Results 1 to 10 of about 1,296 (81)
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 +6 more sources
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
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Topological invariants and a gauge theory of the super-Poincaré algebra in three dimensions
Nuclear Physics B, 1989 Abstract Various aspects of superspace topology and N = 1 supersymmetry in 2 + 1 dimensions are explored. Non-minimal super Yang-Mills theory is used to construct a gauge theory of the N = 1 super-Poincare algebra. A topological super Yang-Mills theory is given and used to compute elements of the cohomology classes of super-monopole moduli space.
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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
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Proceedings of the American Mathematical SocietyWe show that the canonical equivalences of categories between 2-dimensional (unoriented) topological quantum field theories valued in a symmetric monoidal category and (extended) commutative Frobenius algebras in that symmetric monoidal category are symmetric monoidal equivalences.
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, 2018 In computational complexity, a complexity class is given by a set of problems or functions, and a basic challenge is to show separations of complexity classes A != B especially when A is known to be a subset of B. In this paper we introduce a homological theory of functions that can be used to establish complexity separations, while also providing ...
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Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real-World Data. [PDF]
Adv Intell DiscovRen Y, Wei GW.
europepmc +1 more source
CAKR: commutative algebra k-mer representations for genomics. [PDF]
Nat CommunSuwayyid F +5 more
europepmc +1 more source