相关论文: Time Scale Calculus: A New Approach to Multi-Dose …

Stochastic biochemical and transport processes have various final outcomes, and they can be viewed as dynamic systems with multiple exits. Many current theoretical studies, however, typically consider only a single time scale for each…

Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to…

In this review we address to what extent computational techniques can augment our ability to predict toxicity. The first section provides a brief history of empirical observations on toxicity dating back to the dawn of Sumerian…

Understanding the behaviour of biological systems requires a complex setting of in vitro and in vivo experiments, which attracts high costs in terms of time and resources. The use of mathematical models allows researchers to perform…

Machine learning approaches have recently been leveraged as a substitute or an aid for physical/mathematical modeling approaches to dynamical systems. To develop an efficient machine learning method dedicated to modeling and prediction of…

Stochastic, spatial reaction-diffusion simulations have been widely used in systems biology and computational neuroscience. However, the increasing scale and complexity of simulated models and morphologies have exceeded the capacity of any…

A stochastic model for a chemical reaction network is embedded in a one-parameter family of models with species numbers and rate constants scaled by powers of the parameter. A systematic approach is developed for determining appropriate…

Deep reinforcement learning (RL) agents are becoming increasingly proficient in a range of complex control tasks. However, the agent's behavior is usually difficult to interpret due to the introduction of black-box function, making it…

We present a mathematical study for the development of Multiple Sclerosis in which a spatio-temporal kinetic { theory} model describes, at the mesoscopic level, the dynamics of a high number of interacting agents. We consider both…

In this paper a new multiscale modeling technique is proposed. It relies on a recently introduced measure-theoretic approach, which allows to manage the microscopic and the macroscopic scale under a unique framework. In the resulting…

Inspired by the ubiquitous use of differential equations to model continuous dynamics across diverse scientific and engineering domains, we propose a novel and intuitive approach to continuous sequence modeling. Our method interprets…

Time series chain (TSC) is a recently introduced concept that captures the evolving patterns in large scale time series. Informally, a time series chain is a temporally ordered set of subsequences, in which consecutive subsequences in the…

Computing the stationary distributions of a continuous-time Markov chain (CTMC) involves solving a set of linear equations. In most cases of interest, the number of equations is infinite or too large, and the equations cannot be solved…

There are many natural, physical, and biological systems that exhibit multiple time scales. For example, the dynamics of a population of ticks can be described in continuous time during their individual life cycle yet discrete time is used…

Model predictive control (MPC) is a powerful framework for optimal control of dynamical systems. However, MPC solvers suffer from a high computational burden that restricts their application to systems with low sampling frequency. This…

Many real-world processes are trajectories that may be regarded as continuous-time "functional data". Examples include patients' biomarker concentrations, environmental pollutant levels, and prices of stocks. Corresponding advances in data…

Clinical time series data from electronic health records and medical registries offer unprecedented opportunities to understand patient trajectories and inform medical decision-making. However, leveraging such data presents significant…

In this work, we introduce metrics to evaluate the use of simplified time series in the context of interpretability of a TSC -- a Time Series Classifier. Such simplifications are important because time series data, in contrast to text and…

Molecular dynamics (MD) simulations are widely used to study large-scale molecular systems. HPC systems are ideal platforms to run these studies, however, reaching the necessary simulation timescale to detect rare processes is challenging,…

Stochastic agent-based models can account for millions of cells with spatiotemporal movement that can be a function of different factors. However, these simulations can be computationally expensive. In this work, we develop a novel…