Related papers: Discrepancy and numerical integration on metric me…
While sensitivity analysis improves the transparency and reliability of mathematical models, its uptake by modelers is still scarce. This is partially explained by its technical requirements, which may be hard to understand and implement by…
By seeing whether a Liouville type theorem holds for positive, bounded, and/or finite energy $p$-harmonic and $p$-quasiharmonic functions, we classify proper metric spaces equipped with a locally doubling measure supporting a local…
Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…
A marked metric measure space (mmm-space) is a triple (X,r,mu), where (X,r) is a complete and separable metric space and mu is a probability measure on XxI for some Polish space I of possible marks. We study the space of all (equivalence…
The conventional definition of a topological metric over a space specifies properties that must be obeyed by any measure of "how separated" two points in that space are. Here it is shown how to extend that definition, and in particular the…
The application of machine learning to physics problems is widely found in the scientific literature. Both regression and classification problems are addressed by a large array of techniques that involve learning algorithms. Unfortunately,…
I discuss the effects of measurement error on regression and density estimation. I review the statistical methods that have been developed to correct for measurement error that are most popular in astronomical data analysis, discussing…
The distance between the true and numerical solutions in some metric is considered as the discretization error magnitude. If error magnitude ranging is known, the triangle inequality enables the estimation of the vicinity of the approximate…
The concept of angle, angle functions, and the question how to measure angles present old and well-established mathematical topics referring to Euclidean space, and there exist also various extensions to non-Euclidean spaces of different…
Finite metric spaces are the object of study in many data analysis problems. We examine the concept of weak isometry between finite metric spaces, in order to analyse properties of the spaces that are invariant under strictly increasing…
This paper addresses problems in functional metric geometry that arise in the study of data such as signals recorded on geometric domains or on the nodes of weighted networks. Datasets comprising such objects arise in many domains of…
We develop a new functional-analytic technique for investigating the degree of noncompactness of an operator defined on a quasinormed space and taking values in a Marcinkiewicz space. The main result is a general principle from which it can…
Low discrepancy point sets have been widely used as a tool to approximate continuous objects by discrete ones in numerical processes, for example in numerical integration. Following a century of research on the topic, it is still unclear…
In this paper, the Orlicz addition of measures is proposed and an interpretation of the $f$-divergence is provided based on a linear Orlicz addition of two measures. Fundamental inequalities, such as, a dual functional…
We consider finite point subsets (distributions) in compact metric spaces. In the case of general rectifiable metric spaces, non-trivial bounds for sums of distances between points of distributions and for discrepancies of distributions in…
In this paper we study Probability Measures (PM) from a functional point of view: we show that PMs can be considered as functionals (generalized functions) that belong to some functional space endowed with an inner product. This approach…
Identifying the relativistic multipole moments of a spacetime of an astrophysical object that has been constructed numerically is of major interest, both because the multipole moments are intimately related to the internal structure of the…
The main challenges of measuring precipitation are related to the spatio-temporal variability of the drop-size distribution, to the uncertainties that condition the modeling of that distribution, and to the instrumental errors present in…
We study the so-called John-Nirenberg space that is a generalization of functions of bounded mean oscillation in the setting of metric measure spaces with a doubling measure. Our main results are local and global John-Nirenberg…
Kernel embeddings of distributions and the Maximum Mean Discrepancy (MMD), the resulting distance between distributions, are useful tools for fully nonparametric two-sample testing and learning on distributions. However, it is rarely that…