Results 1 to 10 of about 302 (74)

Geometric and homological methods in group theory: constructing small group resolutions [PDF]

, 2011
Given two groups K and H for which we have the free crossed resolutions, B* --> K and C* --> H respectively. Our aim is to construct a free crossed resolution, A* --> G, by way of induction on the degree n, for any semidirect product G = K x H.\ud First we show how to find a set Z1 of generators for the free group A1 and the corresponding unique ...
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Homological methods in rigidity theory using graphs of groups

In recent work, Stokes and Vermant considered graph-of-groups realisations of hypergraphs as a new description of rigidity-theoretic problems. In this paper, we show that the infinitesimal aspects of graph-of-groups realisations can be analysed using cellular sheaves and their cohomology.
openaire   +2 more sources

The metabolomic physics of complex diseases. [PDF]

Proc Natl Acad Sci U S A, 2023
Wu S, Liu X, Dong A, Gragnoli C, Griffin C, Wu J, Yau ST, Wu R.   +7 more
europepmc   +1 more source

Spaces and sequences in the hippocampus: a homological perspective. [PDF]

J Comput Neurosci
Babichev A, Vashin V, Dabaghian Y.
europepmc   +1 more source

Charting higher-order models of brain function beyond pairwise interactions. [PDF]

Nat Commun
Santoro A, Neri M, Poetto S, Orsenigo D, Diano M, Gatica M, Petri G.   +6 more
europepmc   +1 more source

Calix[4]arene Design for Enhanced Carbon Capture via Topological Learning. [PDF]

Chemistry
Laub JA, Vogiatzis KD.
europepmc   +1 more source

CAKR: commutative algebra k-mer representations for genomics. [PDF]

Nat Commun
Suwayyid F, Hozumi Y, Zia M, Wee J, Feng H, Wei GW.   +5 more
europepmc   +1 more source

Persistent Dirac for molecular representation. [PDF]

Sci Rep, 2023
Wee J, Bianconi G, Xia K.
europepmc   +1 more source

Graph statistics theory of individualized quantitative genetics under haplotype-resolved genome assembly. [PDF]

Proc Natl Acad Sci U S A
Sun L, Bian Y, Yang D, Miao R, Meng Y, Che J, Li Z, Li Z, Wang H, Wu S, Meng J, Wang Y, Griffin C, Yau ST, Wu R.   +14 more
europepmc   +1 more source

Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real-World Data. [PDF]

Adv Intell Discov
Ren Y, Wei GW.
europepmc   +1 more source