Hyperbolicity, degeneracy, and expansion of random intersection graphs.

Specifically, we fully characterize the degeneracy of random intersection graphs, and prove that the model asymptotically almost surely produces graphs with hyperbolicity at least n. ... Further, we prove that in the parametric regime where random intersection graphs are degenerate an even stronger notion of sparseness, so called bounded expansion, holds with high probability. ... (ii) For α > 1, w.h.p. random intersection graphs have bounded expansion (and thus constant degeneracy). ...

arXiv:1409.8196v7 fatcat:nvex4vo7yba3hnpiyzboov7sde

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Specifically, we fully characterize the degeneracy of random intersection graphs, and prove that the model asymptotically almost surely produces graphs with hyperbolicity at least log n. ... Further, we prove that in the parametric regime where random intersection graphs are degenerate an even stronger notion of sparseness, so called bounded expansion, holds with high probability. ... (ii) For α > 1, w.h.p. random intersection graphs have bounded expansion (and thus constant degeneracy). ...

doi:10.24166/im.06.2017 fatcat:6ioejr5t6fftfidpsokenntj2u

nodes' popularity, similarity or uniform random. ... with diverse modes and the cascading process of node states. ... This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 71303217 and 61379074) and the Zhejiang Provincial Natural Science Foundation of China (Grant Nos LY17G030030 ...

doi:10.1038/srep42956 pmid:28220840 pmcid:PMC5318875 fatcat:af2xetzkjvavtcxha6jhojvcjq

DOAJ

We study cliques in hyperbolic random graphs G and present new results on the expected number of k-cliques E[K k ] and the size of the largest clique ω(G). ... There is, however, no established and simple model which also has a high clustering of vertices as typically observed in real data. Hyperbolic random graphs bridge this gap. ... Closely related to clustering and community structures, we analyze the emergence of cliques in hyperbolic random graphs. ...

doi:10.1109/infocom.2015.7218533 dblp:conf/infocom/FriedrichK15 fatcat:wnp3xv4xbvbufi3uxzeabahwc4

We sum these contributions for quantum graphs with uniformly hyperbolic dynamics, obtaining +2τ^3, in agreement with random-matrix theory. ... We consider the contributions from pairs of periodic orbits represented by diagrams with up to two self-intersections connected by up to four arcs and explain why all other diagrams are expected to give ... We are grateful to a referee who found a large number of misprints and inconsistencies in the paper and helped us improve the presentation of section 3.2. ...

doi:10.1088/0305-4470/36/31/303 fatcat:cdfngs2tozatlm6ueh2joxojpm

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and prove the existence of physical measures and their stochastical stability. ... We consider diffeomorphisms of a compact manifold with a dominated splitting which is hyperbolic except for a "small" subset of points (Hausdorff dimension smaller than one, e.g. a denumerable subset) ... The expansion on the inner radius of the domains of the graphs is a consequence of the fact that a ball in W cs δ ¢ x£ is a E-disk and any ball in W cu δ ¢ x£ is a F-disk, x Λ. ...

doi:10.3934/dcds.2008.20.849 fatcat:llzbb7tg5betxkd3t2wzrzs6da

We present a new technique of dealing with contribution from the former type of orbits. The technique allows us to derive the third order term of the expansion for general graphs. ... It has been shown that for a certain special type of quantum graphs the random-matrix form factor can be recovered to at least third order in the scaled time \tau using periodic-orbit theory. ... A part of the research was performed while the author was working at the Weizmann Institute of Science, Rehovot, Israel, supported by the Israel Science Foundation, a Minerva grant, and the Minerva Center ...

doi:10.1088/0959-7174/14/1/008 fatcat:wrhmg7xo2vfpvfijeuiaybbg7a

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We present a tutorial treatment of this work and its place in dynamical systems theory, with an emphasis on results that can be checked in specific systems. ... We extend the Melnikov technique to certain non-Hamiltonian systems of ordinary differential equations. The extension is made with a view to applications in the physical sciences and engineering. ... Holmes for inspiration and F. Wu ...

