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Beyond Euclid: an illustrated guide to modern machine learning with geometric, topological, and algebraic structures. [PDF]

Mach Learn Sci Technol
Papillon M, Sanborn S, Mathe J, Cornelis L, Bertics A, Buracas D, J Lillemark H, Shewmake C, Dinc F, Pennec X, Miolane N.   +10 more
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Hodge decomposition of vector fields in Cartesian grids. [PDF]

SIGGRAPH Asia
Su Z, Tong Y, Wei G, Wei G.
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Two-dimensional RMSD projections for reaction path visualization and validation. [PDF]

MethodsX
Goswami R.
europepmc   +1 more source

Equivariant valuations on convex functions. [PDF]

Calc Var Partial Differ Equ
Hofstätter GC, Knoerr J.
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The Polytope Formalism: application to molecular constitution and the prospect of a complete description of Chemical Space. [PDF]

Chem Sci
Canfield PJ, Crossley MJ.
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Decentralized Consensus Protocols on <i>SO</i>(4)^<i>N</i> and <i>TSO</i>(4)^<i>N</i> with Reshaping. [PDF]

Entropy (Basel)
Butcher EA, Spaeth V.
europepmc   +1 more source

Fréchet–Urysohn subspaces of free topological groups

Fréchet–Urysohn subspaces of free topological groups
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COUNTABLE-CODIMENSIONAL SUBSPACES OF TOPOLOGICAL VECTOR SPACES

COUNTABLE-CODIMENSIONAL SUBSPACES OF TOPOLOGICAL VECTOR SPACES
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Algebraic properties of subspace topologies

Advances in Pure and Applied Mathematics
Summary: It is shown that the collection of all topologies on a given set \(X\) coincides with the set of subsemirings of the power set \(\mathcal{P}(X)\) (equipped with union and intersection) if and only if \(X\) is finite. Furthermore, given a topological space \((X, \mathcal{T})\) and a subset \(A\) of \(X\), we characterize when the subspace ...
Jarboui, Noômen, Subaiei, Bana Al
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