Experiments in which monkeys have to select or estimate the location of a target are revealing more about the role of the dorsal premotor cortex in decision making.

We discuss Peter Buneman’s suggestion that a fibre connection to the internet — a hub — should be available within every circle enclosing a population of at least 2,000 people (a b-circle). This poses the problem of finding a small set, H, of hubs, such that every b-circle contains a hub. We show that a greedy algorithm does not lead to an optimal set of hubs. Instead it models market forces, w...

Conditions on the boundary and parameters that produce ordering in the first passage time distributions of two different diffusion processes are proved making use of comparison theorems for stochastic differential equations. Three applications of interest in stochastic modeling are presented: a sensitivity analysis for diffusion models characterized by means of first passage times, the comparis...

It has been known for a long time that for birth-and-death processes started in zero the first passage time of a given level is distributed as a sum of independent exponentially distributed random variables, the parameters of which are the negatives of the eigenvalues of the stopped process. Recently, Diaconis and Miclo have given a probabilistic proof of this fact by constructing a coupling be...

We consider two first passage problems for stable processes, not necessarily symmetric, in one dimension. We make use of a novel method of path censoring in order to deduce explicit formulas for hitting probabilities, hitting distributions and a killed potential measure. To do this, we describe in full detail the Wiener–Hopf factorization of a new Lamperti-stable-type Lévy process obtained via ...

We present an approximation algorithm for the hitting set problem when the VC-dimension of the set system is small. Our algorithm builds on Pach & Agarwal [7], and we show how it can be parallelized and extended to the minimum cost hitting set problem. The running time of the proposed algorithm is comparable with that of Brönnimann & Goodrich [2], and the approximation ratio is smaller by a con...

For random walks on finite graphs, we record some equalities, inequalities and limit theorems (as the size of graph tends to infinity) which hold for vertex-transitive graphs but not for general regular graphs. The main result is a sharp condition for asymptotic exponentiality of the hitting time to a single vertex. Another result is a lower bound for the coefficient of variation of hitting tim...

A collection of landmarks is complete if the cost of a minimum-cost hitting set equals h and there is a minimumcost hitting set that is an optimal relaxed plan. We present an algorithm for generating a complete collection of landmarks and we show that this algorithm can be extended into effective polytime heuristics for optimal and satisficing planning. The new admissible heuristics are compare...

The effect of prior attention was systematically manipulated to study its influence on rates of yelling and head hitting, both maintained by positive reinforcement in the form of attention. Higher levels of head hitting occurred in analogue attention conditions when the person was deprived of attention (no social interactions for 1 hr) prior to the analysis in comparison to when the person rece...