Results 11 to 20 of about 106,327 (167)
Estimate of the Neural Network Dimension Using Algebraic Topology and Lie Theory [PDF]
Lecture Notes in Computer Science, 2021 In this paper we present an approach to determine the smallest possible number of neurons in a layer of a neural network in such a way that the topology of the input space can be learned sufficiently well. We introduce a general procedure based on persistent homology to investigate topological invariants of the manifold on which we suspect the data set.
Luciano Melodia, Richard Lenz
exaly +7 more sources
Global Topological Dirac Synchronization
Journal of Physics: ComplexitySynchronization is a fundamental dynamical state of interacting oscillators, observed, e.g., in natural biological rhythms and in the brain. Global synchronization which occurs when non-linear or chaotic oscillators placed on the nodes of a network ...
Timoteo Carletti +3 more
doaj +2 more sources
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
Graduate Studies in Mathematics, 2020 This lecture covers several basic methods for standard tasks in data analysis and image processing. A non-exclusive and non-exhaustive list of meth-ods: histograms, dimension reduction, clustering, filters, frequency analysis, morphological methods ...
Claudia Scheimbauer
semanticscholar +1 more source
Algebraic methods in approximation theory [PDF]
Computer Aided Geometric Design, 2016 This survey gives an overview of several fundamental algebraic constructions which arise in the study of splines. Splines play a key role in approximation theory, geometric modeling, and numerical analysis; their properties depend on combinatorics ...
H. Schenck
semanticscholar +1 more source
Combinatorial Topology and the Global Dimension of Algebras Arising in Combinatorics [PDF]
, 2012 In a highly influential paper, Bidigare, Hanlon and Rockmore showed that a number of popular Markov chains are random walks on the faces of a hyperplane arrangement.
S. Margolis +2 more
semanticscholar +1 more source
Efficient Hamiltonian encoding algorithms for extracting quantum control mechanism as interfering pathway amplitudes in the Dyson series [PDF]
QuantumHamiltonian encoding is a methodology for revealing the mechanism behind the dynamics governing controlled quantum systems. In this paper, following Mitra and Rabitz \cite{abhra_1}, we define mechanism via pathways of eigenstates that describe the ...
Erez Abrams +4 more
doaj +1 more source
The Origin of Chern-Simons Modified Gravity from an 11 + 3-Dimensional Manifold
Advances in High Energy Physics, 2017 It is our aim to show that the Chern-Simons terms of modified gravity can be understood as generated by the addition of a 3-dimensional algebraic manifold to an initial 11-dimensional space-time manifold; this builds up an 11+3-dimensional space-time. In
J. A. Helayël-Neto +2 more
doaj +1 more source
Categorical cell decomposition of quantized symplectic algebraic varieties [PDF]
, 2016 We prove a new symplectic analogue of Kashiwara’s equivalence from D–module theory. As a consequence, we establish a structure theory for module categories over deformation-quantizations that mirrors, at a higher categorical level, the ...
Bellamy, Gwyn +3 more
core +3 more sources
Quadratic functions in geometry, topology, and M-theory [PDF]
, 2002 We describe an interpretation of the Kervaire invariant of a Riemannian manifold of dimension $4k+2$ in terms of a holomorphic line bundle on the abelian variety $H^{2k+1}(M)\otimes R/Z$.
M. Hopkins, I. Singer
semanticscholar +1 more source