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We propose new continuous-time formulations for first-order stochastic optimization algorithms such as mini-batch gradient descent and variance-reduced methods. We exploit these continuous-time models, together with simple Lyapunov analysis…

We introduce a probabilistic generative model for disentangling spatio-temporal disease trajectories from series of high-dimensional brain images. The model is based on spatio-temporal matrix factorization, where inference on the sources is…

The time process of transport on randomly evolving trees is investigated. By introducing the notions of living and dead nodes a model of random tree evolution is constructed which describes the spreading in time of objects corresponding to…

Tree-based methods are popular nonparametric tools in studying time-to-event outcomes. In this article, we introduce a novel framework for survival trees and ensembles, where the trees partition the dynamic survivor population and can…

Neural differential equations predict the derivative of a stochastic process. This allows irregular forecasting with arbitrary time-steps. However, the expressive temporal flexibility often comes with a high sensitivity to noise. In…

Stochastic Hybrid Systems (SHS) constitute an important class of mathematical models that integrate discrete stochastic events with continuous dynamics. The time evolution of statistical moments is generally not closed for SHS, in the sense…

We consider a broad class of continuous-time two-type population size-dependent Markov Branching Processes. The offspring distribution can depend on the current (alive) and total (dead and alive) populations. Using stochastic approximation…

The ability of a robot to plan complex behaviors with real-time computation, rather than adhering to predesigned or offline-learned routines, alleviates the need for specialized algorithms or training for each problem instance. Monte Carlo…

One of the characteristic features of a stochastic process under resetting is that the probability density converges to a nonequilibrium stationary state (NESS). In addition, the approach to the stationary state exhibits a dynamical phase…

We study a stochastic optimization problem in which the sampling distribution depends on the decision variable, and the available samples are generated through an iterate-dependent Markov chain. Such settings arise naturally in problems…

Spiking Neural Networks (SNNs), recognized as the third generation of neural networks, are known for their bio-plausibility and energy efficiency, especially when implemented on neuromorphic hardware. However, the majority of existing…

We present a novel deep learning method for estimating time-dependent parameters in Markov processes through discrete sampling. Departing from conventional machine learning, our approach reframes parameter approximation as an optimization…

Generating function equation has been derived for the probability distribution of the number of nodes with $k \ge 0$ outgoing lines in randomly evolving special trees. The stochastic properties of end-nodes (k=0) have been analyzed, and it…

Estimating the effective sample size (ESS) is fundamental in Bayesian phylogenetic inference to properly account for autocorrelation in MCMC samples. While methods for continuous parameters are well established, the discrete and…

Latent neural stochastic differential equations (SDEs) have recently emerged as a promising approach for learning generative models from stochastic time series data. However, they systematically underestimate the noise level inherent in…

Stochastic mathematical models are essential tools for understanding and predicting complex phenomena. The purpose of this work is to study the exit times of a stochastic dynamical system-specifically, the mean exit time and the…

Spiking Neural Networks (SNNs) are a promising framework for event-driven temporal processing. Prior work has improved temporal modeling through richer neuron dynamics and network-level mechanisms such as recurrence and delays, but it…

Achieving deterministic computation results in asynchronous neuromorphic systems remains a fundamental challenge due to the inherent temporal stochasticity of continuous-time hardware. To address this, we develop a unified continuous-time…

We have developed a coarse-grained formulation for modeling the dynamic behavior of cells quantitatively, based on stochasticity and heterogeneity, rather than on biochemical reactions. We treat each reaction as a continuous-time stochastic…

With rapid expansion of cellular networks and the proliferation of mobile devices, cellular traffic data exhibits complex temporal dynamics and spatial correlations, posing challenges to accurate traffic prediction. Previous methods often…