Related papers: Variable-free exploration of stochastic models: a …

Hybrid multiscale modelling has emerged as a useful framework for modelling complex biological phenomena. However, when accounting for stochasticity in the internal dynamics of agents, these models frequently become computationally…

Biological neural networks are notoriously hard to model due to their stochastic behavior and high dimensionality. We tackle this problem by constructing a dynamical model of both the expectations and covariances of the fractions of active…

The automated construction of coarse-grained models represents a pivotal component in computer simulation of physical systems and is a key enabler in various analysis and design tasks related to uncertainty quantification. Pertinent methods…

This work explores the trade-off between the number of samples required to accurately build models of dynamical systems and the degradation of performance in various control objectives due to a coarse approximation. In particular, we show…

We focus at the interface between multiscale computations, bifurcation theory and social networks. In particular we address how the Equation-Free approach, a recently developed computational framework, can be exploited to systematically…

We demonstrate how direct simulation of stochastic, individual-based models can be combined with continuum numerical analysis techniques to study the dynamics of evolving diseases. % Sidestepping the necessity of obtaining explicit…

We consider the task of discovering gene regulatory networks, which are defined as sets of genes and the corresponding transcription factors which regulate their expression levels. This can be viewed as a variable selection problem,…

We present a theoretical framework to analyze the dynamics of gene expression with stochastic bursts. Beginning with an individual-based model which fully accounts for the messenger RNA (mRNA) and protein populations, we propose a novel…

Many structural econometric models include latent variables on whose probability distributions one may wish to place minimal restrictions. Leading examples in panel data models are individual-specific variables sometimes treated as "fixed…

This paper considers the problem of learning, from samples, the dependency structure of a system of linear stochastic differential equations, when some of the variables are latent. In particular, we observe the time evolution of some…

Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time…

A general class of stochastic gene expression models with self regulation is considered. One or more genes randomly switch between regulatory states, each having a different mRNA transcription rate. The gene or genes are self regulating…

Modeling a high-dimensional Hamiltonian system in reduced dimensions with respect to coarse-grained (CG) variables can greatly reduce computational cost and enable efficient bottom-up prediction of main features of the system for many…

Distinguishability and, by extension, observability are key properties of dynamical systems. Establishing these properties is challenging, especially when no analytical model is available and they are to be inferred directly from…

The recent experimental progresses in handling microscopic systems have allowed to probe them at levels where fluctuations are prominent, calling for stochastic modeling in a large number of physical, chemical and biological phenomena. This…

We explore the derivation of distributed parameter system evolution laws (and in particular, partial differential operators and associated partial differential equations, PDEs) from spatiotemporal data. This is, of course, a classical…

Mathematical modelling of biological population dynamics often involves proposing high fidelity discrete agent-based models that capture stochasticity and individual-level processes. These models are often considered in conjunction with an…

Although coarse-grained models have been widely used to explain exotic phenomena in complex fluids, such as droplet formation in living cells, these conventional approaches often fail to capture the intricate microscopic degrees of freedom…

Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…

This chapter discusses the interplay between structure and dynamics in complex networks. Given a particular network with an endowed dynamics, our goal is to find partitions aligned with the dynamical process acting on top of the network. We…