehosp Disaster Med. 2014;29(3):307-310. <nowiki>https://doi:10.1017/S1049023X14000296</nowiki> 67. Subhan, I., & Jain, A. (2010). Emergency care in India: the building blocks. International Journal of Emergency Medicine, 3(4), 207–211. <nowiki>https://doi.org/10.1007/s12245-010-0223-7</nowiki> 68. Titoria, R., & Mohandas, A. (2019). A glance on public-private partnership: an opportunity for developing nations to achieve universal health coverage. International Journal Of Community Medicine And Public Health, 6(3), 1353. <nowiki>https://doi.org/10.18203/2394-6040.ijcmph20190640</nowiki> 69. Tserng, H. P., Russell, J. S., Hsu, C. W., & Lin, C. (2012). Analyzing the role of national PPP units in promoting PPPs: Using new institutional economics and a case study. Journal of construction engineering and management, <nowiki>http://doi.org/10.1061/(ASCE)CO.1943-7862.0000398</nowiki> 138(2), 242-249. 99 70. Ho, T.S.Y & Lee, S.B. (2004). The Oxford Guide to Financial Modelling: Applications for Capital Markets, Corporate Finance, Risk Management and Financial Institutions. OUP Publishers, USA. <nowiki>https://doi.org/10.2469/faj.v62.n2.4088</nowiki>. 71. Vasudevan, V., Singh, P., & Basu, S. (2016). Importance of awareness in improving performance of emergency medical services (EMS) systems in enhancing traffic safety: A lesson from India. Traffic Injury Prevention, 17(7), 699–704. <nowiki>https://doi.org/10.1080/15389588.2016.1163689</nowiki> 72. Venkitasubramanian, Akshay, (2010). A Study of PPP Models for Social Healthcare Insurance. Centre for public policy research. Accessed from <nowiki>https://www.cppr.in/wpcontent/uploads/2012/03/A-Study-of-PPP-Models-for-Social</nowiki> Healthcare-Insurance-Akshay-V.pdf 73. Wibowo, A., & Alfen, H. W. (2015a). Critical success factors in public-private partnership (PPP) on infrastructure delivery in Nigeria. Asia-Pacific Journal of Business Administration, 5(1), 212 225. <nowiki>https://doi.org/10.1108/BEPAM-03-2014-0016</nowiki> 74. Wibowo, A., & Alfen, H. W. (2015b). Government-led critical success factors in PPP infrastructure development. Built Environment Project and Asset Management, 5(1), 121–134. <nowiki>https://doi.org/10.1108/BEPAM-03-2014-0016</nowiki> 75. X Guo & B Jiang(2016).Signaling through price and quality to consumers with fairness concerns”. Journal of Marketing Research. <nowiki>https://doi.org/10.1509/jmr.15.0323</nowiki> [[Category:India]] tubd3qj0uckyw4nsgzgvxjezsmikx4l 2720276 2720275 2025-07-01T12:40:59Z MathXplore 2888076 added [[Category:Medicine]] using [[Help:Gadget-HotCat|HotCat]] 2720276 wikitext text/x-wiki Medical emergencies occur anywhere, at any time, in any country irrespective of whether it is a developed, developing or an underdeveloped country. These emergencies occur by the hour, consuming a lot of resources and sometimes, without even achieving the desired results, i.e., to save lives. Medical emergencies have been around since the start of the human civilization, however, they gained recognition as a specialty only around 30 years ago (Chung, 2001). An emergency medical system’s goal should be to provide universal and integrative emergency care right from the time it receives information from an emergency user (Dykstra, E. H, 1997). Further, in a country like India, the seventh largest country, and with the second highest population in the world (David, S. S., & Vasnaik, M, 2007) and high income disparity, the implementation and context of the emergency medical system should be in a way to increase health equity and not worsen the current health disparities (David, S. S., & Vasnaik, M, 2007). This challenge faced by India and similar developing nations can be attended to by promoting systematic development of an evidence-based emergency medical system that is more cost effective than those in developed countries like the USA, Canada and certain European countries where there is lesser income disparity. To design an effective emergency medical system, there is need to address questions such as how it would integrate with the current health-care infrastructure, local communities as well as their values, and the financial resources that would be needed to augment the services step by step (Gupta, M. Das, & Rani, M. 2004). In India, the public sector accounts for less than 20 percent of the total healthcare expenditure, which is the lowest in the world, and is less than 1% of the country’s GDP (KPMG, 2005). Around 94% of the amount of private expenditure is from out of the pockets of citizens, and the remaining 6% is the provision’s expenditure (Development Bank A, 2015). The way forward for the government to address this challenging situation is to consider the Public Private Partnerships (PPP) model in the emergency healthcare sector in India. The emergence v of PPP in India has provided a viable solution wherein the government-led public sector forms a synergetic partnership with the technically advanced and innovative private sector (Raman, A.V et al., 2008). In emergency medical services, the government set-up 108 partnerships in 2005 (Besley, T., & Ghatak, M. 2017) with private organizations, such as GVK, Ziqitza Health Care Ltd., to deal with fatal emergencies, for example, dealing with the medical emergency during the Fani cyclone1 at Odisha in 2019. However, the emergency services are fragmented in India (Subhan, I., & Jain, A. 2010), with many private services having entered the arena without regulation. Though this may look to be a good social and altruistic sign, in the long run, it would hamper the progress of emergency services across the country. These questions will be well-addressed in this study when the rationality of promoting the emergency service systems is evaluated from the financing point of view. Further, in this study, we model the PPP contracts in accordance with the government’s plan to integrate emergency services inclusive of fire and police with emergency health services under a common emergency telephone number, 112. Evidence is available to show that several roles, strategies, rules, and pay-offs govern procedures in the partnerships between the public sector and private firms (Bettignies, J.-E. de, & Ross, T. W, 2004). Thus, modeling them as complex games can help to better understand the failures and difficulties in such partnerships (Scharle, 2002). In this context, the researchers are implementing Nash bargain solutions in their research works to understand financial renegotiations (De Brux, J. 2010). However, there are very few studies to understand why financial renegotiation between government and service provider fails in a PPP contract. Through this study, we hope to provide a solid foundation to the integrated emergency medical services, which in turn, would provide Indian citizens the same equity, access, and quality of services which have been enjoyed by the people in the developing countries for decades. 1Fani cyclone hit many parts of Odisha in April- May of 2019, article by Vishwa Mohan (May 4, 2019), Times of India. vi In the first essay, we have modeled funding mechanisms for Profit-based (Corporate) service providers to provide emergency medical services in PPP during natural disasters such as cyclones and tsunamis or pandemic-like situations such as Covid-19 when there is an unprecedented increase in demand of this service provision. In the second situation, that is, pandemic-like situations, we have considered modeling conditions when the service provider is successful in renegotiating with the government as well as when renegotiation is unsuccessful and investor goes ahead with the funding under government intervention.. Insights from the study indicate that government underinvests during regular situations, whereas during situations which require unprecedented rise in demand, it needs to monitor the service providers to prevent moral hazards. In the second essay, we have modeled funding mechanisms for non-profit-based (NGO) service providers under similar conditions as in the first essay. Further, in case of an unprecedented rise of demand, we have restricted to modeling in renegotiation, as the case of renegotiation failure does not occur in case of non-profit-based service providers. Insights from the study show that the government has preference for investing in non-profit service providers as their pay-off increases with the payoff of the non-profit service provider (SP). In the final essay, we have modeled advertising as a signal to convey the type of service provider (profit/non-profit) to the citizens (/Users/Patients); and also help the service providers decide their service provision. The study reveals that in regular situations, the advertisement strategy may aid to serve the patients when they require the emergency services. Further, the government may prefer either of the SPs (Profit-Oriented or Non-Profit-Oriented) to provide better payoffs in the PPP contractual relationship. We find that the government needs to incentivize service providers to attain demand /service realization. Alternatively, it can penalize service providers by formulating policies if the effort vii decreases with an increase in investment, as in few scenarios. Further, in all scenarios the government needs to formulate policies that aid investment in insurance companies so that citizens have to make less “out of pockets payments” that are quite expensive in emerging economies like India. Though insurance schemes have been launched by the central government in the past few years, various states that have been in PPP -based contracts for emergency health services need to coordinate with the centre to launch more innovative insurance schemes to reduce “out of pocket" expenses” thereby, improving citizen’s welfare. viii{{Article info |journal = WikiJournal Preprints <!-- WikiJournal of Medicine, Science, or Humanities --> |last1 = Lastname |first1 = Firstname |last2 = |first2 = |last3 = |first3 = |last4 = |first4 = <!-- up to 9 authors can be added in this above format --> |et_al = <!-- if there are >9 authors, hyperlink to the list here --> |affiliations = institutes / affiliations |correspondence = email@address.com |keywords = <!-- up to 6 keywords --> |license = <!-- default is CC-BY --> |abstract = Abstract text goes here }} First Heading[[file:example image.png|thumb|left |[[File:IIMFrontpage.jpg|thumb|Senthil Kumar Anantharaman, PhD Thesis IIM Indore]]Image caption text goes here (attribution: name of image creator, [[ccorg:licenses/by/3.0/deed.en|CC-BY 3.0]]) ]] Manuscript text goes re ===Subheading=== ==Second Heading== ==Third Heading, etc== ==Additional information== ===Acknowledgements=== My thanks to all those people who were unmentioned and whose intent helped me in progressing towards completion of my doctoral work ==References== <nowiki> </nowiki>Agheon Phillippe et al. (2000). Agency Costs, Firm Behavior and the Nature of Competition. <nowiki>https://doi.org/10.1016/j.rie.2017.04.005</nowiki>. 2. Akintoye A, Beck M, and Kumaraswamy, M (2016) Public Private Partnership: A Global Review (Edt) Routledge, London, <nowiki>ISBN 978-04-415-72896</nowiki> <nowiki>https://doi.org/10.4324/9781315686516</nowiki> 3. Alonso-Conde, A. B., Brown, C., & Rojo-Suarez, J. (2007). Public-private partnerships: Incentives, risk transfer, and real options. Review of Financial Economics, 16(4), 335 349. <nowiki>https://doi.org/10.1016/j.rfe.2007.03.002</nowiki> 4. Auriol, E., & Picard, P. M. (2013). A theory of BOT concession contracts. Journal of Economic Behavior & Organization, 89, 187-209. <nowiki>https://doi.org/10.1016/j.jebo.2011.10.003</nowiki>. 5. Bagwell.K., and G. Ramey (1990). “Advertising and pricing to deter or accommodate entry when the demand is unknown.” International Journal of Industrial Organization,.93-113. <nowiki>https://doi.org/10.1016/0167-7187(89)90036-2</nowiki>. 6. Baojun Jiang, Jian Ni and Kannan Srinivasan.(2014) “ Signaling Through Pricing by Service Providers with social preferences” Marketing Science. <nowiki>https://doi.org/</nowiki> 10.1287/mksc.2014.0850. 7. Baru, R. V. (2003). Privatisation of Health Services: A South Asian Perspective. Economic and Political Weekly, 38(42), 4433–4437. Accessed from <nowiki>http://www.jstor.org/stable/4414156</nowiki> 8. Bennett, S. and Mills, A.(1998), 'Government capacity to contract: health sector experience and lessons,' Public Administration and Development, vol. 18, no. 4, pp. 307 326. <nowiki>https://doi.org/10.1002/(SICI)1099-162X(1998100)18:4</nowiki><307::AID PAD24>3.0.CO;2-D 9. Michael Bergman & Jan-Erik Lane. (1990). Public Policy in a Principal-Agent Framework, Journal of Theoretical Politics, vol. 2(3), pages 339-352. Accessed from <nowiki>https://ideas.repec.org/a/sae/jothpo/v2y1990i3p339-352.html</nowiki>. 93 10. Besley, T., & Ghatak, M. (2017). Public-private partnerships for the provision of public goods: Theory and an application to NGOs. Research in Economics, 71(2), 356–371. <nowiki>https://doi.org/10.1016/j.rie.2017.04.005</nowiki>. 11. Blanken, A., & Dewulf, G. (n.d.). PPPs in Health: Static or Dynamic? The Australian Journal of Public Administration, 69(S1), 35–47. <nowiki>http://doi.org/10.29145/jmr.72.070204</nowiki> 12. Buso, M. (2019). Bundling versus unbundling: asymmetric information on information externalities. Journal of Economics, 128(1), 1-25. <nowiki>https://doi.org/10.1007/s00712-018-0642-0</nowiki> 13. Carr, B. G., Caplan, J. M., Pryor, J. P., & Branas, C. C. (2006). A Meta-Analysis of Prehospital Care Times for Trauma. Prehospital <nowiki>https://doi.org/10.1080/10903120500541324</nowiki> Emergency Care, 10(2), 198–206. 14. Casady, Carter B., Kent Eriksson, Raymond E. Levitt, and W. Richard Scott. 2020. “(Re)Defining Public-Private Partnerships (PPPs) in the New Public Governance (NPG) Paradigm: An Institutional Maturity Perspective.” Public Management Review 22, no. 2: 161-183. http:// doi:10.1080/14719037.2019.1577909 15. CHO, I. and D.Kreps (1987) Signaling games and stable equilibrium. Quarterly Journal of Economics 102, 179-222. <nowiki>http://dx.doi.org/10.2307/1913604</nowiki> 16. Chou, J.-S., Ping Tserng, H., Lin, C., & Yeh, C.-P. (2012). Critical factors and risk allocation for PPP policy: Comparison between HSR and general infrastructure projects. Transport Policy, 22, 36–48. <nowiki>https://doi.org/10.1016/J.TRANPOL.2012.05.009</nowiki>. 17. Cobb, Barry and Bawsuchoudhary, Atin.(2009) “ A Decision Analysis Approach to Solving the Signaling Game.” <nowiki>https://doi.org/10.1287/deca.1090.0148</nowiki>. 18. Chung, C. (2001). The Evolution of Emergency Medicine. Hong Kong Journal of Emergency Medicine, 8(2), 84–89. <nowiki>https://doi.org/10.1177/102490790100800204</nowiki>. 19. Cooley, Thomas F. and Bruce D. Smith (1987). Equilibrium in Cooperative Games of Policy Formulation. Working Paper No. 84, Rochester Centre of Economic Research. Accessed from <nowiki>https://rcer.econ.rochester.edu/RCERPAPERS/rcer_84.pdf</nowiki> 94 to walk the 20. David, S. S., Vasnaik, M., & TV, R. (2007). Emergency medicine in India: Why are we unable 289–295. talk Emergency Medicine <nowiki>https://doi.org/10.1111/j.1742-6723.2007.00985.x</nowiki> Australasia, 19(4), 21. Baxter D, Casady CB. Proactive and Strategic Healthcare Public-Private Partnerships (PPPs) in the Coronavirus (Covid-19) Epoch. Sustainability. 2020; 12(12):5097. <nowiki>https://doi.org/10.3390/su1212509</nowiki>. 22. De Bettignies, J.