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Phase transition of random non-uniform hypergraphs

Élie de Panafieu
2015 Journal of Discrete Algorithms  
Non-uniform hypergraphs appear in various domains of computer science as in the satisfiability problems and in data analysis.  ...  We show that many analytic tools developed for the analysis of graphs can be extended surprisingly well to non-uniform hypergraphs.  ...  In particular, the analysis of the birth of the complex component in terms of the size of the components and the order of the phase transition can be found in [17] , [6] , [8] , [14] and [25] .  ... 
doi:10.1016/j.jda.2015.01.009 fatcat:xxh3eghn4ratdicbfrwjyedbya

Phase Transition of Random Non-uniform Hypergraphs [chapter]

Élie de Panafieu
2013 Lecture Notes in Computer Science  
Non-uniform hypergraphs appear in various domains of computer science as in the satisfiability problems and in data analysis.  ...  We show that many analytic tools developed for the analysis of graphs can be extended surprisingly well to non-uniform hypergraphs.  ...  It would be interesting to measure the impact of this modification on the phase transition properties described in this paper.  ... 
doi:10.1007/978-3-642-45278-9_12 fatcat:r346m5owafhrtoo45oepwpjo4a

Higher order interactions destroy phase transitions in Deffuant opinion dynamics model [article]

Hendrik Schawe, Laura Hernández
2021 arXiv   pre-print
We show that including higher order interactions induces a drastic change in the onset of consensus for random hypergraphs; instead of the sharp phase transition, characteristic of the dyadic Deffuant  ...  This phenomenon is absent from regular hypergraphs, which conserve a phase transition.  ...  ACKNOWLEDGMENTS The authors acknowledge the OpLaDyn grant obtained in the 4th round of the Trans-Atlantic Platform Digging into Data Challenge (2016-147 ANR OPLADYN TAP-DD2016) and Labex MME-DII (Grant  ... 
arXiv:2111.12165v1 fatcat:pocaqut35vhejgsvu4o33xbbhu

Covering Problems and Core Percolations on Hypergraphs [article]

Bruno Coelho Coutinho, Hai-Jun Zhou, Yang-Yu Liu
2019 arXiv   pre-print
We offer analytical solutions of these two core percolations for random hypergraphs with arbitrary vertex degree and hyperedge cardinality distributions.  ...  We also compute these two cores in several real-world hypergraphs, finding that they tend to be much smaller than their randomized counterparts.  ...  and non-zero for hybrid phase transitions.  ... 
arXiv:1605.00897v2 fatcat:rqosvf35vzeideeqcaawyajeti

Phase transitions in the q-coloring of random hypergraphs

Marylou Gabrié, Varsha Dani, Guilhem Semerjian, Lenka Zdeborová
2017 Journal of Physics A: Mathematical and Theoretical  
We study in this paper the structure of solutions in the random hypergraph coloring problem and the phase transitions they undergo when the density of constraints is varied.  ...  This problem generalizes naturally coloring of random graphs (K=2) and bicoloring of random hypergraphs (q=2), both of which were extensively studied in past works.  ...  Acknowledgments We warmly thank the Simons Institute for the Theory of Computing at UC Berkeley, where this work has been initiated as a working group within the program Counting Complexity and Phase Transitions  ... 
doi:10.1088/1751-8121/aa9529 fatcat:qahzk2p7ereqjc5pt5voagvabe

Clustering Hypergraphs via the MapEquation

Matthew Swan, Justin Zhan
2021 IEEE Access  
In phase two instead of creating a random sequence of nodes, we create a random sequence of community IDs.  ...  The cleaned version is a non-kuniform hypergraph with 1637 nodes and 1524 edges. Since this hypergraph is not K-uniform, the L-S algorithm cannot be applied.  ... 
doi:10.1109/access.2021.3075621 fatcat:4amwonriqbeodiwlpghgfxce3e

Minimum vertex cover problems on random hypergraphs: Replica symmetric solution and a leaf removal algorithm

Satoshi Takabe, Koji Hukushima
2014 Physical Review E  
We study minimum vertex cover problems on random \alpha-uniform hypergraphs using two different approaches, a replica method in statistical mechanics of random systems and a leaf removal algorithm.  ...  It is found that there exists a phase transition at the critical average degree e/(\alpha-1).  ...  The average minimum-cover ratio on random α-uniform hypergraphs with α = 3 as a function of the average degree c.  ... 
doi:10.1103/physreve.89.062139 pmid:25019756 fatcat:mmune5cd6be73npgxhy3offow4

Spectral detection on sparse hypergraphs

Maria Chiara Angelini, Francesco Caltagirone, Florent Krzakala, Lenka Zdeborova
2015 2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)  
We propose a spectral method based on a generalization of the non-backtracking Hashimoto matrix into hypergraphs.  ...  We consider the problem of the assignment of nodes into communities from a set of hyperedges, where every hyperedge is a noisy observation of the community assignment of the adjacent nodes.  ...  V we derive the belief propagation algorithm and the detectability phase transition by linearization around the uniform fixed point. In Sec.  ... 
doi:10.1109/allerton.2015.7446987 dblp:conf/allerton/AngeliniCKZ15 fatcat:mass4a52afayhegmxukkylq3ua

