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The hyperbolic geometry of financial networks [PDF]
Scientific Reports, 2021 Based on data from the European banking stress tests of 2014, 2016 and the transparency exercise of 2018 we construct networks of European banks and demonstrate that the latent geometry of these financial networks can be well-represented by geometry of ...
Martin Keller-Ressel, Stephanie Nargang
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Hyperbolic geometry of gene expression [PDF]
iScience, 2021 Summary: Patterns of gene expressions play a key role in determining cell state. Although correlations in gene expressions have been well documented, most of the current methods treat them as independent variables.
Yuansheng Zhou, Tatyana O. Sharpee
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Contact Geometry of Hyperbolic Equations of Generic Type [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2008 We study the contact geometry of scalar second order hyperbolic equations in the plane of generic type. Following a derivation of parametrized contact-invariants to distinguish Monge-Ampère (class 6-6), Goursat (class 6-7) and generic (class 7-7 ...
Dennis The
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Hyperbolic geometry of complex networks [PDF]
Physical Review E, 2010 We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong clustering in complex networks emerge naturally as simple reflections of the negative curvature and metric property of
Krioukov, Dmitri +4 more
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Visual outdoor space perception [PDF]
Scientific ReportsVisual space perception has been a topic of sustained research since the nineteenth century. Much of this research into the geometry of visual space, however, required observers to make judgments about spatial relationships between isolated points in ...
J. Farley Norman +6 more
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HC-SPA: Hyperbolic Cosine-Based Symplectic Phase Alignment for Fusion Optimization [PDF]
SensorsIn multimodal collaborative learning, the gradient dynamics of heterogeneous modalities face significant challenges due to the curvature heterogeneity of parameter manifolds and mismatches in phase evolution.
Wenlong Zhang +3 more
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METHODOLOGICAL APPROACH TO CONGRUENCE OF QUADRILATERALS IN HYPERBOLIC GEOMETRY
Facta Universitatis. Series, Teaching, Learning and Teacher Education, 2021 In this paper we will prove new criteria for the congruence of convex quadrilaterals in Hyperbolic geometry and consequently, display the appropriate methodological approach in teaching the same.
Milan Zlatanović, Victor Aguilar
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An Extension of Poincare Model of Hyperbolic Geometry with Gyrovector Space Approach [PDF]
Mathematics Interdisciplinary Research, 2016 The aim of this paper is to show the importance of analytic hyperbolic geometry introduced in [9]. In [1], Ungar and Chen showed that the algebra of the group SL(2, C) naturally leads to the notion of gyrogroups and gyrovector spaces for dealing ...
Mahfouz Rostamzadeh +1 more
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Potential Theory on Gromov Hyperbolic Spaces
Analysis and Geometry in Metric Spaces, 2022 Gromov hyperbolic spaces have become an essential concept in geometry, topology and group theory. Herewe extend Ancona’s potential theory on Gromov hyperbolic manifolds and graphs of bounded geometry to a large class of Schrödinger operators on Gromov ...
Kemper Matthias, Lohkamp Joachim
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SciPost Physics, 2023 Hyperbolic geometry on the one-bordered torus is numerically uniformized using Liouville theory. This geometry is relevant for the hyperbolic string tadpole vertex describing the one-loop quantum corrections of closed string field theory.
Atakan Hilmi Firat
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