Results 21 to 30 of about 16,187 (262)
A hyperbolic analogue of the Atiyah-Hitchin manifold
Journal of High Energy Physics, 2022 The Atiyah-Hitchin manifold is the moduli space of parity inversion symmetric charge two SU(2) monopoles in Euclidean space. Here a hyperbolic analogue is presented, by calculating the boundary metric on the moduli space of parity inversion symmetric ...
Paul Sutcliffe
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Greedy routing optimisation in hyperbolic networks
Scientific Reports, 2023 Finding the optimal embedding of networks into low-dimensional hyperbolic spaces is a challenge that received considerable interest in recent years, with several different approaches proposed in the literature. In general, these methods take advantage of
Bendegúz Sulyok, Gergely Palla
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Nonlinear Choquard equations on hyperbolic space [PDF]
Opuscula Mathematica, 2022 In this paper, our purpose is to prove the existence results for the following nonlinear Choquard equation \[-\Delta_{\mathbb{B}^{N}}u=\int_{\mathbb{B}^N}\dfrac{|u(y)|^{p}}{|2\sinh\frac{\rho(T_y(x))}{2}|^\mu} dV_y \cdot |u|^{p-2}u +\lambda u\] on the ...
Haiyang He
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Statistical Hyperbolicity in Teichmüller Space [PDF]
Geometric and Functional Analysis, 2014 In this paper we explore the idea that Teichmüller space is hyperbolic "on average." Our approach focuses on studying the geometry of geodesics which spend a definite proportion of time in some thick part of Teichmüller space. We consider several different measures on Teichmüller space and find that this behavior for geodesics is indeed typical.
Dowdall, Spencer +2 more
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Hyperbolicity in Teichmüller space [PDF]
Geometry & Topology, 2014 We review and organize some results describing the behavior of a Teichmüller geodesic and draw several applications: 1) We show that Teichmüller geodesics do not back track. 2) We show that a Teichmüller geodesic segment whose endpoints are in the thick part has the fellow travelling property.
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Geodesics in Trees of Hyperbolic and Relatively Hyperbolic Spaces [PDF]
Proceedings of the Edinburgh Mathematical Society, 2015 AbstractWe present a careful approximation of the quasi-geodesics of trees of hyperbolic and relatively hyperbolic spaces. As an application we prove a dynamical and geometric combination theorem for trees of relatively hyperbolic spaces, with both Farb's and Gromov's definitions.
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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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Topological Bihyperbolic Modules
Communications in Advanced Mathematical Sciences, 2021 The aim of this article is introducing and researching hyperbolic modules, bihyperbolic modules, topological hyperbolic modules, and topological bihyperbolic modules.
Merve Bilgin, Soley Ersoy
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Translation-Based Embeddings with Octonion for Knowledge Graph Completion
Applied Sciences, 2022 Knowledge representation learning achieves the automatic completion of knowledge graphs (KGs) by embedding entities into continuous low-dimensional vector space.
Mei Yu +7 more
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Analysis and Geometry in Metric Spaces, 2016 We consider a ‘contracting boundary’ of a proper geodesic metric space consisting of equivalence classes of geodesic rays that behave like geodesics in a hyperbolic space.We topologize this set via the Gromov product, in analogy to the topology of the ...
Cashen Christopher H.
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