A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2018; you can also visit the original URL.
The file type is application/pdf.
Filters
Threshold and hitting time for high-order connectedness in random hypergraphs
unpublished
Preserved Fulltext
This generalises the classical hitting time result of Bollobás and Thomason for graphs. ...
We also deduce a hitting time result for the random hypergraph process-the hypergraph becomes j-connected at exactly the moment when the last isolated j-set disappears. ...
Acknowledgement The authors would like to thank an anonymous referee for detailed feedback which greatly improved the quality of the manuscript. ...
fatcat:geqsbyuk3zgtnght2k7vtuunau
Vanishing of Cohomology Groups of Random Simplicial Complexes (Keynote Speakers)
2018
International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is application/pdf.
As a corollary, we deduce a hitting time result for a different model of random simplicial complexes introduced in [Linial and Meshulam, Combinatorica, 2006], a result which has only been known for dimension ...
For each 1 ≤ j ≤ k − 1, we determine when all cohomology groups with coefficients in F 2 from dimension one up to j vanish and the zero-th cohomology group is isomorphic to F 2 . ...
As a corollary, we deduce a hitting time result for Y p in general dimension, thus extending the hitting time result of Kahle and Pittel [15] . ...
doi:10.4230/lipics.aofa.2018.7
dblp:conf/aofa/CooleyGKS18
fatcat:b375abvdfvguza2dzm6okf6aua
Threshold and hitting time for high-order connectivity in random hypergraphs
[article]
2015
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
We also deduce a hitting time result for the random hypergraph process -- the hypergraph becomes j-connected at exactly the moment when the last isolated j-set disappears. ...
We determine the threshold at which the random k-uniform hypergraph with edge probability p becomes j-connected with high probability. ...
Concluding remark In [5] , it is determined for the case j = 1 that the hitting time for d-strong 1-connectedness, i.e. the time at which the hypergraph first has the property that deleting any set of ...
arXiv:1502.07289v1
fatcat:dyv6opjaorg2zcnfkr4usesx4a
Vanishing of cohomology groups of random simplicial complexes
[article]
2018
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
As a corollary, we deduce a hitting time result for a different model of random simplicial complexes introduced in [Linial and Meshulam, Combinatorica, 2006], a result which was previously only known for ...
This property is not deterministically monotone for this model of random complexes, but nevertheless we show that it has a single sharp threshold. ...
An extended abstract of the case k = 2 has appeared in the Proceedings of Eurocomb 2017 [11] . ...
arXiv:1806.04566v1
fatcat:2l62ywhfefh2tjy7rcfso57bom
Homological connectivity of random hypergraphs
[article]
2016
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Although this is not intrinsically a monotone property, we show that it nevertheless has a single sharp threshold, and indeed prove a hitting time result relating the connectedness to the disappearance ...
We consider simplicial complexes that are generated from the binomial random 3-uniform hypergraph by taking the downward-closure. ...
Bollobás and Thomason [2] subsequently proved a hitting time result: With high probability the random graph process, in which edges are added one at a time in random order, becomes connected at exactly ...
arXiv:1604.00842v1
fatcat:72cc2cjxhnac7e7nsy6r3letim
Positional Games
[article]
2014
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
and hypergraphs. ...
We survey the basic notions of the field, its approaches and tools, as well as numerous recent advances, standing open problems and promising research directions. ...
The author wishes to thank Asaf Ferber, Dan Hefetz, Miloš Stojaković and Tibor Szabó for careful reading of the manuscript and many helpful comments, and also for an extensive and fruitful cooperation ...
arXiv:1404.2731v1
fatcat:hlv7jjt4vbgt5kwhr7pc4fgyue
Phase transition in cohomology groups of non-uniform random simplicial complexes
[article]
2020
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Note that this fulltext copy is not of the "primary" version of this work. The version it corresponds to is:
2020 pre-print arXiv:2005.07103v2 fatcat:4xtnocibxngcdhe33hjtrxwj2qOther Versions
We also prove a hitting time result for a natural process interpretation, in which simplices and their downward-closure are added one by one. ...
We prove that this notion of connectedness displays a phase transition and determine the threshold. ...
The vertex-connectedness threshold for uniform random hypergraphs, which we quoted from [9] for the proof of (b), also follows as a special case of earlier and much stronger results from [10] and from ...
arXiv:2005.07103v3
fatcat:vgrsvopfefbuvejew2oz2ez2p4
On Weak Hamiltonicity of a Random Hypergraph
[article]
2014
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
In particular, for d ≥ 3 fixed and p=(d-1)! ...
As a consequence, the probability that the random hypergraph H_d(n, m=n( n + c)/d), where m potential edges are chosen uniformly at random to be present, is weak Hamiltonian also tends to e^-e^-c. ...
