Related papers: Finding Low Star Discrepancy 3D Kronecker Point Se…
Two popular and often applied methods to obtain two-dimensional point sets with the optimal order of $L_p$ discrepancy are digit scrambling and symmetrization. In this paper we combine these two techniques and symmetrize $b$-adic Hammersley…
The construction of low-discrepancy sets, used for uniform sampling and numerical integration, has recently seen great improvements based on optimization and machine learning techniques. However, these methods are computationally expensive,…
The paper addresses parametric inequality systems described by polynomial functions in finite dimensions, where state-dependent infinite parameter sets are given by finitely many polynomial inequalities and equalities. Such systems can be…
We study the smallest possible number of points in a topological space having k open sets. Equivalently, this is the smallest possible number of elements in a poset having k order ideals. Using efficient algorithms for constructing a…
Projection methods are popular algorithms for iteratively solving feasibility problems in Euclidean or even Hilbert spaces. They employ (selections of) nearest point mappings to generate sequences that are designed to approximate a point in…
In 2004 the second author of the present paper proved that a point set in $[0,1]^d$ which has star-discrepancy at most $\varepsilon$ must necessarily consist of at least $c_{abs} d \varepsilon^{-1}$ points. Equivalently, every set of $n$…
The statistical measure of spatial inhomogeneity for n points placed in chi cells each of size kxk is generalized to incorporate finite size objects like black pixels for binary patterns of size LxL. As a function of length scale k, the…
In this paper, we consider the upper bound of the probabilistic star discrepancy based on Hilbert space filling curve sampling. This problem originates from the multivariate integral approximation, but the main result removes the strict…
Two optimization algorithms are proposed for solving a stochastic programming problem for which the objective function is given in the form of the expectation of convex functions and the constraint set is defined by the intersection of…
Chv\'{a}tal and Klincsek (1980) gave an $O(n^3)$-time algorithm for the problem of finding a maximum-cardinality convex subset of an arbitrary given set $P$ of $n$ points in the plane. This paper examines a generalization of the problem,…
Discrepancy measures how uniformly distributed a point set is with respect to a given set of ranges. There are two notions of discrepancy, namely continuous discrepancy and combinatorial discrepancy. Depending on the ranges, several…
We prove upper bounds on the order of convergence of lattice based algorithms for numerical integration in function spaces of dominating mixed smoothness on the unit cube with homogeneous boundary condition. More precisely, we study…
With the high-precision data from current and upcoming experiments, it becomes increasingly important to perform consistency tests of the standard cosmological model. In this work, we focus on consistency measures between different data…
Astronomers generally assume planet-forming disks are aligned with the rotation of their host star. However, recent observations have shown evidence of warping in protoplanetary disks. One can measure the statistical alignment between the…
We discuss the problem of defining an estimate for the error in quasi-Monte Carlo integration. The key issue is the definition of an ensemble of quasi-random point sets that, on the one hand, includes a sufficiency of equivalent point sets,…
Point matching refers to the process of finding spatial transformation and correspondences between two sets of points. In this paper, we focus on the case that there is only partial overlap between two point sets. Following the approach of…
Distributionally balanced sampling designs are low-discrepancy probability designs obtained by minimizing the expected discrepancy between the auxiliary-variable distribution of a random sample and the target population distribution.…
The {\em bottleneck distance} is a natural measure of the distance between two finite point sets of equal cardinality, defined as the minimum over all bijections between the point sets of the maximum distance between any pair of points put…
The major uncertainties in studies of the multi-scale structure of the Universe arise not from observational errors but from the variety of legitimate definitions and detection methods for individual structures. To facilitate the study of…
It is well known that the two-dimensional Hammersley point set consisting of $N=2^n$ elements (also known as Roth net) does not have optimal order of $L_p$-discrepancy for $p \in (1,\infty)$ in the sense of the lower bounds according to…