Related papers: Two models of sparse and clustered dynamic network…

This paper investigates properties of the class of graphs based on exchangeable point processes. We provide asymptotic expressions for the number of edges, number of nodes and degree distributions, identifying four regimes: (i) a dense…

Networks with underlying metric spaces attract increasing research attention in network science, statistical physics, applied mathematics, computer science, sociology, and other fields. This attention is further amplified by the current…

This work presents a framework for studying temporal networks using zigzag persistence, a tool from the field of Topological Data Analysis (TDA). The resulting approach is general and applicable to a wide variety of time-varying graphs. For…

A computer model is described which is used to assess the dynamical complexity of a class of networks of spiking neurons with small-world properties. Networks are constructed by forming an initially segregated set of highly intra-connected…

We introduce a novel training principle for probabilistic models that is an alternative to maximum likelihood. The proposed Generative Stochastic Networks (GSN) framework is based on learning the transition operator of a Markov chain whose…

We consider $N$ counters taking integer values which are subject to the following dynamics. At every time, a pair of distinct counters is chosen uniformly at random and their states are updated according to the following rule. If the states…

In this paper, we consider a one-dimensional random geometric graph process with the inter-nodal gaps evolving according to an exponential AR(1) process, which may serve as a mobile wireless network model. The transition probability matrix…

The way in which different types of dynamics unfold in complex networks is intrinsically related to the propagation of activation along nodes, which is strongly affected by the network connectivity. In this work we investigate to which…

Learning requires the traversal of inherently distinct cognitive states to produce behavioral adaptation. Yet, tools to explicitly measure these states with non-invasive imaging -- and to assess their dynamics during learning -- remain…

Real-world networks often exhibit strong transitivity with nontrivial local clustering spectra and degree correlations. Such features are not easily modeled in tractable network models, creating an obstacle to the theoretical understanding…

The flow of information in networked systems composed of multiple interacting elements strongly depends on the level of connectivity among these elements. Sparse connectivity often hinders the emergence of states in which information is…

Monte Carlo (MC) simulations of transport in random porous networks indicate that for high variances of the log-normal permeability distribution, the transport of a passive tracer is non-Fickian. Here we model this non-Fickian dispersion in…

Consider longitudinal networks whose edges turn on and off according to a discrete-time Markov chain with exponential-family transition probabilities. We characterize when their joint distributions are also exponential families with the…

Many social and biological networks consist of communities - groups of nodes within which connections are dense, but between which connections are sparser. Recently, there has been considerable interest in designing algorithms for detecting…

Although static networks have been extensively studied in machine learning, data mining, and AI communities for many decades, the study of dynamic networks has recently taken center stage due to the prominence of social media and its…

The bivariate distribution of degrees of adjacent vertices (degree-degree distribution) is an important network characteristic defining the statistical dependencies between degrees of adjacent vertices. We show the asymptotic degree-degree…

We study assortative mixing in networks, the tendency for vertices in networks to be connected to other vertices that are like (or unlike) them in some way. We consider mixing according to discrete characteristics such as language or race…

We introduce a random intersection graph process aimed at modeling sparse evolving affiliation networks that admit tunable (power law) degree distribution and assortativity and clustering coefficients. We show the asymptotic degree…

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…

In this work, we focus on the stationary analysis of a specific class of continuous time Markov-modulated reflected random walks in the quarter plane with applications in the modelling of two-node Markov-modulated queueing networks with…