Results 21 to 30 of about 12,053 (292)

On Voronoi Diagrams on the Information-Geometric Cauchy Manifolds

Entropy, 2020
We study the Voronoi diagrams of a finite set of Cauchy distributions and their dual complexes from the viewpoint of information geometry by considering the Fisher-Rao distance, the Kullback-Leibler divergence, the chi square divergence, and a flat ...
Frank Nielsen
doaj   +1 more source

Canonical triangulations of Dehn fillings [PDF]

, 2010
Every cusped, finite-volume hyperbolic three-manifold has a canonical decomposition into ideal polyhedra. We study the canonical decomposition of the hyperbolic manifold obtained by filling some (but not all) of the cusps with solid tori: in a broad ...
Schleimer, Saul, Guéritaud, François
core   +1 more source

An Instrument in Hyperbolic Geometry [PDF]

Proceedings of the American Mathematical Society, 1962
In addition to straight edge and compasses, the classical instruments of Euclidean geometry, we have in hyperbolic geometry the horocompass and the hypercompass. By a straight edge, or ruler, we draw the line joining any two distinct points, and by the compasses we construct a circle with given center and radius.
openaire   +1 more source

Normal automorphisms of relatively hyperbolic groups [PDF]

, 2010
An automorphism of a group G is normal if it fixes every normal subgroup of G setwise. We give an algebraic description of normal automorphisms of relatively hyperbolic groups.
D. Osin, Osin, Denis, Minasyan, Ashot, A. Minasyan   +3 more
core   +1 more source

Hyperbolic Geometry and Neutrosophic Trigonometry: A Unified Approach to Uncertainty Management in Geometric Spaces [PDF]

Neutrosophic Sets and Systems
This paper addresses the challenge of modeling uncertainty in hyperbolic geometry, where non Euclidean properties, such as angle sums in triangles smaller than 180°, complicate traditional trigonometric calculations.
Yismandry González Vargas, Diana Padrón Carrasco   +1 more
doaj   +1 more source

High Dimensional Hyperbolic Geometry of Complex Networks

Mathematics, 2020
High dimensional embeddings of graph data into hyperbolic space have recently been shown to have great value in encoding hierarchical structures, especially in the area of natural language processing, named entity recognition, and machine generation of ...
Weihua Yang, David Rideout
doaj   +1 more source

How the latent geometry of a biological network provides information on its dynamics: the case of the gene network of chronic myeloid leukaemia

Frontiers in Cell and Developmental Biology, 2023
Background: The concept of the latent geometry of a network that can be represented as a graph has emerged from the classrooms of mathematicians and theoretical physicists to become an indispensable tool for determining the structural and dynamic ...
Paola Lecca, Giulia Lombardi, Roberta Valeria Latorre, Claudio Sorio   +3 more
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Conjugacy in normal subgroups of hyperbolic groups [PDF]

, 2012
Let N be a finitely generated normal subgroup of a Gromov hyperbolic group G. We establish criteria for N to have solvable conjugacy problem and be conjugacy separable in terms of the corresponding properties of G/N.
Armando Martino, Ashot Minasyan, Minasyan, Ashot, Martino, Armando   +3 more
core   +1 more source

Conformal hyperbolic optics

Physical Review Research, 2021
Hyperbolic metamaterials have attracted considerable interest in the research community for their peculiar ability to enhance control of electromagnetic waves' propagation.
Shahram Dehdashti, Alireza Shahsafi, Bin Zheng, Lian Shen, Zuojia Wang, Rongrong Zhu, Huanyang Chen, Hongsheng Chen   +7 more
doaj   +1 more source

Hyperbolic Geometry [PDF]

, 2013
The author considers the space of relativistic velocities in the Minkowski vector space \(\mathbb{R}^{1,n}\) as the unit ball \(B^n \subset \mathbb{R}^n \) with the non-commutative non-associative invertible binary operation \(\oplus\), defined by the relativistic addition of velocities.
openaire   +4 more sources