Related papers: Heterogeneous pair-approximation for the contact p…

The concept of entropy rate for a dynamical process on a graph is introduced. We study diffusion processes where the node degrees are used as a local information by the random walkers. We describe analitically and numerically how the degree…

We investigate the contact process on four different types of scale-free inhomogeneous random graphs evolving according to a stationary dynamics, where each potential edge is updated with a rate depending on the strength of the adjacent…

In this paper, we investigate team optimal control of coupled major-minor subsystems with mean-field sharing. In such a model, there is one major subsystem that directly influences the dynamics of $n$ homogeneous minor subsystems; however,…

We study the application of the exact renormalisation group to a many-fermion system with a short-range attractive force. We introduce a boson field to describe pairing effects, and take a simple ansatz for the effective action. We derive a…

The possibility to apply phase-space methods to many-body interacting systems might provide accurate descriptions of correlations with a reduced numerical cost. For instance, the so--called stochastic mean-field phase-space approach, where…

Random walk on changing graphs is considered. For sequences of finite graphs increasing monotonically towards a limiting infinite graph, we establish transition probability upper bounds. It yields sufficient transience criteria for simple…

Moment-closure approximations are an important tool in the analysis of the dynamics on both static and adaptive networks. Here, we provide a broad survey over different approximation schemes by applying each of them to the adaptive voter…

We survey our recent articles dealing with one dimensional attractive zero range processes moving under site disorder. We suppose that the underlying random walks are biased to the right and so hyperbolic scaling is expected. Under the…

Environments with immobile obstacles or void regions that inhibit and alter the motion of individuals within that environment are ubiquitous. Correlation in the location of individuals within such environments arises as a combination of the…

Competition between alternative states is an essential process in social and biological networks. Neutral competition can be represented by an unbiased random drift process in which the states of vertices (e.g., opinions, genotypes, or…

In this article we present very intuitive, easy to follow, yet mathematically rigorous, approach to the so called data fitting process. Rather than minimizing the distance between measured and simulated data points, we prefer to find such…

Random walks have been intensively studied on regular and complex networks, which are used to represent pairwise interactions. Nonetheless, recent works have demonstrated that many real-world processes are better captured by higher-order…

We use the annealed formulation of complex networks to study the dynamical behavior of disease spreading on both static and adaptive networked systems. This unifying approach relies on the annealed adjacency matrix, representing one network…

In this paper, we study the social optimality for mean field linear quadratic control systems following the direct approach, where subsystems are coupled via individual dynamics and costs according to a network topology. A graph is…

We report about the main dynamical features of a model of leaky-integrate-and fire excitatory neurons with short term plasticity defined on random massive networks. We investigate the dynamics by a Heterogeneous Mean-Field formulation of…

In the last few years, distributed machine learning has been usually executed over heterogeneous networks such as a local area network within a multi-tenant cluster or a wide area network connecting data centers and edge clusters. In these…

This paper proposes an adaptation mechanism for heterogeneous multi-agent systems to align the agents' internal parameters, based on enforced consensus through strong couplings. Unlike homogeneous systems, where exact consensus is…

Cluster molecular field approximations represent a substantial progress over the simple Weiss theory where only one spin is considered in the molecular field resulting from all the other spins. In this work we discuss a systematic way of…

Mean-field analysis is an important tool for understanding dynamics on complex networks. However, surprisingly little attention has been paid to the question of whether mean-field predictions are accurate, and this is particularly true for…

Sparse pseudo-point approximations for Gaussian process (GP) models provide a suite of methods that support deployment of GPs in the large data regime and enable analytic intractabilities to be sidestepped. However, the field lacks a…