Zobrazeno 1 - 10
of 456
pro vyhledávání: '"Krioukov, A"'
Publikováno v:
Journal of Physics A 57, 345201 (2024)
Riemann surfaces are among the simplest and most basic geometric objects. They appear as key players in many branches of physics, mathematics, and other sciences. Despite their widespread significance, how to compute distances between pairs of points
Externí odkaz:
http://arxiv.org/abs/2404.19120
Autor:
Boguna, Marian, Krioukov, Dmitri
Causal set theory is perhaps the most minimalistic approach to quantum gravity, in the sense that it makes next to zero assumptions about the structure of spacetime below the Planck scale. Yet even with this minimalism, the continuum limit is still a
Externí odkaz:
http://arxiv.org/abs/2401.17376
Undirected hyperbolic graph models have been extensively used as models of scale-free small-world networks with high clustering coefficient. Here we presented a simple directed hyperbolic model, where nodes randomly distributed on a hyperbolic disk a
Externí odkaz:
http://arxiv.org/abs/2303.01002
Publikováno v:
Computational Methods and Function Theory, 2024
Diameter is one of the most basic properties of a geometric object, while Riemann surfaces are one of the most basic geometric objects. Surprisingly, the diameter of compact Riemann surfaces is known exactly only for the sphere and the torus. For hig
Externí odkaz:
http://arxiv.org/abs/2301.10844
Publikováno v:
Phys. Rev. E 106, 054308 (2022)
The structure of a network is an unlabeled graph, yet graphs in most models of complex networks are labeled by meaningless random integers. Is the associated labeling noise always negligible, or can it overpower the network-structural signal? To addr
Externí odkaz:
http://arxiv.org/abs/2204.08508
Autor:
Bobrowski, Omer, Krioukov, Dmitri
Publikováno v:
Higher-Order Systems (F. Battiston and G. Petri (edt.)), Chapter 2, Springer International Publishing, Cham, Switzerland, 2022
We review a collection of models of random simplicial complexes together with some of the most exciting phenomena related to them. We do not attempt to cover all existing models, but try to focus on those for which many important results have been re
Externí odkaz:
http://arxiv.org/abs/2105.12914
Publikováno v:
Phys. Rev. E 103, 052307 (2021)
Models of complex networks often incorporate node-intrinsic properties abstracted as hidden variables. The probability of connections in the network is then a function of these variables. Real-world networks evolve over time, and many exhibit dynamic
Externí odkaz:
http://arxiv.org/abs/2101.00414
Publikováno v:
Phys. Rev. E 109(5), 054131 (2024)
We consider random hyperbolic graphs in hyperbolic spaces of any dimension $d+1\geq 2$. We present a rescaling of model parameters that casts the random hyperbolic graph model of any dimension to a unified mathematical framework, leaving the degree d
Externí odkaz:
http://arxiv.org/abs/2010.12303
Publikováno v:
Discrete & Computational Geometry, v.70(3), p.671-712 , 2023
Curvature is a fundamental geometric characteristic of smooth spaces. In recent years different notions of curvature have been developed for combinatorial discrete objects such as graphs. However, the connections between such discrete notions of curv
Externí odkaz:
http://arxiv.org/abs/2009.04306
Autor:
van der Hoorn, Pim, Cunningham, William J., Lippner, Gabor, Trugenberger, Carlo, Krioukov, Dmitri
Publikováno v:
Phys. Rev. Research 3, 013211 (2021)
Connections between continuous and discrete worlds tend to be elusive. One example is curvature. Even though there exist numerous nonequivalent definitions of graph curvature, none is known to converge in any limit to any traditional definition of cu
Externí odkaz:
http://arxiv.org/abs/2008.01209