We study the statistical mechanics of classical two-dimensional “Coulomb gases” with general potential and arbitrary β, the inverse of the temperature. Such ensembles also correspond to random matrix models in some particular cases. The formal limit case β =∞ corresponds to “weighted Fekete sets” and also falls within our analysis. It is known that in such a system points should be asymptotical...

We give a rigorous account of an algorithm that provides sequentially consistent replicated data on top of the view synchronous group communication service previously speciied by Fekete, Lynch and Shvartsman. The algorithm performs updates at all members of a majority view, but rotates the work of queries among the members to equalize the load. The algorithm is presented and veriied using I/O a...

Róbert Busa-Fekete [email protected] Eyke Hüllermeier [email protected] Balázs Szörényi [email protected] MTA-SZTE Research Group on Artificial Intelligence, Tisza Lajos krt. 103., H-6720 Szeged, Hungary Department of Computer Science, University of Paderborn, Warburger Str. 100, 33098 Paderborn, Germany INRIA Lille Nord Europe, SequeL project, 40 avenue Halley, 59650 Villeneuve d’Ascq,...

We have implemented a Matlab code to compute Discrete Extremal Sets (of Fekete and Leja type) on convex or concave polygons, together with the corresponding interpolatory cubature formulas. The method works by QR and LU factorizations of rectangular Vandermonde matrices on Weakly Admissible Meshes (WAMs) of polygons, constructed by polygon quadrangulation. 2000 AMS subject classification: 65D05...

We analyze the optimal behavior of two players who are lost on a planar surface and who want to meet each other in least expected time. They each know the initial distribution of the other’s location, but have no common labeling of points, and so cannot simply go to a location agreed to in advance. They have no compasses, so do not even have a common notion of North. For simplicity, we restrict...

Fekete’s lemma is a well known combinatorial result on number sequences. Here we extend it to the multidimensional case, i.e., to sequences of d-tuples, and use it to study the behaviour of a certain class of dynamical systems.

Let n ≥ 4 be even. It is shown that every set S of n points in the plane can be connected by a (possibly self-intersecting) spanning tour (Hamiltonian cycle) consisting of n straight line edges such that the angle between any two consecutive edges is at most 2π/3. For n = 4 and 6, this statement is tight. It is also shown that every even-element point set S can be partitioned into at most two s...