We propose a simple and semi-parametric estimator for the tail index of a regular varying elliptical random vector. Since, for univariate random variables, our estimator boils down to the Hill estimator and it inherits the simplicity and asymptotic properties, we name it after Bruce M. Hill. The estimator is based on the distance between an elliptical probability contour and the outer – or exce...

Enforced hill-climbing is an effective deterministic hillclimbing technique that deals with local optima using breadth-first search (a process called “basin flooding”). We propose and evaluate a stochastic generalization of enforced hill-climbing for online use in goal-oriented probabilistic planning problems. We assume a provided heuristic function estimating expected cost to the goal with fla...

A great deal has been written, especially since the war, on off street parking. You have heard of the crying need for more off street parking in order to meet the needs of shoppers and thereby avoid a process of decentralization. Many parking authorities have been established and millions of dollars of public money invested in park­ ing facilities to provide space for all comers on a completely...

Vimal K. Derebail, JulieAnne G. McGregor, Romulo E. Colindres, Harsharan K. Singh and Abhijit V. Kshirsagar Division of Nephrology and Hypertension, Department of Medicine, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, USA; UNC Kidney Center, Chapel Hill, North Carolina, USA and Department of Pathology and Laboratory Medicine, University of North Carolina at Chapel H...

We show that certain non-linear dynamical systems with non-linearities in the form of Hill functions, can be approximated by piecewise linear dynamical systems. The resulting piecewise systems have closed form solutions that can be used to understand the behavior of the fully nonlinear system. We justify the reduction using geometric singular perturbation theory, and illustrate the results in n...

The aim of the present paper is to study the periodic auto–oscillations of an electric circuit with periodic imperfections on its variables composed by three condensers, one of them without charge, and two bobbins. We model this system by the Lagrangian approach using the morphology of the Hill problem and the main tool used for proving the results is the averaging theory of dynamical systems.

This paper deals with completion of partial latin squares L = (lij) of order n with k cyclically generated diagonals (li+t,j+t = lij + t if lij is not empty; with calculations modulo n). There is special emphasis on cyclic completion. Here, we present results for k = 2, . . . , 7 and odd n ≤ 21, and we describe the computational method used (hill-climbing). Noncyclic completion is investigated ...

In my youth I used to wander in the mountains. I would gain a "feel" of the terrain and gradually build up a reliable intuition of how to get from here to there and back again. Always, on these expeditions, I would discover special places a tiny area, the only one, where fairy slippers grew; a pool in a rushing stream that was deep enough to swim in. Invariably I would find myself excitedly cli...