-E., & Ross, T. W. (2004). The Economics of Public-Private Partnerships. Canadian Public Policy / Analyse de Politiques, 30(2), 135–154. <nowiki>https://doi.org/10.2307/3552389</nowiki> 23. De Brux, J. (2010). The Dark and Bright Sides of Renegotiation: An Application to Transport Concession Contracts. Utilities Policy, 18(2), 77–85. <nowiki>https://doi.org/10.1016/j.jup.2009.07.003</nowiki> 24. Mehta, Anouj; Bhatia, Aparna; Chatterjee, Ameeta. 2010. Improving Health and Education Service Delivery in India through Public-Private Partnerships. © Asian Development Bank. Accessed from <nowiki>http://hdl.handle.net/11540/1036</nowiki>. 25. Dykstra, E. H. (1997). International models for the practice of emergency care. The American Journal of Emergency Medicine, 15(2), 208–209. Accessed from <nowiki>https://doi.org/10.1016/S0735</nowiki> 6757(97)90107-8 26. Elitzur, R., & Gavious, A. (2003). Contracting, signaling, and moral hazard: a model of entrepreneurs, 'angels,' and venture capitalists. Journal of Business Venturing, 18(6), 709–725. <nowiki>https://doi.org/10.1016/S0883-9026(03)00027-2</nowiki> 27. Elitzur, R., & Gavious, A. (2011). Selection of entrepreneurs in the venture capital industry: An asymptotic analysis. <nowiki>https://doi.org/10.1016/j.ejor.2011.06.029</nowiki>. 28. Case Study on “Emergency Medical Service (EMS) in India: A Concept Paper” by National Health Systems Resource Centre (NHSRC) Technical Support Institution with National Rural Health Mission (NRHM) Ministry of Health & Family Welfare, Government of India. Accessed from <nowiki>https://fdocuments.in/document/ems-concept</nowiki> paper.html. 95 29. Sulakshana Nandi, Vandana Prasad, Deepika Joshi, Indira Chakravarthi, Ganapathy Murugan, Shahnawaz Khan, Mohammed Allam Ashraf, Pallavi Gupta, Chandan Kumar. (2021). Public Private Partnerships in healthcare, Evidence from India. Accessed from <nowiki>https://epw.in/journal/2021/36/perspectives/public-private-partnerships-healthcare.html</nowiki> 30. Gregory, A. W., & Hansen, B. E. (1996). Residual-based tests for cointegration in models with regime shifts. Journal of Econometrics, 70(1), 99–126. <nowiki>https://doi.org/10.1016/0304</nowiki> 4076(69)41685-7. 31. Grimsey, D., & Lewis, M. (2007). Public Private Partnerships and Public Procurement. Agenda: A Journal of Policy Analysis and Reform, 14(2), 171 188..<nowiki>https://doi.org/10.22459/AG.14.02.2007.06</nowiki> 32. Gupta, M. Das, & Rani, M. (2004). India's Public Health System: How Well Does It Function at the National Level? The World Bank. <nowiki>https://doi.org/10.1596/1813-9450-3447</nowiki>. 33. Felix Munoz-Garcia (2012). “A systematic procedure for finding perfect equilibria in Incomplete Information Games” vol. 6, no. 1, 2012, pp. <nowiki>https://doi.org/10.1515/1935</nowiki> 5041.1049 34. Frank A Sloan & Chee Ruey Hsieh (2017) Health economics. The MIT Press Jan 27, 2017 | 840 Pages | 8 x 9 | <nowiki>ISBN 9780262035118</nowiki>. 35. Fudenbeg, D., J.Tirole. 1993. Game Theory. MIT Press. Cambridge . MA. 36. Gibbons, R.1992 Game Theory For economists. Princeton University Press, Princeton, NJ. 37. Hart, O. (2003). Incomplete Contracts and Public Ownership: Remarks, and an Application to Public‐Private Partnerships. The <nowiki>https://doi.org/10.1111/1468-0297.00119</nowiki> The Economic Journal, 113(486), C69–C76. 38. Hayllar, M. R., & Wettenhall, R. (2010). Public-Private Partnerships: Promises, Politics, and Pitfalls. Australian Journal of <nowiki>https://doi.org/10.1111/j.1467-8500.2009.00657.x</nowiki> Public Administration, 69(S1), 1–7. 39. Ho, S. P. (2009). Government Policy on PPP Financial Issues: Bid Compensation and Financial Renegotiation. Policy, Finance & Management for Public-Private Partnerships, 267–300. <nowiki>https://doi.org/10.1002/9781444301427.ch15</nowiki> 96 40. Ho, Thomas S. Y. and Lee, Sang Bin, (2004), The Oxford Guide to Financial Modeling: Applications for Capital Markets, Corporate Finance, Risk Management and Financial Institutions, Oxford University Press. Accessed from <nowiki>https://EconPapers.repec.org/RePEc:oxp:obooks:9780195169621</nowiki>. 41. Huige Xing 1, Yuelin Li 1 and Hongyang Li 2,3, (2020). Renegotiation Strategy of Public-Private Partnership Projects with Asymmetric Information— An Evolutionary Game Approach. Sustainability, <nowiki>https://doi.org/10.3390/su12072646</nowiki> 42. Hung, K. K. C., Cheung, C. S. K., Rainer, T. H., & Graham, C. A. (2009). International EMS systems: China. Resuscitation, 80, 732–735. <nowiki>https://doi.org/10.1016/j.resuscitation.2009.04.016</nowiki>. 43. Kennedy, G. M. (2013). Can game theory be used to address PPP renegotiations ? A retrospective study of the of the Metronet - London Underground PPP By Dissertation submitted in partial fulfillment of requirements for the degree of MSc in Business Administration, at the Univers, (June). Accessed from <nowiki>http://hdl.handle.net/10400.14/15839</nowiki> 44. Klijn, E. H., & Koppenjan, J. (2016). Public Money & Management The impact of contract characteristics on the performance of <nowiki>https://doi.org/10.1080/09540962.2016.1206756</nowiki>. public-private partnerships (PPPs). 45. KPMG. (2015). The Emerging Role of PPP in Indian Healthcare Sector Prepared By In collaboration with the Indian government. [White Paper], Accessed from <nowiki>https://www.ibef.org/download/PolicyPaper.pdf</nowiki> 46. Kuruvilla, Sarosh & Liu, Mingwei & Jacob, Priti. (2005). A Case Study of the Yeshasvini Health Insurance Scheme for the Rural Poor in India. International Journal of Self Help and Self Care. 3. 261-306. 10.2190/D60U-5637-M315-3K57. 47. Liu, X., Hotchkiss, D. R., & Bose, S. (2007). The impact of contracting-out on health system performance: A conceptual framework. <nowiki>https://doi.org/10.1016/j.healthpol.2006.09.012</nowiki> Health Policy, 82, 200–211. 48. Lv, J., Ye, G., Liu, W., Shen, L., & Wang, H. (2015). Alternative Model for Determining the Optimal Concession Period in Managing BOT Transportation Projects. Journal of Management in Engineering, 31(4), 04014066. <nowiki>https://doi.org/10.1061/(ASCE)ME.1943-5479.0000291</nowiki>. 97 49. Madhurima Nundy and Rama V Baru. (2013). Private Partnerships of Boundaries: Public- Blurring in Health Services in India. Economic Political Weekly, 43(4), 62–71. Accessed from <nowiki>https://www.epw.in/journal/2008/04</nowiki> 50. MacAl, C. M., & North, M. J. (2010). Tutorial on agent-based modeling and simulation. Journal of Simulation, 4(3), 151–162. Accessed from <nowiki>https://doi.org/10.1057/jos.2010.3</nowiki> 51. Manigart, S., De Waele, K., Wright, M., Robbie, K., Desbrières, P., Sapienza, H. J., & Beekman, A. (2002). Determinants of required return in venture capital investments: a five-country study. Journal of Business Venturing, 17(4), 291–312. <nowiki>https://doi.org/10.1016/S0883-9026(00)00067-7</nowiki> 52. Mason, C. M., & Harrison, R. T. (2002). Is it worth it? The rates of return from informal venture capital investments. Journal of <nowiki>https://doi.org/10.1016/S0883-9026(00)00060-4</nowiki> Business Venturing, 17(3), 211–236. 53. Medda, F. R., Carbonaro, G., & Davis, S. L. (2013). Public-private partnerships in transportation: Some insights from the European experience. IATSS Research, 36(2), 83–87. <nowiki>https://doi.org/10.1016/J.IATSSR.2012.11.002</nowiki> 54. Mitroff, I. I., & Mason, R. O. (2011). The Metaphysics of Policy and Planning: A Reply to Cosier. Academy of Management <nowiki>https://doi.org/10.5465/amr.1981.4285721</nowiki> Review, 6(4), 649–651. 55. Sethi, Nitin & Rao, Menaka. (2017) NITI Aayog and health ministry prepare model contract for privatizing urban health care. Scroll.in. Accessed from <nowiki>https://scroll.in/pulse/844272/niti-aayog</nowiki> and-health-ministry-prepare-model-contract-for-privatising-urban-health-care 56. Oliveira Cruz, C., & Cunha Marques, R. (2014). Theoretical Considerations on Quantitative PPP Viability Analysis. <nowiki>https://doi.org/10.1061/(ASCE)ME.1943-5479.0000184</nowiki> 57. Prakash, G., & Singh, A. (2010). A New Public Management Perspective in Indian E-Governance Initiatives. Accessed from <nowiki>https://www.csi-sigegov.org/critical_pdf/8_71-80.pdf</nowiki> 58. Raman, A. V., Björkman, J. W., & Björkman, J. W. (2008). Public-Private Partnerships in Health Care in India. Routledge. <nowiki>https://doi.org/10.4324/9780203886557</nowiki> 59. Roberts, M. J., Hsiao, W., Berman, P., & Reich, M. R. (2008.). Getting Health Reform Right. <nowiki>https://doi.org/10.1093/acprof:oso/9780195371505.001.0001</nowiki>. 98 60. Ross, T. W., & Yan, J. (2015). Journal of Comparative Policy Analysis: Research and Practice Comparing Public-Private Partnerships and Traditional Public Procurement: Efficiency vs. Flexibility. Journal of Comparative Policy Analysis: Research and Practice, 17(5), 448–466. <nowiki>https://doi.org/10.1080/13876988.2015.1029333</nowiki> 61. Schneider, S. M., Gardner, A. F., Weiss, L. D., Wood, J. P., Ybarra, M., Beck, D. M.,Jouriles, N. J. (2010). The Future of Emergency Medicine. The Journal of Emergency Medicine, 39(2), 210 215. <nowiki>https://doi.org/10.1016/J.JEMERMED.2010.06.001</nowiki> 62. Serra, Danila & Serneels, Pieter & Barr, Abigail,(2010)."Intrinsic Motivations and the Non-Profit Health Sector: Evidence from Ethiopia," IZA Discussion Papers 4746, Institute of Labor Economics. <nowiki>https://ideas.repec.org/p/iza/izadps/dp4746.html</nowiki>. Accessed from 63. Shi, L., Zhang, L., Onishi, M., Kobayashi, K., & Dai, D. (2018). Contractual Efficiency of PPP Infrastructure Projects: An Incomplete Contract Model. Mathematical Problems in Engineering, 2018, 1–13. <nowiki>https://doi.org/10.1155/2018/3631270</nowiki> 64. Singh, A., & Prakash, G. (2010). Public-Private Partnerships in Health Services Delivery. Public Management Review, 12(6), 829–856. <nowiki>https://doi.org/10.1080/14719037.2010.488860</nowiki> 65. Spence. M (1973) “Job Market Signaling” Quarterly Journal of Economics 87, pp 355 371. <nowiki>https://doi.org/10.2307/1882010</nowiki> 66. Sharma M, Brandler ES (2014). Emergency medical services in India: the present and future. Prehosp Disaster Med. 2014;29(3):307-310. <nowiki>https://doi:10.1017/S1049023X14000296</nowiki> 67. Subhan, I., & Jain, A. (2010). Emergency care in India: the building blocks. International Journal of Emergency Medicine, 3(4), 207–211. <nowiki>https://doi.org/10.1007/s12245-010-0223-7</nowiki> 68. Titoria, R., & Mohandas, A. (2019). A glance on public-private partnership: an opportunity for developing nations to achieve universal health coverage. International Journal Of Community Medicine And Public Health, 6(3), 1353. <nowiki>https://doi.org/10.18203/2394-6040.ijcmph20190640</nowiki> 69. Tserng, H. P., Russell, J. S., Hsu, C. W., & Lin, C. (2012). Analyzing the role of national PPP units in promoting PPPs: Using new institutional economics and a case study. Journal of construction engineering and management, <nowiki>http://doi.org/10.1061/(ASCE)CO.1943-7862.0000398</nowiki> 138(2), 242-249. 99 70. Ho, T.S.Y & Lee, S.B. (2004). The Oxford Guide to Financial Modelling: Applications for Capital Markets, Corporate Finance, Risk Management and Financial Institutions. OUP Publishers, USA. <nowiki>https://doi.org/10.2469/faj.v62.n2.4088</nowiki>. 71. Vasudevan, V., Singh, P., & Basu, S. (2016). Importance of awareness in improving performance of emergency medical services (EMS) systems in enhancing traffic safety: A lesson from India. Traffic Injury Prevention, 17(7), 699–704. <nowiki>https://doi.org/10.1080/15389588.2016.1163689</nowiki> 72. Venkitasubramanian, Akshay, (2010). A Study of PPP Models for Social Healthcare Insurance. Centre for public policy research. Accessed from <nowiki>https://www.cppr.in/wpcontent/uploads/2012/03/A-Study-of-PPP-Models-for-Social</nowiki> Healthcare-Insurance-Akshay-V.pdf 73. Wibowo, A., & Alfen, H. W. (2015a). Critical success factors in public-private partnership (PPP) on infrastructure delivery in Nigeria. Asia-Pacific Journal of Business Administration, 5(1), 212 225. <nowiki>https://doi.org/10.1108/BEPAM-03-2014-0016</nowiki> 74. Wibowo, A., & Alfen, H. W. (2015b). Government-led critical success factors in PPP infrastructure development. Built Environment Project and Asset Management, 5(1), 121–134. <nowiki>https://doi.org/10.1108/BEPAM-03-2014-0016</nowiki> 75. X Guo & B Jiang(2016).Signaling through price and quality to consumers with fairness concerns”. Journal of Marketing Research. <nowiki>https://doi.org/10.1509/jmr.15.0323</nowiki> [[Category:India]] [[Category:Medicine]] q33jpnqlcnkt0xg0m36g2py2szj4pxv 0 322274 2720291 2720254 2025-07-01T13:10:00Z Bocardodarapti 289675 2720291 wikitext text/x-wiki {{Linear algebra (Osnabrück 2024-2025)/Part II/Exercise sheet design|56| {{Subtitle|Exercises}} {{ inputexercise |Tensor product/Base change/Computation/1/Exercise|| }} {{ inputexercise |Vector space/Tensor product/Multiplicative properties/Fact/Proof/Exercise|| }} {{ inputexercise |Linear mappings/Tensor product/Matrix representation/1/Exercise|| }} {{ inputexercise |Tensor product/Functoriality/Exercise|| }} {{ inputexercise |Tensor product/Direct sum/Fact/Proof/Exercise|| }} {{ inputexercise |Tensor product/Flags/Exercise|| }} {{ inputexercise |Tensor product/Linear subspaces and residue class spaces/Exercise|| }} {{ inputexercise |Linear mappings/Tensor product/Diagonalizable/Exercise|| }} {{ inputexercise |Linear mappings/Tensor product/Trigonalizable/Exercise|| }} {{:Matrices/Kronecker product/Definition}} {{ inputexercise |Kronecker product/2x2/Computation/Exercise|| }} The {{ Definitionlink |Kronecker product| |Context=| |pm= }} has a tight connection with the {{ Definitionlink |tensor product| |Context=linear| |pm=, }} as the following exercise shows. {{ inputexercise |Matrices/Tensor product/Kronecker product/Exercise|| }} {{ inputexercise |Linear mapping/Tensorization/Jordan matrices/1/Exercise|| }} {{ inputexercise |Linear mapping/Tensor product/Multilinearity/Exercise|| }} {{ inputexercise |Tensor product/Homomorphisms/Relation/Exercise|| }} {{ inputexercise |Field extension/Multiplication is linear/Exercise|| }} {{ inputexercise |Polynomial ring/K/Inserting of a from L/Structure/Exercise|| }} {{ inputexercise |Vector space/Change of base field/Generating system/Basis/Fact/Proof/Exercise|| }} {{ inputexercise |Vector space/Change of base field/Functoriality/Exercise|| }} {{:Field/Finite extension/Definition}} {{:Field/Finite extension/Degree/Definition}} {{ inputexercise |C over R/Degree/Exercise|| }} {{ inputexercise |Field tower/Finite/In between finite/Exercise|| }} {{ inputexercise |Finite field extension/Determination of multiplication on basis/Exercise|| }} {{ inputexercise |Finite field extension/Basis/Multiplication with an element/Exercise|| }} {{ inputexercise |Tensor product/Change of field/Exercise|| }} {{ inputexercise |Field extension/Q in R/Not finite/Exercise|| }} {{:Field/Algebra/Directly/Definition}} Important examples of {{mat|term= K |pm=-}}algebras are given by a field extension {{ Relationchain | K |\subseteq| L || || || |pm=. }} The polynomial ring {{mathl|term= K[X] |pm=}} is a {{mat|term= K |pm=-}}algebra as well. {{ inputexercise |Algebras/Tensor product/Product structure/Exercise|| }} In den following exercises, the symbol {{mat|term= \cong |pm=}} means that these is a correspondence that respects addition, the multiplication, the {{mat|term= 0 |pm=,}} and the {{mat|term= 1 |pm=.