相关论文: Constrained Differential Renormalization
Contrastive dimension reduction (CDR) methods aim to extract signal unique to or enriched in a treatment (foreground) group relative to a control (background) group. This setting arises in many scientific domains, such as genomics, imaging,…
We outline the proofs of several principal statements in conventional renormalization theory. This may be of some use in the light of new trends and new techniques (Hopf algebras, etc.) recently introduced in the field.
The renormalization of the Minimal Supersymmetric Standard Model (MSSM) is presented. We describe symmetry identities that constitute a framework in which the MSSM is completely characterized and renormalizability can be proven.…
An algorithmic method to exploit a general class of infinitesimal symmetries for reducing stochastic differential equations is presented and a natural definition of reconstruction, inspired by the classical reconstruction by quadratures, is…
We review the basic ideas lying at the foundation of the recently developed theory of twisted symmetries of differential equations, and some of its developments.
In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss…
Methods for the reduction of the complexity of computational problems are presented, as well as their connections to renormalization, scaling, and irreversible statistical mechanics. Several statistically stationary cases are analyzed; for…
We stress the potential usefulness of renormalization group invariants. Especially particular combinations thereof could for instance be used as probes into patterns of supersymmetry breaking in the MSSM at inaccessibly high energies. We…
As applied to quantum theories, the program of renormalization is successful for `renormalizable models' but fails for `nonrenormalizable models'. After some conceptual discussion and analysis, an enhanced program of renormalization is…
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…
Renormalization procedure is generalized to be applicable for non renormalizable theories. It is shown that introduction of an extra expansion parameter allows to get rid of divergences and express physical quantities as series of finite…
In this chapter we provide a theoretically founded investigation of state-of-the-art learning approaches for inverse problems from the point of view of spectral reconstruction operators. We give an extended definition of regularization…
We apply the recently developed method of differential renormalization to the Wess-Zumino model. From the explicit calculation of a finite, renormalized effective action, the $\beta$-function is computed to three loops and is found to agree…
This paper studies the problem of reconstructing binary matrices that are only accessible through few evaluations of their discrete X-rays. Such question is prominently motivated by the demand in material science for developing a tool for…
Using resummation in perturbation theories at finite temperature or in non-equilibrium is unavoidable to obtain consistent results. Resummation, however, is often in conflict with renormalization. In this talk we give two possible solutions…
In recent years, some interesting investigations of the non-perturbative renormalization group equations for tensorial group field theories have been done in the truncation method, and completely discarding the Ward identities from their…
A new method, called the method of self-similar approximants, and its recent developments are described. The method is based on the ideas of renormalization group theory and optimal control theory. It allows for the effective extrapolation…
We consider the method of self-similar renormalization for calculating critical temperatures and critical indices. A new optimized variant of the method for an effective summation of asymptotic series is suggested and illustrated by several…
Proceeding by way of examples, we update the combinatorics of the treatment of Feynman diagrams with subdivergences in differential renormalization from more recent viewpoints in Epstein--Glaser renormalization in $x$-space.
The renormalization algorithm based on regularization methods with two regulators is analyzed by means of explicit computations. We show in particular that regularization by higher covariant derivative terms can be complemented with…