Related papers: Measure density for set decompositions and uniform…

We propose a fast and scalable algorithm to project a given density on a set of structured measures defined over a compact 2D domain. The measures can be discrete or supported on curves for instance. The proposed principle and algorithm are…

Shape restriction, like monotonicity or convexity, imposed on a function of interest, such as a regression or density function, allows for its estimation without smoothness assumptions. The concept of $k$-monotonicity encompasses a family…

We give a complete description of sampling and interpolation in the Bargmann-Fock space, based on a density concept of Beurling. Roughly speaking, a discrete set is a set of sampling if and only if its density in every part of the plane is…

The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus to make an approximation of a continuous…

The paper deals with measures of nonlinearity. In state estimation, they are utilized i) to select a suitable state estimation algorithm by assessing the nonlinearity of a system model, ii) to adapt the estimation algorithm structure or…

A.Olevskii and A.Ulanovskii obtained a scale of density results, which correspond to how well an exponential system approximates a uniformly minimal system over a compact set. We extend their result in several directions. First, we show…

We consider the problem of lower bounding a generalized Minkowski measure of subsets of a convex body with a log-concave probability measure, conditioned on the set size. A bound is given in terms of diameter and set size, which is sharp…

This brief paper develops a probability density that models processes for which the physical mechanism is unknown. It has desirable properties which are not realized by densities derived from Gaussian process or other classic methods. In…

We generalise results by Sacks and Tanaka concerning measure-theoretic uniformity for hyperarithmetical sets and a basis theorem for $\Pi^1_1$-sets of positive measure to computability and semicomputability relative to the Suslin…

In this paper, we present a general principle for the Lebesgue measure theory of limsup sets defined by rectangles under the hypothesis of ubiquity for rectangles.

Quantifying the population density of an urban area is a fraught issue. Measures of density are often defined differently from place to place or applied inconsistently, and arguments abound over just how much of the land surrounding a city…

We construct a density estimator in the bivariate uniform deconvolution model. For this model we derive four inversion formulas to express the bivariate density that we want to estimate in terms of the bivariate density of the observations.…

In this paper we present a geometrical framework to study the uniformity of a composite material by means of double groupoid theory. The notions of vertical and horizontal uniformity are introduced, as well as other weaker ones that allows…

A version of Connes trace formula allows to associate a measure on the essential spectrum of a Schr\"odinger operator with bounded potential. In solid state physics there is another celebrated measure associated with such operators --- the…

The notion of metric entropy dimension is introduced to measure the complexity of entropy zero dynamical systems. For measure preserving systems, we define entropy dimension via the dimension of entropy generating sequences. This…

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…

A procedure based on a Mixture Density Model for correcting experimental data for distortions due to finite resolution and limited detector acceptance is presented. Addressing the case that the solution is known to be non-negative, in the…

We study packing densities for set partitions, which is a generalization of packing words. We use results from the literature about packing densities for permutations and words to provide packing densities for set partitions. These results…

The notion of uniform equicontinuity in measure at zero for sequences of additive maps from a normed space into the space of measurable operators associated with a semifinite von Neumann algebra is discussed. It is shown that uniform…

We consider deconvolution from repeated observations with unknown error distribution. So far, this model has mostly been studied under the additional assumption that the errors are symmetric. We construct an estimator for the non-symmetric…