If true, this conjecture would generalize to hypergraphs the weak Hamilton version of Bollobás' [3] hitting time result. ...
arXiv:1410.7446v1
fatcat:lozx7u3vtnc25okh2mbqyjevdi
Thresholds in Random Motif Graphs
2019
International Workshop on Approximation Algorithms for Combinatorial Optimization
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is application/pdf.
Moreover, in the first three cases we give the analogous hitting time results; with high probability, the first graph in the random motif graph process that has minimum degree one (or two) is connected ...
We establish that every monotone property has a threshold in this model, and determine the thresholds for connectivity, Hamiltonicity, the existence of a perfect matching, and subgraph appearance. ...
The analogue hitting time result is also true.
66:4 Thresholds in Random Motif Graphs Next, we describe the threshold for the appearance of a subgraph S. ...
doi:10.4230/lipics.approx-random.2019.66
dblp:conf/approx/AnastosMP19
fatcat:j2tspe36zvcurm4tfiglox3jfq
The sharp threshold for jigsaw percolation in random graphs
[article]
2019
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
We show that this threshold is sharp, and that it lies at 1/4n n. ...
Bollobás, Riordan, Slivken and Smith proved that when the two graphs are independent binomial random graphs, whether the jigsaw process percolates undergoes a phase transition when the product of the two ...
For random graphs, the famous hitting time result of Bollobás and Thomason [6] relates the threshold for connectedness of a random graph to the disappearance of the last isolated vertex, implying that ...
arXiv:1809.01907v2
fatcat:5su4yahvrfd3neaic26gxjsb5u
Resilience for tight Hamiltonicity
[article]
2021
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL.
The file type is application/pdf.
Specifically, for any γ>0 and k≥3, we show that asymptotically almost surely, every subgraph of the binomial random k-uniform hypergraph G^(k)(n,n^γ-1) in which all (k-1)-sets are contained in at least ...
We prove that random hypergraphs are asymptotically almost surely resiliently Hamiltonian. ...
In random hypergraphs, Dudek and Frieze [11, 12] found for several different notions of 'cycle' the threshold for Hamiltonicity in the binomial random hypergraph G (k) (n, p), that is the nvertex k-graph ...
arXiv:2105.04513v1
fatcat:y3gyj67jknc4tkkxsxlv3ltkfy
An Introduction to Metabolic Networks and Their Structural Analysis
2008
IEEE/ACM Transactions on Computational Biology & Bioinformatics
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2010; you can also visit the original URL.
The file type is application/pdf.
The literature is vast enough already, and the thread through it is difficult to follow even for the more experienced worker in the field. ...
There has been a renewed interest for metabolism in the computational biology community, leading to an avalanche of papers coming from methodological network analysis as well as experimental and theoretical ...
Later, the same first author and others [54] extended the distance measure to networks and based it this time on simple operations on hypergraphs, such as union, intersection, and difference of two hypergraphs ...
doi:10.1109/tcbb.2008.79
pmid:18989046
fatcat:iomp7dhnvndgtlwhpeyc4dnvoa
Recent advances in percolation theory and its applications
2015
Physics reports
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Note that this fulltext copy is not of the "primary" version of this work. The version it corresponds to is:
2015 pre-print arXiv:1504.02898v1 fatcat:jzml77er4fcs5bzidj7ugpll5iOther Versions
Recent applications of the percolation theory in natural and artificial landscapes are also reviewed. ...
In this review we will first outline the basic features of the ordinary model and take a glimpse at a number of selective variations and modifications of the original model. ...
Broadbent and Hammersley proposed the concept of a percolation threshold above which the links form an infinite cluster with high probability. ...
doi:10.1016/j.physrep.2015.03.003
fatcat:fwp76ca44vanfh2inf5a6tzjiq
Combinatorial Landscapes
2002
SIAM Review
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
In this review we focus on the connections of landscape theory with algebraic combinatorics and random graph theory, where exact results are available. ...
Fitness landscapes have proven to be a valuable concept in evolutionary biology, combinatorial optimization, and the physics of disordered systems. ...
In the random graph Q n α,λ the probability λ * = 1 − α−1 √ α −1 is the threshold value for connectivity. ...
doi:10.1137/s0036144501395952
fatcat:s46zur5dnrc6rhe7xpdeb3znmi
Social physics
[article]
2021
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL.
The file type is application/pdf.
Other Versions
, cooperation as a basis for civilised life, the structure of (social) networks, and the integration of intelligent machines in such networks. ...
Recent decades have seen a rise in the use of physics-inspired or physics-like methods in attempts to resolve diverse societal problems. ...
In these simulations, the number of hyperlinks equals the critical number that guarantees hypergraph connectedness, l = l c . ...
arXiv:2110.01866v1
fatcat:ccfxyezl6zgddd6uvrxubmaxua
« Previous
Showing results 1 — 15 out of 49 results