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#homology — Public Fediverse posts

Live and recent posts from across the Fediverse tagged #homology, aggregated by home.social.

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  1. Yuriy Karetin @[email protected]

    MVspa_ Stochastic processes
    Стохастические процессы, Випадкові процеси
    #Stochastic processes
    #Стохастическиепроцессы, #Випадковіпроцеси
    t.me/scilib_yura15cbx/230

    MVsa Statistics and applications
    Статистика та додатки, Статистика и приложения
    #Statistics
    t.me/scilib_yura15cbx/229

    EM_ Mechanics of elastic materials
    Механіка пружних матеріалів, Механика упругих материалов
    t.me/scilib_yura15cbx/228

    MPd_ Dynamical systems
    Динамические системы, Динамічні системи
    #Dynamical systems
    t.me/scilib_yura15cbx/227

    MNw_ Wavelets, signal processing
    Вейвлети, обробка сигналів, Вейвлеты, обработка сигналов
    #Wavelets, #signal processing
    t.me/scilib_yura15cbx/226

    MNs_ Simulations of physics
    Физические симуляции
    t.me/scilib_yura15cbx/225

    MNl_ Numerical linear algebra
    Числова лінійна алгебра, Численная линейная алгебра
    t.me/scilib_yura15cbx/224

    MNf_ Finite elements
    Конечные элементы, Скінченні елементи
    t.me/scilib_yura15cbx/223

    MNd_ Numerical calculus
    t.me/scilib_yura15cbx/222

    MDgt_ General topology
    #topology
    Общая топология, Загальна топологія
    t.me/scilib_yura15cbx/221

    MDdg_ Differential geometry
    Диференціальна геометрія, Дифференциальная геометрия
    t.me/scilib_yura15cbx/220

    MDat_ Algebraic and differential topology
    Алгебраическая и дифференциальная топология, Алгебраїчна та диференціальна топологія
    t.me/scilib_yura15cbx/219

    MCv_ Variational calculus
    Варіаційне числення, Вариационное исчисление
    t.me/scilib_yura15cbx/218

    MCta_ Tensor calculus, forms
    Тензорное исчисление, формы, Тензорне числення, форми
    t.me/scilib_yura15cbx/217

    MCsf_ Special functions
    Спеціальні функції, Специальные функции
    t.me/scilib_yura15cbx/216

    MCf_ Functional analysis
    Функциональный анализ, Функціональний аналіз
    t.me/scilib_yura15cbx/215

    MCet_ Elementary calculus textbooks
    Підручники з елементарного числення, Учебники по элементарному исчислению
    t.me/scilib_yura15cbx/214

    MCde_ Differential equations
    Дифференциальные уравнения, Диференціальні рівняння
    #Differential equations
    t.me/scilib_yura15cbx/213

    MCcf_ Continued fractions
    Суцільні дроби, Непрерывные дроби
    t.me/scilib_yura15cbx/212

    MCc_ Complex variable
    Комплексная переменная, Комплексна змінна
    t.me/scilib_yura15cbx/211

    MCat_ Advanced calculus
    t.me/scilib_yura15cbx/210

    Asymptotics, perturbations
    Асимптотика, збурення,
    Асимптотика, возмущения
    #Asymptotics, #perturbations
    #Асимптотика, #збурення,
    #Асимптотика, #возмущения
    t.me/scilib_yura15cbx/209

    Group theory, Теория групп, Теорія груп
    #Group theory, #Теориягрупп, #Теоріягруп
    t.me/scilib_yura15cbx/208

    Algebra textbooks,
    Підручники з алгебри,
    Учебники по алгебре
    t.me/scilib_yura15cbx/207

    Set theory,
    Теория множеств, Теорія множин
    #Set theory,
    #Теория множеств,
    t.me/scilib_yura15cbx/206

    Representation theory
    Теорія репрезентації, Теория представлений
    t.me/scilib_yura15cbx/205

    Quantum groups
    #Quantum groups
    Квантовые группы, Квантові групи
    t.me/scilib_yura15cbx/204

    Mathematical logic
    #Mathematical logic
    Математична логіка, Математическая логика
    t.me/scilib_yura15cbx/203

    Linear algebra
    #Linear algebra
    Линейная алгебра, Лінійна алгебра
    t.me/scilib_yura15cbx/202

    Homology, Гомологія, Гомология
    #Homology, #Гомологія, #Гомология
    t.me/scilib_yura15cbx/201

