Results 31 to 40 of about 3,328,560 (290)
Axioms, 2023 The purpose of this paper is to find some conditions under which the tangent bundle TM has a dualistic structure. Then, we introduce infinitesimal affine transformations on statistical manifolds and investigate these structures on a special statistical ...
Esmaeil Peyghan +2 more
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Quasi-Statistical Schouten–van Kampen Connections on the Tangent Bundle
Mathematics, 2023 We determine the general natural metrics G on the total space TM of the tangent bundle of a Riemannian manifold (M,g) such that the Schouten–van Kampen connection ∇¯ associated to the Levi-Civita connection of G is (quasi-)statistical.
Simona-Luiza Druta-Romaniuc
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Domain Adaptation on the Statistical Manifold [PDF]
2014 IEEE Conference on Computer Vision and Pattern Recognition, 2014 In this paper, we tackle the problem of unsupervised domain adaptation for classification. In the unsupervised scenario where no labeled samples from the target domain are provided, a popular approach consists in transforming the data such that the source and target distributions become similar.
Mahsa Baktashmotlagh +3 more
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Lagrangian and Hamiltonian Mechanics for Probabilities on the Statistical Manifold [PDF]
, 2022 We provide an Information-Geometric formulation of Classical Mechanics on the Riemannian manifold of probability distributions, which is an affine manifold endowed with a dually-flat connection.
Malagò, Luigi +5 more
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Recent Developments on the First Chen Inequality in Differential Geometry
Mathematics, 2023 One of the most fundamental interests in submanifold theory is to establish simple relationships between the main extrinsic invariants and the main intrinsic invariants of submanifolds and find their applications.
Bang-Yen Chen, Gabriel-Eduard Vîlcu
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Mathematics, 2020 In this paper, we prove some inequalities in terms of the normalized δ -Casorati curvatures (extrinsic invariants) and the scalar curvature (intrinsic invariant) of statistical submanifolds in holomorphic statistical manifolds with constant ...
Simona Decu +2 more
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Quantum Statistical Manifolds [PDF]
Entropy, 2018 Quantum information geometry studies families of quantum states by means of differential geometry. A new approach is followed with the intention to facilitate the introduction of a more general theory in subsequent work. To this purpose, the emphasis is shifted from a manifold of strictly positive density matrices to a manifold of faithful quantum ...
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Laplacian operator on statistical manifold
Information Geometry, 2022 In this paper, we define a Laplacian operator on a statistical manifold, called the vector Laplacian. This vector Laplacian incorporates information from the Amari-Chentsov tensor. We derive a formula for the vector Laplacian. We also give two applications using the heat kernel associated with the vector Laplacian.
Ruichao Jiang +2 more
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A New Algebraic Inequality and Some Applications in Submanifold Theory
Mathematics, 2021 We give a simple proof of the Chen inequality involving the Chen invariant δ(k) of submanifolds in Riemannian space forms. We derive Chen’s first inequality and the Chen–Ricci inequality.
Ion Mihai, Radu-Ioan Mihai
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Statistical cosymplectic manifolds and their submanifolds
پژوهشهای ریاضی, 2022 Introduction Let p(x,ζ) be the set of parametric probability distribution with parameter ζ=ζ1,…,ζn∊Rn. This set is called a statistical model or manifold. The distance between two points is measured by the Fisher metric. In general, statistical manifolds
Mohammad Bagher Kazemi, Shiva Salahvarzi
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