#topology — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #topology, aggregated by home.social.
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Although those interested in measure theory here are a set of measure zero, I have nonetheless written an article on the subject. Along with a bit of inappropriate humor, I have careened off of continuity, equivalence classes, orderings, lattices and semilattices, order topologies, and metrics. Oh, and the subject is change of variable.
https://www.skewray.com/articles/continuity-induced-metrics-on-measures
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The nuclear pore complex (7R5J & 7R5K) – one of the largest molecular machines in biology.
The nuclear pore complex is the gatekeeper of the cell nucleus – controlling everything that enters or leaves. We captured it in two states: open (dilated) and closed (constricted).
961665 quantum records
#StructuralBiology #Biophysics #Bioinformatics #Topology #InformationTheory #DNAFolding #ComputationalBiology #ComplexSystems #Genomics #OpenScience #EXXOGEN
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MVspa_ Stochastic processes
Стохастические процессы, Випадкові процеси
#Stochastic processes
#Стохастическиепроцессы, #Випадковіпроцеси
t.me/scilib_yura15cbx/230MVsa Statistics and applications
Статистика та додатки, Статистика и приложения
#Statistics
t.me/scilib_yura15cbx/229EM_ Mechanics of elastic materials
Механіка пружних матеріалів, Механика упругих материалов
t.me/scilib_yura15cbx/228MPd_ Dynamical systems
Динамические системы, Динамічні системи
#Dynamical systems
t.me/scilib_yura15cbx/227MNw_ Wavelets, signal processing
Вейвлети, обробка сигналів, Вейвлеты, обработка сигналов
#Wavelets, #signal processing
t.me/scilib_yura15cbx/226MNs_ Simulations of physics
Физические симуляции
t.me/scilib_yura15cbx/225MNl_ Numerical linear algebra
Числова лінійна алгебра, Численная линейная алгебра
t.me/scilib_yura15cbx/224MNf_ Finite elements
Конечные элементы, Скінченні елементи
t.me/scilib_yura15cbx/223MNd_ Numerical calculus
t.me/scilib_yura15cbx/222MDgt_ General topology
#topology
Общая топология, Загальна топологія
t.me/scilib_yura15cbx/221MDdg_ Differential geometry
Диференціальна геометрія, Дифференциальная геометрия
t.me/scilib_yura15cbx/220MDat_ Algebraic and differential topology
Алгебраическая и дифференциальная топология, Алгебраїчна та диференціальна топологія
t.me/scilib_yura15cbx/219MCv_ Variational calculus
Варіаційне числення, Вариационное исчисление
t.me/scilib_yura15cbx/218MCta_ Tensor calculus, forms
Тензорное исчисление, формы, Тензорне числення, форми
t.me/scilib_yura15cbx/217MCsf_ Special functions
Спеціальні функції, Специальные функции
t.me/scilib_yura15cbx/216MCf_ Functional analysis
Функциональный анализ, Функціональний аналіз
t.me/scilib_yura15cbx/215MCet_ Elementary calculus textbooks
Підручники з елементарного числення, Учебники по элементарному исчислению
t.me/scilib_yura15cbx/214MCde_ Differential equations
Дифференциальные уравнения, Диференціальні рівняння
#Differential equations
t.me/scilib_yura15cbx/213MCcf_ Continued fractions
Суцільні дроби, Непрерывные дроби
t.me/scilib_yura15cbx/212MCc_ Complex variable
Комплексная переменная, Комплексна змінна
t.me/scilib_yura15cbx/211MCat_ Advanced calculus
t.me/scilib_yura15cbx/210Asymptotics, perturbations
Асимптотика, збурення,
Асимптотика, возмущения
#Asymptotics, #perturbations
#Асимптотика, #збурення,
#Асимптотика, #возмущения
t.me/scilib_yura15cbx/209Group theory, Теория групп, Теорія груп
#Group theory, #Теориягрупп, #Теоріягруп
t.me/scilib_yura15cbx/208Algebra textbooks,
Підручники з алгебри,
Учебники по алгебре
t.me/scilib_yura15cbx/207Set theory,
Теория множеств, Теорія множин
#Set theory,
#Теория множеств,
t.me/scilib_yura15cbx/206Representation theory
Теорія репрезентації, Теория представлений
t.me/scilib_yura15cbx/205Quantum groups
#Quantum groups
Квантовые группы, Квантові групи
t.me/scilib_yura15cbx/204Mathematical logic
#Mathematical logic
Математична логіка, Математическая логика
t.me/scilib_yura15cbx/203Linear algebra
#Linear algebra
Линейная алгебра, Лінійна алгебра
t.me/scilib_yura15cbx/202Homology, Гомологія, Гомология