    Algebraic geometry
    Алгебраическая геометрия, Алгебраїчна геометрія
    t.me/scilib_yura15cbx/200

    Algebraic geometry
    #Algebraic geometry
    Алгебраическая геометрия, Алгебраїчна геометрія
    t.me/scilib_yura15cbx/200

    Finite groups
    Скінченні групи, Конечные группы
    t.me/scilib_yura15cbx/199

    Differential algebra
    #Differential algebra
    Дифференциальная алгебра, Диференціальна алгебра
    t.me/scilib_yura15cbx/198

    Category theory
    Теорія категорій, Теория категорий

    #statistics #topology #homology #wavelets #теория #perturbations
  2. Yuriy Karetin @[email protected]

    MVspa_ Stochastic processes
    Стохастические процессы, Випадкові процеси
    #Stochastic processes
    #Стохастическиепроцессы, #Випадковіпроцеси
    t.me/scilib_yura15cbx/230

    MVsa Statistics and applications
    Статистика та додатки, Статистика и приложения
    #Statistics
    t.me/scilib_yura15cbx/229

    EM_ Mechanics of elastic materials
    Механіка пружних матеріалів, Механика упругих материалов
    t.me/scilib_yura15cbx/228

    MPd_ Dynamical systems
    Динамические системы, Динамічні системи
    #Dynamical systems
    t.me/scilib_yura15cbx/227

    MNw_ Wavelets, signal processing
    Вейвлети, обробка сигналів, Вейвлеты, обработка сигналов
    #Wavelets, #signal processing
    t.me/scilib_yura15cbx/226

    MNs_ Simulations of physics
    Физические симуляции
    t.me/scilib_yura15cbx/225

    MNl_ Numerical linear algebra
    Числова лінійна алгебра, Численная линейная алгебра
    t.me/scilib_yura15cbx/224

    MNf_ Finite elements
    Конечные элементы, Скінченні елементи
    t.me/scilib_yura15cbx/223

    MNd_ Numerical calculus
    t.me/scilib_yura15cbx/222

    MDgt_ General topology
    #topology
    Общая топология, Загальна топологія
    t.me/scilib_yura15cbx/221

    MDdg_ Differential geometry
    Диференціальна геометрія, Дифференциальная геометрия
    t.me/scilib_yura15cbx/220

    MDat_ Algebraic and differential topology
    Алгебраическая и дифференциальная топология, Алгебраїчна та диференціальна топологія
    t.me/scilib_yura15cbx/219

    MCv_ Variational calculus
    Варіаційне числення, Вариационное исчисление
    t.me/scilib_yura15cbx/218

    MCta_ Tensor calculus, forms
    Тензорное исчисление, формы, Тензорне числення, форми
    t.me/scilib_yura15cbx/217

    MCsf_ Special functions
    Спеціальні функції, Специальные функции
    t.me/scilib_yura15cbx/216

    MCf_ Functional analysis
    Функциональный анализ, Функціональний аналіз
    t.me/scilib_yura15cbx/215

    MCet_ Elementary calculus textbooks
    Підручники з елементарного числення, Учебники по элементарному исчислению
    t.me/scilib_yura15cbx/214

    MCde_ Differential equations
    Дифференциальные уравнения, Диференціальні рівняння
    #Differential equations
    t.me/scilib_yura15cbx/213

    MCcf_ Continued fractions
    Суцільні дроби, Непрерывные дроби
    t.me/scilib_yura15cbx/212

    MCc_ Complex variable
    Комплексная переменная, Комплексна змінна
    t.me/scilib_yura15cbx/211

    MCat_ Advanced calculus
    t.me/scilib_yura15cbx/210

    Asymptotics, perturbations
    Асимптотика, збурення,
    Асимптотика, возмущения
    #Asymptotics, #perturbations
    #Асимптотика, #збурення,
    #Асимптотика, #возмущения
    t.me/scilib_yura15cbx/209

    Group theory, Теория групп, Теорія груп
    #Group theory, #Теориягрупп, #Теоріягруп
    t.me/scilib_yura15cbx/208

    Algebra textbooks,
    Підручники з алгебри,
    Учебники по алгебре
    t.me/scilib_yura15cbx/207

    Set theory,
    Теория множеств, Теорія множин
    #Set theory,
    #Теория множеств,
    t.me/scilib_yura15cbx/206

    Representation theory
    Теорія репрезентації, Теория представлений
    t.me/scilib_yura15cbx/205

    Quantum groups
    #Quantum groups
    Квантовые группы, Квантові групи
    t.me/scilib_yura15cbx/204

