相关论文: Module Intersection for the Integration-by-Parts R…

We show how a large class of Feynman integrals can be efficiently reduced to master integrals by suitable covariant differentiation on the vector space dual to the one spanned by the master integrals. The connections needed in the covariant…

FIRE7 is a major update to the FIRE program for integration-by-parts (IBP) reduction of Feynman integrals. A large part of improvements is related to the automatic reduction and reconstruction with the modular arithmetic approach, while the…

Many multi-loop calculations make use of integration by parts relations to reduce the large number of complicated Feynman integrals that arise in such calculations to a simpler basis of master integrals. Recently, Gluza, Kajda, and Kosower…

Meshfree methods, including the reproducing kernel particle method (RKPM), have been widely used within the computational mechanics community to model physical phenomena in materials undergoing large deformations or extreme topology…

A new approach to compute Feynman Integrals is presented. It relies on an integral representation of a given Feynman Integral in terms of simpler ones. Using this approach, we present, for the first time, results for a certain family of…

We review the path integral method wherein quantum systems are mapped with Feynman's path integrals onto a classical system of "ring-polymers" and then simulated with the Monte Carlo technique. Bose or Fermi statistics correspond to…

Beam combiners are important components of an optical/infrared astrophysical interferometer, with many variants as to how to optimally combine two or more beams of light to fringe-track and obtain the complex fringe visibility. One such…

Building on the idea of numerically integrating differential equations satisfied by Feynman integrals, we propose a novel strategy for handling branch cuts within a numerical framework. We develop an integrator capable of evaluating a basis…

We propose that the concept of multidimensional residues can be used to directly extracting the coefficients of scalar master integrals (with single propagators only) from one-loop Feynman integrals with generic power of propagators. Unlike…

An important aspect of improving perturbative predictions in high energy physics is efficiently reducing dimensionally regularised Feynman integrals through integration by parts (IBP) relations. The well-known triangle rule has been used to…

FIRE is a program which performs integration-by-parts (IBP) reduction of Feynman integrals. Originally, the C++ version of FIRE relies on the computer algebra system Fermat by Robert Lewis to simplify rational functions. We present an…

We present a simplification of the recursive algorithm for the evaluation of intersection numbers for differential $n$-forms, by combining the advantages emerging from the choice of delta-forms as generators of relative twisted cohomology…

In this paper we consider systems of partial (multidimensional) linear difference equations. Specifically, such systems arise in scientific computing under discretization of linear partial differential equations and in computational high…

We describe how Groebner bases can be used to solve the reduction problem for Feynman integrals, i.e. to construct an algorithm that provides the possibility to express a Feynman integral of a given family as a linear combination of some…

The Zippel algorithm performs a rational reconstruction of multivariate polynomials and aims specifically at the sparse case. It is applied in different fields of science, lately becoming an important step in Feynman integral reduction in…

Approximating solutions of non-linear parametrized physical problems by interpolation presents a major challenge in terms of accuracy. In fact, pointwise interpolation of such solutions is rarely efficient and leads generally to incorrect…

Integration-by-parts reductions of Feynman integrals pose a frequent bottle-neck in state-of-the-art calculations in theoretical particle and gravitational-wave physics, and rely on heuristic approaches for selecting integration-by-parts…

Immersed boundary-lattice Boltzmann method (IB-LBM) has been widely used for simulation of particle-laden flows recently. However, it was limited to small-scale simulations with no more than O(103) particles. Here, we expand IB-LBM for…

A general framework of Numerical Singular Integrals (NSI) method based on the Integration By Parts (IBP) has been developed for integrals involving singular and nearly singular integrands, or NSI-IBP. Through a general integration by parts…

Index modulation (IM) is one of the key enabling technologies for beyond fifth generation (B5G) and sixth generation (6G) wireless systems, attracting attention for its inherent energy and spectral efficiency resulting from conveying…