Aggregation models on hypergraphs

@article{Alberici2016AggregationMO,
  title={Aggregation models on hypergraphs},
  author={Diego Alberici and Pierluigi Contucci and Emanuele Mingione and Marco Molari},
  journal={arXiv: Statistical Mechanics},
  year={2016}
}
3 Citations

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References

SHOWING 1-10 OF 26 REFERENCES
Matchings on infinite graphs
Elek and Lippner (Proc. Am. Math. Soc. 138(8), 2939–2947, 2010) showed that the convergence of a sequence of bounded-degree graphs implies the existence of a limit for the proportion of vertices
Exponential random simplicial complexes
Exponential random graph models have attracted significant research attention over the past decades. These models are maximum-entropy ensembles subject to the constraints that the expected values of
Topological Field Theory of Data: Mining Data Beyond Complex Networks
A Philosophical Introduction It has become increasingly obvious that very detailed, intricate interactions and interdependencies among and within large systems are often central to most of the
Generalized network structures: The configuration model and the canonical ensemble of simplicial complexes.
TLDR
The structure of simplicial complexes is characterized using their generalized degrees that capture fundamental properties of one, two, three, or more linked nodes using the configuration model and the canonical ensemble, enforcing the sequence of generalized degrees of the nodes and the order of the expected generalized degrees.
Statistical mechanics of multiplex networks: entropy and overlap.
  • G. Bianconi
  • Mathematics, Medicine
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2013
TLDR
A statistical mechanics framework is introduced to describe multiplex ensembles in which the existence of a link in one layer is correlated with theexistence of a links in another layer, which implies that a typical multiplex of the ensemble can have a significant overlap of the links in the different layers.
Theory of monomer-dimer systems
We investigate the general monomer-dimer partition function,P(x), which is a polynomial in the monomer activity,x, with coefficients depending on the dimer activities. Our main result is thatP(x) has
The number of matchings in random graphs
TLDR
This work derives an algorithm to compute the leading order of the logarithm of the number of solutions, of matchings with a given size, and an analytic result for the entropy in regular and Erd?s?R?nyi random graph ensembles.
Persistent Homology — a Survey
Persistent homology is an algebraic tool for measuring topological features of shapes and functions. It casts the multi-scale organization we frequently observe in nature into a mathematical
Homological scaffolds of brain functional networks
TLDR
The results show that the homological structure of the brain's functional patterns undergoes a dramatic change post-psilocybin, characterized by the appearance of many transient structures of low stability and of a small number of persistent ones that are not observed in the case of placebo.
Inverse Ising inference using all the data.
We show that a method based on logistic regression, using all the data, solves the inverse Ising problem far better than mean-field calculations relying only on sample pairwise correlation functions,
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