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Complexity of pattern classes and Lipschitz property

, 2004
Rademacher and Gaussian complexities are successfully used in learning theory for measuring the capacity of the class of functions to be learned. One of the most important properties for these complexities is their Lipschitz property: a composition of a ...
J. Shawe-Taylor, M. Ledoux, N. Cristianini, P.L. Bartlett   +3 more
core   +3 more sources

Efficient learning of ground and thermal states within phases of matter [PDF]

Nature Communications
We consider two related tasks: (a) estimating a parameterisation of a given Gibbs state and expectation values of Lipschitz observables on this state; (b) learning the expectation values of local observables within a thermal or quantum phase of matter ...
Cambyse Rouzé, Daniel Stilck França, Emilio Onorati, James D. Watson   +3 more
doaj   +2 more sources

Further results on strictly Lipschitz summing operators

Moroccan Journal of Pure and Applied Analysis, 2022
The aim of this paper is to give some new characterizations of strictly Lipschitz p-summing operators. These operators have been introduced in order to improve the Lipschitz p-summing operators.
Belaala Maatougui, Saadi Khalil
doaj   +1 more source

Representation of Lipschitz Maps and Metric Coordinate Systems

Mathematics, 2022
Here, we prove some general results that allow us to ensure that specific representations (as well as extensions) of certain Lipschitz operators exist, provided we have some additional information about the underlying space, in the context of what we ...
Roger Arnau, Jose M. Calabuig, Enrique A. Sánchez Pérez   +2 more
doaj   +1 more source

Laguerre-Bessel Transform and Generalized Lipschitz Classes

Tatra Mountains Mathematical Publications, 2023
Abstract The aim of this paper is to give necessary and sufficient conditions in terms of the Fourier Laguerre-Bessel transform 𝒲 LB f of the function f to ensure that f belongs to the generalized Lipschitz classes H α
Rakhimi, Larbi, Khadari, Abdelmajid, Daher, Radouan   +2 more
openaire   +2 more sources

Quasi-Copulas, Copulas and Fuzzy Implicators

International Journal of Computational Intelligence Systems, 2020
In this paper, we study relations between fuzzy implicators and some kinds of fuzzy conjunctors, in particular, quasi-copulas and copulas. We show that there is a one-to-one correspondence between the classes of all quasi-copulas and 1-Lipschitz fuzzy ...
Radko Mesiar, Anna Kolesárová
doaj   +1 more source

AN EXISTENCE AND UNIQUENESS OF THE SOLUTION OF SEMILINEAR MONOTONE ELLIPTIC EQUATION WITH THE DATA IN STUMMEL CLASSES

Barekeng, 2023
Let  be a bounded open subset of , ,  be a function in Stummel classes , where , and be a semilinear monotone elliptic equation, where  is  symmetric matrix, elliptic, bounded, and  is non decreasing and Lipschitz. By proving a weighted estimation for
Nicky Kurnia Tumalun
doaj   +1 more source

Lipschitz classes and quasiconformla mappings

Annales Academiae Scientiarum Fennicae. Series A. I. Mathematica, 1985
A domain \(D\subset R^ n\) is a Lip\({}_{\alpha}\)-extension domain if every \(f: D\to R^ p\) which satisfies \(| f(x)-f(y)| \leq m| x-y|^{\alpha ...
Gehring, F. W., Martio, O.
openaire   +2 more sources

Approximation of signals (functions) belonging to certain Lipschitz classes by almost Riesz means of its Fourier series

Journal of Inequalities and Applications, 2016
To start with, signals are dealt with as functions of one variable and images are shown by elements of two variables. The investigation of these ideas is directly related to the transpiring area of information technology.
Deepmala, Laurian-Ioan Piscoran
doaj   +1 more source

Radial variation in some function spaces

Journal of Function Spaces and Applications, 2009
In a previous paper [8] we considered properties of the radial variation of analytic functions in a class of Besov spaces Ap,qs, s≻0. Here we wish to extend these results to certain related spaces.
David Walsh
doaj   +1 more source