#Homology, #Гомологія, #Гомология
t.me/scilib_yura15cbx/201Algebraic geometry
Алгебраическая геометрия, Алгебраїчна геометрія
t.me/scilib_yura15cbx/200Algebraic geometry
#Algebraic geometry
Алгебраическая геометрия, Алгебраїчна геометрія
t.me/scilib_yura15cbx/200Finite groups
Скінченні групи, Конечные группы
t.me/scilib_yura15cbx/199Differential algebra
#Differential algebra
Дифференциальная алгебра, Диференціальна алгебра
t.me/scilib_yura15cbx/198Category theory
Теорія категорій, Теория категорий -
MVspa_ Stochastic processes
Стохастические процессы, Випадкові процеси
#Stochastic processes
#Стохастическиепроцессы, #Випадковіпроцеси
t.me/scilib_yura15cbx/230MVsa Statistics and applications
Статистика та додатки, Статистика и приложения
#Statistics
t.me/scilib_yura15cbx/229EM_ Mechanics of elastic materials
Механіка пружних матеріалів, Механика упругих материалов
t.me/scilib_yura15cbx/228MPd_ Dynamical systems
Динамические системы, Динамічні системи
#Dynamical systems
t.me/scilib_yura15cbx/227MNw_ Wavelets, signal processing
Вейвлети, обробка сигналів, Вейвлеты, обработка сигналов
#Wavelets, #signal processing
t.me/scilib_yura15cbx/226MNs_ Simulations of physics
Физические симуляции
t.me/scilib_yura15cbx/225MNl_ Numerical linear algebra
Числова лінійна алгебра, Численная линейная алгебра
t.me/scilib_yura15cbx/224MNf_ Finite elements
Конечные элементы, Скінченні елементи
t.me/scilib_yura15cbx/223MNd_ Numerical calculus
t.me/scilib_yura15cbx/222MDgt_ General topology
#topology
Общая топология, Загальна топологія
t.me/scilib_yura15cbx/221MDdg_ Differential geometry
Диференціальна геометрія, Дифференциальная геометрия
t.me/scilib_yura15cbx/220MDat_ Algebraic and differential topology
Алгебраическая и дифференциальная топология, Алгебраїчна та диференціальна топологія
t.me/scilib_yura15cbx/219MCv_ Variational calculus
Варіаційне числення, Вариационное исчисление
t.me/scilib_yura15cbx/218MCta_ Tensor calculus, forms
Тензорное исчисление, формы, Тензорне числення, форми
t.me/scilib_yura15cbx/217MCsf_ Special functions
Спеціальні функції, Специальные функции
t.me/scilib_yura15cbx/216MCf_ Functional analysis
Функциональный анализ, Функціональний аналіз
t.me/scilib_yura15cbx/215MCet_ Elementary calculus textbooks
Підручники з елементарного числення, Учебники по элементарному исчислению
t.me/scilib_yura15cbx/214MCde_ Differential equations
Дифференциальные уравнения, Диференціальні рівняння
#Differential equations
t.me/scilib_yura15cbx/213MCcf_ Continued fractions
Суцільні дроби, Непрерывные дроби
t.me/scilib_yura15cbx/212MCc_ Complex variable
Комплексная переменная, Комплексна змінна
t.me/scilib_yura15cbx/211MCat_ Advanced calculus
t.me/scilib_yura15cbx/210Asymptotics, perturbations
Асимптотика, збурення,
Асимптотика, возмущения
#Asymptotics, #perturbations
#Асимптотика, #збурення,
#Асимптотика, #возмущения
t.me/scilib_yura15cbx/209Group theory, Теория групп, Теорія груп
#Group theory, #Теориягрупп, #Теоріягруп
t.me/scilib_yura15cbx/208Algebra textbooks,
Підручники з алгебри,
Учебники по алгебре
t.me/scilib_yura15cbx/207Set theory,
Теория множеств, Теорія множин
#Set theory,
#Теория множеств,
t.me/scilib_yura15cbx/206Representation theory
Теорія репрезентації, Теория представлений
t.me/scilib_yura15cbx/205Quantum groups
#Quantum groups
Квантовые группы, Квантові групи
t.me/scilib_yura15cbx/204Mathematical logic
#Mathematical logic
Математична логіка, Математическая логика
t.me/scilib_yura15cbx/203Linear algebra
#Linear algebra
Линейная алгебра, Лінійна алгебра
t.me/scilib_yura15cbx/202Homology, Гомологія, Гомология
#Homology, #Гомологія, #Гомология
t.me/scilib_yura15cbx/201Algebraic geometry
Алгебраическая геометрия, Алгебраїчна геометрія
t.me/scilib_yura15cbx/200Algebraic geometry
#Algebraic geometry
Алгебраическая геометрия, Алгебраїчна геометрія
t.me/scilib_yura15cbx/200Finite groups
Скінченні групи, Конечные группы
t.me/scilib_yura15cbx/199Differential algebra
#Differential algebra
Дифференциальная алгебра, Диференціальна алгебра
t.me/scilib_yura15cbx/198Category theory
Теорія категорій, Теория категорий -
Probability,
теорія ймовірностей, теория вероятностей
#Probability,
