Related papers: Topological properties of epidemic aftershock proc…
Epidemic disease spreading is conventionally often modelled and analyzed by means of rate and diffusion equations, following the paradigms of well-controlled chemical reactions and diffusive dynamics in a test tube. Yet, serious worries…
According to the Omori-Utsu law, the rate of aftershocks after a mainshock decays as a power law with an exponent close to 1. This well-established law was intensively used in the past to study and model the statistical properties of…
We study asymptotic properties of supercritical Galton-Watson (GW) branching processes in the asymptotic where the mean of the offspring distribution approaches 1 from above. We show that the population-size distribution of the GW branching…
Epilepsy is a neurological disorder characterized by recurrent seizures affecting more than 70 million people worldwide. Often, an individual with epilepsy is more likely to experience subsequent seizures following an initial seizure, a…
We investigate the information-theoretical limits of inference tasks in epidemic spreading on graphs in the thermodynamic limit. The typical inference tasks consist in computing observables of the posterior distribution of the epidemic…
Event-driven systems in fields such as neuroscience, social networks, and finance often exhibit dynamics influenced by continuously evolving external covariates. Motivated by these applications, we introduce a new class of multivariate…
We propose a novel probabilistic framework to model continuous-time interaction events data. Our goal is to infer the \emph{implicit} community structure underlying the temporal interactions among entities, and also to exploit how the…
We consider a threshold epidemic model on a clustered random graph with overlapping communities. In other words, our epidemic model is such that an individual becomes infected as soon as the proportion of her infected neighbors exceeds the…
Studying event time series is a powerful approach for analyzing the dynamics of complex dynamical systems in many fields of science. In this paper, we describe the method of event coincidence analysis to provide a framework for quantifying…
According to some recent analysis (M. Baiesi and M. Paczuski, Phys. Rev. E {\bf 69}, 066106, 2004 \cite{maya1}) of earthquake data, aftershock epicenters can be considered to represent the nodes of a network where the linking scheme depends…
Earthquakes are complex physical processes driven by the stick-slip motion of a sliding fault. After the main quake, a series of aftershocks typically follows. These are loosely defined as events that follow a given event and occur within…
Point processes are widely used statistical models for continuous-time discrete event data, such as medical records, crime reports, and social network interactions, to capture the influence of historical events on future occurrences. In…
Analytical description of propagation phenomena on random networks has flourished in recent years, yet more complex systems have mainly been studied through numerical means. In this paper, a mean-field description is used to coherently…
In this paper, we analyze dynamic switching networks, wherein the networks switch arbitrarily among a set of topologies. For this class of dynamic networks, we derive an epidemic threshold, considering the SIS epidemic model. First, an…
As a tool for capturing irregular temporal dependencies (rather than resorting to binning temporal observations to construct time series), Hawkes processes with exponential decay have seen widespread adoption across many application…
Physics-based and statistic-based models for describing seismic occurrence are two sides of the same coin. In this article we compare the temporal organization of events obtained in a spring-block model for the seismic fault with the one…
Contacts between individuals serve as pathways where infections may propagate. These contact patterns can be represented by network structures. Static structures have been the common modeling paradigm but recent results suggest that…
Our chances to halt epidemic outbreaks rely on how accurately we represent the population structure underlying the disease spread. When analyzing global epidemics this force us to consider metapopulation models taking into account intra-…
Traditionally, Hawkes processes are used to model time--continuous point processes with history dependence. Here we propose an extended model where the self--effects are of both excitatory and inhibitory type and follow a Gaussian Process.…
Existing spatio-temporal Hawkes process models typically rely on either parametric or semiparametric assumptions, limiting the model's ability to capture complex endogenous and exogenous event dynamics. We propose a fully Bayesian…