}} {{ inputexercise |Polynomial ring/Change of field/Exercise|| }} {{ inputexercise |Polynomial ring/Tensor product/Exercise|| }} {{ inputexercise |Field extension/Algebra/Change of field/Exercise|| }} {{Subtitle|Hand-in-exercises}} {{ inputexercise |Tensor product/Base change/Computation/2/Exercise|m| }} {{ inputexercise |Tensor product/Linear mappings/Composition/Exercise|m| }} {{ inputexercise |Tensor product/Eigenvalues/Exercise|m| }} {{ inputexercise |Finite-dimensional vector space/Endomorphism space as tensor product/Trace/Exercise|m| }} {{ inputexercise |Linear mapping/Tensorization/Jordan matrices/2/Exercise|m| }} {{ inputexercise |Tensor product/Modulo tensor product/Kernel/Exercise|m| }} {{ inputexercise |Field extension/Tensor product/No field/Exercise|m| }} }} hw5ed5rtf03jkdp19uzjbzvdo1v3lzc 0 322275 2720297 2720219 2025-07-01T13:44:19Z Bocardodarapti 289675 2720297 wikitext text/x-wiki {{Linear algebra (Osnabrück 2024-2025)/Part II/Exercise sheet design|57| {{Subtitle|Exercises}} {{ inputexercise |Tensor product/Linear mapping/Change of field/Characteristic polynomial/Exercise|| }} However, by going from {{mat|term= K |pm=}} to {{mat|term= L |pm=,}} there may arise new zeroes of the characteristic polynomial and hence also new eigenvalues and eigenvectors. {{ inputexercise |Tensor product/Change of field/Homomorphism space/Exercise|| }} {{ inputexercise |Vector space/To L-vector space/Continuation/Exercise|| }} {{ inputexercise |Wedge product/R^3/Simplify/1/Exercise|| }} {{ inputexercise |Wedge product/R^3/Simplify/2/Exercise|| }} {{ inputexercise |Wedge product/R^3/Simplify/3/Exercise|| }} {{ inputexercise |Wedge product/Construction/n is 1/Exercise|| }} {{ inputexercise |Wedge product/Construction/n is dimension/Not 0/Exercise|| }} {{ inputexercise |Wedge product/Index larger than dimension/0/Exercise|| }} {{ inputexercise |Wedge product/Natural duality/Finite-dimensional/Determinant mapping to fixed dual forms/Exercise|| }} {{ inputexercise |Wedge product/Transformation of the wedge product for subfamilies/Determinant/Exercise|| }} {{ inputexercise |Tensor product/Wedge product/Fact/Via constructions/Exercise|| }} {{ inputexercise |Wedge product/To tensor product/Mapping/Exercise|| }} {{ inputexercise |Wedge product/To tensor product/Permutations/Mapping/Exercise|| }} {{ inputexercise |Wedge product/Change of field/Exercise|| }} {{Subtitle|Hand-in-exercises}} {{ inputexercise |Tensor product/Linear mapping/Change of field/Determinant/Exercise|m| }} {{ inputexercise |Asymptotic properties/Complexification/Exercise|m| }} }} etycz5g4te10ln9fr619umjovqy3hpk 0 322276 2720328 2720220 2025-07-01T15:22:56Z Bocardodarapti 289675 2720328 wikitext text/x-wiki {{Linear algebra (Osnabrück 2024-2025)/Part II/Exercise sheet design|58| {{Subtitle|Exercises}} {{ inputexercise |R^3/(2,3,2) \wedge (4,-1,5)/Standard basis/Exercise|| }} {{ inputexercise |Wedge product/R^2 to R^3/4 -1 0 7 2 3/Second wedge product in standard basis/Exercise|| }} {{ inputexercise |Tensor product/Wedge product/Basis/Exercise|| }} {{ inputexercise |Wedge product/Direct sum/Full dimension/Exercise|| }} {{ inputexercise |Wedge product/Mapping with fixed wedge product/Alternating/Exercise|| }} {{ inputexercise |Wedge product/Eigenvalues/Exercise|| }} {{ inputexercise |Linear mappings/Wedge product/Diagonalizable/Exercise|| }} {{ inputexercise |Linear mappings/Wedge product/Trigonalizable/Exercise|| }} {{ inputexercise |Determinant/Multiplication theorem/Wedge product/Exercise|| }} {{Subtitle|Hand-in-exercises}} {{ inputexercise |Wedge product/Computing example/Exercise|m| }} {{ inputexercise |R^3/(-2,5,-4) \wedge (7,-2,4)/Standard basis/Exercise|m| }} {{ inputexercise |R^4/-2 (3,6,-2,5) \wedge (2,7,4,0) \wedge (0,3,-4,-2) +4 (1,2,3,4) \wedge (1,-1,-2,3) \wedge (7,6,5,-4) /Standard basis/Exercise|m| }} {{ inputexercise |R^3/Second wedge product/Standard basis and wedge basis for (9,8,1), (4,7,-3), (2,5,-2)/Comptation/Exercise|m| }} {{ inputexercise |Wedge product/R^3 to R^3/4 -2 5 6 8 -3 1 4 -1/Second wedge product in standard basis/Exercise|m| }} }} 2wm6xfzjv06gb1vbn3x9d7sk2ncpgxn 2720331 2720328 2025-07-01T15:37:04Z Bocardodarapti 289675 2720331 wikitext text/x-wiki {{Linear algebra (Osnabrück 2024-2025)/Part II/Exercise sheet design|58| {{Subtitle|Exercises}} {{ inputexercise |R^3/(2,3,2) \wedge (4,-1,5)/Standard basis/Exercise|| }} {{ inputexercise |Wedge product/R^2 to R^3/4 -1 0 7 2 3/Second wedge product in standard basis/Exercise|| }} {{ inputexercise |Tensor product/Wedge product/Basis/Exercise|| }} {{ inputexercise |Wedge product/Direct sum/Full dimension/Exercise|| }} {{ inputexercise |Wedge product/Mapping with fixed wedge product/Alternating/Exercise|| }} {{ inputexercise |Wedge product/Eigenvalues/Exercise|| }} {{ inputexercise |Linear mappings/Wedge product/Diagonalizable/Exercise|| }} {{ inputexercise |Linear mappings/Wedge product/Trigonalizable/Exercise|| }} {{ inputexercise |Determinant/Multiplication theorem/Wedge product/Exercise|| }} {{Subtitle|Hand-in-exercises}} {{ inputexercise |Wedge product/Computing example/Exercise|m| }} {{ inputexercise |R^3/(-2,5,-4) \wedge (7,-2,4)/Standard basis/Exercise|m| }} {{ inputexercise |R^4/-2 (3,6,-2,5) \wedge (2,7,4,0) \wedge (0,3,-4,-2) +4 (1,2,3,4) \wedge (1,-1,-2,3) \wedge (7,6,5,-4) /Standard basis/Exercise|m| }} {{ inputexercise |R^3/Second wedge product/Standard basis and wedge basis for (9,8,1), (4,7,-3), (2,5,-2)/Computation/Exercise|m| }} {{ inputexercise |Wedge product/R^3 to R^3/4 -2 5 6 8 -3 1 4 -1/Second wedge product in standard basis/Exercise|m| }} }} 5yhoosha45nwf1nfvv56yit2a2ihyoh 0 322281 2720316 2720227 2025-07-01T14:54:20Z 2C0F:F5C0:B2A:2585:2086:36C6:CC23:50BB Abstract The significance of Emotional Intelligence (EI) in contemporary organizational environments has become increasingly apparent, particularly concerning its influence on leadership effectiveness and employee engagement. As organizations confront complex demands in an era defined by rapid technological change, globalization, and diverse workforce dynamics, emotionally intelligent leadership is now recognized as an indispensable driver of success. This critical review investigates how EI con 2720316 wikitext text/x-wiki {{Article info |journal = WikiJournal Preprints <!-- WikiJournal of Medicine, Science, or Humanities --> |last1 = Lastname |first1 = Firstname |last2 = |first2 = |last3 = |first3 = |last4 = |first4 = <!-- up to 9 authors can be added in this above format --> |et_al = <!-- if there are >9 authors, hyperlink to the list here --> |affiliations = institutes / affiliations |correspondence = email@address.com |keywords = <!-- up to 6 keywords --> |license = <!-- default is CC-BY --> |abstract = Abstract text goes here }} ==First Heading== [[file:example image.png|thumb|left | Image caption text goes here (attribution: name of image creator, [https://creativecommons.org/licenses/by/3.0/deed.en CC-BY 3.0]) ]] ==Additional information== ===Acknowledgements=== Any people, organisations, or funding sources that you would like to thank. ===Competing interests=== Any conflicts of interest that you would like to declare. Otherwise, a statement that the authors have no competing interest. ===Ethics statement=== An ethics statement, if appropriate, on any animal or human research performed should be included here or in the methods section. == Mahbub, A., & Beedle, J. (2025). BEHAVIORISTS, COGNITIVISTS, AND CONSTRUCTIVISTS LEARNING THEORIES: A COMPARISON AND APPLICATION IN INSTRUCTIONAL DESIGN. ''European Journal of Education Studies'', ''12''(6). == {{reflist|35em}} 4d4w7n1bwx09n6c1jyapv6hwl581keg 0 322293 2720294 2720244 2025-07-01T13:11:33Z Bocardodarapti 289675 Bocardodarapti moved page [[Linear mapping/Tensoration/Jordan matrices/2/Exercise]] to [[Linear mapping/Tensorization/Jordan matrices/2/Exercise]] 2720244 wikitext text/x-wiki {{ Mathematical text/Exercise{{{opt|}}} |Text= Suppose that the linear mapping {{ Mapping |name= \varphi | V | V || |pm= }} is given by the {{ Definitionlink |Jordan matrix| |Context=| |pm= }} {{mathl|term= {{op:Matrix22|1|1|0|1|}} |pm=}} with respect to the basis {{mathl|term= v_1,v_2 |pm=,}} and that the linear mapping {{ Mapping |name= \psi | W | W || |pm= }} is given by the Jordan matrix {{mathl|term= {{op:Matrix33|1|1|0|0|1|1|0|0|1}} |pm=}} with respect to the basis {{mathl|term= w_1,w_2,w_3 |pm=.}} {{ Enumeration2 |Determine the matrix of {{ Mapping/display |name= \varphi {{tensor}} \psi | V {{tensor}} W | V {{tensor}} W || |pm= }} with respect to the basis {{mathl|term= v_1 {{tensor}} w_1, v_1 {{tensor}} w_2, v_1 {{tensor}} w_3, v_2 {{tensor}} w_1, v_2 {{tensor}} w_2 , v_2 {{tensor}} w_3 |pm=.}} |Determine the {{ Definitionlink |Jordan normal form| |Context=| |pm= }} of {{mathl|term= \varphi {{tensor}} \psi |pm=.}} }} |Textform=Exercise |Category= |Marks=6 |m1=2 |m2=4 }} gspouqnzd9q3i9745u4fi1shtkwvt5d 0 322301 2720256 2025-07-01T12:00:23Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= {{:Field/Situation|pm=,}} and let {{mathl|term= V_1 {{commadots|}} V_n |pm=}} be {{ Definitionlink |vector spaces| |Context=| |pm= }} over {{mat|term= K|pm=.}} Let {{ Definitionlink |trigonalizable| |Context=| |pm= }} {{ Definitionlink |Premath=K |linear mappings| |Context=| |pm= }} {{ Mapping/display |name=\varphi_i |V_i|V_i || |pm= }} be given. Show that also the {{ Definitionlink |tensor product| |Context=linear| |pm= }} {{ Mappin..." 2720256 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= {{:Field/Situation|pm=,}} and let {{mathl|term= V_1 {{commadots|}} V_n |pm=}} be {{ Definitionlink |vector spaces| |Context=| |pm= }} over {{mat|term= K|pm=.}} Let {{ Definitionlink |trigonalizable| |Context=| |pm= }} {{ Definitionlink |Premath=K |linear mappings| |Context=| |pm= }} {{ Mapping/display |name=\varphi_i |V_i|V_i || |pm= }} be given. Show that also the {{ Definitionlink |tensor product| |Context=linear| |pm= }} {{ Mapping/display |name= \varphi_1 {{tensordots|}} \varphi_n |V_1 {{tensordots|}} V_n |V_1 {{tensordots|}} V_n || |pm= }} is trigonalizable. |Textform=Exercise |Category= |Marks= }} mi53ta2jm41t1po8g6gyawlbqu87a8l 0 322302 2720257 2025-07-01T12:03:33Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= Let {{ Relationchain | K |\subseteq| L || |pm= }} be a {{ Definitionlink |field extension| |Context=| |pm=, }} and let {{mat|term= A|pm=}} be a {{ Definitionlink |Premath=K |algebra| |Context=directly| |pm=. }} Show that {{mathl|term= L {{tensor|K}} A|pm=}} is an {{mat|term= L|pm=-}}algebra. |Textform=Exercise |Category= }}" 2720257 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= Let {{ Relationchain | K |\subseteq| L || |pm= }} be a {{ Definitionlink |field extension| |Context=| |pm=, }} and let {{mat|term= A|pm=}} be a {{ Definitionlink |Premath=K |algebra| |Context=directly| |pm=. }} Show that {{mathl|term= L {{tensor|K}} A|pm=}} is an {{mat|term= L|pm=-}}algebra. |Textform=Exercise |Category= }} 4630xk2ws3g8mdnv1knkp8j83i0alon 0 322303 2720258 2025-07-01T12:05:00Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= {{:Field/Situation|pm=.}} Show that for {{ Definitionlink |polynomial rings| |Context=n, field| |pm=, }} the equality {{ Relationchain/display | K[X] {{tensor|K}} K[Y] |\cong| K[X,Y] || || || |pm= }} holds. |Textform=Exercise |Category= |Marks= }}" 2720258 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= {{:Field/Situation|pm=.}} Show that for {{ Definitionlink |polynomial rings| |Context=n, field| |pm=, }} the equality {{ Relationchain/display | K[X] {{tensor|K}} K[Y] |\cong| K[X,Y] || || || |pm= }} holds. |Textform=Exercise |Category= |Marks= }} cvxc2k898s5e4992qwwt30oqqcmeoh6 0 322304 2720259 2025-07-01T12:05:58Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= {{:Field extension/Situation|pm=.}} Show that for the {{ Definitionlink |polynomial ring| |Context=1 field| |pm=, }} the equality {{ Relationchain/display | L {{tensor|K}} K[X] |\cong| L[X] || || || |pm= }} holds. |Textform=Exercise |Category= |Marks= }}" 2720259 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= {{:Field extension/Situation|pm=.}} Show that for the {{ Definitionlink |polynomial ring| |Context=1 field| |pm=, }} the equality {{ Relationchain/display | L {{tensor|K}} K[X] |\cong| L[X] || || || |pm= }} holds. |Textform=Exercise |Category= |Marks= }} 6klldq1ck1iff3hlibq56kna1x5g9zy 0 322305 2720260 2025-07-01T12:07:03Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Situation{{{opt|}}} |Text= Let {{ Relationchain | {{{K|K}}} | \subseteq| {{{L|L}}} || || || }} be a {{ Definitionlink |field extension| |pm={{{pm|}}} }} |Textform=Situation |}}" 2720260 wikitext text/x-wiki {{ Mathematical text/Situation{{{opt|}}} |Text= Let {{ Relationchain | {{{K|K}}} | \subseteq| {{{L|L}}} || || || }} be a {{ Definitionlink |field extension| |pm={{{pm|}}} }} |Textform=Situation |}} jfxcb6mgk8z9cz9l93kx5whjzldyltj 0 322306 2720261 2025-07-01T12:09:48Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= {{:Field/Situation|pm=,}} and let {{ Mathcor|term1= A |and|term2= B |pm= }} denote {{ Definitionlink |algebras| |Context=field| |pm= }} over {{mat|term= K|pm=.}} Show that {{mathl|term= A {{tensor|K}} B|pm=}} is also a {{mat|term= K|pm=-}}algebra, where the {{mat|term= 1|pm=}} is given by {{mat|term= 1 {{tensor|}} 1|pm=}} and where the multiplication for decomposable tensors are given by {{ Relationchain/display | ( a {{tensor|}} b..." 2720261 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= {{:Field/Situation|pm=,}} and let {{ Mathcor|term1= A |and|term2= B |pm= }} denote {{ Definitionlink |algebras| |Context=field| |pm= }} over {{mat|term= K|pm=.}} Show that {{mathl|term= A {{tensor|K}} B|pm=}} is also a {{mat|term= K|pm=-}}algebra, where the {{mat|term= 1|pm=}} is given by {{mat|term= 1 {{tensor|}} 1|pm=}} and where the multiplication for decomposable tensors are given by {{ Relationchain/display | ( a {{tensor|}} b) \cdot ( c {{tensor|}} d) | {{defeq|}} | (a \cdot c) {{tensor|}} (b \cdot d) || || || |pm=. }} |Textform=Exercise |Category= |Marks= }} 2hwtbjpxl3323kt4iijq4psgeg5tlyo 0 322307 2720262 2025-07-01T12:11:31Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= Show that the {{ Definitionlink |field extension| |Context=| |pm= }} {{ Relationchain | \Q | \subseteq | \R || || || || |pm= }} is not {{ Definitionlink |finite| |Context=field extension| |pm=. }} |Textform=Exercise |Category= |Marks= }}" 2720262 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= Show that the {{ Definitionlink |field extension| |Context=| |pm= }} {{ Relationchain | \Q | \subseteq | \R || || || || |pm= }} is not {{ Definitionlink |finite| |Context=field extension| |pm=. }} |Textform=Exercise |Category= |Marks= }} nhiha3odcnofh0v8oj2j4kb83l2rczv 0 322308 2720263 2025-07-01T12:17:43Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= {{:Field extension/Situation|pm=,}} and let {{mat|term= V_1 {{commadots|}} V_n |pm=}} denote {{ Definitionlink |Premath=K |vector spaces| |Context=| |pm=. }} Show that there exists a canonical isomorphism of {{mat|term= L|pm=-}}vector spaces {{ Relationchain/display | L {{tensor|K}} {{mabr| V_1 {{tensordots|K}} V_n |}} || {{mabr| L {{tensor|K}} V_1 |}} {{tensordots|L}} {{mabr| L {{tensor|K}} V_n |}} || || || |pm=. }} |Textfo..." 