Related papers: Shape-Enforcing Operators for Point and Interval E…
Approximation properties of multivariate quasi-projection operators are studied in the paper. Wide classes of such operators are considered, including the sampling and the Kantorovich-Kotelnikov type operators generated by different…
A height-function-based numerical approach is developed for enforcing contact angles on flat and curved solid surfaces within two-dimensional volume-of-fluid simulations. This method incorporates the contact line position into the curvature…
We develop a general framework for construction and analysis of discrete extension operators with application to unfitted finite element approximation of partial differential equations. In unfitted methods so called cut elements intersected…
We consider a class of linear integral operators with impulse responses varying regularly in time or space. These operators appear in a large number of applications ranging from signal/image processing to biology. Evaluating their action on…
Estimating signals underlying noisy data is a significant problem in statistics and engineering. Numerous estimators are available in the literature, depending on the observation model and estimation criterion. This paper introduces a…
Informed learning is an emerging field in machine learning that aims to compensate for insufficient data with prior knowledge. Shape knowledge covers many types of prior knowledge concerning the relationship of a function's output with…
Industrial and scientific applications handle large volumes of data that render manual validation by humans infeasible. Therefore, we require automated data validation approaches that are able to consider the prior knowledge of domain…
We propose a unified framework for establishing existence of nonparametric M-estimators, computing the corresponding estimates, and proving their strong consistency when the class of functions is exceptionally rich. In particular, the…
We analyse the OPE of any two 1/2 BPS operators of (2,0) SCFT$_6$ by constructing all possible three-point functions that they can form with another, in general long operator. Such three-point functions are uniquely determined by…
In this paper, we study a class of convolution operators on the space of distributions that enlarge the well-studied class of passive operators. In this larger class, we are able to associate, to each operator, a holomorphic function in the…
We propose a new reconstruction operator that aims to recover the missing parts of a function given the observed parts. This new operator belongs to a new, very large class of functional operators which includes the classical regression…
This article addresses structure-preserving smooth approximation of semiconcave functions. semiconcave functions are of particular interest because they naturally arise in a variety of variational problems, including {optimal feedback…
In much of the literature on function approximation by deep networks, the function is assumed to be defined on some known domain, such as a cube or a sphere. In practice, the data might not be dense on these domains, and therefore, the…
Let $A$ be a positive definite operator on a Hilbert space $H$, and $|||.|||$ be a unitarily invariant norm on $B(H)$. We show that if $f$ is an operator monotone function on $(0,\infty)$ and $n\in \mathbb{N}$, then $|||D^n…
We calculate the leading contributions to the connected two-point functions of protected scalar operators in the defect version of N=4 SYM theory which is dual to the D5-D3 probe-brane system with k units of background gauge field flux.…
We study the problem of empirical minimization for variance-type functionals over functional classes. Sharp non-asymptotic bounds for the excess variance are derived under mild conditions. In particular, it is shown that under some…
Shape constraints (such as non-negativity, monotonicity, convexity) play a central role in a large number of applications, as they usually improve performance for small sample size and help interpretability. However enforcing these shape…
This paper develops a uniformly valid and asymptotically nonconservative test based on projection for a class of shape restrictions. The key insight we exploit is that these restrictions form convex cones, a simple and yet elegant structure…
We consider the expectation value of a local operator on a strip with non-trivial boundaries in 1+1 dimensional massive integrable QFT. Using finite volume regularisation in the crossed channel and extending the boundary state formalism to…
Problems in econometrics, insurance, reliability engineering, and statistics quite often rely on the assumption that certain functions are non-decreasing. To satisfy this requirement, researchers frequently model the underlying phenomena…