We develop a systematic matrix-analytic approach, based on intertwinings of Markov semigroups, for proving theorems about hitting-time distributions for finite-state Markov chains—an approach that (sometimes) deepens understanding of the theorems by providing corresponding sample-path-by-sample-path stochastic constructions. We employ our approach to give new proofs and constructions for two th...

We examine the relationship between PageRank and several invariants occurring in the study of random walks and electrical networks. We consider a generalized version of hitting time and effective resistance with an additional parameter which controls the ‘speed’ of diffusion. We will establish their connection with PageRank . Through these connections, a combinatorial interpretation of PageRank...

We consider irreducible Markov chains on a finite state space. We show that the mixing time of any such chain is equivalent to the maximum, over initial states x and moving large sets (As)s, of the hitting time of (As)s starting from x. We prove that in the case of the d-dimensional torus the maximum hitting time of moving targets is equal to the maximum hitting time of stationary targets. Neve...

Previous work has shown the effectiveness of random walk hitting times as a measure of dissimilarity in a variety of graph-based learning problems such as collaborative filtering, query suggestion or finding paraphrases. However, application of hitting times has been limited to small datasets because of computational restrictions. This paper develops a new approximation algorithm with which hit...

In this paper an investigation is carried out to classify the steady state responses of asymmetric piecewise linear vibration isolators as double hitting, single hitting, and no hitting. In each class, the analysis has been carried out using a set of coupled nonlinear algebraic equations following Natsiavas and Gonzalez [1]. Applying perturbation technique, a closed form analytic expression of ...

Consider the random walk on graphs such that, at each step, the next visited vertex is a neighbor of the current vertex, chosen with probability proportional to the inverse of the square root of its degree. On one hand, for every graph with n vertices, the maximal mean hitting time for this degree-biased random walk is asymptotically dominated by n. On the other hand, the maximal mean hitting t...

Data analysis is used to test the hypothesis that "hitting is contagious". A statistical model is described to study the effect of a hot hitter upon his teammates' batting during a consecutive game hitting streak. Box score data for entire seasons comprising [Formula: see text] streaks of length [Formula: see text] games, including a total [Formula: see text] observations were compiled. Treatme...

Given a hypergraph H = (V,E), what is the smallest subset X ⊆ V such that e∩X 6= ∅ holds for all e ∈ E? This problem, known as the hitting set problem, is a basic problem in parameterized complexity theory. There are well-known kernelization algorithms for it, which get a hypergraph H and a number k as input and output a hypergraph H ′ such that (1) H has a hitting set of size k if, and only if...