Related papers: Augmented Transition Path Theory for Sequences of …
Given two metastable states A and B of a biomolecular system, the problem is to calculate the likely paths of the transition from A to B. Such a calculation is more informative and more manageable if done for a reduced set of collective…
Understanding realistic complex systems requires confronting significant conceptual, theoretical and experimental limitations rooted in the persistence of views that originated in the mechanics of simple moving bodies. We define the…
We study an active random walker model in which a particle's motion is determined by a self-generated field. The field encodes information about the particle's path history. This leads to either self-attractive or self-repelling behavior.…
Many processes in chemistry, physics, and biology involve rare events in which the system escapes from a metastable state by surmounting an activation barrier. Examples range from chemical reactions, protein folding, and nucleation events…
We describe an exact approach for calculating transition probabilities and waiting times in finite-state discrete-time Markov processes. All the states and the rules for transitions between them must be known in advance. We can then…
This note shows how classical tools from linear control theory can be leveraged to provide a global analysis of nonlinear reaction-diffusion models. The approach is differential in nature. It proceeds from classical tools of contraction…
Motion of chemically driven droplets is analyzed by applying a solvability condition of perturbed hydrodynamic equations affected by the adsorbate concentration. Conditions for traveling bifurcation analogous to a similar transition in…
Structural transition induced by a local conformational change in biomolecules is formulated based on the generalized Langevin theory for the structural fluctuation of a molecule in solution, and the linear response theory, derived by Kim…
We introduce a representation learning framework for spatial trajectories. We represent partial observations of trajectories as probability distributions in a learned latent space, which characterize the uncertainty about unobserved parts…
The mesosocpic concept is applied to the theory of mixtures. The aim is to investigate the diffusion phenomenon from a mesoscopic point of view. The domain of the field quantities is extended by the set of mesoscopic variables, here the…
We formulate a theory for phase reduction analysis of traveling breathers in reaction--diffusion systems with spatial translational symmetry. In this formulation, the spatial and temporal phases represent the position and oscillation of a…
A plasma transport theory that spans weak to strong coupling is developed from a binary collision picture, but where the interaction potential is taken to be an effective potential that includes correlation effects and screening…
The Average Treatment Effect (ATE) is a foundational metric in causal inference, widely used to assess intervention efficacy in randomized controlled trials (RCTs). However, in many applications -- particularly in healthcare -- this static…
Many biochemical and industrial applications involve complicated networks of simultaneously occurring chemical reactions. Under the assumption of mass action kinetics, the dynamics of these chemical reaction networks are governed by systems…
We propose a definition of phase transitions in finite systems based on topology anomalies of the event distribution in the space of observations. This generalizes all the definitions based on the curvature anomalies of thermodynamical…
After discussing the significance of interactions to understand complex multiscale stochastic systems (CMSS), we turn our attention to the construction of a Generalised Theory of Interactions (GToI). We define interactions as discrete,…
We consider the noise-induced transitions in the randomly perturbed discrete logistic map from a linearly stable periodic orbit consisting of T periodic points. The traditional large deviation theory and asymptotic analysis for small noise…
This paper provides a theoretical framework of deriving the forward and backward Feynman-Kac equations for the distribution of functionals of the path of a particle undergoing both diffusion and chemical reaction. Very general forms of the…
We explore a new framework for describing the kinetics of a heterogeneous chemical reaction where two particles of the same chemical species form a reaction product of another chemical species on the surface of a seed particle. Traditional…
A key overall goal of biomolecular simulations is the characterization of "mechanism" -- the pathways through configuration space of processes such as conformational transitions and binding. Some amount of heterogeneity is intrinsic to the…