Related papers: Rough statistical convergence of sequences in a pa…
In this article pattern statistics of typical cubical cut and project sets are studied. We give estimates for the rate of convergence of appearances of patches to their asymptotic frequencies. We also give bounds for repetitivity and…
Convergence of the solutions of nonhomogeneous linear singularly perturbed systems to that of the corresponding reduced singular system on the half-line [0, $\infty $) is considered. To include the situation on a neighborhood of initial…
Coresets have emerged as a powerful tool to summarize data by selecting a small subset of the original observations while retaining most of its information. This approach has led to significant computational speedups but the performance of…
The Random Sequential Adsorption (RSA) problem holds crucial theoretical and practical significance, serving as a pivotal framework for understanding and optimizing particle packing in various scientific and technological applications. Here…
This article studies the weak convergence and associated Central Limit Theorem for blurring and nonblurring processes. Then, they are applied to the estimation of location parameter. Simulation studies show that the location estimation…
A new type of sectional curvature is introduced. The notion is purely algebraic and can be located in linear algebra as well as in differential geometry.
In this paper, we establish an almost sure central limit theorem for a general random sequence under a strong approximation condition. Additionally, we derive the law of the iterated logarithm for the center of mass corresponding to a…
Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the…
Given $n$ independent random marked $d$-vectors $X_i$ with a common density, define the measure $\nu_n = \sum_i \xi_i $, where $\xi_i$ is a measure (not necessarily a point measure) determined by the (suitably rescaled) set of points near…
This paper introduces a new clustering technique, called {\em dimensional clustering}, which clusters each data point by its latent {\em pointwise dimension}, which is a measure of the dimensionality of the data set local to that point.…
Optimization problems, generalized equations, and the multitude of other variational problems invariably lead to the analysis of sets and set-valued mappings as well as their approximations. We review the central concept of set-convergence…
In this paper we introduce a notion of tightness for a family of nonlinear expectations and show that the tightness can be applied to obtain weak compactness in a framework of nonlinear expectation space. This criterion is very useful for…
Many concrete problems are formulated in terms of a finite set of points in $R^n$ which, via the ambient Euclidean metric, becomes a finite metric space. To obtain information from such a space, it is often useful to associate a graph to…
This article provides an overview on the statistical modeling of complex data as increasingly encountered in modern data analysis. It is argued that such data can often be described as elements of a metric space that satisfies certain…
In this paper we study the coarse Ricci curvature on the space of probability measures on a metric space. The infimum of the $p$-coarse Ricci curvature on the $L^p$-Wasserstein space coincides with that with respect to the original random…
The problem of comparing concepts of dependence in general rough sets with those in probability theory had been initiated by the present author in some of her recent papers. This problem relates to the identification of the limitations of…
This paper proposes a new distance metric between clusterings that incorporates information about the spatial distribution of points and clusters. Our approach builds on the idea of a Hilbert space-based representation of clusters as a…
The mean shift algorithm is a non-parametric and iterative technique that has been used for finding modes of an estimated probability density function. It has been successfully employed in many applications in specific areas of machine…
In the paper we apply some of the results from the theory of ball spaces in the semimetric spaces. This allowed us to obtain some fixed point theorems which we believe to be unknown to this day. We also show the limitations of the ball…
A number of generalizations of stochastic and information-theoretic randomness are known in the literature. However, they are not compatible with handling meaning in vague and dynamic contexts of rough reasoning (and therefore explainable…