Related papers: Analytically Solvable Model of Spreading Dynamics …
We recently introduced idealized mean-field models for networks of integrate-and-fire neurons with impulse-like interactions -- the so-called delayed Poissonian mean-field models. Such models are prone to blowups: for a strong enough…
Recently there has been an increasing interest in studying dynamical processes on networks exhibiting higher-order structures, such as simplicial complexes, where the dynamics acts above and beyond dyadic interactions. Using simulations or…
These are lecture notes for a short course given at the Les Houches Summer School on ``Integrability in Atomic and Condensed Matter Physics'', in summer 2018. Here, I pedagogically discuss recent advances in the study of the entanglement…
Spreading of bacteria in a highly advective, disordered environment is examined. Predictions of super-diffusive spreading for a simplified reaction-diffusion equation are tested. Concentration profiles display anomalous growth and…
This work consists in the asymptotic analysis of the solution of Poisson equation in a bounded domain of $\mathbb{R}^{P}$ $(P=2,3)$ with a thin layer. We use a method based on hierarchical variational equations to derive asymptotic…
Consider a massive (inert) particle impinged from above by N Brownian particles that are instantaneously reflected upon collision with the inert particle. The velocity of the inert particle increases due to the influence of an external…
Count-weighted temporal networks often exhibit unequal dispersion in the edge weights, which cannot be fully explained by modelling observational heterogeneity through latent factors in the conditional mean. Therefore, we propose new…
In this paper we consider a claim that in the natural world there is no fact of the matter about the spatio-temporal separation of events. In order to make sense of such a notion and construct useful models of the world, it is proposed to…
The standard diffusive spreading, characterized by a Gaussian distribution with mean square displacement that grows linearly with time, can break down, for instance, under the presence of correlations and heterogeneity. In this work, we…
Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…
In this work we present a general derivation of the non-Fickian behavior for the self-diffusion of identically interacting particle systems with excluded mutual passage. We show that the conditional probability distribution of finding a…
Studies of human attention dynamics analyses how attention is focused on specific topics, issues or people. In online social media, there are clear signs of exogenous shocks, bursty dynamics, and an exponential or powerlaw lifetime…
In social networks, bursts of activity often result from the imitative behavior between interacting agents. The Ising model, along with its variants in the social sciences, serves as a foundational framework to explain these phenomena…
Stochastic processes can model many emerging phenomena on networks, like the spread of computer viruses, rumors, or infectious diseases. Understanding the dynamics of such stochastic spreading processes is therefore of fundamental interest.…
In this paper we analyze continuous-time SIS epidemics subject to arrivals and departures of agents, by using an approximated process based on replacements. In defining the SIS dynamics in an open network, we consider a stochastic setting…
The Peaks Over Threshold (POT) method is the most popular statistical method for the analysis of univariate extremes. Even though there is a rich applied literature on Bayesian inference for the POT, the asymptotic theory for such proposals…
Approximating the time to extinction of infection is an important problem in infection modelling. A variety of different approaches have been proposed in the literature. We study the performance of a number of such methods, and characterize…
The analysis of diffusion processes in real-world propagation scenarios often involves estimating variables that are not directly observed. These hidden variables include parental relationships, the strengths of connections between nodes,…
Spatio-temporal prediction of levels of an environmental exposure is an important problem in environmental epidemiology. Our work is motivated by multiple studies on the spatio-temporal distribution of mobile source, or traffic related,…
This paper examines a susceptible-infected-susceptible (SIS) epidemic reaction-diffusion model with no-flux boundary conditions and constant total population. The infection mechanism in the model is described by a nonlinear term of the form…