Related papers: On a Subset Metric
This is an exposition of the theory of differentiable structures on metric measures spaces, in the sense of Cheeger and Keith.
In this paper, we give error bounds for the distance distribution of Reed-Muller codes, extending prior work on the distance distribution of Reed-Solomon codes. This is equivalent to the problem of counting multivariate polynomials over a…
We introduce the concept of quotient-convergence for sequences of submodular set functions, providing, among others, a new framework for the study of convergence of matroids through their rank functions. Extending the limit theory of…
Distances are pervasive in machine learning. They serve as similarity measures, loss functions, and learning targets; it is said that a good distance measure solves a task. When defining distances, the triangle inequality has proven to be a…
The main purpose of this paper is to study complex valued metric-like spaces as an extension of metric-like spaces, complex valued partial metric spaces, partial metric spaces, complex valued metric spaces and metric spaces. In this…
We establish a structure theorem for minimizing sequences for the isoperimetric problem on noncompact $\mathsf{RCD}(K,N)$ spaces $(X,\mathsf{d},\mathcal{H}^N)$. Under the sole (necessary) assumption that the measure of unit balls is…
The objective of this manuscript is to introduce and develop the concept of a generalized $\theta$-parametric metric space-a novel extension that enriches the modern metric fixed point theory. We study of its fundamental properties,…
In this paper, we give an interesting extension of the partial S-metric space which was introduced [4] to the M_s-metric space. Also, we prove the existence and uniqueness of a fixed point for a self mapping on an Ms-metric space under…
Measuring inter-dataset similarity is an important task in machine learning and data mining with various use cases and applications. Existing methods for measuring inter-dataset similarity are computationally expensive, limited, or…
We analyze uncertainty relations on finite dimensional Hilbert spaces expressed in terms of classical fidelity, which are stronger then metric uncertainty relations introduced by Fawzi, Hayden and Sen. We establish validity of fidelity…
We consider a new family of codes, termed asymmetric Lee distance codes, that arise in the design and implementation of DNA-based storage systems and systems with parallel string transmission protocols. The codewords are defined over a…
A generalization of the Lebesgue number lemma is obtained. It is proved that, if each countably infinite locally finite open cover of a chainable metric space $X$ has a Lebesgue number, then $X$ is totally bounded. A property of metric…
This paper introduces the notion of multiset codes as relevant to the problem of reliable information transmission over permutation channels. The motivation for studying permutation channels comes from the effect of out of order delivery of…
In topological data science, categories with a flow have become ubiquitous, including as special cases examples like persistence modules and sheaves. With the flow comes an interleaving distance, which has proven useful for applications. We…
The concepts of spread and spread dimension of a metric space were introduced by Willerton in the context of quantifying biodiversity of ecosystems. In previous work, we developed the theoretical basis for applications of spread dimension…
We establish a sharp estimate for a minimal number of binary digits (bits) needed to represent all bounded total generalized variation functions taking values in a general totally bounded metric space $(E,\rho)$ up to an accuracy of…
A time series is a sequence of data items; typical examples are videos, stock ticker data, or streams of temperature measurements. Quite some research has been devoted to comparing and indexing simple time series, i.e., time series where…
Let $(X_1,d_1),\dots, (X_N,d_N)$ be metric spaces, where $d_i: X_i \times X_i \rightarrow [0,1]$ is a distance function for $i=1,\dots,N$. Let $\mathcal{X}$ denote the set theoretic product $X_1\times \cdots \times X_N$. Let $\mathcal{G} =…
The concept of cone metric spaces with $w-$distance was introduced by H. Lakzian and F. Arabyani [16] in $2009.$ In $2020,$ Branga and Olaru [4] put forth the idea of cone metric spaces over topological module. In this paper, we compose…
The metric dimension of a graph is the size of the smallest set of vertices whose distances distinguish all pairs of vertices in the graph. We show that this graph invariant may be calculated by an algorithm whose running time is linear in…