Results 31 to 40 of about 2,657,287 (122)
Apollonian Circle Packings: Geometry and Group Theory I. The Apollonian Group [PDF]
, 2005 Apollonian circle packings arise by repeatedly filling the intersticesbetween four mutually tangent circles with further tangent circles.We observe that there exist Apollonian packings which have strong integralityproperties, in which all circles in the ...
Colin L. Mallows +9 more
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, 2023 The family of planar graphs is a particularly important family and models many real-world networks. In this paper, we propose a principled framework based on the widely-known Apollonian packing process to generate new planar network, i.e., Type-II ...
Ouyang, Jinzhi +4 more
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, 2020 We have discovered the existence of extremely polydisperse High Internal-Phase-Ratio Emulsions (HIPEs) in which the internal-phase droplets, present at 95% volume fraction, remain spherical and organize themselves in the available space according to ...
Botet, Robert +7 more
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Statistical regularity of Apollonian gaskets
, 2021 Apollonian gaskets are formed by repeatedly filling the gaps between three mutually tangent circles with further tangent circles. In this paper we give explicit formulas for the limiting pair correlation and the limiting nearest neighbor spacing of ...
Zhang, X
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Universal Optimality of Apollonian Cell Encoders [PDF]
, 2018 Preserving privacy of private communication against an attacker is a fundamental concern of computer science security. Unconditional encryption considers the case where an attacker has unlimited computational power, hence no complexity result can be ...
Biondi, Fabrizio +5 more
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On Certain Properties of Random Apollonian Networks
, 2018 In this work we analyze fundamental properties of Random Apollonian Networks [34,35], a popular random graph model which generates planar graphs with power law properties.
Alan Frieze (3880564) +1 more
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Energy landscapes, scale-free networks and Apollonian packings
, 2006 We review recent results on the topological properties of two spatial scale-free networks, the inherent structure and Apollonian networks. The similarities between these two types of network suggest an explanation for the scale-free character of the ...
Doye, Jonathan, Massen, CP, Doye, JPK
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High dimensional Apollonian networks
, 2008 . We propose a simple algorithm which produces high dimensional Apollonian networks with both small-world and scale-free characteristics. We derive analytical expressions for the degree distribution, the clustering coefficient and the diameter of the ...
Guillaume Fertin +3 more
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Long paths in random Apollonian networks
, 2014 We consider the length L(n) of the longest path in a randomly generated Apollonian Network (ApN) An. We show that w.h.p. L(n) ≤ ne − logc n for any constant c < 2/3.
Cooper, Colin +5 more
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Degrees and distances in random and evolving apollonian networks
, 2016 In this paper we study random Apollonian networks (RANs) and evolving Apollonian networks (EANs), in d dimensions for any d ≥ 2, i.e. dynamically evolving random ddimensional simplices, looked at as graphs inside an initial d-dimensional simplex.
Komjáthy;, Júlia +3 more
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