Results 1 to 10 of about 4,356 (253)
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.
Jan Naudts
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On Almost Norden Statistical Manifolds [PDF]
Entropy, 2022 We consider a statistical connection ∇ on an almost complex manifold with (pseudo-) Riemannian metric, in particular the Norden metric. We investigate almost Norden (statistical) manifolds under the condition that the almost complex structure J is ...
Leila Samereh +2 more
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Geometry of Statistical Manifolds [PDF]
EntropyA statistical manifold M can be defined as a Riemannian manifold each of whose points is a probability distribution on the same support. In fact, statistical manifolds possess a richer geometric structure beyond the Fisher information metric defined on ...
Paul W. Vos
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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.
Pedro Pessoa +2 more
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Learning on dynamic statistical manifolds. [PDF]
Proc Math Phys Eng Sci, 2020 Hyperbolic balance laws with uncertain (random) parameters and inputs are ubiquitous in science and engineering. Quantification of uncertainty in predictions derived from such laws, and reduction of predictive uncertainty via data assimilation, remain an open challenge.
Boso F, Tartakovsky DM.
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λ-Deformation: A Canonical Framework for Statistical Manifolds of Constant Curvature [PDF]
Entropy, 2022 This paper systematically presents the λ-deformation as the canonical framework of deformation to the dually flat (Hessian) geometry, which has been well established in information geometry.
Jun Zhang, Ting-Kam Leonard Wong
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Conformal Control Tools for Statistical Manifolds and for γ-Manifolds
Mathematics, 2022 The theory of statistical manifolds w.r.t. a conformal structure is reviewed in a creative manner and developed. By analogy, the γ-manifolds are introduced. New conformal invariant tools are defined.
Iulia-Elena Hirica +3 more
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Fisher–Rao Distance for Finite-Energy Signal Manifolds: Geometric Foundations and Numerical Analysis [PDF]
EntropyThis paper introduces a geometric framework for analyzing finite-energy signals observed with additive noise by representing them as points on statistical manifolds equipped with the Fisher–Rao metric. Each signal is associated with a parameter vector θ,
Franck Florin
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Curvature Invariants of Statistical Submanifolds in Kenmotsu Statistical Manifolds of Constant ϕ-Sectional Curvature [PDF]
Entropy, 2018 In this article, we consider statistical submanifolds of Kenmotsu statistical manifolds of constant ϕ-sectional curvature. For such submanifold, we investigate curvature properties. We establish some inequalities involving the normalized δ-Casorati
Simona Decu +3 more
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Correction: Naudts, J. Quantum Statistical Manifolds. Entropy 2018, 20, 472 [PDF]
Entropy, 2018 Section 4 of “Naudts J. Quantum Statistical Manifolds. Entropy 2018, 20, 472” contains errors. They have limited consequences for the remainder of the paper. A new version of this Section is found here.
Jan Naudts
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