2720263 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= {{:Field extension/Situation|pm=,}} and let {{mat|term= V_1 {{commadots|}} V_n |pm=}} denote {{ Definitionlink |Premath=K |vector spaces| |Context=| |pm=. }} Show that there exists a canonical isomorphism of {{mat|term= L|pm=-}}vector spaces {{ Relationchain/display | L {{tensor|K}} {{mabr| V_1 {{tensordots|K}} V_n |}} || {{mabr| L {{tensor|K}} V_1 |}} {{tensordots|L}} {{mabr| L {{tensor|K}} V_n |}} || || || |pm=. }} |Textform=Exercise |Category= |Marks=2 }} cfjf735d51mxgwzxmhi2f3q9419yn35 0 322309 2720264 2025-07-01T12:23:36Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= Determine the {{ Definitionlink |Premath= |degree| |Context=field extension| |pm= }} of the {{ Definitionlink |field extension| |Context=| |pm= }} {{ Relationchain | \R | \subseteq | \Complex || || || || |pm=. }} |Textform=Exercise |Category= |Marks= }}" 2720264 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= Determine the {{ Definitionlink |Premath= |degree| |Context=field extension| |pm= }} of the {{ Definitionlink |field extension| |Context=| |pm= }} {{ Relationchain | \R | \subseteq | \Complex || || || || |pm=. }} |Textform=Exercise |Category= |Marks= }} m106khnvtsohs37h1pn1jzsglw2rrgf 0 322310 2720265 2025-07-01T12:25:32Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= Let {{ Relationchain | K | \subseteq | L | \subseteq | M || || |pm= }} be {{ Definitionlink |field extensions| |Context=| |pm= }} such that {{mat|term= M |pm=}} is {{ Definitionlink |finite| |Context=field extension| |pm= }} over {{mat|term= K |pm=.}} Show that also {{mat|term= M |pm=}} is finite over {{mat|term= L |pm=}} and that {{mat|term= L |pm=}} is finite over {{mat|term= K |pm=.}} |Textform=Exercise |Category= }}" 2720265 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= Let {{ Relationchain | K | \subseteq | L | \subseteq | M || || |pm= }} be {{ Definitionlink |field extensions| |Context=| |pm= }} such that {{mat|term= M |pm=}} is {{ Definitionlink |finite| |Context=field extension| |pm= }} over {{mat|term= K |pm=.}} Show that also {{mat|term= M |pm=}} is finite over {{mat|term= L |pm=}} and that {{mat|term= L |pm=}} is finite over {{mat|term= K |pm=.}} |Textform=Exercise |Category= }} k0iadfh6s95u1t9jtjfapcbwip50n8y 0 322311 2720266 2025-07-01T12:26:42Z Bocardodarapti 289675 New resource with "{{MDLD{{{opt|}}}|Start=tensorization (linear)| |See= |Target=Linear mapping/Change of field/Definition }}" 2720266 wikitext text/x-wiki {{MDLD{{{opt|}}}|Start=tensorization (linear)| |See= |Target=Linear mapping/Change of field/Definition }} n3fkruxgsupzko0vf2y5lwhmspspizl 0 322312 2720267 2025-07-01T12:26:57Z Bocardodarapti 289675 New resource with "{{MDLD{{{opt|}}}|Start=residue class spaces| |See=residue class space |Target=/Definition }}" 2720267 wikitext text/x-wiki {{MDLD{{{opt|}}}|Start=residue class spaces| |See=residue class space |Target=/Definition }} s3f1j8m151l1t2y2g3wkyh8ujpt4r40 0 322313 2720268 2025-07-01T12:28:06Z Bocardodarapti 289675 New resource with "{{MDLD{{{opt|}}}|Start=tensor product (linear)| |See= |Target=Linear mappings/Tensor product/Definition }}" 2720268 wikitext text/x-wiki {{MDLD{{{opt|}}}|Start=tensor product (linear)| |See= |Target=Linear mappings/Tensor product/Definition }} q84pbtghzp127qt8egsviayt9x3fles 0 322314 2720269 2025-07-01T12:28:42Z Bocardodarapti 289675 New resource with "{{MDLD{{{opt|}}}|Start=Kronecker product| |See= |Target=Matrices/Kronecker product/Definition }}" 2720269 wikitext text/x-wiki {{MDLD{{{opt|}}}|Start=Kronecker product| |See= |Target=Matrices/Kronecker product/Definition }} r5z9fq6xpmhz9uynyparseoralu2kdo 0 322315 2720270 2025-07-01T12:31:24Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= {{:Finite field extension/Situation|pm=,}} and let {{ Relationchain | x_1 {{commadots|}} x_n |\in| L || || || |pm= }} denote a {{ Definitionlink |Premath=K|basis| |Context=vs| |pm= }} of {{mat|term= L |pm=.}} Show that the multiplication on {{mat|term= L |pm=}} is uniquely determined by the products {{ Mathbed/display|term= x_i x_j ||condterm1= 1 \leq i\leq j \leq n ||condterm2= |pm=. }} |Textform=Exercise |Category= |Marks=2 }}" 2720270 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= {{:Finite field extension/Situation|pm=,}} and let {{ Relationchain | x_1 {{commadots|}} x_n |\in| L || || || |pm= }} denote a {{ Definitionlink |Premath=K|basis| |Context=vs| |pm= }} of {{mat|term= L |pm=.}} Show that the multiplication on {{mat|term= L |pm=}} is uniquely determined by the products {{ Mathbed/display|term= x_i x_j ||condterm1= 1 \leq i\leq j \leq n ||condterm2= |pm=. }} |Textform=Exercise |Category= |Marks=2 }} 2f3cg7b47yrsc78ea4ap4efig6emust 2720271 2720270 2025-07-01T12:31:37Z Bocardodarapti 289675 2720271 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= {{:Finite field extension/Situation|pm=,}} and let {{ Relationchain | x_1 {{commadots|}} x_n |\in| L || || || |pm= }} denote a {{ Definitionlink |Premath=K|basis| |Context=vs| |pm= }} of {{mat|term= L |pm=.}} Show that the multiplication on {{mat|term= L |pm=}} is uniquely determined by the products {{ Mathcond/display|term= x_i x_j ||condterm1= 1 \leq i\leq j \leq n ||condterm2= |pm=. }} |Textform=Exercise |Category= |Marks=2 }} 8ql0ilgklnfxr7z2gjzl585mogt33e6 0 322316 2720272 2025-07-01T12:32:19Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Situation{{{opt|}}} |Text= Let {{ Relationchain | {{{K|K}}} | \subseteq| {{{L|L}}} || || || }} be a {{ Definitionlink |Premath= |finite| |Context=field extension| |pm= }} {{ Definitionlink |field extension| |pm={{{pm|}}} }} |Textform=Situation |}}" 2720272 wikitext text/x-wiki {{ Mathematical text/Situation{{{opt|}}} |Text= Let {{ Relationchain | {{{K|K}}} | \subseteq| {{{L|L}}} || || || }} be a {{ Definitionlink |Premath= |finite| |Context=field extension| |pm= }} {{ Definitionlink |field extension| |pm={{{pm|}}} }} |Textform=Situation |}} d376xjnxzqcy900llk53ka0nxgquyh0 0 322317 2720273 2025-07-01T12:34:57Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= {{:Finite field extension/Situation|pm=,}} and let {{ Relationchain | v_1 {{commadots|}} v_n |\in| L || || || |pm= }} denote elements that form a {{ Definitionlink |Premath=K |basis| |Context=vs| |pm= }} of {{mat|term= L |pm=.}} Let {{ Mathcond|term= x \in L ||condterm1= x \neq 0 ||condterm2= |pm=. }} Show that also {{ Relationchain | xv_1 {{commadots|}} xv_n |\in| L || || || |pm= }} form a {{mat|term= K |pm=-}}basis of {{mat|t..." 2720273 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= {{:Finite field extension/Situation|pm=,}} and let {{ Relationchain | v_1 {{commadots|}} v_n |\in| L || || || |pm= }} denote elements that form a {{ Definitionlink |Premath=K |basis| |Context=vs| |pm= }} of {{mat|term= L |pm=.}} Let {{ Mathcond|term= x \in L ||condterm1= x \neq 0 ||condterm2= |pm=. }} Show that also {{ Relationchain | xv_1 {{commadots|}} xv_n |\in| L || || || |pm= }} form a {{mat|term= K |pm=-}}basis of {{mat|term= L |pm=.}} |Textform=Exercise |Category= |Marks=3 }} 3uqpmpkz7uf3svvfbpfcvadveacg67i 0 322318 2720274 2025-07-01T12:39:44Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= {{:Field extension/Situation|pm=.}} We consider the assignment {{mathl|term= V \mapsto V_L= L {{tensor|K}} V |pm=,}} that maps a {{ Definitionlink |Premath=K |vector space| |Context=| |pm= }} {{mat|term= V |pm=}} to the {{mat|term= L|pm=-}}vector space {{mathl|term= L {{tensor|K}} V |pm=,}} and a {{ Definitionlink |Premath=K |linear mapping| |Context=| |pm= }} {{ Mapping/display |name= \varphi | V | W || |pm= }} to the {{ Definitio..." 2720274 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= {{:Field extension/Situation|pm=.}} We consider the assignment {{mathl|term= V \mapsto V_L= L {{tensor|K}} V |pm=,}} that maps a {{ Definitionlink |Premath=K |vector space| |Context=| |pm= }} {{mat|term= V |pm=}} to the {{mat|term= L|pm=-}}vector space {{mathl|term= L {{tensor|K}} V |pm=,}} and a {{ Definitionlink |Premath=K |linear mapping| |Context=| |pm= }} {{ Mapping/display |name= \varphi | V | W || |pm= }} to the {{ Definitionlink |tensorization| |Context=linear| |pm= }} {{mat|term= \varphi_L |pm=.}} Show the following statements. {{ Enumeration3 |For the {{ Definitionlink |identity| |Context=| |pm= }} {{ Mapping/display |name= {{op:identity|V|}} | V | V || |pm=, }} also {{ Relationchain/display | {{mabr|{{op:identity|V|}} |}} _L || {{op:identity| L {{tensor|K}} V|}} || || || |pm= }} is the identity. |For linear mappings {{ Math/display|term= U \stackrel{\varphi}{\longrightarrow} V \stackrel{\psi}{\longrightarrow} W |pm= }} we have {{ Relationchain/display | ( \psi \circ \varphi)_L || \psi_L \circ \varphi_L || || || |pm=. }} |For an {{ Definitionlink |isomorphism| |Context=vs| |pm= }} {{ Mapping/display |name= \varphi | V | W || |pm=, }} also {{mathl|term= \varphi_L |pm=}} is an isomorphism, and for the {{ Definitionlink |inverse mapping| |Context=| |pm= }} we have {{ Relationchain/display | {{mabr| \varphi_L |}}^{-1} || {{mabr| \varphi^{-1} |}}_L || || || |pm=. }} }} |Textform=Exercise |Category= |Marks= }} t297mj153zim90dwelles0zb4w9insl 0 322319 2720277 2025-07-01T12:41:36Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= Compute the {{ Definitionlink |Kronecker product| |Context=| |pm= }} of the two matrices {{ Mathcor|term1= {{op:Matrix22|3|-4|5|-2}} |and|term2= {{op:Matrix22|-2|7|6|3}} |pm=. }} |Textform=Exercise |Category= |Marks=2 }}" 2720277 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= Compute the {{ Definitionlink |Kronecker product| |Context=| |pm= }} of the two matrices {{ Mathcor|term1= {{op:Matrix22|3|-4|5|-2}} |and|term2= {{op:Matrix22|-2|7|6|3}} |pm=. }} |Textform=Exercise |Category= |Marks=2 }} pu2jq5pyyzc5ktw1x852s79viatycjw 0 322320 2720278 2025-07-01T12:46:02Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= Let {{mat|term= K |pm=}} be a {{ Definitionlink |field| |Context=| |pm=, }} and let {{ Relationchain/display | A || {{mabr| a_{ij} |}}_{1 \leq i \leq m,\, 1 \leq j \leq n} || || || |pm= }} and {{ Relationchain/display | B || {{mabr| b_{k \ell } |}}_{1 \leq k \leq p,\, 1 \leq \ell \leq r} || || || |pm= }} denote {{ Definitionlink |matrices| |Context=| |pm= }} with the corresponding {{ Definitionlink |linear mappings| |Context=| |pm= }..." 2720278 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= Let {{mat|term= K |pm=}} be a {{ Definitionlink |field| |Context=| |pm=, }} and let {{ Relationchain/display | A || {{mabr| a_{ij} |}}_{1 \leq i \leq m,\, 1 \leq j \leq n} || || || |pm= }} and {{ Relationchain/display | B || {{mabr| b_{k \ell } |}}_{1 \leq k \leq p,\, 1 \leq \ell \leq r} || || || |pm= }} denote {{ Definitionlink |matrices| |Context=| |pm= }} with the corresponding {{ Definitionlink |linear mappings| |Context=| |pm= }} {{ Mapping |name= A | K^n | K^m || |pm= }} and {{ Mapping |name= B | K^r | K^p || |pm=. }} Show that the {{ Definitionlink |tensor product| |Context=linear mapping| |pm= }} of these linear mappings is given by the {{ Definitionlink |Kroneckerprodukt| |Context=| |pm= }} of {{mat|term= A |pm=}} and {{mat|term= B |pm=}} with respect to the bases {{ Mathcond|term= e_j {{tensor|}} e_\ell ||condterm1= 1 \leq j \leq n,\, 1 \leq \ell \leq r ||condterm2= |pm=, }} of {{mathl|term= K^n {{tensor|}} K^r |pm=}} and {{ Mathcond|term= e_i {{tensor|}} e_k ||condterm1= 1 \leq i \leq m,\, 1 \leq k \leq p ||condterm2= |pm=, }} of {{mathl|term= K^m {{tensor|}} K^p |pm=.}} |Textform=Exercise |Category= |Marks= }} qdxp3qveijnggbzxshx2flxzz1syf3o 0 322321 2720279 2025-07-01T12:51:57Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= Suppose that the linear mapping {{ Mapping |name= \varphi | V | V || |pm= }} is given by the {{ Definitionlink |Jordan matrix| |Context=| |pm= }} {{mathl|term= {{op:Matrix22|1|1|0|1|}} |pm=}} with respect to the basis {{mathl|term= v_1,v_2 |pm=,}} and that the linear mapping {{ Mapping |name= \psi | W | W || |pm= }} is given by the Jordan matrix {{mathl|term= {{op:Matrix22|1|1|0|1|}} |pm=}} with respect to the basis {{mathl|term= w_1..." 2720279 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= Suppose that the linear mapping {{ Mapping |name= \varphi | V | V || |pm= }} is given by the {{ Definitionlink |Jordan matrix| |Context=| |pm= }} {{mathl|term= {{op:Matrix22|1|1|0|1|}} |pm=}} with respect to the basis {{mathl|term= v_1,v_2 |pm=,}} and that the linear mapping {{ Mapping |name= \psi | W | W || |pm= }} is given by the Jordan matrix {{mathl|term= {{op:Matrix22|1|1|0|1|}} |pm=}} with respect to the basis {{mathl|term= w_1,w_2|pm=.}} {{ Enumeration2 |Determine the matrix of {{ Mapping/display |name= \varphi {{tensor}} \psi | V {{tensor}} W | V {{tensor}} W || |pm= }} with respect to the basis {{mathl|term= v_1 {{tensor}} w_1, v_1 {{tensor}} w_2, v_2 {{tensor}} w_1, v_2 {{tensor}} w_2 |pm=.}} |Determine the {{ Definitionlink |Jordan normal form| |Context=| |pm= }} of {{mathl|term= \varphi {{tensor}} \psi |pm=.}} }} |Textform=Exercise |Category= |Marks=5 |m1=2 |m2=3 }} 4bhgadbd64svmksrt2ywac3dwtksx3c 2720292 2720279 2025-07-01T13:11:13Z Bocardodarapti 289675 Bocardodarapti moved page [[Linear mapping/Tensoration/Jordan matrices/1/Exercise]] to [[Linear mapping/Tensorization/Jordan matrices/1/Exercise]] 2720279 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= Suppose that the linear mapping {{ Mapping |name= \varphi | V | V || |pm= }} is given by the {{ Definitionlink |Jordan matrix| |Context=| |pm= }} {{mathl|term= {{op:Matrix22|1|1|0|1|}} |pm=}} with respect to the basis {{mathl|term= v_1,v_2 |pm=,}} and that the linear mapping {{ Mapping |name= \psi | W | W || |pm= }} is given by the Jordan matrix {{mathl|term= {{op:Matrix22|1|1|0|1|}} |pm=}} with respect to the basis {{mathl|term= w_1,w_2|pm=.}} {{ Enumeration2 |Determine the matrix of {{ Mapping/display |name= \varphi {{tensor}} \psi | V {{tensor}} W | V {{tensor}} W || |pm= }} with respect to the basis {{mathl|term= v_1 {{tensor}} w_1, v_1 {{tensor}} w_2, v_2 {{tensor}} w_1, v_2 {{tensor}} w_2 |pm=.}} |Determine the {{ Definitionlink |Jordan normal form| |Context=| |pm= }} of {{mathl|term= \varphi {{tensor}} \psi |pm=.}} }} |Textform=Exercise |Category= |Marks=5 |m1=2 |m2=3 }} 4bhgadbd64svmksrt2ywac3dwtksx3c 0 322322 2720280 2025-07-01T12:54:15Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= {{:Field/Situation|pm=,}} and let {{mathl|term= V_1 {{commadots|}} V_n, W_1 {{commadots|}} W_n |pm=}} be {{ Definitionlink |vector spaces| |Context=| |pm= }} over {{mat|term= K|pm=.}} Show that the mapping {{ Mapping/display |name= | {{op:Homomorphisms|V_1|W_1}} {{timesdots}} {{op:Homomorphisms|V_n|W_n}} | {{op:Homomorphisms|V_1 {{tensordots|}} V_n | W_1 {{tensordots|}} W_n}} |(\varphi_1 {{commadots|}} \varphi_n ) | \varphi_1 {{te..." 2720280 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= {{:Field/Situation|pm=,}} and let {{mathl|term= V_1 {{commadots|}} V_n, W_1 {{commadots|}} W_n |pm=}} be {{ Definitionlink |vector spaces| |Context=| |pm= }} over {{mat|term= K|pm=.}} Show that the mapping {{ Mapping/display |name= | {{op:Homomorphisms|V_1|W_1}} {{timesdots}} {{op:Homomorphisms|V_n|W_n}} | {{op:Homomorphisms|V_1 {{tensordots|}} V_n | W_1 {{tensordots|}} W_n}} |(\varphi_1 {{commadots|}} \varphi_n ) | \varphi_1 {{tensordots|}} \varphi_n |pm=, }} is {{ Definitionlink |multilinear| |Context=| |pm=. }} |Textform=Exercise |Category= |Marks= }} ozv5cry0mckmfjrpw2hh87ox89paw5t 0 322323 2720281 2025-07-01T12:56:52Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= {{:Field/Situation|pm=,}} and let {{mathl|term= V_1 {{commadots|}} V_n, W_1 {{commadots|}} W_n |pm=}} denote {{ Definitionlink |finite-dimensional| |Context=vs| |pm= }} {{ Definitionlink |Premath=K |vector spaces| |Context=| |pm=. }} Show that there exists a canonical isomorphism {{ Mapping/display |name= | {{op:Homomorphisms|V_1|W_1}} {{tensordots}} {{op:Homomorphisms|V_n|W_n}} | {{op:Homomorphisms|V_1 {{tensordots|}} V_n|W_1 {{..." 