Results 11 to 20 of about 16,524,402 (288)
Information Geometry, Fluctuations, Non-Equilibrium Thermodynamics, and Geodesics in Complex Systems [PDF]
Entropy, 2021 Information theory provides an interdisciplinary method to understand important phenomena in many research fields ranging from astrophysical and laboratory fluids/plasmas to biological systems.
Eun-jin Kim
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Information Geometry of Nonlinear Stochastic Systems [PDF]
Entropy, 2018 We elucidate the effect of different deterministic nonlinear forces on geometric structure of stochastic processes by investigating the transient relaxation of initial PDFs of a stochastic variable x under forces proportional to -xn (n=3,5,7) and ...
Rainer Hollerbach +2 more
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, 2019 This Special Issue of the journal Entropy, titled “Information Geometry I”, contains a collection of 17 papers concerning the foundations and applications of information geometry. Based on a geometrical interpretation of probability, information geometry has become a rich mathematical field employing the methods of differential geometry.
Verdoolaege, Geert
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Information Geometry of κ-Exponential Families: Dually-Flat, Hessian and Legendre Structures [PDF]
Entropy, 2018 In this paper, we present a review of recent developments on the κ -deformed statistical mechanics in the framework of the information geometry.
Antonio M. Scarfone +2 more
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Information Geometry of Randomized Quantum State Tomography [PDF]
Entropy, 2018 Suppose that a d-dimensional Hilbert space H ≃ C d admits a full set of mutually unbiased bases | 1 ( a ) 〉 , ⋯ , | d ( a ) 〉 , where a = 1 , ⋯ , d + 1 .
Akio Fujiwara, Koichi Yamagata
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Capturing Outlines of Planar Generic Images by Simultaneous Curve Fitting and Sub-division [PDF]
Journal of Artificial Intelligence and Data Mining, 2020 In this paper, a new technique has been designed to capture the outline of 2D shapes using cubic B´ezier curves. The proposed technique avoids the traditional method of optimizing the global squared fitting error and emphasizes the local control of data ...
A.R. Ebrahimi +2 more
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Optimal projection filters with information geometry [PDF]
, 2023 We review the introduction of several types of projection filters. Projection structures coming from information geometry are used to obtain a finite dimensional filter in the form of a stochastic differential equation (SDE), starting from the exact ...
Bernard Hanzon +5 more
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The Information Geometry of UMAP
CoRR, 2023 12 pages, 2 figures, 3 tables ; Github repo (https://github.com/sashakolpakov/info-geometry-umap) ; to appear in Le ...
Alexander Kolpakov \ University of Neuch\^atel, Switzerland +2 more
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Japanese Journal of Mathematics, 2021 SummaryStatistical inference is constructed upon a statistical model consisting of a parameterised family of probability distributions, which forms a manifold. It is important to study the geometry of the manifold. It was Professor C. R. Rao who initiated information geometry in his monumental paper published in 1945.
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Syntax and Geometry of Information
Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), 2023 This paper presents an information-theoretical model of syntactic generalization. We study syntactic generalization from the perspective of the capacity to disentangle semantic and structural information, emulating the human capacity to assign a grammaticality judgment to semantically nonsensical sentences. In order to isolate the structure, we propose
Bailly, Raphaël +2 more
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