Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real-World Data. [PDF]
Adv Intell DiscovThis 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
Algebraic Methods in Mathematical Biology [PDF]
Bulletin of Mathematical Biology, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A Computer Algebra System for R: Macaulay2 and the m2r Package
Journal of Statistical Software, 2020 Algebraic methods have a long history in statistics. Apart from the ubiquitous applications of linear algebra, the most visible manifestations of modern algebra in statistics are found in the young field of algebraic statistics, which brings tools from ...
David Kahle +2 more
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Algebraic Methods for Traffic Flow Densities Estimation
Cybernetics and Information Technologies, 2013 An estimation approach that allows recovering of the traffic state is proposed in this paper. The method used is based on numerical differentiation, which does not need any integration of differential equations and turns out to be quite robust with ...
Abouaïssa H., Iordanova V.
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Nontrivial solutions of linear functional equations: methods and examples [PDF]
Opuscula Mathematica, 2015 For a wide class of linear functional equations the solutions are generalized polynomials. The existence of non-trivial monomial terms of the solution strongly depends on the algebraic properties of some related families of parameters.
Adrienn Varga, Csaba Vincze
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Gelfond's Method for Algebraic Independence [PDF]
Transactions of the American Mathematical Society, 1975 This paper extends Gelfond’s method for algebraic independence to fields K K with transcendence type
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A Granular Computing Based Classification Method From Algebraic Granule Structure
IEEE Access, 2021 Classification, as one of the main task of machine learning, corresponds to the core work of granular computing, namely granulation. Most of granular computing models and related classification methods are uniquely classifying by granule features, but ...
Linshu Chen +4 more
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Stochastic Runge–Kutta methods for multi-dimensional Itô stochastic differential algebraic equations
Results in Applied Mathematics, 2021 In this paper, we discuss the numerical solutions to index 1 stochastic differential algebraic equations. We introduce a new class of weak second-order stochastic Runge–Kutta methods for finding the numerical approximate solutions to multi-dimensional ...
Priya Nair, Anandaraman Rathinasamy
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Method for solving quantifier linear equations based on the algebra of linear predicate operations
Радіоелектронні і комп'ютерні системиThe subject involves structured approaches that extend the existing set of mathematical tools for processing complex relationships within databases and computational systems.
Zoya Dudar, Volodymyr Liashyk
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Intelligent Tutoring Systems for Adult Learning in STEM Disciplines
New Directions for Adult and Continuing Education, EarlyView.ABSTRACT Intelligent tutoring systems (ITS) are reshaping adult learning in STEM by providing adaptive, data‐driven instruction across classrooms, workplaces, and informal environments. In the context of ITS, this article compares generative AI, which creates personalized explanations and practice materials, with explainable AI, which focuses on ...
Jill Zarestky, Amanda R. Lager Gleason
wiley +1 more source