An infinite countable Steiner triple system is called universal if any countable Steiner triple system can be embedded into it. The main result of this paper is the proof of non-existence of a universal Steiner triple system. The fact is proven by constructing a family S of size 2 of infinite countable Steiner triple systems so that no finite Steiner triple system can be embedded into any of th...

The degree of correlation between variables is used in many data analysis applications as a key measure of interdependence. The most common techniques for exploratory analysis of pairwise correlation in multivariate datasets, like scatterplot matrices and clustered heatmaps, however, do not scale well to large datasets, either computationally or visually. We present a new visualization that is ...

It is shown that for a set S of n pairwise disjoint axis-parallel line segments in the plane there is a simple alternating path of length Ω( √ n). This bound is best possible in the worst case. In the special case that the n pairwise disjoint axis-parallel line segments are protruded (that is, if the intersection point of the lines through every two nonparallel segments is not visible from both...

A bstract On-shell methods are particularly suited for exploring the scattering of electrically and magnetically charged objects, which there is no local Lorentz invariant Lagrangian description. In this paper we show how to construct a Lorentz-invariant S -matrix particles, without ever having refer Dirac string. key ingredient revision our fundamental understanding multi-particle representati...

Let X1 X2 be a sequence of pairwise negatively dependent random variables with distributions F1 F2 on − , and let S n be the maximum of its first n partial sums S1 Sn. This article studies the asymptotic tail probabilities of Sn and S n . Under suitable regularity conditions on the distributions F1 Fn, we prove that both P Sn > x and P S n > x are asymptotic to ∑n i=1 1− Fi x as x → , indicatin...

We systematically study pairwise counter-monotonicity, an extremal notion of negative dependence. A stochastic representation and invariance property are established for this dependence structure. show that counter-monotonicity implies association, it is equivalent to joint mix if both possible the same marginal distributions. find intimate connection between risk sharing problems quantile agen...