Results 11 to 20 of about 460 (128)

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

Adv Intell Discov
This article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Ren Y, Wei GW.
europepmc   +2 more sources

Supersymmetric localization in AdS5 and the protected chiral algebra

Journal of High Energy Physics, 2018
N=4 $$ \mathcal{N}=4 $$ super Yang-Mills theory admits [1] a protected subsector isomorphic to a two-dimensional chiral algebra, obtained by passing to the cohomology of a certain supercharge. In the large N limit, we expect this chiral algebra to have a
Federico Bonetti, Leonardo Rastelli
doaj   +1 more source

Analysis of the vacuum solution of the five-dimensional Einstein field equations with negative cosmological constant via variational symmetries [PDF]

AUT Journal of Mathematics and Computing
The Kaluza-Klein theory can be reckoned as a classical unified field theory of two of the significant forces of nature gravitation and electromagnetism.
Fatemeh Ahangari
doaj   +1 more source

Trivalent Categories for Adjoint Representations of Exceptional Lie Algebras

, 2022
We consider the universal pivotal, symmetric, monoidal, $\Bbbk$-linear category, generated by a Schurian object with a skew-symmetric multiplication, and study some of its quotients. We show that these quotients give rise to either vector product algebras or representation categories of exceptional Lie algebras.
openaire   +2 more sources

The Lax Integrable Differential-Difference Dynamical Systems on Extended Phase Spaces

Symmetry, Integrability and Geometry: Methods and Applications, 2010
The Hamiltonian representation for the hierarchy of Lax-type flows on a dual space to the Lie algebra of shift operators coupled with suitable eigenfunctions and adjoint eigenfunctions evolutions of associated spectral problems is found by means of a ...
Oksana Ye. Hentosh
doaj   +1 more source

Lie superalgebra structures in cohomology spaces of Lie algebras with coefficients in the adjoint representation

, 2004
The space of Lie algebra cohomology is usually described by the dimensions of components of certain degree even for the adjoint module as coefficients when the spaces of cochains and cohomology can be endowed with a Lie superalgebra structure. Such a description is rather imprecise: these dimensions may coincide for cohomology spaces of distinct ...
Lebedev, Alexei, Leites, Dimitry, Shereshevskii, Ilya   +2 more
openaire   +2 more sources

On the additive image of zeroth persistent homology

Transactions of the London Mathematical Society, Volume 13, Issue 1, December 2026.
Abstract For a category X$X$ and a finite field F$F$, we study the additive image of the functor H0(−;F)∗:rep(X,Top)→rep(X,VectF)$\operatorname{H}_0(-;F)_* \colon \operatorname{rep}(X, \mathbf {Top}) \rightarrow \operatorname{rep}(X, \mathbf {Vect}_F)$, or equivalently, of the free functor rep(X,Set)→rep(X,VectF)$\operatorname{rep}(X, \mathbf {Set ...
Ulrich Bauer, Magnus B. Botnan, Steffen Oppermann, Johan Steen   +3 more
wiley   +1 more source

On different approaches to IRF lattice models. Part II

Journal of High Energy Physics
This paper represents a continuation of our previous work, where the Boltzmann weights (BWs) for several Interaction-Round-the Face (IRF) lattice models were computed using their relation to rational conformal field theories.
Vladimir Belavin, Doron Gepner, J. Ramos Cabezas, Boris Runov   +3 more
doaj   +1 more source

Stochastic Gradient Descent in High Dimensions for Multi‐Spiked Tensor PCA

Communications on Pure and Applied Mathematics, Volume 79, Issue 10, Page 2291-2369, October 2026.
ABSTRACT We study the high‐dimensional dynamics of online stochastic gradient descent (SGD) for the multi‐spiked tensor model. This multi‐index model arises from the tensor principal component analysis (PCA) problem with multiple spikes, where the goal is to estimate the unknown signal vectors within the N$N$‐dimensional unit sphere through maximum ...
Gérard Ben Arous, Cédric Gerbelot, Vanessa Piccolo   +2 more
wiley   +1 more source

Computable conditions for order-2 CP symmetry in NHDM potentials

Journal of High Energy Physics
We derive necessary and sufficient conditions for order-2 CP (CP2) symmetry in N-Higgs-doublet potentials for N > 2. The conditions, which are formulated as relations between vectors that transform under the adjoint representation of SU(N) under a change
R. Plantey, M. Aa. Solberg
doaj   +1 more source