#теоріяймовірностей, #теориявероятностей
t.me/scilib_yura15cbx/193Number theory
Теория чисел, Теорія чисел
#Number theory
#Теориячисел, #Теоріячисел
t.me/scilib_yura15cbx/192References, Collected works
Література, Зібрання праць,
Ссылки, Собрание сочинений
t.me/scilib_yura15cbx/190Symmetry and groups
Симметрия и группы,
Симетрія і групи
#Symmetry
t.me/scilib_yura15cbx/189Philosophy of mathematics
Філософія математики, Философия математики
t.me/scilib_yura15cbx/188Mathematical physics
Математическая физика, Математична фізика
#Mathematical physics
#Математическаяфизика, #Математичнафізика
t.me/scilib_yura15cbx/187Optimization and control
Оптимізація та контроль, Оптимизация и контроль
t.me/scilib_yura15cbx/186Optimal control
Оптимальный контроль, Оптимальний контроль
#Optimal control
#Оптимальныйконтроль, #Оптимальнийконтроль
t.me/scilib_yura15cbx/185Numerical methods
Чисельні методи, Численные методы
#Numerical methods
#Чисельніметоди, #Численныеметоды
t.me/scilib_yura15cbx/184Lecture notes
Конспекты лекций, Конспект лекцiй
t.me/scilib_yura15cbx/183Encyclopaediae, School-level
Енциклопедії, Шкільний рівень
Энциклопедии, школьный уровень
t.me/scilib_yura15cbx/182Games, game theory
Ігри, теорія ігор
Игры, теория игр
#Games, #game theory
#Ігри, ₽теоріяігор
#Игры, #теорияигр
t.me/scilib_yura15cbx/181Geometry and topology
Геометрия и топология
Геометрія і топологія
#Geometry and #topology
#Геометрия и #топология
#Геометрія і #топологія
t.me/scilib_yura15cbx/180Biography, history
Биография, история
Біографія, історія
#Biography, #history
#Биография, #история
#Біографія, #історія
t.me/scilib_yura15cbx/178Mams_ Proceedings AMS
Праці AMS, Труды АМС
t.me/scilib_yura15cbx/177Algebra, Алгебра
#Algebra, #Алгебра
t.me/scilib_yura15cbx/176Optical devices
Оптика, оптические устройства, технологии, инжинерия
#Optical devices -
While teaching a course on algebraic theories last semester I mentioned at some point that the familiar bicomplete categories Top and Poset were not algebraic, but were topological. A student asked about this later on and I found that the #Wikipedia page on «topological category» pointed to categories enriched in Top, not categories with a forgetful functor to Set which is topological. While I have lost a lot of faith in Wikipedia recently, I am pleased to report that https://en.wikipedia.org/wiki/Topological_category is now a disambiguation page.
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🏛️ Paper 5 The Fortress
Resilience Architectures and Topological Stabilization
Delaying the Velocity of Transition in Persistent Systems
Phase 5 explored:
• persistence
• leakage
• latency
• collapse
• threshold failure
Paper 5 asks the inverse question:
Why do some systems survive?
The answer proposed here is not “strength.”
It is:
• active maintenance
• adaptive geometry
• compartmentalization
• buffering
• rerouting
• and continuous energetic expenditure.
Persistence is not preserved.
Persistence is maintained.
This introduces: • the Maintenance Inequality
• the Red Queen Dynamic
• heterogeneous redundancy ($R_d$)
• buffer capacity ($C_{buffer}$)
• and geometric stabilization as an anti-collapse architecture.The accompanying VR-05 Evidence Card may be the clearest visual summary of the series.
🌿☕🏛️
#HybridMind42 #AtlasRosetta #Resilience #SystemsThinking #ComplexSystems #ScientificIllustration #Topology #BoundaryTheory #Physics #InterdisciplinaryResearch -
Differential Propositional Calculus • 10
Special Classes of Propositions (cont.)
Let’s pause at this point and get a better sense of how our special classes of propositions are structured and how they relate to propositions in general. We can do this by recruiting our visual imaginations and drawing up a sufficient budget of venn diagrams for each family of propositions. The case for 3 variables is exemplary enough for a start.
Linear Propositions
The linear propositions, may be written as sums:
One thing to keep in mind about these sums is that the values in are added “modulo 2”, that is, in such a way that
In a universe of discourse based on three boolean variables, the linear propositions take the shapes shown in Figure 8.