doi:10.1109/tcs.1983.1085413 fatcat:fuwpjkxwyjbx7n7wwbfihgmzj4

We prove that the statistical properties of random perturbations of a nonuniformly hyperbolic diffeomorphism are described by a finite number of stationary measures. ... We show that a certain C^2-open class of nonuniformly hyperbolic diffeomorphisms introduced in [Alves, J; Bonatti, C. and Viana, V., SRB measures for partially hyperbolic systems with mostly expanding ... Then the intersection of E cs x with C cu a (y) is the zero vector. So if x ∈ S then T y S is the graph of a linear map A x (y) : E cu x → E cs x for y ∈ U x ∩ S. ...

arXiv:math/0404160v3 fatcat:ikiogufx7zbtngqebscgeocftq

Multiple Versions

and prove the existence of physical measures and their stochastical stability. ... We consider diffeomorphisms of a compact manifold with a dominated splitting which is hyperbolic except for a "small" subset of points (Hausdorff dimension smaller than one, e.g. a denumerable subset) ... The expansion on the inner radius of the domains of the graphs is a consequence of the fact that a ball in W cs δ (x) is a E-disk and any ball in W cu δ (x) is a F-disk, x ∈ Λ. ...

arXiv:math/0409391v3 fatcat:7ljd5ozhojdp3kf5cu6kglwfcm

Multiple Versions

We show that the maximum algebraic degree required to answer any of the sub-predicates and primitives, and, thus, our main predicate is 10 in non-degenerate configurations when the trisector is of Hausdorff ... Most of our analysis is carried out in the inverted space, which is where our geometric observations and analysis is captured in algebraic terms. ... In any such random layout, it must hold that • Sˆa intersects the negative side of ψ(vik jb ) but does not intersect the negative side of ψ(vi jkb ) and, • Sˆb intersects the negative ...

arXiv:2007.06658v1 fatcat:anudlx3o6bae3j2k577ymn4e2y

TSrSk, and A. Wilkinson for fruitful discussions, and H. Ilyashenko for her help in the preparation of the manuscript. ... Tlm authors are grateful to CIMAT and UNAM, Mexico, where the work was initiated, and to Cornell University, USA, where it was finally written, for their hospitality and creative atmosphere. ... Let S: D --* D ~ be a mapping such that StD~ : Di ~ D~ is the restriction to Di of a linear hyperbolic map with the constants of contrhction and expansion equal to k E (0, 1) and k -1 > 1, respectively ...

doi:10.1007/bf02465190 fatcat:pzrb6g2tgfh4hllcanj55wcz2q

In particular we present Rivin's theorem that gives a characterization of compact convex hyperbolic polyhedra, and Hodgson's proof of the Adreev's theorem. ... We also review the analogous characterization of ideal polyhedra, and give a family of counter-examples that proves that hyperbolic polyhedra are not determined by edge lengths. ... Now consider a closed geodesic γ that does not intersect the interior of any face of Q t . Then γ lives in the t-expansion of the 1-skeleton of Q. ...

arXiv:1006.4445v1 fatcat:sbbf4xf2jvftlptqncpf52q2yq

We explain how these intriguing features are related to the nature of Landau levels in hyperbolic space, and how they could be verified experimentally. ... Our results reveal that the butterfly spectrum with large extended gapped regions prevails and that its shape is universally determined by the number of edges of the fundamental tile, while the fractal ... AS, LKU and RT acknowledge support for funding from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through Project-ID 258499086 -SFB 1170 and ...

arXiv:2111.05779v2 fatcat:dvzpqi2khvduth7qrgdrayiy3u

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At T = 0 K exact ground states are generated by a new algorithm of graph theory and maps of rigid bonds or solidary spins for all ground states are obtained. ... At intermediate x it is found a new phase made up of erratic magnetic walls (lines). At T ~ 0 K a simple renormalization group approach confirms the existence of the random antiphase state. J. ... Uhry from the department of Applied Mathematics of the University of Grenoble, for their initiation to graph theory and the active cooperation on the application of the Edmond's algorithm to the frustration ...

doi:10.1051/jphyslet:019820043010034700 fatcat:qskic4dypjcatjugodhpow4ble

Hyperbolicity, degeneracy, and expansion of random intersection graphs [article]

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