Related papers: Directional metric regularity of multifunctions
This paper studies the problem of integrated distributed network localization and formation maneuver control. We develop an integrated relative-measurement-based scheme, which only uses relative positions, distances, bearings, angles,…
Differential logical relations are a method to measure distances between higher-order programs. They differ from standard methods based on program metrics in that differences between functional programs are themselves functions, relating…
Fractal geometry deals mainly with irregularity and captures the complexity of a structure or phenomenon. In this article, we focus on the approximation of set-valued functions using modern machinery on the subject of fractal geometry. We…
In this article, we present a new characterization of the completeness of a partial metric space--which we call \textit{orbital characterization}-- using fixed point results.
The need for appropriate ways to measure the distance or similarity between data is ubiquitous in machine learning, pattern recognition and data mining, but handcrafting such good metrics for specific problems is generally difficult. This…
It is known that families of graphs with a semialgebraic edge relation of bounded complexity satisfy much stronger regularity properties than arbitrary graphs, and that they can be decomposed into very homogeneous semialgebraic pieces up to…
Given a compact pseudo-metric space, we associate to it upper and lower dimensions, depending only on the metric. Then we construct a doubling metric for which the measure of a dillated ball is closely related to these dimensions.
For a class of integral operators with kernels metric functions on manifold we find some necessary and sufficient conditions to have finite rank. The problem we pose has a stochastic nature and boils down to the following alternative…
Recent progress concerning regularization of supersymmetric theories is reviewed. Dimensional reduction is reformulated in a mathematically consistent way, and an elegant and general method is presented that allows to study the…
We consider mappings satisfying an upper bound for the distortion of families of curves. We establish lower bounds for the distortion of distances under such mappings. As applications, we obtain theorems on the discreteness of the limit…
This paper pursues a twofold goal. First, we introduce and study in detail a new notion of variational analysis called generalized metric subregularity, which is a far-going extension of the conventional metric subregularity conditions. Our…
Geometric quantiles are popular location functionals to build rank-based statistical procedures in multivariate settings. They are obtained through the minimization of a non-smooth convex objective function. As a result, the singularity of…
Deep metrics have been shown effective as similarity measures in multi-modal image registration; however, the metrics are currently constructed from aligned image pairs in the training data. In this paper, we propose a strategy for learning…
In this paper we examine two basic topological properties of partial metric spaces, namely compactness and completeness. Our main result claims that in these spaces compactness is equivalent to sequential compactness. We also show that…
Let X be a smooth projective Berkovich space over a complete discrete valuation field K of residue characteristic zero, endowed with an ample line bundle L. We introduce a general notion of (possibly singular) semipositive (or…
The triangular ratio metric is studied in subdomains of the complex plane and Euclidean $n$-space. Various inequalities are proven for it. The main results deal with the behavior of this metric under quasiconformal maps. We also study the…
There is growing body of learning problems for which it is natural to organize the parameters into matrix, so as to appropriately regularize the parameters under some matrix norm (in order to impose some more sophisticated prior knowledge).…
Regularization is used in many different areas of optimization when solutions are sought which not only minimize a given function, but also possess a certain degree of regularity. Popular applications are image denoising, sparse regression…
In this article, we introduce a notion of relative mean metric dimension with potential for a factor map $\pi: (X,d, T)\to (Y, S)$ between two topological dynamical systems. To link it with ergodic theory, we establish four variational…
Our main aim in this paper is to introduce a general concept of multidimensional fixed point of a mapping in spaces with distance and establish various multidimensional fixed point results. This new concept simplifies the similar notion…