Related papers: Continuous Gated First-Passage Processes
First-passage phenomena play a fundamental role in classical stochastic processes. We here exactly solve a quantum first-passage time problem for quantum diffusion driven by measurement noise, a generalization of classical Brownian motion.…
The first passage time for a single diffusing particle has been studied extensively, but the first passage time of a system of many diffusing particles, as is often the case in physical systems, has received little attention until recently.…
The performance of a quantum information processor depends on the precise control of phases introduced into the system during quantum gate operations. As the number of operations increases with the complexity of a computation, the phases of…
These notes are based on the lectures that I gave (virtually) at the Bruneck Summer School in 2021 on first-passage processes and some applications of the basic theory. I begin by defining what is a first-passage process and presenting the…
In the recent literature, the g-subdiffusion equation involving Caputo fractional derivatives with respect to another function has been studied in relation to anomalous diffusions with a continuous transition between different subdiffusive…
Verification of temporal logic properties plays a crucial role in proving the desired behaviors of continuous systems. In this paper, we propose an interval method that verifies the properties described by a bounded signal temporal logic.…
We investigate the first-passage properties of nearest-neighbor hopping on a finite interval with disordered hopping rates. We develop an approach that relies on the backward equation, in conjunction with probability generating functions,…
Quantifying how spatial disorder affects the movement of a diffusing particle or agent is fundamental to target search studies. When diffusion occurs on a network, that is on a highly disordered environment, we lack the mathematical tools…
We investigate the problem of establishing finite-time probabilistic safety guarantees for discrete-time stochastic dynamical systems subject to unknown disturbance distributions, using barrier certificate methods. Our approach develops a…
We propose an approach for estimating the probability that a given small target, among many, will be the first to be reached in a molecular dynamics simulation. Reaching small targets out of a vast number of possible configurations…
Parallel processing of information plays a critical role in accelerating computation. This includes quantum computers, where parallel processing of quantum information will play a critical role in practical quantum advantage. Here, we…
How long a stochastic process survives before leaving a domain depends not only on its intrinsic dynamics but also on how it is observed. Classical first-passage theory assumes continuous monitoring with absorbing boundaries…
Random search for one or more targets in a bounded domain occurs widely in nature, with examples ranging from animal foraging to the transport of vesicles within cells. Most theoretical studies take a searcher-centric viewpoint, focusing on…
We investigate the work fluctuations in an overdamped non-equilibrium process that is stopped at a stochastic time. The latter is characterized by a first passage event that marks the completion of the non-equilibrium process. In…
We introduce a unified framework for solving first passage times of time-homogeneous diffusion processes. According to the killed version potential theory and the perturbation theory, we are able to deduce closed-form solutions for…
Gating mechanisms are widely used in neural network models, where they allow gradients to backpropagate more easily through depth or time. However, their saturation property introduces problems of its own. For example, in recurrent models…
We address the problem of statically checking safety properties (such as assertions or deadlocks) for parameterized phaser programs. Phasers embody a non-trivial and modern synchronization construct used to orchestrate executions of…
Finding representative reaction pathways is necessary for understanding mechanisms of molecular processes, but is considered to be extremely challenging. We propose a new method to construct reaction paths based on mean first-passage times.…
Extracted event data from information systems often contain a variety of process executions making the data complex and difficult to comprehend. Unlike current research which only identifies the variability over time, we focus on other…
The First Passage Time (FPT) is the time taken for a stochastic process to reach a desired threshold. In this letter we address the FPT of the stochastic measurement current in the case of continuously measured quantum systems. Our approach…