Results 11 to 20 of about 338 (205)

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

Polynomial systems and Kronecker invariants

Linear Algebra and its Applications, 1987
The Kronecker canonical form is generalized from the set of matrix pencils to the set of all the rational matrix functions \(W(\lambda)=\sum^{\ell}_{i=-\infty}W_ i\lambda^ i\), in a way which depends on the choice of \(\ell \in {\mathbb{N}}\). If a polynomial system \(W(\lambda)=C(\lambda I-A)^{-1}B+\sum^{\ell}_{i=0}W_ i\lambda^ i\) is given as a ...
openaire   +2 more sources

A note on generalized invariant cones and the kronecker canonical form

Linear Algebra and its Applications, 1991
There are well-known conditions on the spectrum of a real \(n\times n\) matrix A which are equivalent to the existence of a proper cone \(K\subset {\mathbb{R}}^ n\) such that A(K)\(\subset K\). The authors generalize these results to the case of a pencil A-\(\lambda\) B, A,B \(m\times n\)-matrices.
Stern, Ronald J., Wolkowicz, Henry
openaire   +2 more sources

Wild wall-crossing and symmetric quivers in 4d and 3d N $$ \mathcal{N} $$ = 2 field theories

Journal of High Energy Physics
We reformulate Kontsevich-Soibelman wall-crossing formulae for 4d N $$ \mathcal{N} $$ = 2 class S $$ \mathcal{S} $$ theories and corresponding BPS quivers, including those of wild type, as identities for generating series of symmetric quivers that ...
Daniel Bryan, Piotr Sułkowski
doaj   +1 more source

Electric‐Current‐Assisted Nucleation of Zero‐Field Hopfion Rings

Advanced Materials, EarlyView.
This work reports a novel and efficient nucleation protocol for 3D localized topological magnetic solitons‐hopfion rings in chiral magnets using pulsed electric currents. By using Lorentz transmission electron microscopy and topological analysis, we report characteristic features and extraordinary stability of hopfion rings in zero or inverted external
Xiaowen Chen, Dongsheng Song, Filipp N. Rybakov, Nikolai S. Kiselev, Long Li, Wen Shi, Rui Wu, Xuewen Fu, Olle Eriksson, Stefan Blügel, Rafal E. Dunin‐Borkowski, Haifeng Du, Fengshan Zheng   +12 more
wiley   +1 more source

Photonics of Topological Magnetic Textures

Advanced Optical Materials, EarlyView.
Localized noncollinear magetic textures imprint their geometry and topology onto traversing photonic fields endowing them with orbital angular‐momentum, chirality, and magnetoelectric densities. Abstract Topological textures in magnetically ordered materials are an important case studies for fundamental research with promising applications in data ...
Vakhtang Jandieri, Ramaz Khomeriki, Daniel Erni, Nicolas Tsagareli, Qian Li, Douglas H. Werner, Jamal Berakdar   +6 more
wiley   +1 more source

Modelling A-branes with foliations

Journal of High Energy Physics
A certain class of A-branes in mirrors of toric Calabi-Yau threefolds can be described through the framework of foliations. This allows to develop an explicit description of their moduli spaces based on a cell decomposition, with strata of various ...
Sibasish Banerjee, Pietro Longhi, Mauricio Romo   +2 more
doaj   +1 more source

Invariants, Kronecker products, and combinatorics of some remarkable Diophantine systems

Advances in Applied Mathematics, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Garsia, Adriano, Musiker, Gregg, Wallach, Nolan, Xin, Guoce   +3 more
openaire   +2 more sources

Bayesian Optimisation for the Experimental Sciences: A Practical Guide to Data‐Efficient Optimisation of Laboratory Workflows

Advanced Intelligent Systems, EarlyView.
This study provides an introduction to Bayesian optimisation targeted for experimentalists. It explains core concepts, surrogate modelling, and acquisition strategies, and addresses common real‐world challenges such as noise, constraints, mixed variables, scalability, and automation.
Chuan He, Martin Singull, T. Jesper Jacobsson   +2 more
wiley   +1 more source

Eigenvalue systems for integer orthogonal bases of multi-matrix invariants at finite N

Journal of High Energy Physics
Multi-matrix invariants, and in particular the scalar multi-trace operators of N $$ \mathcal{N} $$ = 4 SYM with U(N) gauge symmetry, can be described using permutation centraliser algebras (PCA), which are generalisations of the symmetric group algebras ...
Adrian Padellaro, Sanjaye Ramgoolam, Ryo Suzuki   +2 more
doaj   +1 more source