Related papers: Range of density measures

We develop a unified approach to defining a point at infinity for an arbitrary space and formalizing convergence to this point. Central to our work is a method to quantify and classify the rates at which functions approach their limits at…

Despite the increasing visibility of fine-grained recognition in our field, "fine-grained'' has thus far lacked a precise definition. In this work, building upon clustering theory, we pursue a framework for measuring dataset granularity. We…

Density mode clustering is a nonparametric clustering method. The clusters are the basins of attraction of the modes of a density estimator. We study the risk of mode-based clustering. We show that the clustering risk over the cluster cores…

For any prime p we consider the density of elements in the multiplicative group of the finite field F_p having order, respectively index, congruent to a(mod d). We compute these densities on average, where the average is taken over all…

The cluster analysis of very large objects is an important problem, which spans several theoretical as well as applied branches of mathematics and computer science. Here we suggest a novel approach: under assumption of local convergence of…

We develop a framework to extend resource measures from one domain to a larger one. We find that all extensions of resource measures are bounded between two quantities that we call the minimal and maximal extensions. We discuss various…

Abstract upper densities are monotone and subadditive functions from the power set of positive integers into the unit real interval that generalize the upper densities used in number theory, including the upper asymptotic density, the upper…

We introduce methods to bound the mean of a discrete distribution (or finite population) based on sample data, for random variables with a known set of possible values. In particular, the methods can be applied to categorical data with…

Density-based clustering aims to find groups of similar objects (i.e., clusters) in a given dataset. Applications include, e.g., process mining and anomaly detection. It comes with two user parameters ({\epsilon}, MinPts) that determine the…

A causal set is a countably infinite poset in which every element is above finitely many others; causal sets are exactly the posets that have a linear extension with the order-type of the natural numbers -- we call such a linear extension a…

Certain countably and finitely additive measures can be associated to a given nonnegative supermartingale. Under weak assumptions on the underlying probability space, existence and (non)uniqueness results for such measures are proven.

In this paper we study some basic properties of strong A-statistical convergence and strong A-statistical Cauchyness of sequences in probabilistic metric spaces not done earlier. We also study some basic properties of strong A-statistical…

In this paper, using the concept of natural density, we have introduced the ideas of statistical and rough statistical convergence in an $S$-metric space. We have investigated some of their basic properties. We have defined statistical…

This paper defines pointwise clustering metrics, a collection of metrics for characterizing the similarity of two clusterings. These metrics have several interesting properties which make them attractive for practical applications. They can…

We prove that certain quotients of entire functions are characteristic functions. Under some conditions, the probability measure corresponding to a characteristic function of that type has a density which can be expressed as a generalized…

In this paper we suggest new effective criteria for the density property. This enables us to give a trivial proof of the original Anders\'en-Lempert result and to establish (almost free of charge) the algebraic density property for all…

This lecture notes are intended for the students taking courses in mathematical control theory. They are concerned with the attainability problem with constraints. The exposition is oriented to the linear control problems with the impulse…

This paper shows that finitely additive measures occur naturally in very general Divergence Theorems. The main results are two such theorems. The first proves the existence of pure normal measures for sets of finite perime- ter, which yield…

Finite mixture models that allow for a broad range of potentially non-elliptical cluster distributions is an emerging methodological field. Such methods allow for the shape of the clusters to match the natural heterogeneity of the data,…

Several measures of non-convexity (departures from convexity) have been introduced in the literature, both for sets and functions. Some of them are of geometric nature, while others are more of topological nature. We address the statistical…