Related papers: Bowen's equations for upper metric mean dimension …
We endeavour to estimate numerous multi-dimensional means of various probability distributions on a common space based on independent samples. Our approach involves forming estimators through convex combinations of empirical means derived…
Metric embedding has become a common technique in the design of algorithms. Its applicability is often dependent on how high the embedding's distortion is. For example, embedding finite metric space into trees may require linear distortion…
A new intrinsic metric called $t$-metric is introduced. Several sharp inequalities between this metric and the most common hyperbolic type metrics are proven for various domains $G\subsetneq\mathbb{R}^n$. The behaviour of the new metric is…
We investigate in this work some situations where it is possible to estimate or determine the upper and the lower $q$-generalized fractal dimensions $D^{\pm}_{\mu}(q)$, $q\in\mathbb{R}$, of invariant measures associated with continuous…
A theory of measurement uncertainty is presented, which, since it is based exclusively on the Bayesian approach and on the subjective concept of conditional probability, is applicable in the most general cases. The recent International…
Wu and Verd\'u developed a theory of almost lossless analog compression, where one imposes various regularity conditions on the compressor and the decompressor with the input signal being modelled by a (typically infinite-entropy)…
This paper investigates the relationship between quantization of measures and metric mean dimension of topological dynamical systems. We introduce the concept of mean quantization dimension for invariant probability measures and establish a…
In this paper, we introduce the mean $\Psi$-intermediate dimension which has a value between the mean Hausdorff dimension and the metric mean dimension, and prove the equivalent definition of the mean Hausdorff dimension and the metric mean…
A generic massive Thirring Model in three space-time dimensions exhibits a correspondence with a topologically massive bosonized gauge action associated to a self-duality constraint, and we write down a general expression for this…
{Researchers recently introduced interpolative metric spaces and established fixed-point theorems in this setting. We demonstrate that these metrics are a special case of b-metrics. On the other hand, suprametrics and b-suprametrics have…
The aim of the paper is twofold. Firstly, by using the constant rank level set theorem from differential geometry, we establish sharp upper bounds for the dimensions of the solution sets of polynomial variational inequalities under mild…
In Generalised Bayesian Inference (GBI), the learning rate and hyperparameters of the loss must be estimated. These inference-hyperparameters can't be estimated jointly with the other parameters, from the data, by giving them a prior.…
This article is an introductory work to a larger research project devoted to pure, applied and philosophical aspects of dimension theory. It concerns a novel approach toward an alternate dimension theory foundation: the point-dimension…
In this paper we shall consider some famous means such as arithmetic, harmonic, geometric, root square mean, etc. Considering the difference of these means, we can establish. some inequalities among them. Interestingly, the difference of…
The main purpose of this survey is to gather results on the boundedness of the Bergman projection. First, we shall go over some equivalent norms on weighted Bergman spaces $A^p_\omega$ which are useful in the study of this question. In…
Pointwise tangential dimensions are introduced for metric spaces. Under regularity conditions, the upper, resp. lower, tangential dimensions of X at x can be defined as the supremum, resp. infimum, of box dimensions of the tangent sets, a…
The goal of this paper is to define and investigate those topological pressures, which is an extension of topological entropy presented by Feng and Huang [13], of continuous transformations. This study reveals the similarity between many…
Bayesian statistics is based on the subjective definition of probability as {\it ``degree of belief''} and on Bayes' theorem, the basic tool for assigning probabilities to hypotheses combining {\it a priori} judgements and experimental…
Well-established methods for the solution of stochastic partial differential equations (SPDEs) typically struggle in problems with high-dimensional inputs/outputs. Such difficulties are only amplified in large-scale applications where even…
We formulate a general statement of the problem of defining invariant measures with certain properties and suggest an ergodic method of perturbations for describing such measures.