25 papers · ranked by Valyu relevance
Marian-Andrei Rizoiu, Young Lee, Swapnil Mishra, Lexing Xie
This chapter provides an accessible introduction for point processes, and especially Hawkes processes, for modeling discrete, inter-dependent events over continuous time. We start by reviewing the definitions and the key concepts in point processes. We then introduce the Hawkes process, its event intensity function, as…
Thomas A. Trikalinos, Yuliia Sereda, Abhik Ghosh
We introduce the nhppp package for simulating events from one dimensional non-homogeneous Poisson point processes (NHPPPs) in R fast and with a small memory footprint. We developed it to facilitate the sampling of event times in discrete event and statistical simulations. The package’s functions are based on three…
Thomas A Trikalinos, Yuliia Sereda
We introduce the nhppp package for simulating events from one dimensional nonhomogeneous Poisson point processes (NHPPPs) in R. Its functions are based on three algorithms that provably sample from a target NHPPP: the time-transformation of a homogeneous Poisson process (of intensity one) via the inverse of the…
Thomas Freud, Pablo M. Rodríguez
The Poisson process is one of the simplest stochastic processes defined in continuous time, having interesting mathematical properties, leading, in many situations, to applications mathematically treatable. One of the limitations of the Poisson process is the rare events hypothesis; which is the hypothesis of unitary…
Nicolas Lanchier
Poisson processes and one-dimensional Poisson point processes satisfy three main properties: superposition, thinning, and conditioning. The proof of the first two relies on basic estimates involving the Poisson distribution that are also true for multi-dimensional Poisson point processes. In contrast, the proof of…
Marco Raberto, Fabio Rapallo, Enrico Scalas, Matjaz Perc
In this paper, we outline a model of graph (or network) dynamics based on two ingredients. The first ingredient is a Markov chain on the space of possible graphs. The second ingredient is a semi-Markov counting process of renewal type. The model consists in subordinating the Markov chain to the semi-Markov counting…
Andi Kresna Jaya, Nurtiti Sunusi, Erna Tri Herdiani
The point process model effectively represents the number of random events occurring over time through its intensity function. When events are of two types, a bivariate point process allows simultaneous analysis of each event’s intensity. This study develops a conditional intensity model for a non-homogeneous bivariate…
Régis Houssou, Jérôme Bovay, Stephan Robert
This paper discusses financial fraud detection in imbalanced dataset using homogeneous and non-homogeneous Poisson processes. The probability of predicting fraud on the financial transaction is derived. Applying our methodology to the financial dataset shows a better predicting power than a baseline approach…
Antonio Di Crescenzo, Barbara Martinucci, Shelemyahu Zacks
A compound Poisson process whose randomized time is an independent Poisson process is called compound Poisson process with Poisson subordinator. We provide its probability distribution, which is expressed in terms of the Bell polynomials, and investigate in detail both the special cases in which the compound Poisson…
Adam J. Peterson
The inhomogeneous Poisson point process is a common model for time series of discrete, stochastic events. When an event from a point process is detected, it may trigger a random dead time in the detector, during which subsequent events will fail to be detected. It can be difficult or impossible to obtain a closed-form…
Viola Priesemann, Oren Shriki, Francesco P. Battaglia
The finding of power law scaling in neural recordings lends support to the hypothesis of critical brain dynamics. However, power laws are not unique to critical systems and can arise from alternative mechanisms. Here, we investigate whether a common time-varying external drive to a set of Poisson units can give rise to…
Niklas Hohmann
In this paper, a test for hypotheses on population dynamics is presented alongside an implementation of said test for R. The test is based on the assumption that the sample, consisting of points on a time axis, is a realization of a Poisson point process (PPP). There are no restrictions on the shapes of the rate…
Sultan Hussain, Anwar Zeb, Akhter Rasheed, Tareq Saeed
This work is devoted to a stochastic model on the spread and control of corona virus (COVID-19), in which the total population of a corona infected area is divided into susceptible, infected, and recovered classes. In reality, the number of individuals who get disease, the number of deaths due to corona virus, and the…
Carl P. Dettmann
Random geometric graphs consist of randomly distributed nodes (points), with pairs of nodes within a given mutual distance linked. In the usual model the distribution of nodes is uniform on a square, and in the limit of infinitely many nodes and shrinking linking range, the number of isolated nodes is Poisson…
Sean Bellew, Ian Flint, Yan Wang
Poisson processes have become a prominent tool in species distribution modelling when analysing citizen science data based on presence records. This study examines four distinct statistical approaches, each of which utilises a different approximation to fit a Poisson point process. These include two Poisson regressions…
Jakob Gulddahl Rasmussen
These short lecture notes contain a not too technical introduction to point processes on the time line. The focus lies on defining these processes using the conditional intensity function. Furthermore, likelihood inference, methods of simulation and residual analysis for temporal point processes specified by a…
Xinyu Wang, Youming Li, Chen Jia
Stochastic gene expression dynamics can be modeled either discretely or continuously. Previous studies have shown that the mRNA or protein number distributions of some simple discrete and continuous gene expression models are related by Gardiner’s Poisson representation. Here we systematically investigate the Poisson…
Authors not listed
Classical molecular dynamics (MD) simulation is the most computationally efficient way to model large molecular systems atomistically for extended periods; however, due to fixed forcefield parameters, incorporating on-the-fly quantum reactions is not straightforward. Reactive Step-Based Molecular Dynamics (RSMD) is a…
Ulisse Ferrari, Stéphane Deny, Olivier Marre, Thierry Mora
Neural noise sets a limit to information transmission in sensory systems. In several areas, the spiking response (to a repeated stimulus) has shown a higher degree of regularity than predicted by a Poisson process. However, a simple model to explain this low variability is still lacking. Here we introduce a new model…
Neha Gupta, Arun Kumar, Nikolai Leonenko
In this article, we introduce the Skellam process of order k and its running average. We also discuss the time-changed Skellam process of order k. In particular, we discuss the space-fractional Skellam process and tempered space-fractional Skellam process via time changes in Skellam process by independent stable…
Lucy Ham, Rowan D. Brackston, Michael P.H. Stumpf
Noise in gene expression is one of the hallmarks of life at the molecular scale. Here we derive analytical solutions to a set of models describing the molecular mechanisms underlying transcription of DNA into RNA. Our Ansatz allows us to incorporate the effects of extrinsic noise – encompassing factors external to the…
Mohamed Y. Hassan
In this study, we propose an Equi-Under-dispersed Poisson distribution derived from a finite mixture of weighted Poisson distributions. This probability distribution is a simple, parsimonious, and flexible option suitable for modeling under-dispersed count data. It aims to overcome some of the weaknesses of existing…
Authors not listed
The polarizable continuum model (PCM) is a computationally efficient way to incorporate dielectric boundary conditions into electronic structure calculations, via a boundary-element reformulation of Poisson's equation. This transformation is only rigorously valid for an isotropic dielectric medium. To simulate…
Authors not listed
The screening of chemical libraries is an essential starting point in the drug discovery process. While some researchers desire a more thorough screening of drug targets against a narrower scope of molecules, it is not uncommon for diverse screening sets to be favored during early stages of drug discovery. However, a…
Authors not listed
Quantitative analysis of small extracellular vesicles (sEVs) at single-particle resolution remains challenging due to their nanoscale dimensions and compositional heterogeneity. Existing methods often rely on specialized and costly instrumentation, limiting accessibility for many researchers and necessitates extensive…