Results 11 to 20 of about 4,356 (253)

Explosive neural networks via higher-order interactions in curved statistical manifolds [PDF]

Nature Communications
Higher-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, Pablo A. Morales, Fernando E. Rosas, Hideaki Shimazaki   +3 more
doaj   +2 more sources

Curvature Invariants for Statistical Submanifolds of Hessian Manifolds of Constant Hessian Curvature

Mathematics, 2018
We consider statistical submanifolds of Hessian manifolds of constant Hessian curvature. For such submanifolds we establish a Euler inequality and a Chen-Ricci inequality with respect to a sectional curvature of the ambient Hessian manifold.
Adela Mihai, Ion Mihai, Mihai Adela
exaly   +3 more sources

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, K. S. Subrahamanian Moosath   +1 more
openaire   +3 more sources

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, Mohd Danish Siddiqi, Ali Hussain Alkhaldi   +2 more
doaj   +1 more source

Screen Semi-Invariant Lightlike Hypersurfaces on Hermite-Like Manifolds

Journal of New Theory, 2023
Hermite-like manifolds, which admit two different, almost complex structures, can be considered a general concept of Hermitian manifolds. Factoring in the effects of these two complex structures on the radical, screen, and transversal spaces, a new ...
Ömer Aksu, Mehmet Gülbahar
doaj   +1 more source

Some Results on Statistical Hypersurfaces of Sasakian Statistical Manifolds and Holomorphic Statistical Manifolds

International Electronic Journal of Geometry, 2021
In this paper, we study the statistical immersion of codimension one from a Sasakian statistical manifold of constant φ− curvature to a holomorphic statistical manifold of constant holomorphic curvature and its converse. We prove that in both cases the constant φ− curvature equals to one and the constant holomorphic curvature must be zero. Moreover, we
Feng Wu, Yan Jıang, Liang Zhang
openaire   +4 more sources

General Chen Inequalities for Statistical Submanifolds in Hessian Manifolds of Constant Hessian Curvature

Mathematics, 2022
Chen’s first inequality for statistical submanifolds in Hessian manifolds of constant Hessian curvature was obtained by B.-Y. Chen et al. Other particular cases of Chen inequalities in a statistical setting were given by different authors.
Ion Mihai, Radu-Ioan Mihai
doaj   +1 more source

Basic inequalities for statistical submanifolds in Golden-like statistical manifolds

Open Mathematics, 2022
In this paper, we introduce and study Golden-like statistical manifolds. We obtain some basic inequalities for curvature invariants of statistical submanifolds in Golden-like statistical manifolds.
Lone Mohamd Saleem, Bahadir Oğuzhan, Park Choonkil, Hwang Inho   +3 more
doaj   +1 more source

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, Mehrtash Tafazzoli Harandi, Brian C. Lovell, Mathieu Salzmann   +3 more
openaire   +4 more sources

Inequalities for the Casorati Curvature of Statistical Manifolds in Holomorphic Statistical Manifolds of Constant Holomorphic Curvature

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, Stefan Haesen, Leopold Verstraelen   +2 more
doaj   +1 more source