When does a diffusing particle reach its target for the first time? This first-passage time (FPT) problem is central to the kinetics of molecular reactions in chemistry and molecular biology. Here, we explain the behavior of smooth FPT densities, for which all moments are finite, and demonstrate universal yet generally non-Poissonian long-time asymptotics for a broad variety of transport proces...

Every economic model should include an estimate of its stability and predictability. A new measure, the first passage time (FPT) which is defined as the time period when the model error first exceeds a pre-determined criterion (i.e., the tolerance level), is proposed here to estimate the model predictability. A theoretical framework is developed to determine the mean and variance of FPT. The cl...

Evaluation of default correlation is an important task in credit risk analysis. In many practical situations, it concerns the joint defaults of several correlated firms, the task that is reducible to a first passage time (FPT) problem. This task represents a great challenge for jump-diffusion processes (JDP), where except for very basic cases, there are no analytical solutions for such problems...

Abstract We introduce a framework for the verification of protocols involving distinguished machine (referred to as leader) orchestrating operation an arbitrary number identical machines followers) in network. At core our is high-level formalism capturing these types together with their network interactions. show that this automatically translates tractable form first-order temporal logic. Chec...

Abstract. We present exact results for the spectrum of the fractional Laplacian in a bounded domain and apply them to First Passage Time (FPT) Statistics of Lévy flights. We specifically show that the average is insufficient to describe the distribution of FPT, although it is the only quantity available in the existing literature. In particular, we show that the FPT distribution is not peaked a...

The parameterized complexity classes of the W -hierarchy are usually defined as the problems reducible to certain natural complete problems by means of fixed-parameter tractable (fpt) reductions. We investigate whether the classes can be characterised by means of weaker, logical reductions. We show that each class W [t] has complete problems under slicewise bounded-variable firstorder reduction...

The undecidability of first-order logic implies that there is no computable bound on the length of shortest proofs of valid sentences of first-order logic. Some valid sentences can only have quite long proofs. How hard is it to prove such “hard” valid sentences? The polynomial time tractability of this problem would imply the fixed-parameter tractability of the parameterized problem that, given...

In this article we study the parameterized complexity of problems consisting in finding degree-constrained subgraphs, taking as the parameter the number of vertices of the desired subgraph. Namely, given two positive integers d and k, we study the problem of finding a d-regular (induced or not) subgraph with at most k vertices and the problem of finding a subgraph with at most k vertices and of...