Related papers: Regularisation of functional determinants using bo…
We establish an algorithm for a criterion of the diagonalisability of a matrix over a local field by a unitary matrix. For this sake, we define the notion of normality of a $p$-adic operator, and give several criteria for the normality. We…
Depending of the geometry of the domain, one can define --at least-- three different Stokes operators with Dirichlet boundary conditions. We describe how the resolvents of these Stokes operators converge with respect to a converging…
Some prominent discretisation methods such as finite elements provide a way to approximate a function of $d$ variables from $n$ values it takes on the nodes $x_i$ of the corresponding mesh. The accuracy is $n^{-s_a/d}$ in $L^2$-norm, where…
A general method of regularisation of classical self interaction in strings is extended from the electromagnetic case (for which it was originally developed) to the gravitation case, for which the result can also be represented as a…
In this paper, we develop a new regularized version of the Factorization Method for positive operators mapping a complex Hilbert Space into it's dual space. The Factorization Method uses Picard's Criteria to define an indicator function to…
We obtain regularity conditions of a new type of problems of the calculus of variations with second-order derivatives. As a corollary, we get non-occurrence of the Lavrentiev phenomenon. Our main result asserts that autonomous integral…
In this report we introduce a \texttt{Matlab} toolbox for the regularization of descriptor systems. We apply it, in particular, for systems resulting from the generalized realization procedure of \cite{MayA07}, which generates, via rational…
The BV formalism is a well-established method for analyzing symmetries and quantization of field theories. In this paper we use the BV formalism to derive partition functions of gauge invariant operators up to equations of motions and their…
Neural operators have emerged as transformative tools for learning mappings between infinite-dimensional function spaces, offering useful applications in solving complex partial differential equations (PDEs). This paper presents a rigorous…
A formulation of quantum mechanics with additive and multiplicative (q-)difference operators instead of differential operators is studied from first principles. Borel-quantisation on smooth configuration spaces is used as guiding…
Phase equations describing the evolution of large scale modulation of spatially periodic patterns in two dimensional systems are derived by employing the renormalization group method. A general formula for phase diffusion coefficients is…
We propose a generalization of separability in the context of global optimization. Our results apply to objective functions implemented as differentiable computer programs. They are presented in the context of a simple branch and bound…
The determinant and higher loop terms, usually treated with the Pauli-Villars and higher covariant derivatives methods, in the background field method in 4 dimensions can hardly be regularized simultaneously. At the same time we observe…
I am showing how the ideas behind the renormalisation group can be generalised in order to produce the desired reduction in the degrees of freedom other that the ones considered up to now. Instead of looking only at the renormalisation…
The aim of this paper is to design a theoretical framework that allows us to perform the computation of regular expression derivatives through a space of generic structures. Thanks to this formalism, the main properties of regular…
The article $-$ part of a larger thesis which aims to give a detailed description of the generalisation to the category of groups with operators of the classical theory of semisimplicity for modules $-$ presents a straightforward…
Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and…
We present a novel procedure where a stationary point process is regularized through the convolution with a continuous random field with stationary increments, in the sense that the dependency between distant points is weakened; and the…
In high-dimensional and/or non-parametric regression problems, regularization (or penalization) is used to control model complexity and induce desired structure. Each penalty has a weight parameter that indicates how strongly the structure…
This paper addresses explainability of the operator-regularization approach under the use of monotone Lipschitz-gradient (MoL-Grad) denoiser -- an operator that can be expressed as the Lipschitz continuous gradient of a differentiable…