Related papers: From molecular dynamics to coarse self-similar sol…

In this paper we propose an approach for solving systems of nonlinear equations without computing function derivatives. Motivated by the application area of tomographic absorption spectroscopy, which is a highly-nonlinear problem with…

We propose a new multi-scale molecular dynamics simulation method which can achieve high accuracy and high sampling efficiency simultaneously without aforehand knowledge of the coarse grained (CG) potential and test it for a biomolecular…

The simulation of large nonlinear dynamical systems, including systems generated by discretization of hyperbolic partial differential equations, can be computationally demanding. Such systems are important in both fluid and kinetic…

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

We discovered a class of self-similar solutions in nonlinear models describing the formation of morphogen gradients, the concentration fields of molecules acting as spatial regulators of cell differention in developing tissues. These models…

We present a new adaptive resolution technique for efficient particle-based multiscale molecular dynamics (MD) simulations. The presented approach is tailor-made for molecular systems where atomistic resolution is required only in spatially…

Neuro-dynamic programming is a class of powerful techniques for approximating the solution to dynamic programming equations. In their most computationally attractive formulations, these techniques provide the approximate solution only…

We propose a combination of cluster analysis and stochastic process analysis to characterize high-dimensional complex dynamical systems by few dominating variables. As an example, stock market data are analyzed for which the dynamical…

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…

We present a systematic computational approach to the study of self-similar dynamics. The approach, through the use of what can be thought of as a ``dynamic pinning condition" factors out self-similarity, and yields a transformed, non-local…

Developing physics-based models for molecular simulation requires fitting many unknown parameters to diverse experimental datasets. Traditionally, this process is piecemeal and difficult to reproduce, leading to a fragmented landscape of…

-Molecular simulations allow the study of properties and interactions of molecular systems. This article presents an improved version of the Adaptive Resolution Scheme that links two systems having atomistic (also called fine-grained) and…

An efficient and flexible engine for computing fixed points is critical for many practical applications. In this paper, we firstly present a goal-directed fixed point computation strategy in the logic programming paradigm. The strategy…

We propose a data-driven, coarse-graining formulation in the context of equilibrium statistical mechanics. In contrast to existing techniques which are based on a fine-to-coarse map, we adopt the opposite strategy by prescribing a…

The adoption of detailed mechanisms for chemical kinetics often poses two types of severe challenges: First, the number of degrees of freedom is large; and second, the dynamics is characterized by widely disparate time scales. As a result,…

Atomistic or ab-initio molecular dynamics simulations are widely used to predict thermodynamics and kinetics and relate them to molecular structure. A common approach to go beyond the time- and length-scales accessible with such…

We propose a multiscale approach for predicting quantities in dynamical systems which is explicitly structured to extract information in both fine-to-coarse and coarse-to-fine directions. We envision this method being generally applicable…

In this paper we study the randomized non-autonomous complete linear differential equation. The diffusion coefficient and the source term in the differential equation are assumed to be stochastic processes and the initial condition is…

The macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction-diffusion processes in periodic porous media is analyzed. Our mathematical model can be used for studying…

We present a dual-resolution molecular dynamics (MD) simulation of liquid water employing a recently introduced Adaptive Resolution Scheme (AdResS). The spatially adaptive molecular resolution procedure allows for changing from a…