Results 31 to 40 of about 1,008,318 (283)

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

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

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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The theorems of Stewart and Steiner in the Poincaré disc model of hyperbolic geometry [PDF]

, 2009
summary:In [Comput. Math. Appl. 41 (2001), 135--147], A. A. Ungar employs the Möbius gyrovector spaces for the introduction of the hyperbolic trigonometry.
Demirel, Oğuzhan
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

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

Impulse Gauss Curvatures [PDF]

, 2004
In Riemannian (differential) geometry, the differences between Euclidean geometry, elliptic geometry, and hyperbolic geometry are understood in terms of curvature.
Iseri, Howard
core   +1 more source

The Formulas of Möbius-Bretschneider and Möbius-Cagnoli in the Poincaré Disc Model of Hyperbolic Geometry

Al-Mustansiriyah Journal of Science, 2021
In this paper, we present two gyroarea formulas (Möbius-Bretschneider’s formula and Möbius-Cagnoli’s formula) for Möbius gyroquadrilaterals in the Poincaré disc model of hyperbolic geometry.
Gülcan Balakan, Oğuzhan Demirel
doaj   +1 more source

Supersymmetry and geometry of hyperbolic monopoles [PDF]

, 2015
This thesis studies the geometry of hyperbolic monopoles using supersymmetry in four and six dimensions. On the one hand, we show that starting with a four dimensional supersymmetric Yang-Mills theory provides the necessary information to study the ...
Gharamti, Moustafa
core   +3 more sources

A New Hyperbolic Area Formula of a Hyperbolic Triangle and Its Applications

Journal of Mathematics, 2014
We study some characterizations of hyperbolic geometry in the Poincaré disk. We first obtain the hyperbolic area and length formula of Euclidean disk and a circle represented by its Euclidean center and radius.
Hui Bao, Xingdi Chen
doaj   +1 more source