Related papers: Accurate estimates of dynamical statistics using m…
Understanding the stability and long-time behavior of generative models is a fundamental problem in modern machine learning. This paper provides quantitative bounds on the sampling error of score-based generative models by leveraging…
There are multiple ways in which a stochastic system can be out of statistical equilibrium. It might be subject to time-varying forcing; or be in a transient phase on its way towards equilibrium; it might even be in equilibrium without us…
We study an approximation method for partially observed Markov decision processes (POMDPs) with continuous spaces. Belief MDP reduction, which has been the standard approach to study POMDPs requires rigorous approximation methods for…
The formal verification and controller synthesis for Markov decision processes that evolve over uncountable state spaces are computationally hard and thus generally rely on the use of approximations. In this work, we consider the…
In this paper we propose two behavioral distances that support approximate reasoning on Stochastic Markov Models (SMMs), that are continuous-time stochastic transition systems where the residence time on each state is described by a generic…
Markov processes with stochastic resetting towards the origin generically converge towards non-equilibrium steady-states. Long dynamical trajectories can be thus analyzed via the large deviations at Level 2.5 for the joint probability of…
When clustering molecular dynamics (MD) trajectories into a few metastable conformational states, the Markov state models (MSMs) assumption of timescale separation between fast intrastate fluctuations and rarely occurring interstate…
These lecture notes introduce the statistical analysis of continuous-time generative models built from Markov dynamics. We begin with the stochastic-calculus foundations of score-based diffusion models, including time reversal, score…
Learning unknown stochastic differential equations (SDEs) from observed data is a significant and challenging task with applications in various fields. Current approaches often use neural networks to represent drift and diffusion functions,…
After reviewing the behavioral studies of working memory and of the cellular substrate of the latter, we argue that metastable states constitute candidates for the type of transient information storage required by working memory. We then…
Multi-adaptive Galerkin methods are extensions of the standard continuous and discontinuous Galerkin methods for the numerical solution of initial value problems for ordinary or partial differential equations. In particular, the…
Leveraging recent work on data-driven methods for constructing a finite state space Markov process from dynamical systems, we address two problems for obtaining further reduced statistical representations. The first problem is to extract…
Advection-dominated dynamical systems, characterized by partial differential equations, are found in applications ranging from weather forecasting to engineering design where accuracy and robustness are crucial. There has been significant…
Markov state models (MSMs) have been broadly adopted for analyzing molecular dynamics trajectories, but the approximate nature of the models that results from coarse-graining into discrete states is a long-known limitation. We show…
The Dynamical Graph Grammar (DGG) formalism can describe complex system dynamics with graphs that are mapped into a master equation. An exact stochastic simulation algorithm may be used, but it is slow for large systems. To overcome this…
Stochasticity plays a fundamental role in various biochemical processes, such as cell regulatory networks and enzyme cascades. Isothermal, well-mixed systems can be modelled as Markov processes, typically simulated using the Gillespie…
We introduce and analyze a discontinuous Galerkin method for the numerical modelling of the equations of Multiple-Network Poroelastic Theory (MPET) in the dynamic formulation. The MPET model can comprehensively describe functional changes…
We propose a flexible Bayesian approach for sparse Gaussian graphical modeling of multivariate time series. We account for temporal correlation in the data by assuming that observations are characterized by an underlying and unobserved…
Molecular Dynamics (MD) is a powerful computational microscope for probing protein functions. However, the need for fine-grained integration and the long timescales of biomolecular events make MD computationally expensive. To address this,…
Point and interval estimation of future disability inception and recovery rates are predominantly carried out by combining generalized linear models (GLM) with time series forecasting techniques into a two-step method involving parameter…