This definition makes sense without extra mathematical technicalities if Xt is a continuous function of t and S is a closed set. In that case, Xτ ∈ S and Xt / ∈ S if t < τ . Many practical problems may be formulated using hitting times. When does something break? How long does it take to travel a given distance? A hitting time is an important example of the more general idea of a stopping time....

Therapies consisting of a combination of agents are an attractive proposition, especially in the context of diseases such as cancer, which can manifest with a variety of tumor types in a single case. However uncovering usable drug combinations is expensive both financially and temporally. By employing computational methods to identify candidate combinations with a greater likelihood of success ...

A k-hitting set in a hypergraph is a set of at most k vertices that intersects all hyperedges. We study the union of all inclusion-minimal khitting sets in hypergraphs of rank r (where the rank is the maximum size of hyperedges). We show that this union is relevant for certain combinatorial inference problems and give worst-case bounds on its size, depending on r and k. For r = 2 our result is ...

Algorithms based on the enumeration of implicit hitting sets find a growing number of applications, which include maximum satisfiability and model based diagnosis, among others. This paper exploits enumeration of implicit hitting sets in the context of Quantified Boolean Formulas (QBF). The paper starts by developing a simple algorithm for QBF with two levels of quantification, which is shown t...

Many aspects of the relation of different decision tree and DNF complexity measures of Boolean functions have been more or less substantially explored. This paper adds a new detail to the picture: we prove that DNF tautologies with terms conflicting in one or two variables pairwise possess a tree-like structure. An equivalent reformulation of this result (adopting the terminology of [7, 8, 9]) ...

We characterize the hitting sets for read-once branching programs of width 3 by a so-called richness condition which is independent of a rather technical definition of branching programs. The richness property proves to be (in certain sense) necessary and sufficient condition for such hitting sets. In particular, we show that any rich set extended with all strings within Hamming distance of 3 i...