Results 211 to 220 of about 235,971 (249)

Image biomarkers and explainable AI: handcrafted features versus deep learned features. [PDF]

Eur Radiol Exp
Rundo L, Militello C.
europepmc   +1 more source

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The tangent space in sub-Riemannian geometry

Journal of Mathematical Sciences, 1994
Tangent spaces of a sub-Riemannian manifold are themselves sub-Riemannian manifolds. They can be defined as metric spaces, using Gromov’s definition of tangent spaces to a metric space, and they turn out to be sub-Riemannian manifolds. Moreover, they come with an algebraic structure: nilpotent Lie groups with dilations.
A. Bellaïche
openaire   +3 more sources

Topics in sub-Riemannian geometry

Russian Mathematical Surveys, 2016
Subriemannian geometry is geometry of the spaces with nonholonomic constraints. In this paper, we give an informal survey of some topics from the subject starting from the construction of geodesic lines and arriving to the recent definition of the curvature.
A. Agrachev
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Geometry, Analysis and Dynamics on sub-Riemannian Manifolds

2016
These lectures focus on some probabilistic aspects related to sub-Riemannian geometry. The main intention is to give an introduction to hypoelliptic and subelliptic diffusions. The notes are written from a geometric point of view trying to minimize the weight of “probabilistic baggage” necessary to follow the arguments.
Andrei A. Agrachev, Davide Barilari, Ugo Boscain, Ugo Boscain   +3 more
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Geometric Control Theory and Sub-Riemannian Geometry

, 2014
This volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language for studying controllability, motion planning, stabilizability and optimality for control systems. The geometric approach turned out to
STEFANI, GIANNA, Ugo Boscain, Mario Sigalotti, SARYCHEV, ANDREY, Jean Paul Gauthier   +4 more
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Sub-Riemannian Geometry and Optimal Transport

2014
The book provides an introduction to sub-Riemannian geometry and optimal transport and presents some of the recent progress in these two fields. The text is completely self-contained: the linear discussion, containing all the proofs of the stated results, leads the reader step by step from the notion of distribution at the very beginning to the ...
L. Rifford
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The Sub-Riemannian Geometry of Screw Motions with Constant Pitch

Journal of Geometric Analysis, 2023
We consider a family of Riemannian manifolds M such that for each unit speed geodesic γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs ...
Eduardo Hulett, R. P. Moas, M. Salvai
semanticscholar   +1 more source

Sub-Riemannian Geometry, Mixing, and the Holonomy of Optimal Mass Transport

arXiv.org
The theory of Monge-Kantorovich Optimal Mass Transport (OMT) has in recent years spurred a fast developing phase of research in stochastic control, control of ensemble systems, thermodynamics, data science, and several other fields in engineering and ...
Mahmoud Abdelgalil, T. Georgiou
semanticscholar   +1 more source

Volumes in Sub-Riemannian Geometry

2019
In this chapter we investigate the notion of the intrinsic volume in sub-Riemannian geometry in the case of "equiregular" structures. In particular we consider the Popp and the Hausdorff volumes. On
Ugo Boscain, Davide Barilari, Andrei A. Agrachev   +2 more
openaire   +2 more sources