    Mathematical logic
    #Mathematical logic
    Математична логіка, Математическая логика
    t.me/scilib_yura15cbx/203

    Linear algebra
    #Linear algebra
    Линейная алгебра, Лінійна алгебра
    t.me/scilib_yura15cbx/202

    Homology, Гомологія, Гомология
    #Homology, #Гомологія, #Гомология
    t.me/scilib_yura15cbx/201

    Algebraic geometry
    Алгебраическая геометрия, Алгебраїчна геометрія
    t.me/scilib_yura15cbx/200

    Algebraic geometry
    #Algebraic geometry
    Алгебраическая геометрия, Алгебраїчна геометрія
    t.me/scilib_yura15cbx/200

    Finite groups
    Скінченні групи, Конечные группы
    t.me/scilib_yura15cbx/199

    Differential algebra
    #Differential algebra
    Дифференциальная алгебра, Диференціальна алгебра
    t.me/scilib_yura15cbx/198

    Category theory
    Теорія категорій, Теория категорий

    #statistics #topology #homology #wavelets #теория #perturbations
  3. Papers We Love @[email protected]

    Gershom Bazerman on "Homological Computations for Term Rewriting Systems" [PWL NYC] (2017)

    youtube.com/watch?v=WdawrT-6Qzk

    #Homology #KnuthBendixalgorithm #termrewriting

    #homology #knuthbendixalgorithm #termrewriting
  4. Knowledge Zone @[email protected]

    #KnowledgeBit: In biology, #Homology is similarity due to shared ancestry between a pair of structures or genes in different taxa.

    A common example of homologous structures is the forelimbs of vertebrates, where the wings of bats and birds, the arms of primates, the front flippers of whales and the forelegs of four-legged vertebrates like dogs and crocodiles are all derived from the same ancestral tetrapod structure.

    knowledgezone.co.in/kbits/6303

    #knowledgebit #homology
  5. Ehud @[email protected]

    The main point ofc is the notion of #homology being proposed. #evolution #philbio

    RE: https://bsky.app/profile/did:plc:i7lv3abpcflafgtnc3nf5vlb/post/3m4b4pjnf3s24

    #homology #evolution #philbio
  6. Oscar Cunningham @[email protected]

    #Mathober #Mathober2025

    The prompt for day 4 was 'Strongly'. In linear algebra, the dual of a vector space V is the space V* of linear maps from V to the field. There's a natural inclusion 𝑉⊗𝑉* → Hom(𝑉,𝑉) and we call V *strongly* dualisable if and only if this map has an inverse.

    The strongly dualisable vector spaces are precisely the finite dimensional ones. This is useful because it allows us to prove statements about finite dimensional vector spaces in a basis-free way. For example the trace is easy to define for strongly dualisable objects without mentioning any basis.

    The same approach works for modules over a commutative ring. The strongly dualisable objects are precisely the finitely-generated projective modules. For example for ℤ this includes free modules like ℤ¹⁰ but not quotients like ℤ/12ℤ.

    But if we work in higher algebra something interesting happens! In the category of chain complexes a chain is strongly dualisable if and only if it has finitely many nonzero modules, all of which are themselves strongly dualisable.

    The ∞-category of chain complexes include the category of modules by sending V to … → 0 → 0 → 𝑉. But the chain complex … → 0 → 0 → ℤ/12ℤ is equivalent to … → 0 → ℤ → ℤ, which is dualisable!

    So using ∞-categories we can extend the methods of finite-dimensional linear algebra to modules that were previously out of reach!

    #Math #Maths #Mathematics #CategoryTheory #Homology #HomologyTheory

    #homologytheory #homology #categorytheory #mathematics #maths #math
  7. Knowledge Zone @[email protected]

    #DidYouKnow: In biology, #Homology is similarity due to shared ancestry between a pair of structures or genes in different taxa.

    A common example of homologous structures is the forelimbs of vertebrates, where the wings of bats and birds, the arms of primates, the front flippers of whales and the forelegs of four-legged vertebrates like dogs and crocodiles are all derived from the same ancestral tetrapod structure.

    knowledgezone.co.in/kbits/6303

    #didyouknow #homology
  8. CellBioNews @[email protected]

    #Bacterial species study challenges assumption that #structural similarity predicts #protein behavior

    #Escherichia #Mycobacterium #cAMP #CRP #Allosteric #homology

    phys.org/news/2025-02-bacteria

    #bacterial #structural #protein #escherichia #mycobacterium #camp
  9. Knowledge Zone @[email protected]

    #DidYouKnow: In biology, #Homology is similarity due to shared ancestry between a pair of structures or genes in different taxa.

