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We find the static displacement, stress, strain and the modified Columb failure stress produced in an elastic medium by a finite size rectangular fault after its dislocation with uniform stress drop but a non uniform dislocation on the…
Analysis of gun violence in the United States has utilized various models based on spatiotemporal point processes. Previous studies have identified a contagion effect in gun violence, characterized by bursts of diffusion across urban…
The correct identification of clusters is crucial for an accurate monitoring of the spread of a disease and also in many other natural, social and physical phenomena which exhibit an epidemic structure. Nevertheless, even when an accurate…
In this note we highlight the role of fractional linear birth and linear death processes recently studied in \citet{sakhno} and \citet{pol}, in relation to epidemic models with empirical power law distribution of the events. Taking…
The statistics of natural catastrophes contains very counter-intuitive results. Using earthquakes as a working example, we show that the energy radiated by such events follows a power-law or Pareto distribution. This means, in theory, that…
Standard epidemic models based on compartmental differential equations are investigated under continuous parameter change as external forcing. We show that seasonal modulation of the contact parameter superimposed a monotonic decay needs a…
We consider online monitoring of the network event data to detect local changes in a cluster when the affected data stream distribution shifts from one point process to another with different parameters. Specifically, we are interested in…
Learning causal structure among event types on multi-type event sequences is an important but challenging task. Existing methods, such as the Multivariate Hawkes processes, mostly assumed that each sequence is independent and identically…
The probability distribution of inter-event time (IET) between two consecutive earthquakes is a measure for the uncertainty in the occurrence time of earthquakes in a region of interest. It is well known that the IET distribution for…
Recent observation studies have revealed that earthquakes are classified into several different categories. Each category might be characterized by the unique statistical feature in the time series, but the present understanding is still…
We study the seismicity (global seismic activity) that occurred in Greece between 1976 and 2009 based on the dataset reported in Makropoulos et al., 2012, using concepts of Non-extensive Statistical Physics. By considering the entire and…
Spatio-temporal Hawkes point processes are a particularly interesting class of stochastic point processes for modeling self-exciting behavior, in which the occurrence of one event increases the probability of other events occurring. These…
In this article, we study concave recursions on trees, which appear widely in information theory through algorithms such as belief propagation, and in statistical mechanics through models on tree-like graphs, including the Ising model,…
The social contagion literature makes a distinction between simple (independent cascade or bond percolation processes that pass infections through edges) and complex contagions (bootstrap percolation or threshold processes that require…
This paper is second in the series, following Pranav et al. (2019), focused on the characterization of geometric and topological properties of 3D Gaussian random fields. We focus on the formalism of persistent homology, the mainstay of…
We discuss various statistical distributions of earthquake numbers. Previously we derived several discrete distributions to describe earthquake numbers for the branching model of earthquake occurrence: these distributions are the Poisson,…
The Hawkes process is a simple point process that has long memory, clustering effect, self-exciting property and is in general non-Markovian. The future evolution of a self-exciting point process is influenced by the timing of the past…
The author previously presented an event window segmentation (EWS) algorithm [5] that uses purely statistical methods to learn to recognize recurring patterns in an input stream of events. In the following discussion, the EWS algorithm is…
Discontinuous percolation transitions and the associated tricritical points are manifest in a wide range of both equilibrium and non-equilibrium cooperative phenomena. To demonstrate this, we present and relate the continuous and first…
Self-exciting processes of Hawkes type have been used to model various phenomena including earthquakes, neural activities, and views of online videos. Studies of temporal networks have revealed that sequences of social interevent times for…