Related papers: Consistency Relations for an Implicit n-dimensiona…
The numerical properties of algorithms for finding the intersection of sets depend to some extent on the regularity of the sets, but even more importantly on the regularity of the intersection. The alternating projection algorithm of von…
It is shown that regularisation by dimensional reduction is a viable alternative to dimensional regularisation in non-supersymmetric theories.
We study regular inclusions of finite-dimensional von Neumann algebras from a matrix-theoretic perspective. To this end, we introduce a new combinatorial invariant of an inclusion, called the normalizer matrix, which encodes the structure…
These lecture notes evolve around mathematical concepts arising in inverse problems. We start by introducing inverse problems through examples such as differentiation, deconvolution, computed tomography and phase retrieval. This then leads…
We have investigated the perturbative ambiguity of the radiatively induced Chern-Simons term in differential regularization. The result obtained in this method contains all those obtained in other regularization schemes and the ambiguity is…
We propose a variational regularization approach based on a multiscale representation called cylindrical shearlets aimed at dynamic imaging problems, especially dynamic tomography. The intuitive idea of our approach is to integrate a…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
A regularization algorithm using inexact function values and inexact derivatives is proposed and its evaluation complexity analyzed. This algorithm is applicable to unconstrained problems and to problems with inexpensive constraints (that…
We consider the inverse problem of reconstructing inhomogeneities by performing a finite number of scattering measurements of acoustic type in the time-harmonic setting. We set up the reconstruction as a fully discrete variational problem…
We present an approach to learning regular spatial transformations between image pairs in the context of medical image registration. Contrary to optimization-based registration techniques and many modern learning-based methods, we do not…
For supersymmetric gauge theories a consistent regularization scheme that preserves supersymmetry and gauge invariance is not known. In this article we tackle this problem for supersymmetric QED within the framework of algebraic…
Recently \cite{Horowitz:2022rpp,Horowitz:2022uak}, denominator regularisation (Den. Reg.) scheme has been proposed to handle divergences in quantum field theory. It is shown to yield results as simple as in dimensional regularisation scheme…
The O(N) non-linear sigma model in a $D$-dimensional space of the form ${\bf R}^{D-M} \times {\bf T}^M$, ${\bf R}^{D-M} \times {\bf S}^M$, or ${\bf T}^M \times {\bf S}^P$ is studied, where ${\bf R}^M$, ${\bf T}^M$ and ${\bf S}^M$ correspond…
The goal of this paper is to further develop an approach to inverse problems with imperfect forward operators that is based on partially ordered spaces. Studying the dual problem yields useful insights into the convergence of the…
This work introduces topological regularization as a framework for handling ultraviolet divergences in quantum field theory, reinterpreting infinities as topological obstructions at spacetime boundaries. Through geometric compactification…
A regularization procedure developed in [1] for the integral curvature invariants on manifolds with conical singularities is generalized to the case of squashed cones. In general, the squashed conical singularities do not have rotational…
Many robotics applications require alignment and fusion of observations obtained at multiple views to form a global model of the environment. Multi-way data association methods provide a mechanism to improve alignment accuracy of pairwise…
Differential flatness serves as a powerful tool for controlling continuous time nonlinear systems in problems such as motion planning and trajectory tracking. A similar notion, called difference flatness, exists for discrete-time systems.…
To study asymptotic structures, we regularize Einstein's field equations by means of conformal transformations. The conformal factor is chosen so that it carries a dimensional scale that captures crucial asymptotic features. By choosing a…
We numerically investigate a lattice regularized version of quantum electrodynamics in one spatial dimension (Schwinger model). We work at a density where lattice commensuration effects are important, and preclude analytic solution of the…