Related papers: Shape-Enforcing Operators for Point and Interval E…
Overlap functions are a class of aggregation functions that measure the overlapping degree between two values. Interval-valued overlap functions were defined as an extension to express the overlapping of interval-valued data, and they have…
The operator product expansion (OPE) in 4d (super)conformal field theory is of broad interest, for both formal and phenomenological applications. In this paper, we use conformal perturbation theory to study the OPE of nearly-free fields…
Perspective functions arise explicitly or implicitly in various forms in applied mathematics and in statistical data analysis. To date, no systematic strategy is available to solve the associated, typically nonsmooth, optimization problems.…
In this paper, we introduce a new operator, $\mathcal{S}$, which is closely related to the restriction problem for spheres in $\mathbb{F}_q^d$, the $d$-dimensional vector space over the finite field $\mathbb{F}_q$ with $q$ elements. The…
Quantifying the influence of infinitesimal changes in training data on model performance is crucial for understanding and improving machine learning models. In this work, we reformulate this problem as a weighted empirical risk minimization…
Convex regression is a method for estimating the convex function from a data set. This method has played an important role in operations research, economics, machine learning, and many other areas. However, it has been empirically observed…
The paper examines the construction and analysis of a new class of mixed exponential statistical structures that combine the properties of stochastic models and linear positive operators. The relevance of the topic is driven by the growing…
We consider the application of feedback control strategies with point actuators to stabilise desired interface shapes. We take a multidimensional Kuramoto--Sivashinsky equation as a test case; this equation arises in the study of thin…
In [R. J. Baraldi and D. P. Kouri, Math. Program., 201:1 (2023), pp. 559-598], the authors introduced a trust-region method for minimizing the sum of a smooth nonconvex and a nonsmooth convex function, the latter of which has an analytical…
We consider nonconforming methods for symmetric elliptic problems and characterize their quasi-optimality in terms of suitable notions of stability and consistency. The quasi-optimality constant is determined and the possible impact of…
We study minimax lower bounds for function estimation problems on large graph when the target function is smoothly varying over the graph. We derive minimax rates in the context of regression and classification problems on graphs that…
It is expected that conformal symmetry is an emergent property of many systems at their critical point. This imposes strong constraints on the critical behavior of a given system. Taking them into account in theoretical approaches can lead…
Given additional distributional information in the form of moment restrictions, kernel density and distribution function estimators with implied generalised empirical likelihood probabilities as weights achieve a reduction in variance due…
We discuss ways in which momentum operators can be introduced on an oriented metric graph. A necessary condition appears to the balanced property, or a matching between the numbers of incoming and outgoing edges; we show that a graph…
Many studies have been conducted on statistical convergence, and it remains an area of active research. Since its introduction, statistical convergence has found applications many fields. Nevertheless, there is a shortage of research…
Superconformal transformations are derived for the $\N=2,4 supermultiplets corresponding to the simplest chiral primary operators. These are applied to two, three and four point correlation functions. When $\N=4$, results are obtained for…
We introduce an algorithm of joint approximation of a function and its first derivative by alternative orthogonal polynomials on the interval [0,1].The algorithm exhibits properties of shape preserving approximation for the function. A weak…
We study the momentum-space 4-point correlation function of identical scalar operators in conformal field theory. Working specifically with null momenta, we show that its imaginary part admits an expansion in conformal blocks. The blocks…
In many image analysis problems, the contours of objects carry important statistical information about shape. Such contours are typically affected by deformation variables including scaling, translation, rotation, and reparametrization.…
Lifting operators play an important role in starting a lattice Boltzmann model from a given initial density. The density, a macroscopic variable, needs to be mapped to the distribution functions, mesoscopic variables, of the lattice…