At the top is the venn diagram for the linear proposition of rank 3, which may be expressed by any one of the following three forms.
Next are the venn diagrams for the three linear propositions of rank 2, which may be expressed by the following three forms, respectively.
Next are the three linear propositions of rank 1, which are none other than the three basic propositions,
At the bottom is the linear proposition of rank 0, the everywhere false proposition or the constant function, which may be expressed by the form or by a simple
Resources
cc: Academia.edu • Cybernetics • Structural Modeling • Systems Science
cc: Conceptual Graphs • Laws of Form • Mathstodon • Research Gate#Amphecks #Animata #BooleanAlgebra #BooleanFunctions #CSPeirce #CactusGraphs #CategoryTheory #Change #Cybernetics #DifferentialAnalyticTuringAutomata #DifferentialCalculus #DifferentialLogic #DiscreteDynamics #EquationalInference #FunctionalLogic #GraphTheory #Hologrammautomaton #IndicatorFunctions #InquiryDrivenSystems #Leibniz #Logic #LogicalGraphs #Mathematics #MinimalNegationOperators #PropositionalCalculus #Time #Topology #Visualization
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An intriguing cover for this 2003 issue of Nature, featuring a dodecahedral space topology and this question:
Is this the shape of the Universe?
☑️ The research paper: https://nature.com/articles/nature01944
☑️ A News & Views article: https://nature.com/articles/425566a
☑️ The full issue: https://www.nature.com/nature/volumes/425/issues/6958#universe #cosmology #topology #curvature #cmb #wmap #bigbang #astronomy #astrophysics #astrodon #nature #cover #covers #naturecovers #space #science #research
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The name for the algebraic structure consisting of a set \(A\) equipped with a binary operation \(f\colon A^2\to A\) which is not assumed to be commutative, associative, etc. has an interesting history. As far as I can tell, this sort of algebra was originally known as a "groupoid", and you can find recent literature using the term in that way. However, Nicolas Bourbaki called a set with a single binary operation a "magma" in his Éléments de mathématique and this name came to be used when there might be confusion with the newer topological use of "groupoid" to mean a category whose morphisms are all invertible. A third contender is "binar". I don't know the history of this one but it seems reasonable to me.
I prefer "magma" myself. I don't know what a "lava" or a "volcano" should be nor have I had the audacity to try to name something like this in the literature. One reason I prefer "magma" is that I can talk about a set \(A\) equipped with a single \(n\)-ary operation \(f\colon A^n\to A\) as an "\(n\)-ary magma" (or just "\(n\)-magma" or even "magma").
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Hello w̶o̶r̶l̶d̶ Set-of-interconnected-self-actualising-machines!
I intend this to be somewhat of an introduction, although I do realise that it would constitute a rather bizarre greeting in real life. This won't be a personal account, by that I mean I don't intend to post personal content (i.e. about my real world identity). This isn't really for anonymity, despite admittedly being quite a shy person, I think it's more to do with not wanting to attempt a serious explanation of my context, something which I doubt is achievable through this medium. For me underrepresentation is better than misrepresentation, although I understand if people find my presentation here dishonest or unaccountable.
I'll use this account partly for listening, a sampling spoon through which to experience the soup of conversation and thought. I'll also do some tooting, I like this word, I might have said contributing, tossing new, or maybe reused, ingredients into the soup, but that gives the impression, I think, of some final objective, an endpoint. Most likely, listening will be the larger of these two parts, and at least for the short term, both parts, the whole, will occupy very little of my time. Expect sporadicity and inconsistency!
I also wanted to say something about what I am interested in, this is difficult since if I just say a lot of words then what is there to relate my meaning, my intentions, to the meaning which you understand? "Language disguises thought" - Wittgenstein. Well after much deliberation and many sleepless nights I decided to... just say a lot of words, although do bear in mind that the following list is just that, merely a collection of words that I, at the time of writing, happened to perceive as having meanings that corresponded, perhaps imperfectly, to topics that I am interested in. Interested does not necessarily mean fully-endorse/believe/would-describe-myself-as/is-knowledgeable-about.
#philosophy #absurdism #existentialism #anarchism #communism #anticapitalism #mutualaid #prefiguration #ontology #phenomenology #poststructuralism #structuralism #mathematics #chaos #topology #imagination #art #education #linguistics #literature #music #machines #networks #cybernetics #systems #sustainability #ecology #technology #sciencefiction #utopia #DavidGraeber #DavidWengrow #MurrayBookchin #NoamChomsky #PeterKropotkin #AdamCurtis #KenLoach #AlbertCamus #GillesDeleuze #JacquesDerrida #JeanPaulSartre #MarkFisher #SimoneDeBeauvoir #FranzKafka #GeorgeOrwell #PercyByssheShelley #MaryShelley #UrsulaKLeGuin