Given a set S of points in the plane representing wireless devices, each point equipped with a directional antenna of radius r and aperture angle α ≥ 180◦, our goal is to find orientations and a minimum r for these antennas such that the induced communication graph is strongly connected. We show that r = √ 3 suffices to establish strong connectivity, assuming that the longest edge in the Euclid...

The connection between sense of direction and communication complexity in distributed complete networks is studied for two basic problems: finding a minimum-weight spanning tree (MST) and finding a spanning tree (SP). Several models of the complete network are defined, the difference being the amount (and type) of sense of direction available, forming a hierarchy which includes the models previ...

Statistical learning and sequential prediction are two different but related formalisms to study the quality of predictions. Mapping out their relations and transferring ideas is an active area of investigation. We provide another piece of the puzzle by showing that an important concept in sequential prediction, the mixability of a loss, has a natural counterpart in the statistical setting, whi...

Color superconductivity of QCD at finite density, temperature and flavor asymmetry is studied within an approximation which the interaction is modeled upon four–fermion interactions. We calculate the thermodynamic potential in the socalled NJL-type model and study the phase structure at finite density, temperature and flavor asymmetry. We find that a mixed phase appears at sufficiently large fl...

Given a set of points S = {x1, . . . , xm} ⊂ R and > 0, we propose and analyze an algorithm for the problem of computing a (1 + )-approximation to the minimum-volume axis-aligned ellipsoid enclosing S . We establish that our algorithm is polynomial for fixed . In addition, the algorithm returns a small core set X ⊆ S , whose size is independent of the number of points m, with the property that ...

Given a binary nonlinear code, we provide a deterministic algorithm to compute its weight and distance distribution, and in particular its minimum weight and its minimum distance, which takes advantage of fast Fourier techniques. This algorithm’s performance is similar to that of best-known algorithms for the average case, while it is especially efficient for codes with low information rate. We...

We present an average case analysis of the minimum spanning tree heuristic for the power assignment problem. The worst-case approximation ratio of this heuristic is 2. We have the following results: (a) In the one-dimensional case, with uniform [0, 1]-distributed distances, the expected approximation ratio is bounded above by 2− 2/(p+ 2), where p denotes the distance power gradient. (b) For the...

We consider robust adaptive control designs for relative degree one, minimum phase linear systems of known high frequency gain. The designs are based on the dead-zone and projection modifications, and we compare their performance w.r.t. a worst case transient cost functional with a penalty on the L∞ norm of the output, control and control derivative. We establish two qualitative results. If a b...

We consider the minimum spanning tree (MST) problem in an uncertainty model where uncertain edge weights can be explored at extra cost. The task is to find an MST by querying a minimum number of edges for their exact weight. This problem has received quite some attention from the algorithms theory community. In this paper, we conduct the first practical experiments for MST under uncertainty, th...

This paper presents some complexity results for the specific case of a VLSI friendly neural network used in classification problems. A VLSI-friendly neural network is a neural network using exclusively integer weights in a narrow interval. The results presented here give updated worst-case lower bounds for the number of weights used by the network. It is shown that the number of weights can be ...