Related papers: Kinetic distance and kinetic maps from molecular d…
Errors in the kinematic distances, under the assumption of circular gas orbits, were estimated by performing synthetic observations of a model disk galaxy. It was found that the error is < 0.5 kpc for most of the disk when the measured…
Distances to high mass star forming regions (HMSFRs) in the Milky Way are a crucial constraint on the structure of the Galaxy. Only kinematic distances are available for a majority of the HMSFRs in the Milky Way. Here we compare the…
For a given Markov chain Monte Carlo algorithm we introduce a distance between two configurations that quantifies the difficulty of transition from one configuration to the other configuration. We argue that the distance takes a universal…
Small integration time steps limit molecular dynamics (MD) simulations to millisecond time scales. Markov state models (MSMs) and equation-free approaches learn low-dimensional kinetic models from MD simulation data by performing…
In this review paper, we will present different data-driven dimension reduction techniques for dynamical systems that are based on transfer operator theory as well as methods to approximate transfer operators and their eigenvalues,…
The internal dynamics of macro-molecular systems is characterized by widely separated time scales, ranging from fraction of ps to ns. In ordinary molecular dynamics simulations, the elementary time step dt used to integrate the equation of…
For a given Markov chain Monte Carlo (MCMC) algorithm, we define the distance between configurations that quantifies the difficulty of transitions. This distance enables us to investigate MCMC algorithms in a geometrical way, and we…
Molecular dynamics simulates the~movements of atoms. Due to its high cost, many methods have been developed to "push the~simulation forward". One of them, metadynamics, can hasten the~molecular dynamics with the~help of variables describing…
We present a mathematical framework for constructing and analyzing parallel algorithms for lattice Kinetic Monte Carlo (KMC) simulations. The resulting algorithms have the capacity to simulate a wide range of spatio-temporal scales in…
Relative fluctuations of observables in discrete stochastic systems are bounded at all times by the mean dynamical activity in the system, quantified by the mean number of jumps. This constitutes a kinetic uncertainty relation that is…
This study introduces a novel computational approach based on ratchet-and-pawl molecular dynamics (rMD) for accurately estimating ligand dissociation kinetics in protein-ligand complexes. By integrating Kramers' theory with Bell's equation,…
To develop and investigate detailed mathematical models of cellular metabolic processes is one of the primary challenges in systems biology. However, despite considerable advance in the topological analysis of metabolic networks, explicit…
In this paper we propose two behavioral distances that support approximate reasoning on Stochastic Markov Models (SMMs), that are continuous-time stochastic transition systems where the residence time on each state is described by a generic…
Protein-ligand (un)binding simulations are a recent focus of biased molecular dynamics simulations. Such binding and unbinding can occur via different pathways in and out of a binding site. We here present a theoretical framework how to…
Molecular dynamics (MD) simulations are used in biochemistry, physics, and other fields to study the motions, thermodynamic properties, and the interactions between molecules. Computational limitations and the complexity of these problems,…
Calculating the inverse kinematics (IK) is a fundamental challenge in robotics. Compared to numerical or learning-based approaches, analytical IK provides higher efficiency and accuracy. However, existing analytical approaches are difficult…
In this work, we derive particle schemes, based on micro-macro decomposition, for linear kinetic equations in the diffusion limit. Due to the particle approximation of the micro part, a splitting between the transport and the collision part…
A dilute gas of hard disks confined between two straight parallel lines is considered. The distance between the two boundaries is in between one and two particle diameters, so that the system is quasi-one-dimensional. A Boltzmann-like…
Recent experimental studies on the stepwize motion of biological molecular motors have revealed that the ``characteristic distance'' of a step is usually less than the actual step size. This observation implies that the detailed-balance…
Many chemical reactions and molecular processes occur on timescales that are significantly longer than those accessible by direct simulation. One successful approach to estimating dynamical statistics for such processes is to use many short…