2720281 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= {{:Field/Situation|pm=,}} and let {{mathl|term= V_1 {{commadots|}} V_n, W_1 {{commadots|}} W_n |pm=}} denote {{ Definitionlink |finite-dimensional| |Context=vs| |pm= }} {{ Definitionlink |Premath=K |vector spaces| |Context=| |pm=. }} Show that there exists a canonical isomorphism {{ Mapping/display |name= | {{op:Homomorphisms|V_1|W_1}} {{tensordots}} {{op:Homomorphisms|V_n|W_n}} | {{op:Homomorphisms|V_1 {{tensordots|}} V_n|W_1 {{tensordots|}} W_n}} || |pm=. }} |Textform=Exercise |Category= |Marks= }} dxppxa35iy9uoa46cy87gclgjq7j882 0 322324 2720282 2025-07-01T12:58:37Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= {{:Field extension/Situation|pm=,}} and let {{ Relationchain | f |\in| L || || || |pm=. }} Show that the mapping {{ Mapping/display |name= \mu_f | L | L | x | fx |pm=, }} is {{ Definitionlink |Premath=K |linear| |Context=| |pm=. }} |Textform=Exercise |Category= |Marks= }}" 2720282 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= {{:Field extension/Situation|pm=,}} and let {{ Relationchain | f |\in| L || || || |pm=. }} Show that the mapping {{ Mapping/display |name= \mu_f | L | L | x | fx |pm=, }} is {{ Definitionlink |Premath=K |linear| |Context=| |pm=. }} |Textform=Exercise |Category= |Marks= }} 9vfhbsi7gqavpr62qmogvsqroeqo27o 0 322325 2720283 2025-07-01T13:01:12Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text={{:Field extension/Situation|pm=,}} and let {{ Relationchain | a |\in| L || || || |pm=. }} Show that the inserting mapping, that is, the assignment {{ Mapping/display |name= \psi | K[X] | L | P | P(a) |pm=, }} fulfills the following properties {{ Extra/Bracket |text=for {{ Relationchain/b | P,Q |\in| K[X] || || || |pm= }}| |Ipm=|Epm=. }} {{ Enumeration3 |{{ Relationchain | (P + Q)(a) || P(a) +Q(a) || || || |pm=, }} |{{ Relationc..." 2720283 wikitext text/x-wiki {{ Mathematical text/Exercise |Text={{:Field extension/Situation|pm=,}} and let {{ Relationchain | a |\in| L || || || |pm=. }} Show that the inserting mapping, that is, the assignment {{ Mapping/display |name= \psi | K[X] | L | P | P(a) |pm=, }} fulfills the following properties {{ Extra/Bracket |text=for {{ Relationchain/b | P,Q |\in| K[X] || || || |pm= }}| |Ipm=|Epm=. }} {{ Enumeration3 |{{ Relationchain | (P + Q)(a) || P(a) +Q(a) || || || |pm=, }} |{{ Relationchain | (P \cdot Q)(a) || P(a) \cdot Q(a) || || || |pm=, }} |{{ Relationchain | 1(a) || 1 || || || |pm=. }} }} |Textform=Exercise |Category= |Marks= }} 6q5nti89qqkmmxmedd1j3k1r7ko5ku2 0 322326 2720284 2025-07-01T13:03:43Z Bocardodarapti 289675 New resource with "{{MDLD{{{opt|}}}|Start=finite field extension| |See= |Target=Field/Finite extension/Definition }}" 2720284 wikitext text/x-wiki {{MDLD{{{opt|}}}|Start=finite field extension| |See= |Target=Field/Finite extension/Definition }} eleb3gei67ez84f9mv5l3xw2nyna347 0 322327 2720285 2025-07-01T13:03:54Z Bocardodarapti 289675 New resource with "{{MDLD{{{opt|}}}|Start=finite (field extension)| |See= |Target=Field/Finite extension/Definition }}" 2720285 wikitext text/x-wiki {{MDLD{{{opt|}}}|Start=finite (field extension)| |See= |Target=Field/Finite extension/Definition }} 9vmecg0vd24s8ws8cs7nmjwqm6xtrb3 0 322328 2720286 2025-07-01T13:04:18Z Bocardodarapti 289675 New resource with "{{MDLD{{{opt|}}}|Start=degree (field extension)| |See= |Target=Field/Finite extension/Degree/Definition }}" 2720286 wikitext text/x-wiki {{MDLD{{{opt|}}}|Start=degree (field extension)| |See= |Target=Field/Finite extension/Degree/Definition }} 7809db6ww5dol2fa02bxs9nwfnp1mji 0 322329 2720287 2025-07-01T13:05:07Z Bocardodarapti 289675 New resource with "{{MDLD{{{opt|}}}|Start=algebra (directly)| |See= |Target=Field/Algebra/Directly/Definition }}" 2720287 wikitext text/x-wiki {{MDLD{{{opt|}}}|Start=algebra (directly)| |See= |Target=Field/Algebra/Directly/Definition }} iqsyoyu5c60pkfgsjdle36vsek2e1o2 0 322330 2720288 2025-07-01T13:05:22Z Bocardodarapti 289675 New resource with "{{MDLD{{{opt|}}}|Start=algebras (field)| |See=algebra (field) |Target=/Definition }}" 2720288 wikitext text/x-wiki {{MDLD{{{opt|}}}|Start=algebras (field)| |See=algebra (field) |Target=/Definition }} 15w0oyh96gj70hjn8hok3gv9sam20rw 0 322331 2720289 2025-07-01T13:05:33Z Bocardodarapti 289675 New resource with "{{MDLD{{{opt|}}}|Start=algebra (field)| |See= |Target=Field/Algebra/Directly/Definition }}" 2720289 wikitext text/x-wiki {{MDLD{{{opt|}}}|Start=algebra (field)| |See= |Target=Field/Algebra/Directly/Definition }} 9m92bfcak1n6gmya3yumy9pacfmvl8w 0 322332 2720290 2025-07-01T13:06:41Z Bocardodarapti 289675 New resource with "{{MDLD{{{opt|}}}|Start=polynomial ring (1 field)| |See= |Target=Polynomials/Field/Introduction/Section }}" 2720290 wikitext text/x-wiki {{MDLD{{{opt|}}}|Start=polynomial ring (1 field)| |See= |Target=Polynomials/Field/Introduction/Section }} 7weo5v419pxl2b7kck137wlmj1miaq4 0 322333 2720293 2025-07-01T13:11:14Z Bocardodarapti 289675 Bocardodarapti moved page [[Linear mapping/Tensoration/Jordan matrices/1/Exercise]] to [[Linear mapping/Tensorization/Jordan matrices/1/Exercise]] 2720293 wikitext text/x-wiki #REDIRECT [[Linear mapping/Tensorization/Jordan matrices/1/Exercise]] sonenucfj3wlsrfbamqcgxgudstfce2 0 322334 2720295 2025-07-01T13:11:33Z Bocardodarapti 289675 Bocardodarapti moved page [[Linear mapping/Tensoration/Jordan matrices/2/Exercise]] to [[Linear mapping/Tensorization/Jordan matrices/2/Exercise]] 2720295 wikitext text/x-wiki #REDIRECT [[Linear mapping/Tensorization/Jordan matrices/2/Exercise]] rqd3xyvmoyrqu2way93yl52f5swl4v6 0 322335 2720298 2025-07-01T13:53:08Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= {{:Field extension/Situation|pm=,}} {{mat|term= V|pm=}} be a {{ Definitionlink |finite-dimensional| |Context=vs| |pm= }} {{ Definitionlink |Premath=K |vector space| |Context=| |pm=, }} and let {{ Mapping/display |name= \varphi | V | V || |pm= }} be a {{ Definitionlink |linear mapping| |Context=| |pm=. }} Show that the {{ Definitionlink |characteristic polynomial| |Context=| |pm= }} of {{mat|term= \varphi |pm=}} coincides with the char..." 2720298 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= {{:Field extension/Situation|pm=,}} {{mat|term= V|pm=}} be a {{ Definitionlink |finite-dimensional| |Context=vs| |pm= }} {{ Definitionlink |Premath=K |vector space| |Context=| |pm=, }} and let {{ Mapping/display |name= \varphi | V | V || |pm= }} be a {{ Definitionlink |linear mapping| |Context=| |pm=. }} Show that the {{ Definitionlink |characteristic polynomial| |Context=| |pm= }} of {{mat|term= \varphi |pm=}} coincides with the characteristic polynomial of the {{ Definitionlink |tensorization| |Context=linear| |pm= }} {{mat|term= \varphi_L |pm=.}} |Textform=Exercise |Category= |Marks= }} 4hjza9y8ru5ik3pv0e9hs83y8968xod 0 322336 2720299 2025-07-01T13:59:05Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= {{:Field extension/Situation|pm=,}} and let {{ Mathcor|term1= V |and|term2= W |pm= }} be {{ Definitionlink |vector spaces| |Context=| |pm= }} over {{mat|term= K|pm=.}} {{ Enumeration2/a |Define an {{ Definitionlink |Premath=L |linear mapping| |Context=| |pm= }} {{ Mapping/display |name= | L {{tensor|K}} {{op:Homomorphisms| V | W | K }} |{{op:Homomorphisms| V_L | W_L | L }} || |pm= }} that maps {{mathl|term= c {{tensor|}} \varphi |..." 2720299 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= {{:Field extension/Situation|pm=,}} and let {{ Mathcor|term1= V |and|term2= W |pm= }} be {{ Definitionlink |vector spaces| |Context=| |pm= }} over {{mat|term= K|pm=.}} {{ Enumeration2/a |Define an {{ Definitionlink |Premath=L |linear mapping| |Context=| |pm= }} {{ Mapping/display |name= | L {{tensor|K}} {{op:Homomorphisms| V | W | K }} |{{op:Homomorphisms| V_L | W_L | L }} || |pm= }} that maps {{mathl|term= c {{tensor|}} \varphi |pm=}} to {{mathl|term= c {{mabr|{{op:identity|L|}} {{tensor|}} \varphi |}} |pm=.}} |Suppose that the two vector spaces are {{ Definitionlink |finite-dimensional| |Context=| |pm=. }} Show that the mapping from part (a) is an {{ Definitionlink |isomorphism| |Context=linear| |pm=. }} }} |Textform=Exercise |Category= |Marks= }} 3byqx05w29z7efef519nvcwwz9q8kle 2720300 2720299 2025-07-01T14:00:27Z Bocardodarapti 289675 2720300 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= {{:Field extension/Situation|pm=,}} and let {{ Mathcor|term1= V |and|term2= W |pm= }} be {{ Definitionlink |vector spaces| |Context=| |pm= }} over {{mat|term= K|pm=.}} {{ Enumeration2/a |Define an {{ Definitionlink |Premath=L |linear mapping| |Context=| |pm= }} {{ Mapping/display |name= | L {{tensor|K}} {{op:Homomorphisms| V | W | K }} |{{op:Homomorphisms| V_L | W_L | K= L }} || |pm= }} that maps {{mathl|term= c {{tensor|}} \varphi |pm=}} to {{mathl|term= c {{mabr|{{op:identity|L|}} {{tensor|}} \varphi |}} |pm=.}} |Suppose that the two vector spaces are {{ Definitionlink |finite-dimensional| |Context=| |pm=. }} Show that the mapping from part (a) is an {{ Definitionlink |isomorphism| |Context=linear| |pm=. }} }} |Textform=Exercise |Category= |Marks= }} 9nebqquf41lz1a9xtou7cgeapzm595q 0 322337 2720302 2025-07-01T14:28:59Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise{{{opt|}}} |Text= Let {{ Mapping/display |name=\varphi |V|V || |pm= }} be an {{ Definitionlink |endomorphism| |Context=linear| |pm= }} on a {{ Definitionlink |finite-dimensional| |Context=| |pm= }} {{ Definitionlink |real vector space| |Context=| |pm= }} {{mat|term= V |pm=,}} and let {{ Mapping/display |name= \varphi_\Complex | V_\Complex | V_\Complex || |pm= }} be the corresponding {{ Definitionlink |complexification| |Context=linear| |pm=...." 2720302 wikitext text/x-wiki {{ Mathematical text/Exercise{{{opt|}}} |Text= Let {{ Mapping/display |name=\varphi |V|V || |pm= }} be an {{ Definitionlink |endomorphism| |Context=linear| |pm= }} on a {{ Definitionlink |finite-dimensional| |Context=| |pm= }} {{ Definitionlink |real vector space| |Context=| |pm= }} {{mat|term= V |pm=,}} and let {{ Mapping/display |name= \varphi_\Complex | V_\Complex | V_\Complex || |pm= }} be the corresponding {{ Definitionlink |complexification| |Context=linear| |pm=. }} Show that {{mat|term= \varphi |pm=}} is {{ Extra/Bracket |text={{ Definitionlink |asymptotically| |Context=stable| |pm= }}| |Ipm=|Epm= }} {{ Definitionlink |stable| |Context=linear| |pm= }} if and only if this holds for {{mat|term= \varphi_\Complex |pm=.}} |Textform=Exercise |Category= |Marks=4 }} g6k44j1jecv8eq9wm31fxxdaafb7bk4 6 322338 2720303 2025-07-01T14:29:08Z Young1lim 21186 {{Information |Description=VLSI.Arith: Carry Lookahead Adders 1A (20250628 - 20250627) |Source={{own|Young1lim}} |Date=2025-07-01 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} 2720303 wikitext text/x-wiki == Summary == {{Information |Description=VLSI.Arith: Carry Lookahead Adders 1A (20250628 - 20250627) |Source={{own|Young1lim}} |Date=2025-07-01 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} fl0muvoq887sc9g3xk417gqgkchdng0 0 322339 2720304 2025-07-01T14:31:02Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise{{{opt|}}} |Text= {{:Field extension/Situation|pm=,}} let {{mat|term= V|pm=}} be a {{ Definitionlink |finite-dimensional| |Context=vs| |pm= }} {{ Definitionlink |Premath=K |vector space| |Context=| |pm=, }} and let {{ Mapping/display |name=\varphi | V | V || |pm= }} denote a {{ Definitionlink |linear mapping| |Context=| |pm=. }} Show {{ Relationchain/display | {{op:Determinant|\varphi|}} || {{op:Determinant|\varphi_L|}} || || || |pm=. }} |..." 2720304 wikitext text/x-wiki {{ Mathematical text/Exercise{{{opt|}}} |Text= {{:Field extension/Situation|pm=,}} let {{mat|term= V|pm=}} be a {{ Definitionlink |finite-dimensional| |Context=vs| |pm= }} {{ Definitionlink |Premath=K |vector space| |Context=| |pm=, }} and let {{ Mapping/display |name=\varphi | V | V || |pm= }} denote a {{ Definitionlink |linear mapping| |Context=| |pm=. }} Show {{ Relationchain/display | {{op:Determinant|\varphi|}} || {{op:Determinant|\varphi_L|}} || || || |pm=. }} |Textform=Exercise |Category= |Marks=2 }} 37eycxayo0uicuw08v6oq7hezwfmnuw 0 322340 2720305 2025-07-01T14:33:23Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= {{:Field extension/Situation|pm=,}} let {{mat|term= V|pm=}} be a {{ Definitionlink |Premath=K |vector space| |Context=| |pm=, }} and {{ Relationchain | n |\in| \N || || || |pm=. }} Show that there exists a canonical isomorphy of {{mat|term= L |pm=-}}vector spaces {{ Mathcor/display|term1= \bigwedge^n V_L |and|term2= ( \bigwedge^n V )_L |pm= }} {{ Extra/Bracket |text=where on the left-hand side, we have the {{ Definitionlink |wedge..." 2720305 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= {{:Field extension/Situation|pm=,}} let {{mat|term= V|pm=}} be a {{ Definitionlink |Premath=K |vector space| |Context=| |pm=, }} and {{ Relationchain | n |\in| \N || || || |pm=. }} Show that there exists a canonical isomorphy of {{mat|term= L |pm=-}}vector spaces {{ Mathcor/display|term1= \bigwedge^n V_L |and|term2= ( \bigwedge^n V )_L |pm= }} {{ Extra/Bracket |text=where on the left-hand side, we have the {{ Definitionlink |wedge product| |Context=| |pm= }} over {{mat|term= L |pm=}}| |Ipm=|Epm=. }} |Textform=Exercise |Category= |Marks=2 }} 2omn0pzlx9cks2n8lbsyljvnz5bjjd7 0 322341 2720306 2025-07-01T14:33:42Z Bocardodarapti 289675 New resource with "{{refcontrol}}" 2720306 wikitext text/x-wiki {{refcontrol}} fm6x64t6vw5xxjlwo10fad26g9okvho 0 322342 2720307 2025-07-01T14:35:11Z Bocardodarapti 289675 New resource with "{{MDLD{{{opt|}}}|Start=asymptotically (stable)| |See= |Target=Endomorphism/K/Power/Zero convergence/Asymptotically stable/Definition }}" 2720307 wikitext text/x-wiki {{MDLD{{{opt|}}}|Start=asymptotically (stable)| |See= |Target=Endomorphism/K/Power/Zero convergence/Asymptotically stable/Definition }} 90ot5b1tf7zkqisrswdecwtblcys41y 0 322343 2720308 2025-07-01T14:36:09Z Bocardodarapti 289675 New resource with "{{MDLD{{{opt|}}}|Start=complexification (linear)| |See= |Target=Real vector space/Complexification/Tensor product/Example }}" 2720308 wikitext text/x-wiki {{MDLD{{{opt|}}}|Start=complexification (linear)| |See= |Target=Real vector space/Complexification/Tensor product/Example }} f591x29lz9aiwwexu1jk9h32qdti6w2 0 322344 2720309 2025-07-01T14:37:17Z Bocardodarapti 289675 New resource with "{{MDLD{{{opt|}}}|Start=wedge product| |See= |Target=Vector space/Wedge product/Construction/Section }}" 2720309 wikitext text/x-wiki {{MDLD{{{opt|}}}|Start=wedge product| |See= |Target=Vector space/Wedge product/Construction/Section }} tw8cdt0tikad17jn7odlb91k3z5dv0j 0 322345 2720310 2025-07-01T14:37:36Z Bocardodarapti 289675 New resource with "{{refcontrol}}" 2720310 wikitext text/x-wiki {{refcontrol}} fm6x64t6vw5xxjlwo10fad26g9okvho 0 322346 2720311 2025-07-01T14:41:43Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= Let {{mat|term= V |pm=}} be a {{ Definitionlink |Premath=K |vector space| |Context=| |pm=, }} and let {{ Mapping/display |name= \pi | V {{timesdots}} V | V {{tensordots}} V || |pm= }} {{ Extra/Bracket |text={{mat|term= n|pm=}} factors| |Ipm=|Epm= }} the canonical multilinear mapping. {{ Enumeration3 |Let {{ Relationchain | \sigma |\in| S_n || || || |pm= }} be a {{ Definitionlink |permutation| |Context=| |pm=. }} Show that there exi..." 2720311 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= Let {{mat|term= V |pm=}} be a {{ Definitionlink |Premath=K |vector space| |Context=| |pm=, }} and let {{ Mapping/display |name= \pi | V {{timesdots}} V | V {{tensordots}} V || |pm= }} {{ Extra/Bracket |text={{mat|term= n|pm=}} factors| |Ipm=|Epm= }} the canonical multilinear mapping. {{ Enumeration3 |Let {{ Relationchain | \sigma |\in| S_n || || || |pm= }} be a {{ Definitionlink |permutation| |Context=| |pm=. }} Show that there exists a multilinear mapping {{ Mapping/display |name= \pi \circ \sigma | V {{timesdots}} V | V {{tensordots}} V || |pm= }} with {{ Relationchain/display | (\pi \circ \sigma )(v_1 {{commadots|}} v_n) || v_{\sigma (1) } {{tensordots|}} v_{\sigma (n)} || || || |pm=. }} |Show that {{mathl|term= \sum_{\sigma \in S_n} {{op:Sign|\sigma}} \pi \circ \sigma |pm=}} is multilinear and {{ Definitionlink |alternating| |Context=| |pm=. }} |Show that there exists a linear mapping {{ Mapping/display |name= \Psi | \bigwedge^n V | V {{tensordots}} V || |pm= }} with {{ Relationchain/display | \Psi ( v_1 {{wedgedots}} v_n) || \sum_{\sigma \in S_n} {{op:Sign|\sigma}} v_{\sigma (1) } {{tensordots|}} v_{\sigma (n)} || || || |pm=. }} }} |Textform=Exercise |Category= |Marks= }} mfdwszjqn9ag501wnaavfhgklohbkx4 0 322347 2720312 2025-07-01T14:45:49Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= Let {{mat|term= V|pm=}} be a {{ Definitionlink |Premath=K |vector space| |Context=| |pm=, }} and {{ Relationchain | n |\in| \N || || || |pm=. }} {{ Enumeration2 |Can we define by the assignment {{ Math/display|term= v_1 {{wedgedots|}} v_n \mapsto v_1 {{tensordots|}} v_n |pm= }} a {{ Extra/Bracket |text=linear| |Ipm=|Epm= }} mapping from {{mathl|term= \bigwedge^n V |pm=}} to {{mathl|term= V {{tensordots}} V |pm=?