Results 1 to 10 of about 53,985 (263)
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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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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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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Classification and Geometry of General Perceptual Manifolds [PDF]
Physical Review X, 2018 Perceptual manifolds arise when a neural population responds to an ensemble of sensory signals associated with different physical features (e.g., orientation, pose, scale, location, and intensity) of the same perceptual object.
SueYeon Chung +2 more
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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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Bounds for Statistical Curvatures of Submanifolds in Kenmotsu-like Statistical Manifolds
Mathematics, 2022 In this article, we obtain certain bounds for statistical curvatures of submanifolds with any codimension of Kenmotsu-like statistical manifolds. In this context, we construct a class of optimum inequalities for submanifolds in Kenmotsu-like statistical ...
Aliya Naaz Siddiqui +2 more
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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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Explosive neural networks via higher-order interactions in curved statistical manifolds [PDF]
Nature CommunicationsHigher-order interactions underlie complex phenomena in systems such as biological and artificial neural networks, but their study is challenging due to the scarcity of tractable models. By leveraging a generalisation of the maximum entropy principle, we
Miguel Aguilera +3 more
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