Beyond Euclid: an illustrated guide to modern machine learning with geometric, topological, and algebraic structures. [PDF]
Mach Learn Sci TechnolPapillon M +10 more
europepmc +1 more source
Equivariant multiplicities via representations of quantum affine algebras. [PDF]
Sel Math New Ser, 2023 Casbi E, Li JR.
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Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract Heilbronn's triangle problem is a classical question in discrete geometry. It asks to determine the smallest number Δ=Δ(N)$\Delta = \Delta (N)$ for which every collection in N$N$ points in the unit square spans a triangle with area at most Δ$\Delta$.
Dmitrii Zakharov
wiley +1 more source
New quantum LDPC codes based on projective geometry. [PDF]
Sci RepTang C, Bai C, Feng Y.
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Diophantine tuples and product sets in shifted powers
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract Let k⩾2$k\geqslant 2$ and n≠0$n\ne 0$. A Diophantine tuple with property Dk(n)$D_k(n)$ is a set of positive integers A$A$ such that ab+n$ab+n$ is a k$k$th power for all a,b∈A$a,b\in A$ with a≠b$a\ne b$. Such generalizations of classical Diophantine tuples have been studied extensively.
Ernie Croot, Chi Hoi Yip
wiley +1 more source
Osculating geometry and higher‐order distance Loci
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract We discuss the problem of optimizing the distance function from a given point, subject to polynomial constraints. A key algebraic invariant that governs its complexity is the Euclidean distance degree, which pertains to first‐order tangency. We focus on the data locus of points possessing at least one critical point of the distance function ...
Sandra Di Rocco +2 more
wiley +1 more source
Multireference Equation-of-Motion Driven Similarity Renormalization Group: Theoretical Foundations and Applications to Ionized States. [PDF]
J Chem Theory ComputZhao Z, Li S, Evangelista FA.
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Toral symmetries of collapsed ancient solutions to the homogeneous Ricci flow
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract Collapsed ancient solutions to the homogeneous Ricci flow on compact manifolds occur only on the total space of principal torus bundles. Under an algebraic assumption that guarantees flowing through diagonal metrics and a tameness assumption on the collapsing directions, we prove that such solutions have additional symmetries, that is, they ...
Anusha M. Krishnan +2 more
wiley +1 more source
Image generator for tabular data based on non-Euclidean metrics for CNN-based classification. [PDF]
PLoS OneLin YR, Wu HM.
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Excited States, Symmetry Breaking, and Unphysical Solutions in State-Specific CASSCF Theory. [PDF]
J Phys Chem A, 2023 Marie A, Burton HGA.
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