}} |Can we apply to..." 2720312 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= Let {{mat|term= V|pm=}} be a {{ Definitionlink |Premath=K |vector space| |Context=| |pm=, }} and {{ Relationchain | n |\in| \N || || || |pm=. }} {{ Enumeration2 |Can we define by the assignment {{ Math/display|term= v_1 {{wedgedots|}} v_n \mapsto v_1 {{tensordots|}} v_n |pm= }} a {{ Extra/Bracket |text=linear| |Ipm=|Epm= }} mapping from {{mathl|term= \bigwedge^n V |pm=}} to {{mathl|term= V {{tensordots}} V |pm=?}} |Can we apply to the canonical mapping {{ Mapping/display |name= \pi | V {{timesdots}} V | V {{tensordots}} V || |pm= }} the {{ Factlink |Preword=|universal property of the wedge product|Factname= Wedge product/Universal property/Fact |Nr= |pm=, }} in order to obtain a linear mapping from {{mathl|term= \bigwedge^n V |pm=}} to {{mathl|term= V {{tensordots}} V |pm=?}} }} |Textform=Exercise |Category= |Marks= }} 35xk95pxygunhip6xzlf1y0q9a7eti8 0 322348 2720313 2025-07-01T14:48:46Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= Prove {{ Factlink |Factname=Tensor product/Wedge product/Fact |Nr= |pm= }} directly from the {{ Factlink |Preword=|construction|Factname=Vector spaces/Finite family/Tensor product/Definition |pm= }} of the tensor product and the {{ Factlink |Preword=|construction|Factname=Vector space/Wedge product/Construction/Section |pm= }} of the wedge product. |Textform=Exercise |Category= |Marks= }}" 2720313 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= Prove {{ Factlink |Factname=Tensor product/Wedge product/Fact |Nr= |pm= }} directly from the {{ Factlink |Preword=|construction|Factname=Vector spaces/Finite family/Tensor product/Definition |pm= }} of the tensor product and the {{ Factlink |Preword=|construction|Factname=Vector space/Wedge product/Construction/Section |pm= }} of the wedge product. |Textform=Exercise |Category= |Marks= }} 8xmzhm6tdzq3j3sjdm3ueetb0rw3c9l 0 322349 2720314 2025-07-01T14:49:24Z Bocardodarapti 289675 New resource with "{{Number in course{{{opt|}}}|Theorem|57|9|}}" 2720314 wikitext text/x-wiki {{Number in course{{{opt|}}}|Theorem|57|9|}} 5k5f6umu547lrwce4w0b1zlb2m15b99 0 322350 2720315 2025-07-01T14:53:59Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= Show the following statement for the wedge product: {{:Vector space/Situation|pm=}} of {{ Definitionlink |dimension| |Context=vs| |pm= }} {{mat|term= n |pm=.}} Let {{ Mathcor|term1= v_1 {{commadots|}} v_r |and|term2= w_1 {{commadots|}} w_r |pm= }} be vectors in {{mat|term= V |pm=,}} related by {{ Relationchain/display | {{op:Column vector| w_1|\vdots| w_r}} || M {{op:Column vector|v_1|\vdots|v_r}} || || || |pm=, }} where {{mat|t..." 2720315 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= Show the following statement for the wedge product: {{:Vector space/Situation|pm=}} of {{ Definitionlink |dimension| |Context=vs| |pm= }} {{mat|term= n |pm=.}} Let {{ Mathcor|term1= v_1 {{commadots|}} v_r |and|term2= w_1 {{commadots|}} w_r |pm= }} be vectors in {{mat|term= V |pm=,}} related by {{ Relationchain/display | {{op:Column vector| w_1|\vdots| w_r}} || M {{op:Column vector|v_1|\vdots|v_r}} || || || |pm=, }} where {{mat|term= M |pm=}} is an {{ Definitionlink |Premath=r \times r |matrix| |Context=| |pm=. }} Then in {{mathl|term= \bigwedge^r V |pm=}} the relation {{ Relationchain/display | w_1 {{wedgedots|}} w_r || ( {{op:Determinant|M|}}) v_1 {{wedgedots|}} v_r || || || |pm= }} holds. |Textform=Exercise |Category= }} 1cgyo37s0rfsgbopol3nlgc9ckn8xgl 0 322351 2720317 2025-07-01T14:55:42Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text={{:Vector space/Finite-dimensional/Situation|pm=.}} Let {{ Relationchain | f_1 {{commadots|}} f_k |\in| V^* || || || |pm=. }} Show that the {{ Definitionlink |mapping| |Context=| |pm= }} {{ Mapping/display |name= | V {{timesdots|}} V | K | (v_1 {{commadots|}} v_k) | {{op:Determinant| (f_i (v_j))_{1 \leq i ,j \leq k}|}} |pm=, }} is {{ Definitionlink |multilinear| |Context=| |pm= }} and {{ Definitionlink |alternating| |Context=|..." 2720317 wikitext text/x-wiki {{ Mathematical text/Exercise |Text={{:Vector space/Finite-dimensional/Situation|pm=.}} Let {{ Relationchain | f_1 {{commadots|}} f_k |\in| V^* || || || |pm=. }} Show that the {{ Definitionlink |mapping| |Context=| |pm= }} {{ Mapping/display |name= | V {{timesdots|}} V | K | (v_1 {{commadots|}} v_k) | {{op:Determinant| (f_i (v_j))_{1 \leq i ,j \leq k}|}} |pm=, }} is {{ Definitionlink |multilinear| |Context=| |pm= }} and {{ Definitionlink |alternating| |Context=| |pm=. }} |Textform=Exercise |Category= }} esnbvymrka11kfruoeeqr33m19ylnaa 0 322352 2720318 2025-07-01T14:57:04Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= Let {{mat|term= K |pm=}} be a {{ Definitionlink |field| |Context=| |pm=, }} and let {{mat|term= V |pm=}} be an {{ Definitionlink |Premath=m |dimensional| |Context=vs| |pm= }} {{ Definitionlink |Premath=K |vector space| |Context=| |pm=. }} Let {{ Relationchain | n | < | m || || || |pm=. }} Show {{ Relationchain | \bigwedge^n V || 0 || || || |pm=. }} |Textform=Exercise |Category= }}" 2720318 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= Let {{mat|term= K |pm=}} be a {{ Definitionlink |field| |Context=| |pm=, }} and let {{mat|term= V |pm=}} be an {{ Definitionlink |Premath=m |dimensional| |Context=vs| |pm= }} {{ Definitionlink |Premath=K |vector space| |Context=| |pm=. }} Let {{ Relationchain | n | < | m || || || |pm=. }} Show {{ Relationchain | \bigwedge^n V || 0 || || || |pm=. }} |Textform=Exercise |Category= }} ri129sp7e9lqzed73ecil95cq8xsy6g 0 322353 2720320 2025-07-01T14:59:10Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= Let {{mat|term= K |pm=}} be a {{ Definitionlink |field| |pm=, }} and let {{mat|term= V |pm=}} be a {{ Definitionlink |Premath=K |vector space| |pm= }} of {{ Definitionlink |dimension| |Context=vs| |pm= }} {{mat|term= n |pm=.}} Show that {{mathl|term= \bigwedge^n V |pm=}} is not the zero space. |Textform=Exercise |Category= }}" 2720320 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= Let {{mat|term= K |pm=}} be a {{ Definitionlink |field| |pm=, }} and let {{mat|term= V |pm=}} be a {{ Definitionlink |Premath=K |vector space| |pm= }} of {{ Definitionlink |dimension| |Context=vs| |pm= }} {{mat|term= n |pm=.}} Show that {{mathl|term= \bigwedge^n V |pm=}} is not the zero space. |Textform=Exercise |Category= }} 6np9c9nzur75qa196wisvw6az6q8qj2 0 322354 2720321 2025-07-01T15:00:19Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= Let {{mat|term= K |pm=}} be a {{ Definitionlink |field| |pm=, }} and let {{mat|term= V|pm=}} be a {{ Definitionlink |Premath=K |vector space| |pm=. }} Show the equality {{ Relationchain | V || \bigwedge^1 V || || || |pm=. }} |Textform=Exercise |Category= }}" 2720321 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= Let {{mat|term= K |pm=}} be a {{ Definitionlink |field| |pm=, }} and let {{mat|term= V|pm=}} be a {{ Definitionlink |Premath=K |vector space| |pm=. }} Show the equality {{ Relationchain | V || \bigwedge^1 V || || || |pm=. }} |Textform=Exercise |Category= }} hiuunvrrwdeyl07jkm4dna4omt558jc 0 322355 2720322 2025-07-01T15:02:10Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= Simplify in {{mathl|term= \bigwedge^3 \R^3 |pm=}} the expression {{ Math/display|term= - 7e_1 \wedge e_2 \wedge e_3 + 6 e_2 \wedge e_3 \wedge e_1 + 4 e_3 \wedge e_2 \wedge e_1 +3 e_2 \wedge e_1 \wedge e_3 +5 e_3 \wedge e_1 \wedge e_2 -11 e_2 \wedge e_3 \wedge e_1 |pm=. }} |Textform=Exercise |Category= }}" 2720322 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= Simplify in {{mathl|term= \bigwedge^3 \R^3 |pm=}} the expression {{ Math/display|term= - 7e_1 \wedge e_2 \wedge e_3 + 6 e_2 \wedge e_3 \wedge e_1 + 4 e_3 \wedge e_2 \wedge e_1 +3 e_2 \wedge e_1 \wedge e_3 +5 e_3 \wedge e_1 \wedge e_2 -11 e_2 \wedge e_3 \wedge e_1 |pm=. }} |Textform=Exercise |Category= }} 8b70zgdgda3cmd9yw0geyovf1nv0l1w 0 322356 2720323 2025-07-01T15:02:40Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= Simplify in {{mathl|term= \bigwedge^3 \R^3 |pm=}} the expression {{ Math/display|term= ( e_1-e_2) \wedge (e_2 -4 e_3) \wedge (3e_1-5e_2+4e_3) + {{mabr| 7e_3 |}} \wedge {{mabr| e_1 -4 e_3 |}} \wedge {{mabr| 5 e_3 -e_1|}} -(4e_3-2 e_2 ) \wedge e_2 \wedge (4 e_1 +3e_2-4e_3) |pm=. }} |Textform=Exercise |Category= }}" 2720323 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= Simplify in {{mathl|term= \bigwedge^3 \R^3 |pm=}} the expression {{ Math/display|term= ( e_1-e_2) \wedge (e_2 -4 e_3) \wedge (3e_1-5e_2+4e_3) + {{mabr| 7e_3 |}} \wedge {{mabr| e_1 -4 e_3 |}} \wedge {{mabr| 5 e_3 -e_1|}} -(4e_3-2 e_2 ) \wedge e_2 \wedge (4 e_1 +3e_2-4e_3) |pm=. }} |Textform=Exercise |Category= }} qbu11qr57c1lsicmtwy9rwm20y9fo6w 0 322357 2720324 2025-07-01T15:03:08Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= Simplify in {{mathl|term= \bigwedge^2 \R^3 |pm=}} the expression {{ Math/display|term= e_1 \wedge (e_2 -4 e_3) - e_2 \wedge (5 e_1 +3e_2-4e_3) + {{mabr| 7e_3 |}} \wedge e_1 -4 {{mabr| 5e_1 \wedge 2 e_3 |}} + (2e_1-8e_2) \wedge (2e_1-8e_2) |pm=. }} |Textform=Exercise |Category= }}" 2720324 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= Simplify in {{mathl|term= \bigwedge^2 \R^3 |pm=}} the expression {{ Math/display|term= e_1 \wedge (e_2 -4 e_3) - e_2 \wedge (5 e_1 +3e_2-4e_3) + {{mabr| 7e_3 |}} \wedge e_1 -4 {{mabr| 5e_1 \wedge 2 e_3 |}} + (2e_1-8e_2) \wedge (2e_1-8e_2) |pm=. }} |Textform=Exercise |Category= }} 6c0714umtb58w6bdp96aollknrgrjrt 0 322358 2720325 2025-07-01T15:15:10Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= {{:Field extension/Situation|pm=,}} let {{mat|term= V|pm=}} be a {{ Definitionlink |Premath=K |vector space| |Context=| |pm= }} and {{mat|term= W |pm=}} an {{mat|term= L|pm=-}}vector space. Let {{ Mapping/display |name= \varphi | V | W || |pm= }} be a {{ Definitionlink |Premath=K |linear mapping| |Context=| |pm=. }} Show that there exists an {{mat|term= L|pm=-}}linear mapping {{ Mapping/display |name= \tilde{ \varphi } | V_L | W || |p..." 2720325 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= {{:Field extension/Situation|pm=,}} let {{mat|term= V|pm=}} be a {{ Definitionlink |Premath=K |vector space| |Context=| |pm= }} and {{mat|term= W |pm=}} an {{mat|term= L|pm=-}}vector space. Let {{ Mapping/display |name= \varphi | V | W || |pm= }} be a {{ Definitionlink |Premath=K |linear mapping| |Context=| |pm=. }} Show that there exists an {{mat|term= L|pm=-}}linear mapping {{ Mapping/display |name= \tilde{ \varphi } | V_L | W || |pm= }} that extends {{mat|term= \varphi |pm=}} {{ Extra/Bracket |text=that is, coincides on {{ Relationchain/b | V | \subseteq | V_L || || || |pm= }} with {{mat|term= \varphi |pm=.}}| |Ipm=|Epm=. }} |Textform=Exercise |Category= |Marks= }} siy6gbakjz7hfo03eytto77gbjenx1o 0 322359 2720329 2025-07-01T15:25:50Z Bocardodarapti 289675 New resource with " {{ Mathematical text/Exercise |Text= Express the {{ Definitionlink |wedge product| |Context=| |pm= }} {{mathl|term= {{op:Column vector|2|3|2}} \wedge {{op:Column vector|4|-1|5}} |pm=}} in the standard basis of {{mathl|term= \bigwedge^2 \R^3|pm=.}} |Textform=Exercise |Category= |Marks=2 }}" 2720329 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= Express the {{ Definitionlink |wedge product| |Context=| |pm= }} {{mathl|term= {{op:Column vector|2|3|2}} \wedge {{op:Column vector|4|-1|5}} |pm=}} in the standard basis of {{mathl|term= \bigwedge^2 \R^3|pm=.}} |Textform=Exercise |Category= |Marks=2 }} iikl51rhuy2prlf44dhbmezjl9m2o7g 2720341 2720329 2025-07-01T15:45:17Z Bocardodarapti 289675 2720341 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= Express the {{ Definitionlink |wedge product| |Context=| |pm= }} {{mathl|term= {{op:Column vector|2|3|2}} \wedge {{op:Column vector|4|-1|5}} |pm=}} in the standard basis of {{mathl|term= \bigwedge^2 \R^3|pm=.}} |Textform=Exercise |Category= |Marks=2 }} lrgui8463qfwr0nsicckkgriw2maglh 0 322360 2720330 2025-07-01T15:36:05Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise{{{opt|}}} |Text= Let {{ Mapping/display |name=\varphi |\R^3|\R^3 || |pm= }} be the {{ Definitionlink |linear mapping| |Context=| |pm= }} given by the {{ Definitionlink |matrix| |Context=| |pm= }} {{ Math/display|term= {{op:Matrix33|4|-2|5|6|8|-3|1|4|-1}} |pm=. }} Determine the matrix of {{mathl|term= \bigwedge^2 \varphi|pm=}} with respect to the standard bases of the wedge products. |Textform=Exercise |Category= |Marks=5 }}" 2720330 wikitext text/x-wiki {{ Mathematical text/Exercise{{{opt|}}} |Text= Let {{ Mapping/display |name=\varphi |\R^3|\R^3 || |pm= }} be the {{ Definitionlink |linear mapping| |Context=| |pm= }} given by the {{ Definitionlink |matrix| |Context=| |pm= }} {{ Math/display|term= {{op:Matrix33|4|-2|5|6|8|-3|1|4|-1}} |pm=. }} Determine the matrix of {{mathl|term= \bigwedge^2 \varphi|pm=}} with respect to the standard bases of the wedge products. |Textform=Exercise |Category= |Marks=5 }} t1snutndh2i85rwij8fdja82kf6holk 0 322361 2720332 2025-07-01T15:38:15Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise{{{opt|}}} |Text= We consider the {{ Definitionlink |basis| |Context=vs| |pm= }} {{ Math/display|term= v_1= {{op:Column vector|9|8|1}} ,\, v_2 = {{op:Column vector|4|7|-3}} ,\, v_3= {{op:Column vector|2|5|-2}} |pm= }} of {{mat|term= \R^3|pm=,}} and the corresponding induced basis {{ Relationchain/display | {{basis|v}} || v_1 \wedge v_2,\, v_1 \wedge v_3 , \, v_2 \wedge v_3 || || || |pm= }} of {{mathl|term= \bigwedge^2 \R^3 |pm=.}}..." 2720332 wikitext text/x-wiki {{ Mathematical text/Exercise{{{opt|}}} |Text= We consider the {{ Definitionlink |basis| |Context=vs| |pm= }} {{ Math/display|term= v_1= {{op:Column vector|9|8|1}} ,\, v_2 = {{op:Column vector|4|7|-3}} ,\, v_3= {{op:Column vector|2|5|-2}} |pm= }} of {{mat|term= \R^3|pm=,}} and the corresponding induced basis {{ Relationchain/display | {{basis|v}} || v_1 \wedge v_2,\, v_1 \wedge v_3 , \, v_2 \wedge v_3 || || || |pm= }} of {{mathl|term= \bigwedge^2 \R^3 |pm=.