Results 11 to 20 of about 225,797 (277)

Point Cloud Denoising Algorithm via Geometric Metrics on the Statistical Manifold

Applied Sciences, 2023
A denoising algorithm was proposed for point cloud with high-density noise. The algorithm utilized geometric metrics on the statistical manifold and applied the idea of clustering K-means based on local statistical characteristics between noise and valid
Xiaomin Duan, Li Feng, Xinyu Zhao
doaj   +3 more sources

Analyzing Curvature Properties and Geometric Solitons of the Twisted Sasaki Metric on the Tangent Bundle over a Statistical Manifold

Mathematics
Let (M,∇,g) be a statistical manifold and TM be its tangent bundle endowed with a twisted Sasaki metric G. This paper serves two primary objectives. The first objective is to investigate the curvature properties of the tangent bundle TM.
Lixu Yan, Yanlin Li, Lokman Bilen, Aydın Gezer   +3 more
doaj   +3 more sources

Casorati Inequalities for Statistical Submanifolds in Kenmotsu Statistical Manifolds of Constant ϕ-Sectional Curvature with Semi-Symmetric Metric Connection

Entropy, 2022
In this paper, we prove some inequalities between intrinsic and extrinsic curvature invariants, namely the normalized δ-Casorati curvatures and the scalar curvature of statistical submanifolds in Kenmotsu statistical manifolds of constant ϕ-sectional ...
Simona Decu, Gabriel-Eduard Vîlcu
doaj   +1 more source

Casorati Inequalities for Spacelike Submanifolds in Sasaki-like Statistical Manifolds with Semi-Symmetric Metric Connection

Mathematics, 2022
In this paper, we establish some inequalities between the normalized δ-Casorati curvatures and the scalar curvature (i.e., between extrinsic and intrinsic invariants) of spacelike statistical submanifolds in Sasaki-like statistical manifolds, endowed ...
Simona Decu
doaj   +1 more source

Infinitesimal Affine Transformations and Mutual Curvatures on Statistical Manifolds and Their Tangent Bundles

Axioms, 2023
The purpose of this paper is to find some conditions under which the tangent bundle TM has a dualistic structure. Then, we introduce infinitesimal affine transformations on statistical manifolds and investigate these structures on a special statistical ...
Esmaeil Peyghan, Davood Seifipour, Ion Mihai   +2 more
doaj   +1 more source

Quasi-Statistical Schouten–van Kampen Connections on the Tangent Bundle

Mathematics, 2023
We determine the general natural metrics G on the total space TM of the tangent bundle of a Riemannian manifold (M,g) such that the Schouten–van Kampen connection ∇¯ associated to the Levi-Civita connection of G is (quasi-)statistical.
Simona-Luiza Druta-Romaniuc
doaj   +1 more source

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
doaj   +1 more source

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

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 ...
openaire   +5 more sources

Learning on dynamic statistical manifolds

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 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.
F. Boso, D. M. Tartakovsky
openaire   +5 more sources