21 papers · ranked by Valyu relevance
Ivan N. Burenev, M.J. Kearney, Satya N. Majumdar
The time to first crossing for the Poisson counting process with respect to a linear moving barrier with offset is a classic problem, although key results remain scattered across the literature and their equivalence is often unclear. Here we present a unified and pedagogical treatment of two approaches: the direct…
Pradeep Vishwakarma
Spatial Poisson point processes on finite-dimensional Euclidean space provide fundamental mathematical tools for modeling random spatial point patterns. In this paper, we introduce and analyze several Poisson-type spatial point processes. In particular, we propose and study a point process, namely, the generalized…
Tathe, Kartik, Ghosh, Sayan
This paper investigates the martingale characterizations of non-homogeneous counting processes and their fractional generalizations. We show that the weighted sum of non-homogeneous Poisson processes (NPPs) is the non-homogeneous generalized counting process (NGCP). Both the compensated and exponential forms of…
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…
An Wang, Donald Geman, Uthsav Chitra, Laurent Younes
Spatial transcriptomics (ST) technologies measure gene expression at thousands of locations within a two-dimensional tissue slice, enabling the study of spatial gene expression patterns. Spatial variation in gene expression is characterized by spatial gradients, or the collection of vector fields describing the…
Xuhua Xia, Daria Sanna
Classical branching-process theory, developed by Galton and Watson in the nineteenth century and later refined by Fisher and Haldane, provides the formal framework for quantifying the fate of new mutants, new viral and bacterial pathogens, new colonization of invasive species, etc. It is a powerful tool to quantify and…
Xiaokai Luo, Haotian Xu, Yanzhen Chen, Oscar Hernán Madrid Padilla
We study online change point detection for multivariate inhomogeneous Poisson point process time series. This setting arises commonly in applications such as earthquake seismology, climate monitoring, and epidemic surveillance, yet remains underexplored in the machine learning and statistics literature. We propose a…
José Giral-Barajas, Samantha Linn, Paul C. Bressloff
Stochastic search processes in which searchers are continuously introduced to and removed from a target search domain are fundamental to a wide class of physical and artificial systems. The theory of such non-conservative search processes is, however, much less developed than for search processes with a fixed number of…
Sergey Vinogradov, Fabio Acerbi
This paper presents an order statistic approach to the time distribution of the first detected event following a primary avalanche pulse, considering a mixture of correlated and primary dark counts. The well-known order statistic method, commonly used to describe the time resolution of scintillation detectors, is…
Sophie Jaffard, Giulia Mezzadri, Patricia Reynaud-Bouret, Etienne Tanré
In cognition, response times and choices in decision-making tasks are commonly modeled using Drift Diffusion Models (DDMs), which describe the accumulation of evidence for a decision as a stochastic process, specifically a Brownian motion, with the drift rate reflecting the strength of the evidence. In the same vein…
Kumar Utkarsh, Nirmish R. Shah, Tanvi Banerjee, Daniel M. Abrams + 1 more
Researchers across different fields, including but not limited to ecology, biology, and healthcare, often face the challenge of sparse data. Such sparsity can lead to uncertainties, estimation difficulties, and potential biases in modeling. Here we introduce a novel data augmentation method that combines multiple…
Golam M Kashef, Rob de Ruyter van Steveninck
Early studies of synaptic transmission by Bernard Katz and colleagues suggested that neurotransmitter release at graded-potential synapses occurs through statistically independent (i.e. Poissonian) quanta [1, 2]. Subsequent experimental work supported this framework [3]. However, these measurements were performed in…
Wanrudee Skulpakdee, Mongkol Hunkrajok
A mixture of two or more count distributions has become deeply embedded in the analysis of excess counts, often relative to the stationary (equilibrium) distributions of birth-death processes such as the geometric, Poisson, Poisson-Lindley (PL), negative binomial (NB), hyper-Poisson (HP), and Conway-Maxwell-Poisson…
Baoyin Yuan, Feng Jiao
Understanding extinction probabilities in branching processes is pivotal for epidemiology and population dynamics. Traditional models often assume a fixed generation time, resulting in extinction probabilities determined solely by offspring distributions and remaining unchanged over time. By contrast, our study…
Stephen Keeley, David Zoltowski, Adam Charles, Jonathan Pillow
Calcium imaging (CI) is a standard method for recording neural population activity, as it enables simultaneous recording of hundreds-to-thousands of individual somatic signals. Accordingly, CI recordings are prime candidates for population-level latent variable analyses, for example, using models such as Gaussian…
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…
Martin Bladt, Rasmus Frigaard Lemvig
We investigate the Poisson regression method for Markov and semi-Markov jump processes from a nonparametric angle, allowing the lengths of the time and duration intervals in the partition to vary with the number of observations. Imposing no structural assumptions on the true intensities, we obtain asymptotic normality…
Fernando Alcalde Cuesta, Gustavo Guerberoff, Álvaro Lozano Rojo
In this paper, we study the absorption and fixation times for evolutionary processes on graphs, under different updating rules. While in Moran process a single neighbour is randomly chosen to be replaced, in proliferation processes other neighbours can be replaced using Bernoulli or binomial draws depending on 0 < p ≤…
Arunendra Kumar Verma, Hillol Kumar Barman, Krishna Rijal, Dibyendu Das
Within the studies of stochastic gene expression, apart from the variability of copy number of gene products, the problems of threshold crossing of those products are biologically important as they often lead to terminal cellular events. Here, we study the threshold crossing problem of the messenger ribonucleic acid…
Bjarki Eldon
Recruitment dynamics, or the distribution of the number of offspring among individuals, is fundamental to ecology and evolution. We take sweepstakes reproduction to mean a skewed (heavy right-tailed) offspring number distribution without natural selection being involved. Sweepstakes may be generated by chance matching…
Authors not listed
The GENERIC framework provides a robust structure for nonequilibrium dynamics but lacks a principled method to select reversible ($L$) and irreversible ($M$) brackets. Similarly, finite-time optimizations minimizing path-averaged reciprocal temperature exist but remain isolated. Here, we introduce the \textbf{Entropy…