Related papers: Stochastic Sandpile Model: exact sampling and comp…
Population structure can have a significant effect on evolution. For some systems with sufficient symmetry, analytic results can be derived within the mathematical framework of evolutionary graph theory which relate to the outcome of the…
This article consists in two independent parts. In the first one, we investigate the geometric properties of almost periodicity of model sets (or cut-and-project sets, defined under the weakest hypotheses); in particular we show that they…
Given a finite sequence of graphs, e.g., coming from technological, biological, and social networks, the paper proposes a methodology to identify possible changes in stationarity in the stochastic process generating the graphs. In order to…
There are two distinct regimes commonly used to model traveling waves in stratified water: continuous stratification, where the density is smooth throughout the fluid, and layer-wise continuous stratification, where the fluid consists of…
This paper studies a stochastic model that describes the evolution of vehicle densities in a road network. It is consistent with the class of (deterministic) kinematic wave models, which describe traffic flows on the basis of conservation…
A popular theory of self-organized criticality relates driven dissipative systems to systems with conservation. This theory predicts that the stationary density of the abelian sandpile model equals the threshold density of the fixed-energy…
We establish and generalise several bounds for various random walk quantities including the mixing time and the maximum hitting time. Unlike previous analyses, our derivations are based on rather intuitive notions of local expansion…
Cellular automata have been mainly studied on very regular graphs carrying the vertices (like lines or grids) and under synchronous dynamics (all vertices update simultaneously). In this paper, we study how the asynchronism and the graph…
Stochastic dynamic models have been extensively used for the description of processes with uncertainties arising in the operations research, behavioral sciences, and many other application areas. A large class of the problems from these…
Graph representations offer powerful and intuitive ways to describe data in a multitude of application domains. Here, we consider stochastic processes generating graphs and propose a methodology for detecting changes in stationarity of such…
In this paper we study dynamic averaging load balancing on general graphs. We consider infinite time and dynamic processes, where in every step new load items are assigned to randomly chosen nodes. A matching is chosen, and the load is…
The aim of this paper is to provide conditions which ensure that the affinely transformed partial sums of a strictly stationary process converge in distribution to an infinite variance stable distribution. Conditions for this convergence to…
A dissipative stochastic sandpile model is constructed on one and two dimensional small-world networks with different shortcut densities $\phi$ where $\phi=0$ and $1$ represent a regular lattice and a random network respectively. In the…
This paper considers a Markov-modulated duplication-deletion random graph where at each time instant, one node can either join or leave the network; the probabilities of joining or leaving evolve according to the realization of a finite…
Let $F$ be a probability distribution with support on the non-negative integers. A model is proposed for generating stationary simple graphs on $\mathbb{Z}$ with degree distribution $F$ and it is shown for this model that the expected total…
We study the dynamics of a continuous-time model of the Stochastic Gradient Descent (SGD) for the least-square problem. Indeed, pursuing the work of Li et al. (2019), we analyze Stochastic Differential Equations (SDEs) that model SGD either…
A popular theory of self-organized criticality relates the critical behavior of driven dissipative systems to that of systems with conservation. In particular, this theory predicts that the stationary density of the abelian sandpile model…
We study stochastic pairwise interaction network systems whereby a finite population of agents, identified with the nodes of a graph, update their states in response to both individual mutations and pairwise interactions with their…
We introduce a new approach to model and analyze \emph{Mobility}. It is fully based on discrete mathematics and yields a class of mobility models, called the \emph{Markov Trace} Model. This model can be seen as the discrete version of the…
We consider the problem of model selection in Gaussian Markov fields in the sample deficient scenario. In many practically important cases, the underlying networks are embedded into Euclidean spaces. Using the natural geometric structure,…