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Symplectic Geometry and Its Applications on Time Series Analysis
Structure Topology and Symplectic Geometry, 2020 This chapter serves to introduce the symplectic geometry theory in time series analysis and its applications in various fields. The basic concepts and basic elements of mathematics relevant to the symplectic geometry are introduced in the second section.
Min Lei
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An approach to stability analyses in general relativity via symplectic geometry [PDF]
Arabian Journal of Mathematics, 2019 We begin with a review of the statements of non-linear, linear and mode stability of autonomous dynamical systems in classical mechanics, using symplectic geometry.
Prashant Kocherlakota, P. Joshi
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Airy structures and symplectic geometry of topological recursion [PDF]
Proceedings of Symposia in Pure Mathematics, 2017 We propose a new approach to the topological recursion of Eynard-Orantin based on the notion of Airy structure, which we introduce in the paper. We explain why Airy structure is a more fundamental object than the one of the spectral curve. We explain how
M. Kontsevich, Y. Soibelman
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Symplectic geometry and connectivity of spaces of frames [PDF]
Advances in Computational Mathematics, 2018 Frames provide redundant, stable representations of data which have important applications in signal processing. We introduce a connection between symplectic geometry and frame theory and show that many important classes of frames have natural symplectic
Tom Needham, C. Shonkwiler
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Fast symplectic integrator for Nesterov-type acceleration method [PDF]
Japan journal of industrial and applied mathematics, 2021 In this paper, explicit stable integrators based on symplectic and contact geometries are proposed for a family of non-autonomous ordinarily differential equations (ODEs) found in improving convergence rate of Nesterov’s accelerated gradient method ...
S. Goto, H. Hino
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Symplectic geometric flows [PDF]
Pure and Applied Mathematics Quarterly, 2021 Several geometric flows on symplectic manifolds are introduced which are potentially of interest in symplectic geometry and topology. They are motivated by the Type IIA flow and T-duality between flows in symplectic geometry and flows in complex geometry.
Teng Fei, D. Phong
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Symplectic Geometry of a Moduli Space of Framed Higgs Bundles [PDF]
International mathematics research notices, 2018 Let $X$ be a compact connected Riemann surface and $D$ an effective divisor on $X$. Let ${\mathcal N}_H(r,d)$ denote the moduli space of $D$-twisted stable Higgs bundles (a special class of Hitchin pairs) on $X$ of rank $r$ and degree $d$.
I. Biswas +2 more
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Quantized anti de Sitter spaces and non-formal deformation quantizations of symplectic symmetric spaces [PDF]
, 2007 We realize quantized anti de Sitter space black holes, building Connes spectral triples, similar to those used for quantized spheres but based on Universal Deformation Quantization Formulas (UDF) obtained from an oscillatory integral kernel on an ...
Bieliavsky, Pierre +3 more
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From symplectic cohomology to Lagrangian enumerative geometry [PDF]
Advances in Mathematics, 2017 We build a bridge between Floer theory on open symplectic manifolds and the enumerative geometry of holomorphic disks inside their Fano compactifications, by detecting elements in symplectic cohomology which are mirror to Landau-Ginzburg potentials.
D. Tonkonog
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Symplectic and Poisson geometry on b-manifolds [PDF]
, 2012 Let $M^{2n}$ be a Poisson manifold with Poisson bivector field $\Pi$. We say that $M$ is b-Poisson if the map $\Pi^n:M\to\Lambda^{2n}(TM)$ intersects the zero section transversally on a codimension one submanifold $Z\subset M$.
Ana Rita Pires +30 more
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