Related papers: Random Abstract Cell Complexes
For many probability distributions of interest, it is quite difficult to obtain samples efficiently. Often, Markov chains are employed to obtain approximately random samples from these distributions. The primary drawback to traditional…
Given a chain complex with the only modification that each cell of the complex has a probability distribution assigned. We will call this complex - a random complex and what should be understood in practice, is that we have a classical…
Although random cell complexes occur throughout the physical sciences, there does not appear to be a standard way to quantify their statistical similarities and differences. The various proposals in the literature are usually motivated by…
I report on the development of a novel statistical mechanical formalism for the analysis of random graphs with many short loops, and processes on such graphs. The graphs are defined via maximum entropy ensembles, in which both the degrees…
Controlled branching processes are stochastic growth population models in which the number of individuals with reproductive capacity in each generation is controlled by a random control function. The purpose of this work is to examine the…
Random graph generation is an important tool for studying large complex networks. Despite abundance of random graph models, constructing models with application-driven constraints is poorly understood. In order to advance state-of-the-art…
We give alternate constructions of (i) the scaling limit of the uniform connected graphs with given fixed surplus, and (ii) the continuum random unicellular map (CRUM) of a given genus that start with a suitably tilted Brownian continuum…
Networks are often studied using the eigenvalues of their adjacency matrix, a powerful mathematical tool with a wide range of applications. Since in real systems the exact graph structure is not known, researchers resort to random graphs to…
It appeared recently that the classical random graph model used to represent real-world complex networks does not capture their main properties. Since then, various attempts have been made to provide accurate models. We study here a model…
Approximate Bayesian computation (ABC) methods provide an elaborate approach to Bayesian inference on complex models, including model choice. Both theoretical arguments and simulation experiments indicate, however, that model posterior…
We provide dual algorithms for sampling the space of abstract simplicial complexes on a fixed number of vertices. We develop a generative and descriptive sampler designed with heuristics to help balance the combinatorial multiplicities of…
In this paper, a sample-based procedure for obtaining simple and computable approximations of chance-constrained sets is proposed. The procedure allows to control the complexity of the approximating set, by defining families of…
Cell complexes are topological spaces constructed from simple blocks called cells. They generalize graphs, simplicial complexes, and polyhedral complexes that form important domains for practical applications. They also provide a…
We describe a new method for the random sampling of connected networks with a specified degree sequence. We consider both the case of simple graphs and that of loopless multigraphs. The constraints of fixed degrees and of connectedness are…
We study the large-deviation properties of minimum spanning trees for two ensembles of random graphs with $N$ nodes. First, we consider complete graphs. Second, we study Erd\H{o}s-R\'{e}nyi (ER) random graphs with edge probability $p=c/N$…
In many areas of applied statistics and machine learning, generating an arbitrary number of independent and identically distributed (i.i.d.) samples from a given distribution is a key task. When the distribution is known only through…
This work will appear as a chapter in a forthcoming volume titled "Topics in Probabilistic Graph Theory". A theory of scaling limits for random graphs has been developed in recent years. This theory gives access to the large-scale geometric…
The emergence of complex behaviors in cellular automata is an area that has been widely developed in recent years with the intention to generate and analyze automata that produce space-moving patterns or gliders that interact in a periodic…
On a finite graph, there is a natural family of Boltzmann probability measures on cycle-rooted spanning forests, parametrized by weights on cycles. For a certain subclass of those weights, we construct Gibbs measures in infinite volume, as…
At the intersection of dynamical systems, control theory, and formal methods lies the construction of symbolic abstractions: these typically represent simpler, finite-state models whose behavior mimics that of an underlying concrete system…