相关论文: Loop integration results using numerical extrapola…
One remaining problem of unitarity cut method for one-loop integral reduction is that tadpole coefficients can not be straightforward obtained through this way. In this paper, we reconsider the problem by applying differential operators…
Trace formulas are investigated in non-commutative integration theory. The main result is to evaluate the standard trace of a Takesaki dual and, for this, we introduce the notion of interpolator and accompanied boundary objects. The formula…
Real and imaginary part of the limit 2N->infinity of the integral int_{x=1..2N} exp(i*pi*x)*x^(1/x) dx are evaluated to 20 digits with brute force methods after multiple partial integration, or combining a standard Simpson integration over…
This paper describes a very efficient algorithm for image signal extrapolation. It can be used for various applications in image and video communication, e.g. the concealment of data corrupted by transmission errors or prediction in video…
We introduce a technique to estimate a linear operator by embedding it in a family $A_t$ of operators, $t\in(\sigma_0,\infty)$, with suitable curvature properties. One can then estimate the norm of each $A_t$ by bounds that hold in the…
Some finite series of harmonic numbers involving certain reciprocals are evaluated. Products of such reciprocals are expanded in a sum of the individual reciprocals, leading to a computer program. A list of examples is provided.
As dynamical systems equipped with neural network controllers (neural feedback systems) become increasingly prevalent, it is critical to develop methods to ensure their safe operation. Verifying safety requires extending control theoretic…
Late-lumping feedback design for infinite-dimensional linear systems with unbounded input operators is considered. The proposed scheme is suitable for the approximation of backstepping and flatness-based designs and relies on a…
This paper presents a method for enhancing the gray level images. This method takes part from the category of point transforms and it is based on interpolation functions. The latter have a graphic represented by polygonal lines. The…
We study the problem of data integration from sources that contain probabilistic uncertain information. Data is modeled by possible-worlds with probability distribution, compactly represented in the probabilistic relation model. Integration…
Calculations in field theory are usually accomplished by employing some variants of perturbation theory, for instance using loop expansions. These calculations result in asymptotic series in powers of small coupling parameters, which as a…
A technique for avoiding infinite integrals in the calculation of the one-loop diagram contribution to the vacuum polarization component of an atomic energy level is presented. This makes renormalization unnecessary. Infinite integrals do…
Graph signal processing benefits significantly from the direct and highly adaptable supplementary techniques offered by partition of unity methods (PUMs) on graphs. In our approach, we demonstrate the generation of a partition of unity…
The purpose of this paper is to introduce a very efficient algorithm for signal extrapolation. It can widely be used in many applications in image and video communication, e. g. for concealment of block errors caused by transmission errors…
We present a semi-analytic method for the integrand reduction of one-loop amplitudes, based on the systematic application of the Laurent expansions to the integrand-decomposition. In the asymptotic limit, the coefficients of the master…
We consider the most general loop integral that appears in non-relativistic effective field theories with no light particles. The divergences of this integral are in correspondence with simple poles in the space of complex space-time…
The effective potential is known to be given by the vacuum diagrams. In this paper we show that the massive loop integrations corresponding to the vacuum diagrams can be expressed through the massless loop integrations with the…
Low rank matrix approximation is a popular topic in machine learning. In this paper, we propose a new algorithm for this topic by minimizing the least-squares estimation over the Riemannian manifold of fixed-rank matrices. The algorithm is…
The inference and the verification of numerical relationships among variables of a program is one of the main goals of static analysis. In this paper, we propose an Abstract Interpretation framework based on higher-dimensional ellipsoids to…
Numerical integration over the implicitly defined domains is challenging due to topological variances of implicit functions. In this paper, we use interval arithmetic to identify the boundary of the integration domain exactly, thus getting…