Related papers: Accurate multiple time step in biased molecular si…
Bayesian forecasting is developed in multivariate time series analysis for causal inference. Causal evaluation of sequentially observed time series data from control and treated units focuses on the impacts of interventions using…
Multiscale is a hallmark feature of complex nonlinear systems. While the simulation using the classical numerical methods is restricted by the local \textit{Taylor} series constraints, the multiscale techniques are often limited by finding…
In this short note, we discuss the basic approach to computational modeling of dynamical systems. If a dynamical system contains multiple time scales, ranging from very fast to slow, computational solution of the dynamical system can be…
Kinetic equations model distributions of particles in position-velocity phase space. Often, one is interested in studying the long-time behavior of particles in high-collisional regimes in which an approximate (advection)-diffusion model…
We provide a general mathematical framework for selective inference with supervised model selection procedures characterized by quadratic forms in the outcome variable. Forward stepwise with groups of variables is an important special case…
The era of huge data necessitates highly efficient machine learning algorithms. Many common machine learning algorithms, however, rely on computationally intensive subroutines that are prohibitively expensive on large datasets. Oftentimes,…
We introduce the class of multistage stochastic optimization problems with a random number of stages. For such problems, we show how to write dynamic programming equations and detail the Stochastic Dual Dynamic Programming algorithm to…
Automated variable selection is widely applied in statistical model development. Algorithms like forward, backward or stepwise selection are available in statistical software packages like R and SAS. Many researchers have criticized the use…
We present an explicit multiscale algorithm for solving differential equations for problems with high-frequency modes that can be averaged over by separating and scaling the fast and slow dynamics within a single equation. We introduce a…
Approximate numerical methods are one of the most used strategies to extract information from many-interacting-agents systems. In particular, numerical approximations are of extended use to deal with epidemic, ecological and biological…
Large molecular dynamics simulations (millions of atoms, tens of microseconds, thousands of processors) hit the strong scalability wall: simulation on twice as many processors does not take half the time. Inspired by large N-body space…
A computer simulation has to be fast to be helpful, if it is employed to study the behavior of a multicomponent dynamic system. This paper discusses modeling concepts and algorithmic techniques useful for creating such fast simulations.…
Motivation: In systems biology, modelling strategies aim to decode how molecular components interact to generate dynamical behaviour. Boolean modelling is more and more used, but the description of the dynamics from two-levels components…
Stochastic computational models in the form of pure jump processes occur frequently in the description of chemical reactive processes, of ion channel dynamics, and of the spread of infections in populations. For spatially extended models,…
In a world made of atoms, the computer simulation of molecular systems, such as proteins in water, plays an enormous role in science. Software packages that perform these computations have been developed for decades. In molecular…
Bidimensional spiking models currently gather a lot of attention for their simplicity and their ability to reproduce various spiking patterns of cortical neurons, and are particularly used for large network simulations. These models…
Our ability to calculate rates of biochemical processes using molecular dynamics simulations is severely limited by the fact that the time scales for reactions, or changes in conformational state, scale exponentially with the relevant…
Multiscale models allow for the treatment of complex phenomena involving different scales, such as remodeling and growth of tissues, muscular activation, and cardiac electrophysiology. Numerous numerical approaches have been developed to…
Biased sampling of collective variables is widely used to accelerate rare events in molecular simulations and to explore free energy surfaces. However, computational efficiency of these methods decreases with increasing number of collective…
Complex biological processes are usually experimented along time among a collection of individuals. Longitudinal data are then available and the statistical challenge is to better understand the underlying biological mechanisms. The…