#homology — Public Fediverse posts

#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.

https://knowledgezone.co.in/kbits/63030b3ccdab15e41dd0aa7d

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

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

#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

#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.

https://knowledgezone.co.in/kbits/63030b3ccdab15e41dd0aa7d

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

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

https://phys.org/news/2025-02-bacterial-species-assumption-similarity-protein.html

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

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

https://phys.org/news/2025-02-bacterial-species-assumption-similarity-protein.html

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

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

https://phys.org/news/2025-02-bacterial-species-assumption-similarity-protein.html

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

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

https://phys.org/news/2025-02-bacterial-species-assumption-similarity-protein.html

#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.

https://knowledgezone.co.in/kbits/63030b3ccdab15e41dd0aa7d

"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

https://academic.oup.com/nar/advance-article/doi/10.1093/nar/gkad1260/7517491

Christmas tree with non trivial #homology...

-- Is Homology REALLY Evidence for Evolution? (yes) | Reacteria --
(from Forrest Valkai)
https://www.youtube.com/watch?v=hDo3a8Z55lw

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

-- Is Homology REALLY Evidence for Evolution? (yes) | Reacteria --
(from Forrest Valkai)
https://www.youtube.com/watch?v=hDo3a8Z55lw

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

-- Is Homology REALLY Evidence for Evolution? (yes) | Reacteria --
(from Forrest Valkai)
https://www.youtube.com/watch?v=hDo3a8Z55lw

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

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
https://bioportal.bioontology.org/ontologies/HOM/?p=classes&conceptid=http%3A%2F%2Fpurl.obolibrary.org%2Fobo%2FHOM_0000004
https://doi.org/10.1016/j.tig.2009.12.012
#SMBE2023

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 https://bgee.org/gene/ENSG00000198586/#orthologs -> https://bgee.org/analysis/expr-comparison?data=4a7fc4f9fba1b1e63c458881a6ca8f5b61367fd2
HAT1 https://bgee.org/analysis/expr-comparison?data=d9510c624d21931605aa16a7c378f8ede9ce4fe6
#bioinformatics #biocuration #evodevo #ortholog #homology

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

http://jmlr.org/papers/v24/21-1526.html

#homology #outliers #topological

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

http://jmlr.org/papers/v24/21-1044.html

#manifold #homology #topological

Two p-cycles a and b are "homologous" (i.e. belong to the same #Homology class) if there exists a (p+1)-chain c, such that b = a + ∂c (mod-2 sum)
👇
https://arxiv.org/abs/2206.13932
#TopologicalDataAnalysis #TopologyToolKit #PersistentHomology #Visualization #DataScience #MachineLearning
Funded by the European Research Council (ERC) (project TORI, https://erc-tori.github.io/)

#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:

https://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!

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