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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Inequalities for the Casorati Curvature of Statistical Manifolds in Holomorphic Statistical Manifolds of Constant Holomorphic Curvature [PDF]
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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Explicit Geodesic Projection Distance on the Statistical Manifold of Multivariate Elliptical Distributions [PDF]
EntropyGeodesic projection distances on statistical manifolds have been widely applied across various research fields. Nevertheless, the existing closed-form solution is only available for the Gaussian manifold.
Xiangbing Chen +2 more
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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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Relations between Extrinsic and Intrinsic Invariants of Statistical Submanifolds in Sasaki-Like Statistical Manifolds [PDF]
Mathematics, 2021 The Chen first inequality and a Chen inequality for the δ(2,2)-invariant on statistical submanifolds of Sasaki-like statistical manifolds, under a curvature condition, are obtained.
Hülya Aytimur +2 more
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Entropy, 2015 In this paper we investigate statistical manifolds with almost quaternionic structures. We define the concept of quaternionic Kähler-like statistical manifold and derive the main properties of quaternionic Kähler-like statistical submersions, extending ...
Alina-Daniela Vîlcu +1 more
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Lifts of a Semi-Symmetric Metric Connection from Sasakian Statistical Manifolds to Tangent Bundle
MathematicsThe lifts of Sasakian statistical manifolds associated with a semi-symmetric metric connection in the tangent bundle are characterized in the current research.
Rajesh Kumar +4 more
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Homogeneous statistical manifolds [PDF]
Information GeometryThe methods of Information geometry have been glowing up to develop various subjects of theoretical physics, including quantum information systems. The present article has two purposes. The first one is to develop general theory of homogeneous statistical manifolds.
Inoguchi, Jun-ichi, Ohno, Yu
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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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Immersions into Statistical Manifolds
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 2021 This paper studies the geometry of immersions into statistical manifolds. A necessary and sufficient condition is obtained for statistical manifold structures to be dual to each other for a non-degenerate equiaffine immersion. Then we obtain conditions for realizing an n-dimensional statistical manifold in an (n+1)-dimensional statistical manifold and ...
T. V. Mahaesh +1 more
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