Results 31 to 40 of about 17,583 (186)

Stability of the Mezard-Parisi solution for random manifolds

, 1996
The eigenvalues of the Hessian associated with random manifolds are constructed for the general case of $R$ steps of replica symmetry breaking. For the Parisi limit $R\to\infty$ (continuum replica symmetry breaking) which is relevant for the manifold ...
Carlucci, D. M., De Dominicis, C., Temesvari, T.   +2 more
core   +3 more sources

Duality between Ahlfors-Liouville and Khas'minskii properties for nonlinear equations

, 2020
In recent years, the study of the interplay between (fully) non-linear potential theory and geometry received important new impulse. The purpose of this work is to move a step further in this direction by investigating appropriate versions of ...
Mari, Luciano, Pessoa, Leandro F.
core   +1 more source

Reaction Kinetics Path Based on Entropy Production Rate and Its Relevance to Low-Dimensional Manifolds

Entropy, 2014
The equation that approximately traces the trajectory in the concentration phase space of chemical kinetics is derived based on the rate of entropy production.
Shinji Kojima
doaj   +1 more source

A Riemannian View on Shape Optimization

, 2014
Shape optimization based on the shape calculus is numerically mostly performed by means of steepest descent methods. This paper provides a novel framework to analyze shape-Newton optimization methods by exploiting a Riemannian perspective.
Schulz, Volker
core   +1 more source

Robust Hessian Locally Linear Embedding Techniques for High-Dimensional Data

Algorithms, 2016
Recently manifold learning has received extensive interest in the community of pattern recognition. Despite their appealing properties, most manifold learning algorithms are not robust in practical applications.
Xianglei Xing, Sidan Du, Kejun Wang
doaj   +1 more source

Moduli spaces of G2 manifolds

, 2010
This paper is a review of current developments in the study of moduli spaces of G2 manifolds. G2 manifolds are 7-dimensional manifolds with the exceptional holonomy group G2.
Beasley C., Becker K., Berger M., Bonan E., Cvetic M., Harvey F. R., Hori K., Joyce D. D., Joyce D. D., Nordström J., SERGEY GRIGORIAN   +10 more
core   +1 more source

Geometry of Manifolds and Applications

Mathematics
This editorial presents 24 research articles published in the Special Issue entitled Geometry of Manifolds and Applications of the MDPI Mathematics journal, which covers a wide range of topics from the geometry of (pseudo-)Riemannian manifolds and their ...
Adara M. Blaga
doaj   +1 more source

The Soliton-Ricci Flow with variable volume forms

Complex Manifolds, 2016
We introduce a flow of Riemannian metrics and positive volume forms over compact oriented manifolds whose formal limit is a shrinking Ricci soliton. The case of a fixed volume form has been considered in our previouswork.We still call this new flow, the ...
Pali Nefton
doaj   +1 more source

Information Geometry of κ-Exponential Families: Dually-Flat, Hessian and Legendre Structures

Entropy, 2018
In this paper, we present a review of recent developments on the κ -deformed statistical mechanics in the framework of the information geometry.
Antonio M. Scarfone, Hiroshi Matsuzoe, Tatsuaki Wada   +2 more
doaj   +1 more source

Hessian manifolds of constant Hessian sectional curvature

Journal of the Mathematical Society of Japan, 1995
Let \(M\) be a flat affine manifold with a flat affine connection \(D\). If \(M\) admits a Riemannian metric \(g\) such that \(g\) is locally expressed by \(g= D^2 u\), then \((M, D, g)\) is said to be a Hessian manifold. We define Hessian sectional curvatures (these correspond to holomorphic sectional curvatures for Kählerian manifolds) and construct ...
openaire   +3 more sources