Topological graph persistence
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
- MathematicsSojourns in Probability Theory and Statistical Physics - I
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…
Human-AI ecosystem with abrupt changes as a function of the composition
- BiologyPloS one
A model that simulate a Human-AI ecosystem and evidence that for suitable values of the interaction parameters, arbitrarily small changes in such percentage may trigger dramatic changes for the system that can be either in one of the two polarised states or in an undecided state is presented.
Networks beyond pairwise interactions: structure and dynamics
- Computer ScienceArXiv
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
- Computer Science
This work introduces and analyzes the most general random simplicial complex ensemble with statistically independent simplices, and proves that ensemble is maximum-entropy subject to the two types of constraints which fix the expected numbers of simplices and their boundaries.
Topological Field Theory of Data: Mining Data Beyond Complex Networks
- Computer Science
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.
- Computer SciencePhysical review. E
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.
- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
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
- Computer Science, MathematicsArXiv
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 ScienceJournal of The Royal Society Interface
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.