相关论文: Integral Reduction with Kira 2.0 and Finite Field …

In this technical report, we present the Ring-linear model series, specifically including Ring-mini-linear-2.0 and Ring-flash-linear-2.0. Ring-mini-linear-2.0 comprises 16B parameters and 957M activations, while Ring-flash-linear-2.0…

In a recent paper \cite{ft} a new powerful method to calculate Feynman diagrams was proposed. It consists in setting up a Taylor series expansion in the external momenta squared. The Taylor coefficients are obtained from the original…

Discretizations of the Feynman-Kac path integral representation of the quantum mechanical density matrix are investigated. Each infinite-dimensional path integral is approximated by a Riemann integral over a finite-dimensional function…

It is shown how strictly four-dimensional integration by parts combined with differential renormalization and its infrared analogue can be applied for calculation of Feynman diagrams.

We present a new FORM program for analytically evaluating four-loop massless propagator-type Feynman integrals in an efficient way. Our program Forcer implements parametric reductions of the aforementioned class of Feynman integrals into a…

We introduce the tools of intersection theory to the study of Feynman integrals, which allows for a new way of projecting integrals onto a basis. In order to illustrate this technique, we consider the Baikov representation of maximal cuts…

$\mathcal{H}\Phi$ [$aitch$-$phi$] is an open-source software package of numerically exact and stochastic calculations for a wide range of quantum many-body systems. In this paper, we present the newly added functions and the implemented…

We propose that Feynman integral reduction is controlled by solutions of the Landau equations. We study integral relations with prescribed propagator powers using syzygy methods and discuss how syzygies can be expressed as a sum over…

High precision calculations in perturbative QFT often require evaluation of big collection of Feynman integrals. Complexity of this task can be greatly reduced via the usage of linear identities among Feynman integrals. Based on…

We discuss the systematic evaluation of 3-loop vacuum integrals with arbitrary masses. Using integration by parts, the general integral of this type can be reduced algebraically to a few basis integrals. We define a set of modified finite…

In this presentation, we review the general features of integrand-reduction techniques, with a particular focus on their generalization beyond one loop. We start with a brief discussion of the one-loop scenario, a case in which…

INTEGRAL observations provide a large amount of data on accreting binary systems. The interpretation of the spectral emission of these sources needs timing analysis and phase resolved spectroscopy, which are really cumbersome tasks if…

Numerous tasks at the core of statistics, learning and vision areas are specific cases of ill-posed inverse problems. Recently, learning-based (e.g., deep) iterative methods have been empirically shown to be useful for these problems.…

An efficient computational approach for optimal reconstructing parameters of binary-type physical properties for models in biomedical applications is developed and validated. The methodology includes gradient-based multiscale optimization…

Standard integration-by-parts (IBP) reduction methods typically yield Feynman integral bases where the reduction of some integrals gives rise to coefficients singular as the dimensional regulator $\epsilon\rightarrow 0$. These singular…

In earlier work, we developed an approach for automatic complexity analysis of integer programs, based on an alternating modular inference of upper runtime and size bounds for program parts. In this paper, we show how recent techniques to…

Feature pyramids and iterative refinement have recently led to great progress in optical flow estimation. However, downsampling in feature pyramids can cause blending of foreground objects with the background, which will mislead subsequent…

This paper provides a new way of developing the fast iterative shrinkage/thresholding algorithm (FISTA) that is widely used for minimizing composite convex functions with a nonsmooth term such as the $\ell_1$ regularizer. In particular,…

We present a Mathematica package which finds a basis of master integrals for the Feynman integral reduction. In this basis the dependence on the dimensional regularization in the denominators factorizes in kinematic independent polynomials.

Analyzing high-dimensional data presents challenges due to the "curse of dimensionality'', making computations intensive. Dimension reduction techniques, categorized as linear or non-linear, simplify such data. Non-linear methods are…