}} Determine the {{ Definitionlink |base change matrices| |Context=| |pm= }} {{ Extra/Bracket |text=in both directions| |Ipm=|Epm= }} betwee the basis {{mat|term= {{basis|v}} |pm=}} and the standard basis {{mathl|term= e_1 \wedge e_2,\, e_1 \wedge e_3 , \, e_2 \wedge e_3 |pm=.}} |Textform=Exercise |Category= |Marks=5 }} 9f5mbbqxn3akws11n1l2kbdd2ee0snr 0 322362 2720333 2025-07-01T15:39:37Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= Express the {{ Definitionlink |wedge product| |Context=| |pm= }} {{Math/display|term= -2 {{op:Column vector|3|6|-2|5}} \wedge {{op:Column vector|2|7|4|0}} \wedge {{op:Column vector|0|3|-4|-2}} + 4 {{op:Column vector|1|2|3|4}} \wedge {{op:Column vector|1|-1|-2|3}} \wedge {{op:Column vector|7|6|5|-4}} |pm=}} in the standard basis of {{mathl|term= \bigwedge^3 \R^4 |pm=.}} |Textform=Exercise |Category= |Marks=4 }}" 2720333 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= Express the {{ Definitionlink |wedge product| |Context=| |pm= }} {{Math/display|term= -2 {{op:Column vector|3|6|-2|5}} \wedge {{op:Column vector|2|7|4|0}} \wedge {{op:Column vector|0|3|-4|-2}} + 4 {{op:Column vector|1|2|3|4}} \wedge {{op:Column vector|1|-1|-2|3}} \wedge {{op:Column vector|7|6|5|-4}} |pm=}} in the standard basis of {{mathl|term= \bigwedge^3 \R^4 |pm=.}} |Textform=Exercise |Category= |Marks=4 }} mkb7y6lb82gsffa1o1ax4ob38x1m1jl 2720334 2720333 2025-07-01T15:39:45Z Bocardodarapti 289675 2720334 wikitext text/x-wiki {{ Mathematical text/Exercise{{{opt|}}} |Text= Express the {{ Definitionlink |wedge product| |Context=| |pm= }} {{Math/display|term= -2 {{op:Column vector|3|6|-2|5}} \wedge {{op:Column vector|2|7|4|0}} \wedge {{op:Column vector|0|3|-4|-2}} + 4 {{op:Column vector|1|2|3|4}} \wedge {{op:Column vector|1|-1|-2|3}} \wedge {{op:Column vector|7|6|5|-4}} |pm=}} in the standard basis of {{mathl|term= \bigwedge^3 \R^4 |pm=.}} |Textform=Exercise |Category= |Marks=4 }} pni4fu4b3ldb2lyq7vtboxz3kj7updn 0 322363 2720335 2025-07-01T15:40:38Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise{{{opt|}}} |Text= Express the {{ Definitionlink |wedge product| |Context=| |pm= }} {{mathl|term= {{op:Column vector|-2|5|-4}} \wedge {{op:Column vector|7|-2|4}} |pm=}} in the standard basis of {{mathl|term= \bigwedge^2 \R^3 |pm=.}} |Textform=Exercise |Category= |Marks=2 }}" 2720335 wikitext text/x-wiki {{ Mathematical text/Exercise{{{opt|}}} |Text= Express the {{ Definitionlink |wedge product| |Context=| |pm= }} {{mathl|term= {{op:Column vector|-2|5|-4}} \wedge {{op:Column vector|7|-2|4}} |pm=}} in the standard basis of {{mathl|term= \bigwedge^2 \R^3 |pm=.}} |Textform=Exercise |Category= |Marks=2 }} 785veoyvpjamo7c9x90q46xjfrr6fs9 0 322364 2720336 2025-07-01T15:41:52Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise{{{opt|}}} |Text= Express the {{ Definitionlink |wedge product| |Context=| |pm= }} {{Math/display|term= 4 {{op:Column vector|2|3|4}} \wedge {{op:Column vector|1|0|3}} + 5{{op:Column vector|-3|2|3}} \wedge {{op:Column vector|0|0|1}} -2 {{op:Column vector|7|-5|3}} \wedge {{op:Column vector|1|3|-4}} |pm=}} in {{mathl|term= \bigwedge^2 \R^3 |pm=}} as a linear combination of the wedge products {{mathl|term= e_1 \wedge e_2 |pm=,}} {{mathl|term= e_..." 2720336 wikitext text/x-wiki {{ Mathematical text/Exercise{{{opt|}}} |Text= Express the {{ Definitionlink |wedge product| |Context=| |pm= }} {{Math/display|term= 4 {{op:Column vector|2|3|4}} \wedge {{op:Column vector|1|0|3}} + 5{{op:Column vector|-3|2|3}} \wedge {{op:Column vector|0|0|1}} -2 {{op:Column vector|7|-5|3}} \wedge {{op:Column vector|1|3|-4}} |pm=}} in {{mathl|term= \bigwedge^2 \R^3 |pm=}} as a linear combination of the wedge products {{mathl|term= e_1 \wedge e_2 |pm=,}} {{mathl|term= e_1 \wedge e_3 |pm=,}} and {{mathl|term= e_2 \wedge e_3 |pm=.}} |Textform=Exercise |Category= |Marks=4 }} rztlhs1nr7q9j6fs3i0bj5a9nh1qrq9 0 322365 2720338 2025-07-01T15:43:09Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= Prove {{ Factlink |Preword=the|multiplication theorem for the determinant|Factname= Determinant/Multiplication/Fact |Nr= |pm= }} with the help of the {{ Definitionlink |wedge product| |Context=| |pm=. }} |Textform=Exercise |Category= |Marks= }}" 2720338 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= Prove {{ Factlink |Preword=the|multiplication theorem for the determinant|Factname= Determinant/Multiplication/Fact |Nr= |pm= }} with the help of the {{ Definitionlink |wedge product| |Context=| |pm=. }} |Textform=Exercise |Category= |Marks= }} 9pcbjn1p29pkvvn9scbldm4d19cjbf9 2720339 2720338 2025-07-01T15:43:39Z Bocardodarapti 289675 2720339 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= Prove {{ Factlink |Preword=the|multiplication theorem for the determinant|Factname= Determinant/Multiplication theorem/Fact |Nr= |pm= }} with the help of the {{ Definitionlink |wedge product| |Context=| |pm=. }} |Textform=Exercise |Category= |Marks= }} 8x8jww2cnt33u4qr4x6z4cho41tbz17 0 322366 2720340 2025-07-01T15:45:00Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= {{:Vector space/Situation|pm=.}} Let {{ Mapping/display |name= \varphi | V | V || |pm= }} be a {{ Definitionlink |trigonalizable| |Context=| |pm= }} {{ Definitionlink |Premath=K |linear mapping| |Context=| |pm=. }} Show that also the {{ Definitionlink |wedge product| |Context=linear| |pm= }} {{ Mapping/display |name= \bigwedge^n \varphi | \bigwedge^n V | \bigwedge^n V || |pm= }} is trigonalizable. |Textform=Exercise |Category= |Mar..." 2720340 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= {{:Vector space/Situation|pm=.}} Let {{ Mapping/display |name= \varphi | V | V || |pm= }} be a {{ Definitionlink |trigonalizable| |Context=| |pm= }} {{ Definitionlink |Premath=K |linear mapping| |Context=| |pm=. }} Show that also the {{ Definitionlink |wedge product| |Context=linear| |pm= }} {{ Mapping/display |name= \bigwedge^n \varphi | \bigwedge^n V | \bigwedge^n V || |pm= }} is trigonalizable. |Textform=Exercise |Category= |Marks= }} rj4of0kro6bnmyma7fmrysfvoag5oj6 0 322367 2720342 2025-07-01T15:45:49Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= {{:Vector space/Situation|pm=.}} Let {{ Mapping/display |name= \varphi | V | V || |pm= }} be a {{ Definitionlink |diagonalizable| |Context=| |pm= }} {{ Definitionlink |Premath=K |linear mapping| |Context=| |pm=. }} Show that also the {{ Definitionlink |wedge product| |Context=linear| |pm= }} {{ Mapping/display |name= \bigwedge^n \varphi | \bigwedge^n V | \bigwedge^n V || |pm= }} is diagonalizable. |Textform=Exercise |Category= |Mar..." 2720342 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= {{:Vector space/Situation|pm=.}} Let {{ Mapping/display |name= \varphi | V | V || |pm= }} be a {{ Definitionlink |diagonalizable| |Context=| |pm= }} {{ Definitionlink |Premath=K |linear mapping| |Context=| |pm=. }} Show that also the {{ Definitionlink |wedge product| |Context=linear| |pm= }} {{ Mapping/display |name= \bigwedge^n \varphi | \bigwedge^n V | \bigwedge^n V || |pm= }} is diagonalizable. |Textform=Exercise |Category= |Marks= }} 3tntcrhuyfs70yj6ocrittjyq1q6o0j 0 322368 2720343 2025-07-01T15:48:47Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= Let {{mat|term= V |pm=}} be a {{ Definitionlink |vector space| |Context=| |pm= }} over the {{ Definitionlink |field| |Context=| |pm= }} {{mat|term= K|pm=,}} and let {{ Mapping/display |name= \varphi | V | V || |pm= }} be an {{ Definitionlink |endomorphism| |Context=linear| |pm=. }} Let {{ Mapping/display |name= \bigwedge^m \varphi | \bigwedge^m V | \bigwedge^m V || |pm= }} be the {{mat|term= m|pm=-}}th {{ Definitionlink |wedge produc..." 2720343 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= Let {{mat|term= V |pm=}} be a {{ Definitionlink |vector space| |Context=| |pm= }} over the {{ Definitionlink |field| |Context=| |pm= }} {{mat|term= K|pm=,}} and let {{ Mapping/display |name= \varphi | V | V || |pm= }} be an {{ Definitionlink |endomorphism| |Context=linear| |pm=. }} Let {{ Mapping/display |name= \bigwedge^m \varphi | \bigwedge^m V | \bigwedge^m V || |pm= }} be the {{mat|term= m|pm=-}}th {{ Definitionlink |wedge product| |Context=linear mapping| |pm= }} of {{mat|term= \varphi |pm=.}} Let {{mathl|term= v_1 {{commadots|}} v_m |pm=}} be {{ Definitionlink |linearly independent| |Context=| |pm= }} {{ Definitionlink |eigenvectors| |Context=| |pm= }} of {{mat|term= \varphi |pm=}} with {{ Definitionlink |eigenvalues| |Context=| |pm= }} {{mathl|term= a_1 {{commadots|}} a_m |pm=.}} Show that {{mathl|term= a_1 \cdots a_m |pm=}} is an eigenvalue of {{mat|term= \bigwedge^m \varphi |pm=.}} |Textform=Exercise |Category= |Marks=3 }} fkqxpwfnjzjrfwblje3hjk4b0xjmcb6 0 322369 2720344 2025-07-01T15:50:30Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= {{:Vector space/Situation|pm=.}} Let {{ Relationchain | u_1 {{commadots|}} u_n |\in| V || || || |pm=. }} Show that for every {{ Relationchain | k |\in| \N || || || |pm=, }} there exists a uniquely determined {{ Definitionlink |linear mapping| |Context=| |pm= }} {{ Mapping/display |name= | \bigwedge^k V | \bigwedge^{k+n} V || |pm= }} satisfying {{mathl|term= v_1 {{wedgedots|}} v_k \mapsto v_1 {{wedgedots|}} v_k \wedge u_1 {{wedgedots..." 2720344 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= {{:Vector space/Situation|pm=.}} Let {{ Relationchain | u_1 {{commadots|}} u_n |\in| V || || || |pm=. }} Show that for every {{ Relationchain | k |\in| \N || || || |pm=, }} there exists a uniquely determined {{ Definitionlink |linear mapping| |Context=| |pm= }} {{ Mapping/display |name= | \bigwedge^k V | \bigwedge^{k+n} V || |pm= }} satisfying {{mathl|term= v_1 {{wedgedots|}} v_k \mapsto v_1 {{wedgedots|}} v_k \wedge u_1 {{wedgedots|}} u_n |pm=.}} |Textform=Exercise |Category= |Marks=4 }} jt4yhmh1zk0yeebpswr6497hw9d57er 0 322370 2720345 2025-07-01T15:52:56Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= Let {{ Relationchain | V || U \oplus W || || || |pm= }} be a {{ Definitionlink |direct sum decomposition| |Context=| |pm= }} in {{ Definitionlink |linear subspaces| |Context=| |pm= }} of {{ Definitionlink |dimension| |Context=vs| |pm= }} {{ Relationchain | {{op:Dimension vector space|U|}} || r || || || |pm= }} and {{ Relationchain | {{op:Dimension vector space|U|}} || s || || || |pm=. }} Show that there exists a canonical isomorph..." 2720345 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= Let {{ Relationchain | V || U \oplus W || || || |pm= }} be a {{ Definitionlink |direct sum decomposition| |Context=| |pm= }} in {{ Definitionlink |linear subspaces| |Context=| |pm= }} of {{ Definitionlink |dimension| |Context=vs| |pm= }} {{ Relationchain | {{op:Dimension vector space|U|}} || r || || || |pm= }} and {{ Relationchain | {{op:Dimension vector space|U|}} || s || || || |pm=. }} Show that there exists a canonical isomorphy {{ Relationchain/display | \bigwedge^{r+s} V |\cong| \bigwedge^r U {{tensor}} \bigwedge^s W || || || |pm=. }} |Textform=Exercise |Category= |Marks= }} imhxq9xvxu0nf7rbpjs5pthbkvrpeb7 0 322371 2720346 2025-07-01T15:55:08Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= Let {{mat|term= V |pm=}} be a {{ Definitionlink |finite-dimensional| |Context=| |pm= }} {{ Definitionlink |Premath=K |vector space| |Context=| |pm=, }} and let {{mathl|term= v_1 {{commadots|}} v_m |pm=}} be a {{ Definitionlink |basis| |Context=vs| |pm= }} of {{mat|term= V|pm=.}} Determine the matrix of the natural mapping {{ Extra/Bracket |text={{mat|term= n|pm=}} factors| |Ipm=|Epm= }} {{ Mapping/display |name= | V {{tensordots|K}}..." 2720346 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= Let {{mat|term= V |pm=}} be a {{ Definitionlink |finite-dimensional| |Context=| |pm= }} {{ Definitionlink |Premath=K |vector space| |Context=| |pm=, }} and let {{mathl|term= v_1 {{commadots|}} v_m |pm=}} be a {{ Definitionlink |basis| |Context=vs| |pm= }} of {{mat|term= V|pm=.}} Determine the matrix of the natural mapping {{ Extra/Bracket |text={{mat|term= n|pm=}} factors| |Ipm=|Epm= }} {{ Mapping/display |name= | V {{tensordots|K}} V | \bigwedge^n V || |pm= }} with respect to the corresponding bases. |Textform=Exercise |Category= |Marks= }} jvamjwhj69gcqodsfjmc945p1n465y1 0 322372 2720347 2025-07-01T15:57:13Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Exercise |Text= Let {{ Mapping/display |name= \varphi | \R^2 | \R^3 || |pm= }} be the {{ Definitionlink |linear mapping| |Context=| |pm= }} given by the {{ Definitionlink |matrix| |Context=| |pm= }} {{ Math/display|term= {{op:Matrix32|4|-1|0|7|2|3}} |pm=. }} Determine the matrix of {{mathl|term= \bigwedge^2 \varphi|pm=}} with respect to the standard bases of the {{ Definitionlink |Premath= |wedge products| |Context=| |pm=. }} |Textform=Exercise..." 2720347 wikitext text/x-wiki {{ Mathematical text/Exercise |Text= Let {{ Mapping/display |name= \varphi | \R^2 | \R^3 || |pm= }} be the {{ Definitionlink |linear mapping| |Context=| |pm= }} given by the {{ Definitionlink |matrix| |Context=| |pm= }} {{ Math/display|term= {{op:Matrix32|4|-1|0|7|2|3}} |pm=. }} Determine the matrix of {{mathl|term= \bigwedge^2 \varphi|pm=}} with respect to the standard bases of the {{ Definitionlink |Premath= |wedge products| |Context=| |pm=. }} |Textform=Exercise |Category= }} 9natpmp9rmhfccz6i5arij5mmg3ueuw 0 322373 2720348 2025-07-01T15:58:41Z Bocardodarapti 289675 New resource with "{{MDLD{{{opt|}}}|Start=wedge products| |See=wedge product |Target=/Definition }}" 2720348 wikitext text/x-wiki {{MDLD{{{opt|}}}|Start=wedge products| |See=wedge product |Target=/Definition }} 8qsvy59ycrzc1vzj4ivauk3rznsmgoo 0 322374 2720349 2025-07-01T15:59:57Z Bocardodarapti 289675 New resource with "{{MDLD{{{opt|}}}|Start=wedge product (linear mapping)| |See= |Target=Wedge product/Canonical mapping for linear mapping/Existence/Fact }}" 2720349 wikitext text/x-wiki {{MDLD{{{opt|}}}|Start=wedge product (linear mapping)| |See= |Target=Wedge product/Canonical mapping for linear mapping/Existence/Fact }} se0sae55ertj28adusof5wy6b1kpg1k 0 322375 2720350 2025-07-01T16:00:11Z Bocardodarapti 289675 New resource with "{{MDLD{{{opt|}}}|Start=wedge product (linear)| |See= |Target=Wedge product/Canonical mapping for linear mapping/Existence/Fact }}" 2720350 wikitext text/x-wiki {{MDLD{{{opt|}}}|Start=wedge product (linear)| |See= |Target=Wedge product/Canonical mapping for linear mapping/Existence/Fact }} czmargiovu6unisat4ab2dht2u1v3j0 0 322376 2720351 2025-07-01T16:03:23Z Bocardodarapti 289675 New resource with "{{MDLD{{{opt|}}}|Start=rings| |See=ring |Target=/Definition }}" 2720351 wikitext text/x-wiki {{MDLD{{{opt|}}}|Start=rings| |See=ring |Target=/Definition }} 6ampnqh26n4mbrew6ed5z3oannl1vdh 0 322377 2720352 2025-07-01T16:04:40Z Bocardodarapti 289675 New resource with "{{MDLD{{{opt|}}}|Start=vector space structure| |See=vector space |Target=/Definition }}" 2720352 wikitext text/x-wiki {{MDLD{{{opt|}}}|Start=vector space structure| |See=vector space |Target=/Definition }} pyjxmoj7m402svvbnys3vy2hmy7hyf6 0 322378 2720353 2025-07-01T16:06:38Z Bocardodarapti 289675 New resource with "{{MDLD{{{opt|}}}|Start=kernel (ring)| |See= |Target=Group homomorphism/Kernel/Definition }}" 2720353 wikitext text/x-wiki {{MDLD{{{opt|}}}|Start=kernel (ring)| |See= |Target=Group homomorphism/Kernel/Definition }} iufojgcmfwat9bym1j8hvj3alhx94j8 0 322379 2720354 2025-07-01T16:07:06Z Bocardodarapti 289675 New resource with "{{MDLD{{{opt|}}}|Start=cosets (group)| |See=coset (group) |Target=/Definition }}" 2720354 wikitext text/x-wiki {{MDLD{{{opt|}}}|Start=cosets (group)| |See=coset (group) |Target=/Definition }} l7dgawvr8cmzfid1logn4liiqoilbhu 0 322380 2720355 2025-07-01T16:08:17Z Bocardodarapti 289675 New resource with "{{MDLD{{{opt|}}}|Start=coset (group)| |See= |Target=Group theory/Left and right coset/Definition }}" 2720355 wikitext text/x-wiki {{MDLD{{{opt|}}}|Start=coset (group)| |See= |Target=Group theory/Left and right coset/Definition }} nwv4kg4joq4u49pugaltfz908og8guu 0 322381 2720356 2025-07-01T16:08:43Z Bocardodarapti 289675 New resource with "{{MDLD{{{opt|}}}|Start=cosets (ideal)| |See=coset (group) |Target=/Definition }}" 2720356 wikitext text/x-wiki {{MDLD{{{opt|}}}|Start=cosets (ideal)| |See=coset (group) |Target=/Definition }} 9ipxun60sdk3hu5ns6nd5033r4dqid6 0 322382 2720357 2025-07-01T16:12:11Z Bocardodarapti 289675 New resource with "{{MDLD{{{opt|}}}|Start=same orientation| |See= |Target=Real finite-dimensional vector space/Bases with same orientation/Definition }}" 2720357 wikitext text/x-wiki {{MDLD{{{opt|}}}|Start=same orientation| |See= |Target=Real finite-dimensional vector space/Bases with same orientation/Definition }} tpz95n957qen68g5ysfwl6cs2j4s5wq 0 322383 2720359 2025-07-01T16:15:12Z Bocardodarapti 289675 New resource with "{{MDLD{{{opt|}}}|Start=linear isomorphism| |See= |Target=Linear mapping/Field/Isomorphism/Definition }}" 2720359 wikitext text/x-wiki {{MDLD{{{opt|}}}|Start=linear isomorphism| |See= |Target=Linear mapping/Field/Isomorphism/Definition }} hzdxqpw04oi66jgqthpq2mpv146d1k1 0 322384 2720360 2025-07-01T16:15:26Z Bocardodarapti 289675 New resource with "{{MDLD{{{opt|}}}|Start=vector space isomorphism| |See= |Target=Linear mapping/Field/Isomorphism/Definition }}" 2720360 wikitext text/x-wiki {{MDLD{{{opt|}}}|Start=vector space isomorphism| |See= |Target=Linear mapping/Field/Isomorphism/Definition }} b5avai562j3w0hyq3k6e6f54qm2kozb 10 322385 2720361 2025-07-01T16:57:39Z Atcovi 276019 Create. 