In this article, we give the sharp bounds of probabilistic Kolmogorov N,δ-widths and linear multivariate Sobolev space W2A with common smoothness on a Sq norm equipped Gaussian measure μ, where A⊂Rd is finite set. And obtain average width from results widths. These develop theory approximation functions play important roles in research related algorithms for spaces.

In this paper we lay the semantic basis for a quantitative security analysis of probabilistic systems by introducing notions of approximate confinement based on various process equivalences. We re-cast the operational semantics classically expressed via probabilistic transition systems (PTS) in terms of linear operators and we present a technique for defining approximate semantics as probabilis...

Quantitative researchers need a probabilistic sample to generalise their findings, but research constraints often compel them use non-probabilistic samples. The of non-probability sampling methods in quantitative studies has therefore become norm. Interestingly, even published top-quality journals compromise best practices that the samples requires. Based on thorough review relevant studies, we...

Sparse coding algorithms are about finding a linear basis in which signals can be represented by a small number of active (non-zero) coefficients. Such coding has many applications in science and engineering and is believed to play an important role in neural information processing. However, due to the computational complexity of the task, only approximate solutions provide the required efficie...

In this letter, we analyze a two-stage cluster-then-l(1)-optimization approach for sparse representation of a data matrix, which is also a promising approach for blind source separation (BSS) in which fewer sensors than sources are present. First, sparse representation (factorization) of a data matrix is discussed. For a given overcomplete basis matrix, the corresponding sparse solution (coeffi...

The Kolmogorov and total variation distance between the laws of random variables have upper bounds represented by L1-norm densities when densities. In this paper, we derive an bound, in terms such as distance, for several probabilistic distances (e.g., Wasserstein Forter–Mourier etc.) F G case where a variable follows invariant measure that admits density differentiable G, sense Malliavin calcu...

The idea of probabilistic metric space was introduced by Menger and he showed that probabilistic metric spaces are generalizations of metric spaces. Thus, in this paper, we prove some of the important features and theorems and conclusions that are found in metric spaces. At the beginning of this paper, the distance distribution functions are proposed. These functions are essential in defining p...

In this contribution, we first introduce the concept of metrical T-norm-based similarity measure for hesitant fuzzy sets (HFSs) {by using the concept of T-norm-based distance measure}. Then,the relationship of the proposed {metrical T-norm-based} similarity {measures} with the {other kind of information measure, called the metrical T-norm-based} entropy measure {is} discussed. The main feature ...