A common measure for the uniformity of point distributions is the star discrepancy. Let λ s denote the s-dimensional Lebesgue measure. Then the star discrepancy of a mul-tiset P = {p 1 ,. .. , p N } ⊂ [0, 1] s is given by D * N (P) := sup α∈[0,1] s λ s ([0, α)) − 1 N N k=1 1 [0,α) (p k) ; here [0, α) denotes the s-dimensional axis-parallel box [0, α 1) × · · · × [0, α s) and 1 [0,α) its charact...

BACKGROUND Beckwith-Wiedemann syndrome (BWS) is a congenital disorder that involves a somatic overgrowth during the patient's first years of life. Exomphalos, macroglossia and gigantism are the main clinical symptoms. CASE DESCRIPTION The authors describe a 15-year follow-up in a patient with BWS. They focus on a multidisciplinary approach to treating the patient's oral manifestations from ag...

We introduce a new construction method for digital nets which yield point sets in the s-dimensional unit cube with small star discrepancy. The digital nets are constructed using polynomials over finite fields. It has long been known that there exist polynomials which yield point sets with small (unweighted) star discrepancy. This result was obtained by Niederreiter by the means of averaging ove...

Polynomial lattice point sets (PLPSs) (of rank 1) are special constructions of finite point sets which may have outstanding equidistribution properties. Such point sets are usually required as nodes in quasi-Monte Carlo rules. Any PLPS is a special instance of a (t,m, s)-net in base b as introduced by Niederreiter. In this paper we generalize PLPSs of rank 1 to what we call then PLPSs of rank r...

It is known that there is a constant c > 0 such that for every sequence x1, x2, . . . in [0, 1) we have for the star discrepancy D ∗ N of the first N elements of the sequence that ND∗ N ≥ c · logN holds for infinitely many N . Let c∗ be the supremum of all such c with this property. We show c∗ > 0.065664679 . . ., thereby slightly improving the estimates known until now.

We study (0, 1)-sequences in arbitrary base b and derive a new upper bound on the star discrepancy of these. Moreover, we show that the van der Corput sequence is the sequence with the highest star discrepancy among all (0, 1)-sequences. The key property of the van der Corput sequence leading to this result is that its points are in a certain sense as close to the origin as possible. The main t...

The pairwise comparisonsmethod is a convenient tool used when the relative order among different concepts (alternatives) needs to be determined. There are several popular implementations of this method, including the Eigenvector Method, the Least Squares Method, the Chi Squares Method and others. Each of the above methods comes with one or more inconsistency indices that help to decide whether ...