2720361 wikitext text/x-wiki [[Image:Pictogram voting wait orange.svg|17px|link=|alt=]] '''{{{1|In progress}}}...'''<!--template:in progress--><noinclude> {{documentation}} [[Category:Image insertion templates|{{PAGENAME}}]] </noinclude> ro0u8xru0hmfhu5n2yb7fsa8iyllff9 2 322386 2720362 2025-07-01T16:59:49Z Atcovi 276019 Create. 2720362 wikitext text/x-wiki == About == Aaqib Azeez (User:Atcovi) – undergraduate psychology researcher & data analyst in training. Portfolio includes statistical projects using SPSS, SQL, R, and Excel, aimed at real-world problems in clinical psychology and business analytics. == Skills == * SPSS (syntax & GUI) {{Done}} * SQL (PostgreSQL / SQLite) {{In progress}} * Excel (pivot tables, data cleaning) {{In progress}} * R {{In progress}} == Portfolio Projects == * [[/Project 1 – CBT vs Medication Study]] * [[User:Atcovi/Data Analyst Portfolio/Project 2 – business analytics project|/Project 2 – TBD]] * ... [[Category:Atcovi's Work]] jvetcbwm80i0qly73qo8zwjd21k9nu3 2720363 2720362 2025-07-01T17:11:15Z Atcovi 276019 for future start 2720363 wikitext text/x-wiki == About == Aaqib Azeez (User:Atcovi) – undergraduate psychology researcher & data analyst in training. Portfolio includes statistical projects using SPSS, SQL, R, and Excel, aimed at real-world problems in clinical psychology and business analytics. == Skills == * SPSS (syntax & GUI) {{Done}} * SQL (PostgreSQL / SQLite) {{In progress}} * Excel (pivot tables, data cleaning) {{In progress}} * R {{In progress}} == Online Course Progress == https://www.datasciencehive.com/data-analyst-path == Portfolio Projects == * [[/Project 1 – CBT vs Medication Study]] * [[User:Atcovi/Data Analyst Portfolio/Project 2 – business analytics project|/Project 2 – TBD]] * ... [[Category:Atcovi's Work]] 8w8laoqbnn86sym95qu5y5zuz6xfgzj 2720373 2720363 2025-07-01T22:44:36Z Atcovi 276019 /* Skills */ 2720373 wikitext text/x-wiki == About == Aaqib Azeez (User:Atcovi) – undergraduate psychology researcher & data analyst in training. Portfolio includes statistical projects using SPSS, SQL, R, and Excel, aimed at real-world problems in clinical psychology and business analytics. == Skills == * SPSS (syntax & GUI) {{Done}} * SQL (PostgreSQL / SQLite) {{In progress}} * Excel (pivot tables, data cleaning; complete mastery) {{In progress}} * R {{In progress}} == Online Course Progress == https://www.datasciencehive.com/data-analyst-path == Portfolio Projects == * [[/Project 1 – CBT vs Medication Study]] * [[User:Atcovi/Data Analyst Portfolio/Project 2 – business analytics project|/Project 2 – TBD]] * ... [[Category:Atcovi's Work]] hvtad2pnsjbswr4rn0feyo2y2q0q8gj 2720377 2720373 2025-07-02T00:18:42Z Atcovi 276019 /* Skills */ +Tableu; per https://www.youtube.com/watch?v=dJA7k58zlA8 2720377 wikitext text/x-wiki == About == Aaqib Azeez (User:Atcovi) – undergraduate psychology researcher & data analyst in training. Portfolio includes statistical projects using SPSS, SQL, R, and Excel, aimed at real-world problems in clinical psychology and business analytics. == Skills == * SPSS (syntax & GUI) {{Done}} * SQL (PostgreSQL / SQLite) {{In progress}} * Excel (pivot tables, data cleaning; complete mastery) {{In progress}} * Tableu {{In progress}} * R {{In progress}} == Online Course Progress == https://www.datasciencehive.com/data-analyst-path == Portfolio Projects == * [[/Project 1 – CBT vs Medication Study]] * [[User:Atcovi/Data Analyst Portfolio/Project 2 – business analytics project|/Project 2 – TBD]] * ... [[Category:Atcovi's Work]] nu3p343v0j9q7xkxiyu9esh7d0peznn 2720378 2720377 2025-07-02T00:26:25Z Atcovi 276019 /* Skills */ 2720378 wikitext text/x-wiki == About == Aaqib Azeez (User:Atcovi) – undergraduate psychology researcher & data analyst in training. Portfolio includes statistical projects using SPSS, SQL, R, and Excel, aimed at real-world problems in clinical psychology and business analytics. == Skills == * SPSS (syntax & GUI) {{Done}} * SQL (select, where, group by, having, joins, window functions) {{In progress}} * Excel (pivot tables, VLOOKUP, data cleaning, visualizations; complete mastery) {{In progress}} * Tableu (BI tool; connect to data, add data sources, create visualizations) {{In progress}} * R {{In progress}} == Online Course Progress == https://www.datasciencehive.com/data-analyst-path == Portfolio Projects == * [[/Project 1 – CBT vs Medication Study]] * [[User:Atcovi/Data Analyst Portfolio/Project 2 – business analytics project|/Project 2 – TBD]] * ... [[Category:Atcovi's Work]] b86yhpmpsiomsnenbued784800bzk5t 2720379 2720378 2025-07-02T00:40:31Z Atcovi 276019 /* Portfolio Projects */ 2720379 wikitext text/x-wiki == About == Aaqib Azeez (User:Atcovi) – undergraduate psychology researcher & data analyst in training. Portfolio includes statistical projects using SPSS, SQL, R, and Excel, aimed at real-world problems in clinical psychology and business analytics. == Skills == * SPSS (syntax & GUI) {{Done}} * SQL (select, where, group by, having, joins, window functions) {{In progress}} * Excel (pivot tables, VLOOKUP, data cleaning, visualizations; complete mastery) {{In progress}} * Tableu (BI tool; connect to data, add data sources, create visualizations) {{In progress}} * R {{In progress}} == Online Course Progress == https://www.datasciencehive.com/data-analyst-path == Portfolio Projects == '''Aim''': Projects with combinations of different skills, an analysis that meaningfully solves a problem and tells a story. * [[/Project 1]] * [[User:Atcovi/Data Analyst Portfolio/Project 2 – business analytics project|/Project 2]] * ... [[Category:Atcovi's Work]] 7iduzilry72afy75gyizlli3dg79xyb 0 322387 2720365 2025-07-01T19:55:22Z Stevesuny 294667 New resource with "This is clearly a work in progress, and to the extent that this should be a conversation, we can have" 2720365 wikitext text/x-wiki This is clearly a work in progress, and to the extent that this should be a conversation, we can have rtypeccuxcjdexkardunn9fpo6cjujk 2720366 2720365 2025-07-01T19:59:31Z Stevesuny 294667 2720366 wikitext text/x-wiki This is clearly a work in progress, and to the extent that this should be a conversation, we can have it in the Discuss section of this page. But here I'll lay out an initial vision of the process I imagine. End goal: A manuscript approved by participating authors that can be published on an open-source platforms such as arxiv, and the Poly AIX web site, as a working paper. The manuscript will be generated from this wikiversity collection of pages. Authors will include at least two categories: # Participating authors. Those who install open web ui, and share their use case / participant story with us, in dnxyv5iswfu1rwoe9tozbilxw76glan 2720367 2720366 2025-07-01T20:05:25Z Stevesuny 294667 added content 2720367 wikitext text/x-wiki This is clearly a work in progress, and to the extent that this should be a conversation, we can have it in the Discuss section of this page. But here I'll lay out an initial vision of the process I imagine. End goal: A manuscript approved by participating authors that can be published on an open-source platforms such as arxiv, and the Poly AIX web site, as a working paper. The manuscript will be generated from this wikiversity collection of pages. Authors will include at least two categories: # Participating authors. Those who install open web ui, and share their use case / participant story with us, in "Use Cases of Open WebUI from participants in June Working Group". They will need some sort of participation agreement. # Contributing authors. Those who contribute any content to sections other than "Use Cases of Open WebUI from participants in June Working Group". They will need some sort of agreement as well, including references, edits, etc. # Senior authors. Probably, the project directors (Steve Schneider & Asela Abeyaa), and others who write significant chunks of sections. This is an open invitation to anyone to nominate themselves to be primary author of section. 5rwxcnevvfgbr9szaypjtynw1qbttes 2720369 2720367 2025-07-01T20:08:38Z Stevesuny 294667 2720369 wikitext text/x-wiki This process for writing a collaborative paper is, itself, its own work in progress, and to the extent that this should be a conversation, we can have it in the Discuss section of this page. But here I'll lay out an initial vision of the process I imagine. End goal: A manuscript approved by participating authors that can be published on an open-source platforms such as arxiv, and the Poly AIX web site, as a working paper. The manuscript will be generated from this wikiversity collection of pages. Authors will include at least two categories: # Participating authors. Those who install open web ui, and share their use case / participant story with us, in "Use Cases of Open WebUI from participants in June Working Group". They will need some sort of participation agreement. # Contributing authors. Those who contribute any content to sections other than "Use Cases of Open WebUI from participants in June Working Group". They will need some sort of agreement as well, including references, edits, etc. # Senior authors. Probably, the project directors (Steve Schneider & Asela Abeyaa), and others who write significant chunks of sections. This is an open invitation to anyone to nominate themselves to be primary author of section. qvrkog3ezhuvrphv3p23whgphmj79wi 2720371 2720369 2025-07-01T20:09:57Z Stevesuny 294667 added link to talk page 2720371 wikitext text/x-wiki This process for writing a collaborative paper is, itself, its own work in progress, and to the extent that this should be a conversation, we can have it in the [[Talk:AIXworkbench/Papers/Building-the-Workbench/Paper-writing-process|Discuss section of this page]]. But here I'll lay out an initial vision of the process I imagine. End goal: A manuscript approved by participating authors that can be published on an open-source platforms such as arxiv, and the Poly AIX web site, as a working paper. The manuscript will be generated from this wikiversity collection of pages. Authors will include at least two categories: # Participating authors. Those who install open web ui, and share their use case / participant story with us, in "Use Cases of Open WebUI from participants in June Working Group". They will need some sort of participation agreement. # Contributing authors. Those who contribute any content to sections other than "Use Cases of Open WebUI from participants in June Working Group". They will need some sort of agreement as well, including references, edits, etc. # Senior authors. Probably, the project directors (Steve Schneider & Asela Abeyaa), and others who write significant chunks of sections. This is an open invitation to anyone to nominate themselves to be primary author of section. 0xz9qqzhlg2hihsg9xe91mw2y98l013 1 322388 2720370 2025-07-01T20:08:59Z Stevesuny 294667 /* What do you think? */ new section 2720370 wikitext text/x-wiki == What do you think? == Interested in writing collaboratively in wikiversity? [[User:Stevesuny|Stevesuny]] ([[User talk:Stevesuny|discuss]] • [[Special:Contributions/Stevesuny|contribs]]) 20:08, 1 July 2025 (UTC) bl34lyh8anytabvjwmzd7kzq46lrvid 1 322390 2720411 2025-07-02T11:40:47Z 175.176.64.180 /* Shabu shouldering foil iron melting crystal support government police department and mellittar */ new section 2720411 wikitext text/x-wiki == Shabu shouldering foil iron melting crystal support government police department and mellittar == shabu shouldering foil iron melting crystal supported police department and government [[Special:Contributions/175.176.64.180|175.176.64.180]] ([[User talk:175.176.64.180|discuss]]) 11:40, 2 July 2025 (UTC) lv8d4i7qx423zrtloekiz7div3ecck6 2720412 2720411 2025-07-02T11:41:55Z 175.176.64.180 /* Shabu shouldering foil iron melting crystal support government police department and mellittar */ Reply 2720412 wikitext text/x-wiki == Shabu shouldering foil iron melting crystal support government police department and mellittar == shabu shouldering foil iron melting crystal supported police department and government [[Special:Contributions/175.176.64.180|175.176.64.180]] ([[User talk:175.176.64.180|discuss]]) 11:40, 2 July 2025 (UTC) :shabu shouldering foil iron melting crystal supported police department and mellittar [[Special:Contributions/175.176.64.180|175.176.64.180]] ([[User talk:175.176.64.180|discuss]]) 11:41, 2 July 2025 (UTC) 9yfn5a1rd9r9gnvz60k32gs73z5bhl5 2720413 2720412 2025-07-02T11:43:43Z 175.176.64.180 /* Shabu shouldering foil iron melting crystal support government police department and mellittar */ Reply 2720413 wikitext text/x-wiki == Shabu shouldering foil iron melting crystal support government police department and mellittar == shabu shouldering foil iron melting crystal supported police department and government [[Special:Contributions/175.176.64.180|175.176.64.180]] ([[User talk:175.176.64.180|discuss]]) 11:40, 2 July 2025 (UTC) :shabu shouldering foil iron melting crystal supported police department and mellittar [[Special:Contributions/175.176.64.180|175.176.64.180]] ([[User talk:175.176.64.180|discuss]]) 11:41, 2 July 2025 (UTC) :UtC validation for reconcellation approve to drugs shabu shouldering foil iron melting crystal supported police department and mellittar [[Special:Contributions/175.176.64.180|175.176.64.180]] ([[User talk:175.176.64.180|discuss]]) 11:43, 2 July 2025 (UTC) g2mhpo75xus3zna9nz1nlt8mcfqzpgv 2720419 2720413 2025-07-02T11:51:36Z MathXplore 2888076 Reset talk page with [[:w:simple:User:DannyS712/Reset talk|reset talk]] (version 1.1) 2720419 wikitext text/x-wiki {{Talk header}} 6ujz0t3lkt6jsf7d1r360l6l7wj3njb