    A common example of homologous structures is the forelimbs of vertebrates, where the wings of bats and birds, the arms of primates, the front flippers of whales and the forelegs of four-legged vertebrates like dogs and crocodiles are all derived from the same ancestral tetrapod structure.

    knowledgezone.co.in/kbits/6303

    #homology #didyouknow
  10. katch wreck @[email protected]

    "Contrary to the model, we found that the double helix was not unwound even a single turn during search for #sequence homology, but rather was unwound only after the homologous sequence was recognized... The search for homologous sequence with homologous ssDNA without dsDNA-strand separation does not generate stress within the dsDNA; this would be an advantage for dsDNA to express #homology-dependent functions in vivo and also in vitro"

    #DNA

    academic.oup.com/nar/advance-a

    #sequence #homology #dna
  11. Paolo Caressa @[email protected]

    Christmas tree with non trivial #homology...

    #homology
  12. Atheism Actually @[email protected]

    -- Is Homology REALLY Evidence for Evolution? (yes) | Reacteria --
    (from Forrest Valkai)
    youtube.com/watch?v=hDo3a8Z55l

    #homology #evolution #science #creationism #biology #commonDescent

    #commondescent #biology #creationism #science #evolution #homology
  13. Marc Robinson-Rechavi @[email protected]

    Taking the opportunity to advertise that we have an ontology of #homology related concepts since 2010, which tries to formalise many of the related concepts, with references and relations between the concepts
    bioportal.bioontology.org/onto
    doi.org/10.1016/j.tig.2009.12.
    #SMBE2023

    #homology #smbe2023
  14. Bgee database @[email protected]

    These observations of conserved homologous expression are easy to reproduce! Go to a gene page, click "orthologs", and chose a taxonomic level, here Theria:
    TLK1 bgee.org/gene/ENSG00000198586/ -> bgee.org/analysis/expr-compari
    HAT1 bgee.org/analysis/expr-compari
    #bioinformatics #biocuration #evodevo #ortholog #homology

    #bioinformatics #biocuration #evodevo #ortholog #homology
  15. JMLR @[email protected]

    'Outlier-Robust Subsampling Techniques for Persistent Homology', by Bernadette J. Stolz.

    jmlr.org/papers/v24/21-1526.ht

    #homology #outliers #topological

    #homology #outliers #topological
  16. JMLR @[email protected]

    'Intrinsic Persistent Homology via Density-based Metric Learning', by Ximena Fernández, Eugenio Borghini, Gabriel Mindlin, Pablo Groisman.

    jmlr.org/papers/v24/21-1044.ht

    #manifold #homology #topological

    #manifold #homology #topological
  17. Knowledge Zone @[email protected]

    #DidYouKnow: In biology, #Homology is similarity due to shared ancestry between a pair of structures or genes in different taxa.

    A common example of homologous structures is the forelimbs of vertebrates, where the wings of bats and birds, the arms of primates, the front flippers of whales and the forelegs of four-legged vertebrates like dogs and crocodiles are all derived from the same ancestral tetrapod structure.

    knowledgezone.co.in/kbits/6303

    #homology #didyouknow
  18. Julien Tierny @julientierny

    Two p-cycles a and b are "homologous" (i.e. belong to the same class) if there exists a (p+1)-chain c, such that b = a + ∂c (mod-2 sum)
    👇
    arxiv.org/abs/2206.13932

    Funded by the European Research Council (ERC) (project TORI, erc-tori.github.io/)

    #homology #topologicaldataanalysis #topologytoolkit #persistenthomology #visualization #datascience
  19. Refurio Anachro @[email protected]

    #Matroid s are a specific kind of sets that contain other sets, but for any set they contain, they also need to contain its subsets. For more look here:

    en.wikipedia.org/wiki/Matroid

    Looking oddly specific, they're in fact an interesting structure which pops out in the study of many combinatorial subjects like graph theory, and, as I just learned, #homology!

    #homology #matroid
  20. Refurio Anachro @[email protected]

    Well, actually, it’s a bit annoying that \(\delta\) returns lots of n-1 simplices for any n-simplex: it is a multifunction. If we instead map the other way around, from the boundary to the inside, we simply get a function! And that’s called cohomology, and is what the cool kids do all the time!

    4/end

    #homology #cohomology

    #cohomology #homology
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