Poisson Cloning Model for Random Graphs

Jeong Han Kim
2007 Expositions of Current Mathematics  
Particularly, the phase transition for the existence of non-empty 2-core is not sharp.  ...  Actually, for k• †3, it turns out that the phase transition is similar to that of the 2-core in the random hypergraphs.  ... 
doi:10.11429/emath1996.2007.autumn-meeting1_104 fatcat:qhnzr56u2nhv7ns3eeavluzmfm

Phase transition in a power-law uniform hypergraph [article]

Mingao Yuan
2021 arXiv   pre-print
We propose a power-law m-uniform random hypergraph on n vertexes.  ...  Interestingly, for the number of loose 2-cycle, phase transition occurs at both α=1 and α=2.  ...  Keywords: uniform hypergraph; power-law; phase transition. 1.  ... 
arXiv:2105.04296v2 fatcat:m4rrk5vm3bbyzksjik3f5bjhhq

Algorithmic Barriers from Phase Transitions

Dimitris Achlioptas, Amin Coja-Oghlan
2008 2008 49th Annual IEEE Symposium on Foundations of Computer Science  
We prove that a completely analogous phase transition also occurs both in random k-SAT and in random hypergraph 2-coloring.  ...  We prove that the factor of 2 corresponds in a precise mathematical sense to a phase transition in the geometry of this set.  ...  We also prove that an analogous phase transition occurs both in random k-SAT and in random hypergraph 2-coloring.  ... 
doi:10.1109/focs.2008.11 dblp:conf/focs/AchlioptasC08 fatcat:aygz6dfyxfhg3b3ativ3o3o2jm

Phase transition in the spanning-hyperforest model on complete hypergraphs

Andrea Bedini, Sergio Caracciolo, Andrea Sportiello
2009 Nuclear Physics B  
By using our novel Grassmann formulation we study the phase transition of the spanning-hyperforest model of the k-uniform complete hypergraph for any k>= 2.  ...  The phase transition occurs when the number of hyperforests is a fraction (k-1)/k of the total number of vertices.  ...  In [26] a phase transition is detected in the random k-uniform hypergraph when a number of hyperedges |E| = n/k(k − 1) of the total number of vertices n = |V | is chosen uniformly at random.  ... 
doi:10.1016/j.nuclphysb.2009.07.008 fatcat:42cozbwrsvhdhd7eyez6nixiee

Satisfiability Thresholds for Regular Occupation Problems

Konstantinos Panagiotou, Matija Pasch, Michael Wagner
2019 International Colloquium on Automata, Languages and Programming  
The two most popular types of such CSPs are the Erdős-Rényi and the random regular CSPs.  ...  The diversity of the developed methods, on the rigorous and non-rigorous side, has led to major advances regarding both the theoretical as well as the applied viewpoints.  ...  Since the 1980s non-rigorous methods have been introduced in statistical physics that are targeted at the analysis of phase transitions in random CSPs [37, 36, 33] .  ... 
doi:10.4230/lipics.icalp.2019.90 dblp:conf/icalp/PanagiotouP19 fatcat:tvqr6ugbhveqdpkemm5ybrsiiy

Effective epidemic containment strategy in hypergraphs [article]

Bukyoung Jhun
2021 arXiv   pre-print
We also show that immunizing hyperedges with high H-eigenscore effectively contains the epidemics in uniform hypergraphs.  ...  Recently, hypergraphs have attracted considerable interest from the research community as a generalization of networks capable of encoding higher-order interactions, which commonly appear in both natural  ...  For continuous phase transitions, where p i vanishes in the vicinity of the phase transition, the equation can be linearized as p i (t+1) = j βa i j + (1 − µ)δ i j p j and the epidemic threshold β µ is  ... 
arXiv:2108.04568v2 fatcat:jv3ekslfcfhefphvslhovgeirm

Thermodynamics of spin systems on small-world hypergraphs

D. Bollé, R. Heylen, N. S. Skantzos
2006 Physical Review E  
We study the thermodynamic properties of spin systems on small-world hypergraphs, obtained by superimposing sparse Poisson random graphs with p-spin interactions onto a one-dimensional Ising chain with  ...  In the more general case where the number of connections is finite we determine the static and dynamic ferromagnetic-paramagnetic transitions using population dynamics.  ...  Just as in the p = 2 case, the small-world hypergraph has its ferromagnetic transition at finite temperatures for all non-zero values of c.  ... 
doi:10.1103/physreve.74.056111 pmid:17279972 fatcat:pr35r2ukancnxe3zkvjjs7xb7y
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