Results 31 to 40 of about 59,568 (301)
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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Entropic Dynamics on Gibbs Statistical Manifolds [PDF]
Entropy, 2021 Entropic dynamics is a framework in which the laws of dynamics are derived as an application of entropic methods of inference. Its successes include the derivation of quantum mechanics and quantum field theory from probabilistic principles. Here, we develop the entropic dynamics of a system, the state of which is described by a probability distribution.
Pedro Pessoa +2 more
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Lagrangian and Hamiltonian Mechanics for Probabilities on the Statistical Manifold
, 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 +2 more
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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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Information-Geometric Markov Chain Monte Carlo Methods Using Diffusions [PDF]
, 2014 Recent work incorporating geometric ideas in Markov chain Monte Carlo is reviewed in order to highlight these advances and their possible application in a range of domains beyond statistics. A full exposition of Markov chains and their use in Monte Carlo
Livingstone, Samuel +5 more
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Geodesic Monte Carlo on Embedded Manifolds [PDF]
, 2013 Markov chain Monte Carlo methods explicitly defined on the manifold of probability distributions have recently been established. These methods are constructed from diffusions across the manifold and the solution of the equations describing geodesic flows
Simon Byrne +5 more
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Information-Geometric Approach for a One-Sided Truncated Exponential Family
Entropy, 2023 In information geometry, there has been extensive research on the deep connections between differential geometric structures, such as the Fisher metric and the α-connection, and the statistical theory for statistical models satisfying regularity ...
Masaki Yoshioka, Fuyuhiko Tanaka
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