Results 11 to 20 of about 135,287 (264)

The Beckman–Quarles Theorem in Hyperbolic Geometry

Journal of Mathematics, 2021
In this paper, we present the counterpart of the Beckman–Quarles theorem in the Poincaré disc model of hyperbolic geometry to characterize the gyroisometries (hyperbolic isometries) with a single nonzero distance a∈0,1 satisfying a2∈ℚ.
Oğuzhan Demirel, Damla Topal, Leyla Aslan   +2 more
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KONFLIK KOGNITIF MAHASISWA DALAM MEMAHAMI KONSEP GEOMETRI HIPERBOLIK DAN ELLIPTIK

Jupitek, 2020
Using schemes of Euclid's geometrical concepts in long-term memory to understand hyperbolic geometry and elliptic geometry concepts with assimilation and accommodation allows for cognitive conflict.
Mega Teguh Budiarto, Rini Setyaningsih
doaj   +1 more source

Hyperbolic matrix factorization improves prediction of drug-target associations

Scientific Reports, 2023
Past research in computational systems biology has focused more on the development and applications of advanced statistical and numerical optimization techniques and much less on understanding the geometry of the biological space.
Aleksandar Poleksic
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Link prediction with hyperbolic geometry

Physical Review Research, 2020
Link prediction is a paradigmatic problem in network science with a variety of applications. In latent space network models this problem boils down to ranking pairs of nodes in the order of increasing latent distances between them. The network model with
Maksim Kitsak, Ivan Voitalov, Dmitri Krioukov   +2 more
doaj   +1 more source

On a family of pseudohyperbolic disks [PDF]

, 2015
Hyperbolic geometry plays an important role within function theory of the disk. For example, via the Schwarz-Pick Lemma, the isometries of the unit disk $\mathbb D$ with respect to this geometry are the conformal self-maps of $\mathbb D$.
Mortini, Raymond, Rupp, Rudolf
core   +2 more sources

Random Motions at Finite Velocity on Non-Euclidean Spaces

Mathematics, 2022
In this paper, random motions at finite velocity on the Poincaré half-plane and on the unit-radius sphere are studied. The moving particle at each Poisson event chooses a uniformly distributed direction independent of the previous evolution. This implies
Francesco Cybo Ottone, Enzo Orsingher
doaj   +1 more source

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
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Menelaus's theorem for hyperbolic quadrilaterals in the Einstein relativistic velocity model of hyperbolic geometry [PDF]

, 2010
Hyperbolic Geometry appeared in the first half of the 19th century as an attempt to understand Euclid's axiomatic basis of Geometry.
Barbu, Catalin
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
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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