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Encounter-based models of diffusion provide a probabilistic framework for analyzing the effects of a partially absorbing reactive surface, in which the probability of absorption depends upon the amount of surface-particle contact time.…

Evaluating the performance of a prediction model is a common task in medical statistics. Standard accuracy metrics require the observation of the true outcomes. This is typically not possible in the setting with time-to-event outcomes due…

This paper introduces a run-and-tumble model with self-reinforcing directionality and rests. We derive a single governing hyperbolic partial differential equation for the probability density of random walk position, from which we obtain the…

We study the statistics of the first-passage time of a single run and tumble particle (RTP) in one spatial dimension, with or without resetting, to a fixed target located at $L>0$. First, we compute the first-passage time distribution of a…

Analytical expressions are put forward to investigate the forced spiking activity of abstract neuron models such as the driven leaky integrate-and-fire (LIF) model. The method is valid in a wide parameter regime beyond the restraining…

We present a general theoretical model for the spatio-temporal dynamics of animal contests. Inspired by interactions between physical particles, the model is formulated in terms of effective interaction potentials, which map typical…

During an infectious disease outbreak, public health decision-makers require real-time monitoring of disease transmission to respond quickly and intelligently. In these settings, a key measure of transmission is the instantaneous…

We consider the distribution of the duration time, the time elapsed since it began, of a diffusion process given its present position, under the assumption that the process began at the origin. For unbiased diffusion, the distribution does…

Motivated by various recent experimental findings, we propose a dynamical model of intermittently self-propelled particles: active particles that recurrently switch between two modes of motion, namely an active run-state and a turn state,…

Real-world reinforcement learning often faces environment drift, but most existing methods rely on static entropy coefficients/target entropy, causing over-exploration during stable periods and under-exploration after drift, and leaving…

Often, constraints arise in deployment settings where even lightweight parameter updates e.g. parameter-efficient fine-tuning could induce model shift or tuning instability. We study test-time adaptation of foundation models for few-shot…

Motivated by applications in movement ecology, in this paper I propose a new class of integrated continuous-time hidden Markov models in which each observation depends on the underlying state of the process over the whole interval since the…

In many areas of the brain, neural spiking activity covaries with features of the external world, such as sensory stimuli or an animal's movement. Experimental findings suggest that the variability of neural activity changes over time and…

Utilizing non-concurrent control data (NCC) in the analysis of late-entering arms in platform trials has recently received considerable attention. While incorporating NCC can lead to increased power and lower sample sizes, it might…

In applied machine learning, concept drift, which is either gradual or abrupt changes in data distribution, can significantly reduce model performance. Typical detection methods,such as statistical tests or reconstruction-based models,are…

We study a two state ``jumping diffusivity'' model for a Brownian process alternating between two different diffusion constants, $D_{+}>D_{-}$, with random waiting times in both states whose distribution is rather general. In the limit of…

The passage-time distribution for a spread-out quantum particle to traverse a specific region is calculated using a detailed quantum model for the detector involved. That model, developed and investigated in earlier works, is based on the…

Temporal point processes are the dominant paradigm for modeling sequences of events happening at irregular intervals. The standard way of learning in such models is by estimating the conditional intensity function. However, parameterizing…

System-prompting is a standard tool for customizing language-model chatbots, enabling them to follow a specific instruction. An implicit assumption in the use of system prompts is that they will be stable, so the chatbot will continue to…

Let $X_1,X_2,\ldots $ be independent random variables observed sequentially and such that $X_1,\ldots,X_{\theta-1}$ have a common probability density $p_0$, while $X_\theta,X_{\theta+1},\ldots $ are all distributed according to $p_1\neq…