Related papers: Enclosing Depth and other Depth Measures
We solve the truncated K-moment problem when $K\subseteq R^n$ is the closure of a, not necessarily bounded, open set (which includes the important cases $K=R^n$ and $K=R^n_+$). That is, we completely characterize the interior of the convex…
We construct with full rigorous mathematical proof a family of approximate solutions to the Cauchy problem for the standard system of two fluid flows with energy equations and we pass to the limit by weak compactness to obtain Radon…
We compute the Stanley depth for a particular, but important case, of the quotient of complete intersection monomial ideals. Also, in the general case, we give sharp bounds for the Stanley depth of a quotient of complete intersection…
We propose a unified scaling theory of entanglement entropy in the confinements of finite bond dimensions, dynamics and system sizes. Within the theory, the finite-entanglement scaling introduced recently is generalized to the dynamics…
We show that in many parametrized families of self-similar measures, their projections, and their convolutions, the set of parameters for which the measure fails to be absolutely continuous is very small - of co-dimension at least one in…
Intrinsic volumes of convex sets are natural geometric quantities that also play important roles in applications, such as linear inverse problems with convex constraints, and constrained statistical inference. It is a well-known fact that,…
Consider a measurable space with an atomless finite vector measure. This measure defines a mapping of the $\sigma$-field into an Euclidean space. According to the Lyapunov convexity theorem, the range of this mapping is a convex compactum.…
The long-standing topological Tverberg conjecture claimed, for any continuous map from the boundary of an $N(q,d):=(q-1)(d+1)$-simplex to $d$-dimensional Euclidian space, the existence of $q$ pairwise disjoint subfaces whose images have…
We study the Hausdorff dimension of self-similar sets and measures on the line. We show that if the dimension is smaller than the minimum of 1 and the similarity dimension, then at small scales there are super-exponentially close cylinders.…
We show that Stanley's Conjecture holds for square free monomial ideals in five variables, that is the Stanley depth of a square free monomial ideal in five variables is greater or equal with its depth.
We introduce a new information-theoretic formulation of quantum measurement uncertainty relations, based on the notion of relative entropy between measurement probabilities. In the case of a finite-dimensional system and for any approximate…
The Assouad and quasi-Assouad dimensions of a metric space provide information about the extreme local geometric nature of the set. The Assouad dimension of a set has a measure theoretic analogue, which is also known as the upper regularity…
Current methods for depth map prediction from monocular images tend to predict smooth, poorly localized contours for the occlusion boundaries in the input image. This is unfortunate as occlusion boundaries are important cues to recognize…
We introduce new families of quandles that serve as invariants for classifying closed orientable surfaces. These families generalize the classical Dehn quandle and are defined, respectively, on isotopy classes of unoriented closed curves…
We establish numerical lower bounds for the monochromatic connectivity measure in two dimensions introduced by Sarnak and Wigman. This measure dictates among the nodal domains of a random plane wave what proportion have any given number of…
Relative entropy is a powerful measure of the dissimilarity between two statistical field theories in the continuum. In this work, we study the relative entropy between Gaussian scalar field theories in a finite volume with different masses…
The Collatz Conjecture's connection to dynamical systems opens it to a variety of techniques aimed at recurrence and density results. First, we turn to density results and strengthen the result of Terras through finding a strict rate of…
For infinite measure-theoretic entropy systems, we introduce the notion of measure-theoretic metric mean dimension of invariant measures for different types of measure-theoretic $\epsilon$-entropies, and show that measure-theoretic metric…
An universal approximation technique for analysis of different characteristics of states of composite infinite-dimensional quantum systems is proposed and used to prove general results concerning the properties of correlation and…
A brief overview of dimensional reductions for diffeomorphism invariant theories is given. The distinction between the physical idea of compactification and the mathematical problem of a consistent truncation is discussed, and the typical…