Related papers: Perspective: Markov Models for Long-Timescale Biom…

Machine learning techniques not only offer efficient tools for modelling dynamical systems from data, but can also be employed as frontline investigative instruments for the underlying physics. Nontrivial information about the original…

A new methodology is developed to integrate numerically the equations of motion for classical many-body systems in molecular dynamics simulations. Its distinguishable feature is the possibility to preserve, independently on the size of the…

We extend the phase field crystal model to accommodate exact atomic configurations and vacancies by requiring the order parameter to be non-negative. The resulting theory dictates the number of atoms and describes the motion of each of…

Models for open quantum systems, which play important roles in electron transport problems and quantum computing, must take into account the interaction of the quantum system with the surrounding environment. Although such models can be…

A realistic long-term microscopic traffic simulator is necessary for understanding how microscopic changes affect traffic patterns at a larger scale. Traditional simulators that model human driving behavior with heuristic rules often fail…

Markov chains are a class of probabilistic models that have achieved widespread application in the quantitative sciences. This is in part due to their versatility, but is compounded by the ease with which they can be probed analytically.…

Generative tasks about molecules, including but not limited to molecule generation, are crucial for drug discovery and material design, and have consistently attracted significant attention. In recent years, diffusion models have emerged as…

Time-resolved investigations of ultrafast electronic and molecular dynamics were not possible until recently. The typical time scale of these processes is in the picosecond to attosecond realm. The tremendous technological progress in…

Biochemical networks play a crucial role in biological systems, implementing a broad range of vital functions. They normally operate at low copy numbers and in spatial settings, but this is often ignored and well-stirred conditions are…

Markov chains are fundamental models for stochastic dynamics, with applications in a wide range of areas such as population dynamics, queueing systems, reinforcement learning, and Monte Carlo methods. Estimating the transition matrix and…

One of the main tasks in the study of financial and economic processes is forecasting and analysis of the dynamics of these processes. Within this task lie important research questions including how to determine the qualitative properties…

We present a continuum model trained on molecular dynamics (MD) simulations for cellular membranes composed of an arbitrary number of lipid types. The model is constructed within the formalism of dynamic density functional theory and can be…

Stochastic reaction networks are mathematical models with a wide range of applications in biochemistry, ecology, and epidemiology, and are often complex to analyze. Except for some special cases, it is generally difficult to predict how the…

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…

At present it is still quite difficult to match the vast knowledge on the behavior of individual tumor cells with macroscopic measurements on clinical tumors. On the modeling side, we already know how to deal with many molecular pathways…

Understanding the dynamical processes that govern the performance of functional materials is essential for the design of next generation materials to tackle global energy and environmental challenges. Many of these processes involve the…

Unraveling the dynamical motions of biomolecules is essential for bridging their structure and function, yet it remains a major computational challenge. Molecular dynamics (MD) simulation provides a detailed depiction of biomolecular…

Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching…

Developing accurate and efficient coarse-grained representations of proteins is crucial for understanding their folding, function, and interactions over extended timescales. Our methodology involves simulating proteins with molecular…

Bisimulation metrics are powerful tools for measuring similarities between stochastic processes, and specifically Markov chains. Recent advances have uncovered that bisimulation metrics are, in fact, optimal-transport distances, which has…