## 3 Citations

Networks beyond pairwise interactions: structure and dynamics

- Computer Science, PhysicsArXiv
- 2020

Topological graph persistence

- Mathematics
- 2017

Abstract Graphs are a basic tool in modern data representation. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional…

Mean-Field Monomer-Dimer Models. A Review

- Physics, MathematicsSojourns in Probability Theory and Statistical Physics - I
- 2019

A collection of rigorous results for a class of mean-field monomer-dimer models is presented. It includes a Gaussian representation for the partition function that is shown to considerably simplify…

## References

SHOWING 1-10 OF 26 REFERENCES

Matchings on infinite graphs

- Mathematics
- 2011

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

- Mathematics, Physics
- 2015

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

- Mathematics
- 2016

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.

- Mathematics, MedicinePhysical review. E
- 2016

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.

- Mathematics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2013

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

- 1972

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

- Mathematics, PhysicsArXiv
- 2006

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

- Computer Science, MedicineJournal of The Royal Society Interface
- 2014

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.

- Mathematics, MedicinePhysical review letters
- 2012

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,…