Related papers: A Recursive Method to Calculate UV-divergent Parts…
An analytical-numeric calculation method of extremely complicated integrals is presented. These integrals appear often in magnet soliton theory. The appropriate analytical continuation and a corresponding integration contour allow to reduce…
The vertex function is analyzed using covariant spectral regularization without encountering any divergence, either UV or IR. The mathematics of covariant spectral regularization for covariant matrix valued measures with one Lorentz index…
The chapter contains a detailed presentation of the surface integral theory for modelling light diffraction by surface-relief diffraction gratings having a one-dimensional periodicity. Several different approaches are presented, leading…
A recursive calculational scheme is developed for matrix elements in the generalized seniority scheme for the nuclear shell model. Recurrence relations are derived which permit straightforward and efficient computation of matrix elements of…
The calculation of one loop integrals at finite temperature requires the evaluation of certain series, which converge very slowly or can even be divergent. Here we review a new method, recently devised by the author, for obtaining…
We develop a basis--covariant one--loop renormalization framework for two interacting real scalars in $D=4-\epsilon$ with the most general two--derivative Lorentz--violating quadratic form, allowing anisotropic spatial gradients and…
Stratified digraphs are popular models for feedforward neural networks. However, computation of their path homologies has been limited to low dimensions due to high computational complexity. A recursive algorithm is proposed to compute…
We introduce a new Partition of Unity Method for the numerical homogenization of elliptic partial differential equations with arbitrarily rough coefficients. We do not restrict to a particular ansatz space or the existence of a finite…
In this book chapter, we briefly describe the main components that constitute the gradient descent method and its accelerated and stochastic variants. We aim at explaining these components from a mathematical point of view, including…
Regularization is used in many different areas of optimization when solutions are sought which not only minimize a given function, but also possess a certain degree of regularity. Popular applications are image denoising, sparse regression…
A new iterative technique is presented for solving of initial value problem for certain classes of multidimensional linear and nonlinear partial differential equations. Proposed iterative scheme does not require any discretization,…
The differential equation method is applied to evaluate analytically two-loop vertex Feynman diagrams. Three on-shell infrared divergent planar two-loop diagrams with zero thresholds contributing to the processes Z --> bb bar (for zero b…
We discuss how to apply regularization by dimensional reduction for computing hadronic cross sections at next-to-leading order. We analyze the infrared singularity structure, demonstrate that there are no problems with factorization, and…
We describe methods for evaluating one-loop integrals in $4-2\e$ dimensions. We give a recursion relation that expresses the scalar $n$-point integral as a cyclicly symmetric combination of $(n-1)$-point integrals. The computation of such…
We describe the on-shell method to deriving the Renormalization Group (RG) evolution of Wilson coefficients of high dimensional operators at one loop, which is a necessary part in the on-shell construction of the Standard Model Effective…
A new method is presented for the simplification of loop integrals in one particle irreducible diagrams with large numbers of external lines, based on the partial fractioning of products of propagators. Whenever a loop diagram in $d$…
A technique for reducing the number of integrals in a Monte Carlo calculation is introduced. For integrations relying on classical or mean-field trajectories with local weighting functions, it is possible to integrate analytically at least…
We investigate the issue of regularization/renormalization in the presence of a nontrivial background in the case of 1+1-(supersymmetric) solitons. In particular we study and compare the commonly employed regularization methods (mode-…
We investigate some recursive procedures based on an exact or ``approximate'' Euler scheme with decreasing step in vue to computation of invariant measures of solutions to S.D.E. driven by a L\'evy process. Our results are valid for a large…
We discuss a systematic way to dimensionally regularize divergent sums arising in field theories with an arbitrary number of physical compact dimensions or finite temperature. The method preserves the same symmetries of the action as the…