Results 1 to 10 of about 2,851,799 (287)

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
doaj   +1 more source

A universal sum over topologies in 3d gravity

SciPost Physics
We explore the sum over topologies in $\mathrm{AdS}_3$ quantum gravity and its relationship with the statistical interpretation of the boundary theory.
Alexandre Belin, Scott Collier, Lorenz Eberhardt, Diego Liska, Boris Post
doaj   +1 more source

Classification and Geometry of General Perceptual Manifolds

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, Daniel D. Lee, Haim Sompolinsky   +2 more
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On the α-connections and the α-conformal equivalence on statistical manifolds [PDF]

Arab Journal of Mathematical Sciences
Purpose – In this paper, we give some properties of the α-connections on statistical manifolds and we study the α-conformal equivalence where we develop an expression of curvature R¯ for ∇¯ in relation to those for ∇ and ∇^. Design/methodology/approach –
Khadidja Addad, Seddik Ouakkas
doaj   +1 more source

Black-Box Optimization Using Geodesics in Statistical Manifolds

Entropy, 2015
Information geometric optimization (IGO) is a general framework for stochastic optimization problems aiming at limiting the influence of arbitrary parametrization choices: the initial problem is transformed into the optimization of a smooth function on a
Jérémy Bensadon
doaj   +1 more source

Sasakian Statistical Manifolds with Semi-Symmetric Metric Connection

Universal Journal of Mathematics and Applications, 2018
In the present paper, firstly we express the relation between the semi-symmetric metric connection $\tilde{\nabla}$ and the torsion-free connection $\nabla$ and obtain the relation between the curvature tensors $\tilde{R}$ of $\tilde{\nabla}$ and $R$ of $
Ahmet Kazan, Sema Kazan
doaj   +1 more source

Generalization of the maximum entropy principle for curved statistical manifolds

Physical Review Research, 2021
The maximum entropy principle (MEP) is one of the most prominent methods to investigate and model complex systems. Despite its popularity, the standard form of the MEP can only generate Boltzmann-Gibbs distributions, which are ill-suited for many ...
Pablo A. Morales, Fernando E. Rosas
doaj   +1 more source

Implications and Consequences of SL(2R) as Invariance Group in the Description of Complex Systems Dynamics from a Multifractal Perspective of Motion

Entropy, 2022
Possible implications and consequences of using SL(2R) as invariance groups in the description at any scale resolution of the dynamics of any complex system are analyzed.
Lucian Dobreci, Oana Rusu, Decebal Vasincu, Mihaela Jarcău, Cristina Marcela Rusu, Silviu Gurlui, Vlad Ghizdovat, Alina Gavrilut, Maricel Agop   +8 more
doaj   +1 more source

Some Applications of Casorati Curvature for Statistical Submanifolds of Sasakian Statistical Manifolds and Locally Homogeneous, Quasi-Umbilical Hypersurfaces

پژوهش‌های ریاضی, 2021
In this paper, in the first part, the affine geometry is assumed as the main framework. Then we have a spacious explanation of necessary introduction in rather different subjects.
Azam Etemad Dehkordy
doaj  

Differentiable Manifolds and Geometric Structures

Mathematics
This editorial presents 26 research articles published in the Special Issue entitled Differentiable Manifolds and Geometric Structures of the MDPI Mathematics journal, which covers a wide range of topics particularly from the geometry of (pseudo ...
Adara M. Blaga
doaj   +1 more source