相关论文: Equipartitions of a Mass in Boxes
In this note we show that the volume of axis-parallel boxes in $\mathbb{R}^d$ which do not intersect an admissible lattice $\mathbb{L}\subset\mathbb{R}^d$ is uniformly bounded. In particular, this implies that the dispersion of the dilated…
This paper consists of two (still only vaguely) related parts: in the first, we briefly review work done in the past three years on the ``planar equivalence" between a class of non-supersymmetric theories (including limiting cases of QCD)…
Let $n$ be the order of a (quaternary) Hadamard matrix. It is shown that the existence of a projective plane of order $n$ is equivalent to the existence of a balancedly multi-splittable (quaternary) Hadamard matrix of order $n^2$.
We present an optimal mass transport framework on the space of Gaussian mixture models, which are widely used in statistical inference. Our method leads to a natural way to compare, interpolate and average Gaussian mixture models.…
Keller packings and tilings of boxes are investigated. Certain general inequality measuring a complexity of such systems is proved. A straightforward application to the unit cube tilings is given.
The aim of this paper is to prove an improved version of the bounded differences inequality for matrix valued functions, by developing the methods of Mackey et al.: "Matrix Concentration Inequalities via the Method of Exchangeable Pairs".…
We discuss combinatorial conditions for the existence of various types of reductions between equivalence relations, and in particular identify necessary and sufficient conditions for the existence of injective reductions.
Based on the ranks of reduced density matrices, we derive necessary conditions for the separability of multiparticle arbitrary-dimensional mixed states, which are equivalent to sufficient conditions for entanglement. In a similar way we…
While effective concentration inequalities for suprema of empirical processes exist under boundedness or strict tail assumptions, no comparable results have been available under considerably weaker assumptions. In this paper, we derive…
In the paper the main attention is paid to conditions on algebras from a given variety which provide coincidence of their algebraic geometries. The main part here play the notions mentioned in the title of the paper.
In this era of large-scale data, distributed systems built on top of clusters of commodity hardware provide cheap and reliable storage and scalable processing of massive data. Here, we review recent work on developing and implementing…
The Ham-Sandwich theorem is a well-known result in geometry. It states that any $d$ mass distributions in $\mathbb{R}^d$ can be simultaneously bisected by a hyperplane. The result is tight, that is, there are examples of $d+1$ mass…
In the standard ball-in-bins experiment, a well-known scheme is to sample $d$ bins independently and uniformly at random and put the ball into the least loaded bin. It can be shown that this scheme yields a maximum load of $\log\log n/\log…
Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…
We study parallelisms on Veronese spaces associated with affine spaces, determine hyperplanes in Veronese spaces associated with projective spaces, and analyse the geometry of parallelisms determined by these hyperplanes.
Let X(t) be a Gaussian random field R d $\rightarrow$ R. Using the notion of (d -- 1)-integral geometric measures, we establish a relation between (a) the volume of the level set (b) the number of crossings of the restriction of the random…
Motivated by the study of the propagation of convexity by semi-groups of stochastic differential equations and convex comparison between the distributions of solutions of two such equations, we study the comparison for the convex order…
I review our current knowledge of the mass distribution in clusters, as obtained from the analysis of the projected phase-space distribution of cluster galaxies. I discuss the methods of analysis, their relative advantages and…
The task of mixture proportion estimation (MPE) is to estimate the weight of a component distribution in a mixture, given observations from both the component and mixture. Previous work on MPE adopts the irreducibility assumption, which…
Sphere packings are essential to the development of physical models for powders, composite materials, and the atomic structure of the liquid state. There is a strong scientific need to be able to assess the fit of packing models to data,…