Related papers: Poissonian bursts in e-mail correspondence
Human behaviour is heterogeneous and temporally fluctuates. Many studies have focused on inter-event time (IET) fluctuations and have reported that the IET distributions have a long-tailed distribution, which cannot be explained by a…
We consider the problem of leakage or effusion of an ensemble of independent stochastic processes from a region where they are initially randomly distributed. The case of Brownian motion, initially confined to the left half line with…
It is commonly believed that the correlations between stock returns increase in high volatility periods. We investigate how much of these correlations can be explained within a simple non-Gaussian one-factor description with time…
We demonstrate the presence of chaos in stochastic simulations that are widely used to study biodiversity in nature. The investigation deals with a set of three distinct species that evolve according to the standard rules of mobility,…
The concept of temporal networks provides a framework to understand how the interaction between system components changes over time. In empirical communication data, we often detect non-Poissonian, so-called bursty behavior in the activity…
Little attention has been given to the correlation coefficient when data come from discrete or continuous non-normal populations. In this article, we consider the efficiency of two correlation coefficients which are from the same family,…
Consider two forms of sampling from a population: (i) drawing $s$ samples of $n$ elements with replacement and (ii) drawing a single sample of $ns$ elements. In this paper, under the setting where the descending order population frequency…
For time series with high temporal correlation, the empirical process converges rather slowly to its limiting distribution. Many statistics in change-point analysis, goodness-of-fit testing and uncertainty quantification admit a…
A validated simulation model primarily requires performing an appropriate input analysis mainly by determining the behavior of real-world processes using probability distributions. In many practical cases, probability distributions of the…
Current models for opinion dynamics typically utilize a Poisson process for speaker selection, making the waiting time between events exponentially distributed. Human interaction tends to be bursty, though, having higher probabilities of…
We provide a complete solution of the problems of the probability distribution and the escape rate in Poisson-noise driven systems. It includes both the exponents and the prefactors. The analysis refers to an overdamped particle in a…
Information diagram and the I-measure are useful mnemonics where random variables are treated as sets, and entropy and mutual information are treated as a signed measure. Although the I-measure has been successful in machine proofs of…
Poisson-like behavior for event count data is ubiquitous in nature. At the same time, differencing of such counts arises in the course of data processing in a variety of areas of application. As a result, the Skellam distribution -- defined…
Records of social interactions provide us with new sources of data for understanding how interaction patterns affect collective dynamics. Such human activity patterns are often bursty, i.e., they consist of short periods of intense activity…
The Poisson distribution arises naturally when dealing with data involving counts, and it has found many applications in inverse problems and imaging. In this work, we develop an approximate Bayesian inference technique based on expectation…
It is demonstrated that in a two-stage scenario with elementary Poissonian emitters of particles (colour strings) arbitrarily distributed in their number and average multiplicities, the forward- backward correlations are completely…
Recently the interest of researchers has shifted from the analysis of synchronous relationships of financial instruments to the analysis of more meaningful asynchronous relationships. Both of those analyses are concentrated only on…
The dynamics of interference over space and time influences the performance of wireless communication systems, yet its features are still not fully understood. This article analyzes the temporal dynamics of the interference in Poisson…
Human social interactions in local settings can be experimentally detected by recording the physical proximity and orientation of people. Such interactions, approximating face-to-face communications, can be effectively represented as time…
An information-theoretic development is given for the problem of compound Poisson approximation, which parallels earlier treatments for Gaussian and Poisson approximation. Let $P_{S_n}$ be the distribution of a sum $S_n=\Sumn Y_i$ of…