In this paper various measures for the uniformity of distribution of a point set in the unit cube are studied. We show how the diaphony and spectral test based on Walsh functions appear naturally as the worst-case error of integration in certain Hilbert spaces which are based on Walsh functions. Furthermore, it has been shown that this worst-case error equals to the root mean square discrepancy...

We consider the problem of minimizing the makespan when scheduling tasks on two uniform parallel machines, where one machine is q times as efficient on each task as is the other. We compute the maximum relative error of the LPT (largest processing time first) heuristic as an explicit function of q. In the special case that the two machines are identical (q = 1), our problem and heuristic reduce...

We derive new margin-based inequalities for the probability of error of classifiers. The main feature of these bounds is that they can be calculated using the training data and therefore may be effectively used for model selection purposes. In particular, the bounds involve empirical complexities measured on the training data (such as the empirical fatshattering dimension) as opposed to their w...

Despite all of the publicity surrounding the Pentium bug of 1994, the mathematical details of the bug are poorly understood. We discuss these details and supply a new proof of the Coe–Tang result that the at-risk divisors have six consecutive ones in positions 5 through 10. Also, we prove that the worst-case absolute error for arguments in [1, 2) is on the order of 1e–5.

We study the quantum summation (QS) algorithm of Brassard, Høyer, Mosca and Tapp, see [1], which approximates the arithmetic mean of a Boolean function defined on N elements. We present sharp error bounds of the QS algorithm in the worst-average setting with the average performance measured in the Lq norm, q ∈ [1,∞]. We prove that the QS algorithm with M quantum queries, M < N , has the worst-a...

We consider the problem of recovering a symmetric, positive semidefinite (SPSD) matrix from a subset of its entries, possibly corrupted by noise. In contrast to previous matrix recovery work, we drop the assumption of a random sampling of entries in favor of a deterministic sampling of principal submatrices of the matrix. We develop a set of sufficient conditions for the recovery of a SPSD matr...

Abstract. Cyclic nets are a special case of digital nets and were recently introduced by Niederreiter. Here we present a construction algorithm for such nets, where we use the root mean square worst-case error of a randomly digitally shifted point set in a weighted Sobolev space as a selection criterion. This yields a feasible construction algorithm since for a cyclic net with qm points (with f...

Algebraic space–time coding allows for reliable data exchange across fading multiple-input multiple-output channels. A powerful technique for decoding space–time codes is Maximum-Likelihood (ML) decoding, but well-performing and widely-used codes such as the Golden code often suffer from high ML-decoding complexity. In this article, a recursive algorithm for decoding general algebraic space–tim...

The power of an accurate model for describing a physical process or designing a physical system is beyond doubt. The currently used reliability model for physically unclonable functions (PUFs) assumes an equally likely error for every evaluation of every PUF response bit. This limits an accurate description since experiments show that certain responses are more error-prone than others, but this...

In this paper we introduce a new class of search problem which we calìalternating search'. Two searchers starting at given points in diierent search regions, who can move alternately with speed one, or (as a limiting case) simultaneously with combined speed one, seek to nd (reach) an object in least expected time. The hidden object is stationary and its location is given by a known distribution...