Related papers: Rapid Determination of Multiple Reaction Pathways …

Path planning in the multi-robot system refers to calculating a set of actions for each robot, which will move each robot to its goal without conflicting with other robots. Lately, the research topic has received significant attention for…

Mobile robots frequently navigate on roadmaps, i.e., graphs where edges represent safe motions, in applications such as healthcare, hospitality, and warehouse automation. Often the environment is quasi-static, i.e., it is sufficient to…

We propose a technique to detect and generate patterns in a network of locally interacting dynamical systems. Central to our approach is a novel spatial superposition logic, whose semantics is defined over the quad-tree of a partitioned…

We investigate several important issues regarding the Random Batch Method (RBM) for second order interacting particle systems. We first show the uniform-in-time strong convergence for second order systems under suitable contraction…

We derive a reduction formula for singularly perturbed ordinary differential equations (in the sense of Tikhonov and Fenichel) with a known parameterization of the critical manifold. No a priori assumptions concerning separation of slow and…

A combination of first principle molecular dynamics (MD) simulations with a rate equation model (MD-RE approach) is presented to study the trapping and the scattering of rare gas atoms from metal surfaces. The temporal evolution of the atom…

The discerning behavior of living systems relies on accurate interactions selected from the lot of molecular collisions occurring in the cell. To ensure the reliability of interactions, binding partners are classically envisioned as finely…

The inherent complexity of biological agents often leads to motility behavior that appears to have random components. Robust stochastic inference methods are therefore required to understand and predict the motion patterns from time…

For the investigation of chemical reaction networks, the efficient and accurate determination of all relevant intermediates and elementary reactions is mandatory. The complexity of such a network may grow rapidly, in particular if reactive…

In this paper mathematical models for the evolutionary conserved Notch-Delta pathway are developed and analyzed in order to better understand how two neighboring biological cells can become different. We pursue a structure-based…

This paper studies the problem of multi-agent trajectory prediction in crowded unknown environments. A novel energy function optimization-based framework is proposed to generate prediction trajectories. Firstly, a new energy function is…

Executing various sequences of system functions in a system under test represents one of the primary techniques in software testing. The natural way to create effective, consistent and efficient test sequences is to model the system under…

Numerous algorithms and parallelisations have been developed for short-range particle simulations; however, none are optimally performant for all scenarios. Such a concept led to the prior development of the particle simulation library…

This chapter discusses the way in which dimensionality reduction algorithms such as diffusion maps and sketch-map can be used to analyze molecular dynamics trajectories. The first part discusses how these various algorithms function, as…

Particle dynamics and multi-agent systems provide accurate dynamical models for studying and forecasting the behavior of complex interacting systems. They often take the form of a high-dimensional system of differential equations…

The probability distribution describing the state of a Stochastic Reaction Network evolves according to the Chemical Master Equation (CME). It is common to estimated its solution using Monte Carlo methods such as the Stochastic Simulation…

We propose a generalization of the stochastic resetting mechanism for a Brownian particle diffusing in a one-dimensional periodic potential: randomly in time, the particle gets reset at the bottom of the potential well it was in. Numerical…

Motivation: Stochastic reaction networks are a widespread model to describe biological systems where the presence of noise is relevant, such as in cell regulatory processes. Unfortu-nately, in all but simplest models the resulting discrete…

Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose…

Logistic regression is a well-known statistical model which is commonly used in the situation where the output is a binary random variable. It has a wide range of applications including machine learning, public health, social sciences,…