Related papers: On I-statistical cluster point of double sequences

We explore some convergence notions for set-convergence coming from modern summability methods. Specifically we will see the connections between Wijsman $f$-statistical convergence and Wijsman $f$-strong Ces\`aro convergence, when $f$ is a…

In this article, after recalling and discussing the conventional extremality, local extremality, stationarity and approximate stationarity properties of collections of sets and the corresponding (extended) extremal principle, we focus on…

Sum-of-norms clustering is a method for assigning $n$ points in $\mathbb{R}^d$ to $K$ clusters, $1\le K\le n$, using convex optimization. Recently, Panahi et al.\ proved that sum-of-norms clustering is guaranteed to recover a mixture of…

There are many physically interesting superconformal gauge theories in four dimensions. In this talk I discuss a common phenomenon in these theories: the existence of continuous families of infrared fixed points. Well-known examples include…

Let $X,X_1,X_2,\ldots$ be i.i.d. mean zero random vectors with values in a separable Banach space $B$, $S_n=X_1+\cdots+X_n$ for $n\ge1$, and assume $\{c_n:n\ge1\}$ is a suitably regular sequence of constants. Furthermore, let…

This Meeting featured the recent advancements in our understanding of galaxy clusters and the distant Universe, achieved by the past and new generation of X-ray satellites. I summarize here the main themes that have been discussed: (a)…

In this paper, we generalized the Wijsman statistical convergence of closed sets in metric space by introducing the $f$-Wijsman statistical convergence these of sets, where $f$ is an unbounded modulus. It is shown that the Wijsman…

We prove a collection of asymptotic density results for several interesting classes of the $I$-graphs. Specifically, we quantify precisely the proportion of $I$-graphs that are generalised Petersen graphs as well as those that are…

Organising the relevant literature and by letting statistical convergence play the main role in the theory of compactness, a variant of compactness called statistical compactness has been achieved. As in case of sequential compactness, one…

The Cauchy-Schwarz (CS) divergence was developed by Pr\'{i}ncipe et al. in 2000. In this paper, we extend the classic CS divergence to quantify the closeness between two conditional distributions and show that the developed conditional CS…

Clusters of galaxies are important targets in observationally cosmology, as they can be used both to study the evolution of the galaxies themselves and to constrain cosmological parameters. Here we report on the first results of a major…

In the context of count-in-cells statistics, the joint probability distribution of the density in two concentric spherical shells is predicted from first first principle for sigmas of the order of one. The agreement with simulation is found…

This is an expanded version of the notes for the two lectures at the 2004 International Mathematics Conference (Chonbuk National University, August 4-6, 2004). The first lecture discusses the origins of cluster algebras, with the focus on…

Here we have studied the notion of rough $I$-convergence as an extension of the idea of rough convergence in a cone metric space using ideals. We have further introduced the notion of rough $I^*$-convergence of sequences in a cone metric…

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 develop a simple and unified approach to investigate several aspects of the cluster statistics of random expansive (multi-)sets. In particular, we determine the limiting distribution of the size of the smallest and largest clusters, we…

We propose a simple and efficient clustering method for high-dimensional data with a large number of clusters. Our algorithm achieves high-performance by evaluating distances of datapoints with a subset of the cluster centres. Our…

This Living Review updates a previous version which its itself an update of a review article. Numerical exploration of the properties of singularities could, in principle, yield detailed understanding of their nature in physically realistic…

Every set $A$ of positive integers with upper Banach density 1 contains an infinite sequence of pairwise disjoint subsets $(B_i)_{i=1}^{\infty}$ such that $B_i$ has upper Banach density 1 for all $i \in \mathbf{N}$ and $\sum_{i\in I} B_i…

Clusters of galaxies are studied from a theoretical point of view, comparing with observational results whenever possible. The problem is approached both analytically as well as by means of high-resoultion numerical simulations. The dark…