Related papers: Equipartitions of a Mass in Boxes
Rooted, weighted continuum random trees are used to describe limits of sequences of random discrete trees. Formally, they are random quadruples $(\mathcal{T},d,r,p)$, where $(\mathcal{T},d)$ is a tree-like metric space, $r\in\mathcal{T}$ is…
The paper deals with a generalisation of uniform distribution. The analogues of Weyl's criterion are derived.
In the mixture models problem it is assumed that there are $K$ distributions $\theta_{1},\ldots,\theta_{K}$ and one gets to observe a sample from a mixture of these distributions with unknown coefficients. The goal is to associate instances…
We prove a Harnack inequality for the solutions of a difference equation with non-elliptic balanced i.i.d. coefficients. Along the way we prove a (weak) quantitative homogenisation result, which we believe is of some interest too.
Let $H$ be an arbitrary family of hyper-planes in $d$-dimensions. We show that the point-location problem for $H$ can be solved by a linear decision tree that only uses a special type of queries called \emph{generalized comparison queries}.…
In this study, the orthogonalization process for different inner products is applied to pairwise comparisons. Properties of consistent approximations of a given inconsistent pairwise comparisons matrix are examined. A method of a derivation…
The goal of this paper is to establish certain inequalities between the numbers of convex polytopes in the d-dimensional space "containing" and "avoiding" zero provided that their vertex sets are subsets of a given finite set of points in…
In this paper, we prove new upper bounds for sums of reciprocals of fractional parts over general aligned boxes, thus extending a previous result of the author concerning bounds for sums of reciprocals over symmetric boxes. These new upper…
The aim of this note is a combinatorial description of a category of $D$-modules over an affine space, smooth along the stratification defined by an arrangement of hyperplanes. These $D$-modules are assumed to satisfy certain non-resonance…
An ordered $r$-matching is an $r$-uniform hypergraph matching equipped with an ordering on its vertices. These objects can be viewed as natural generalisations of $r$-dimensional orders. The theory of ordered 2-matchings is well-developed…
N-body simulations of major spiral-spiral mergers with different mass ratios q <= 4:1 are presented. All mergers lead to spheroidal stellar systems with de Vaucouleurs-like surface density profiles, resembling elliptical galaxies. The…
This paper introduces constrained mixtures for continuous distributions, characterized by a mixture of distributions where each distribution has a shape similar to the base distribution and disjoint domains. This new concept is used to…
The interaction between a large number of laser filaments brought together using weak external focusing leads to the emergence of few filamentary structures reminiscent of standard filaments, but carrying a higher intensity. The resulting…
We give a sufficient condition in order that $n$ closed connected subsets in the $n$-dimensional real projective space admit a common multitangent hyperplane.
We discuss a sufficient condition for a space to be filled with an arbitrary finite number of self-similar spaces using a topological concept.
We study edge-isoperimetric inequalities in chamber graphs of affine hyperplane arrangements. Our approach is topological: to a set of chambers we associate its thickening in Euclidean space and estimate its edge boundary through the…
We consider coherent sublinear expectations on a measurable space, without assuming the existence of a dominating probability measure. By considering a decomposition of the space in terms of the supports of the measures representing our…
Let $R$ be a finite ring and $r \in R$. The aim of this paper is to study the probability that the commutator of a randomly chosen pair of elements of $R$ equals $r$.
We introduce a new class of balanced allocation processes which are primarily characterized by ``filling'' underloaded bins. A prototypical example is the Packing process: At each round we only take one bin sample, if the load is below the…
We establish necessary and sufficient conditions for consistency of estimators of mixing distribution in linear latent structure analysis.