Related papers: Approximating First Hitting Point Distribution in …
Milestoning is a computational procedure that reduces the dynamics of complex systems to memoryless jumps between intermediates, or milestones, and only retains some information about the probability of these jumps and the time lags between…
Milestoning is an accurate and efficient method for rare event kinetics calculations by constructing a continuous-time kinetic network connecting the reactant and product states. However, even with adequate sampling, its accuracy can also…
Computing long-timescale kinetics of biomolecular processes remains a major challenge for atomistic simulations. A way out is to exploit local kinetic information to construct the global stationary flux across the reaction space. The…
The first-passage time (FPT), i.e., the moment when a stochastic process reaches a given threshold value for the first time, is a fundamental mathematical concept with immediate applications. In particular, it quantifies the statistics of…
The Milestoning algorithm created by Ron Elber et al. is a method for determining the time scale of processes too complex to be studied using brute force simulation methods. The fundamental objects implemented in the Milestoning algorithm…
We present a reduction of Milestoning (ReM) algorithm to analyze the high-dimensional Milestoning kinetic network. The algorithm reduces the Milestoning network to low dimensions but preserves essential kinetic information, such as local…
The first passage is a generic concept for quantifying when a random quantity such as the position of a diffusing molecule or the value of a stock crosses a preset threshold (target) for the first time. The last decade saw an enlightening…
We give a mathematical framework for Exact Milestoning, a recently introduced algorithm for mapping a continuous time stochastic process into a Markov chain or semi-Markov process that can be efficiently simulated and analyzed. We…
As an optimal one-dimensional reaction coordinate, the committor function not only describes the probability of a trajectory initiated at a phase space point first reaching the product state before reaching the reactant state, but also…
The first passage time (FPT) is a generic measure that quantifies when a random quantity reaches a specific state. We consider the FTP distribution in nonlinear stochastic biochemical networks, where obtaining exact solutions of the…
To directly simulate rare events using atomistic molecular dynamics is a significant challenge in computational biophysics. Well-established enhanced-sampling techniques do exist to obtain the thermodynamic functions for such systems. But…
The generalized master equation or the equivalent continuous time random walk equations can be used to compute the macroscopic first passage time distribution (FPTD) of a complex stochastic system from short-term microscopic simulation…
We develop novel numerical methods and perturbation approaches to determine the mean first passage time (MFPT) for a Brownian particle to be captured by either small stationary or mobile traps inside a bounded 2-D confining domain. Of…
Many transport processes in ecology, physics and biochemistry can be described by the average time to first find a site or exit a region, starting from an initial position. Typical mathematical treatments are based on formulations that…
The transport properties of discrete-time random walks on ring networks with deterministic shortcuts are investigated through analytical and numerical methods. The network consists of a periodic chain where each node is connected to its…
First-passage probability estimation of high-dimensional nonlinear stochastic systems is a significant task to be solved in many science and engineering fields, but remains still an open challenge. The present paper develops a novel…
The ``first passage-time'' (FPT) problem is an important problem with a wide range of applications in mathematics, physics, biology and finance. Mathematically, such a problem can be reduced to estimating the probability of a (stochastic)…
An approach was developed to describe the first passage time (FPT) in multistep stochastic processes with discrete states governed by a master equation (ME). The approach is an extension of the totally absorbing boundary approach given for…
A new mechanism for efficiently solving the Markov decision processes (MDPs) is proposed in this paper. We introduce the notion of reachability landscape where we use the Mean First Passage Time (MFPT) as a means to characterize the…
Biological events are often initiated when a random "searcher" finds a "target," which is called a first passage time (FPT). In some biological systems involving multiple searchers, an important timescale is the time it takes the slowest…