相关论文: Automatic Integral Reduction for Higher Order Pert…

Integration by parts reduction is a standard component of most modern multi-loop calculations in quantum field theory. We present a novel strategy constructed to overcome the limitations of currently available reduction programs based on…

The reduction of a large number of scalar integrals to a small set of master integrals via Laporta's algorithm is common practice in multi-loop calculations. It is also a major bottleneck in terms of running time and memory consumption. It…

Ihe first author presented an efficient algorithm for computing involutive (and reduced Groebner) bases. In this paper, we consider a modification of this algorithm which simplifies matters to understand it and to implement. We prove…

Studies in thermodynamics often require the reduction of some first or second order partial derivatives in terms of a smaller basic set. A simple algorithm to perform such a reduction is presented here, together with a review of earlier…

Large language model (LLM) agents have emerged as powerful tools for complex tasks, yet their ability to adapt to individual users remains fundamentally limited. We argue this limitation stems from a critical architectural conflation:…

We propose new methods for optimizing the integration-by-parts (IBP) reduction of Feynman integrals, an important computational bottleneck in modern perturbative calculations in quantum field theory. Using the simple example of one-loop…

The recently developed algorithm FIRE performs the reduction of Feynman integrals to master integrals. It is based on a number of strategies, such as applying the Laporta algorithm, the s-bases algorithm, region-bases and integrating…

In this paper we introduce a generic model for multiplicative algorithms which is suitable for the MapReduce parallel programming paradigm. We implement three typical machine learning algorithms to demonstrate how similarity comparison,…

Optimizing parallel programs for distributed systems is a complex task, often requiring significant code modifications. Task-based programming systems improve modularity by separating performance decisions from application logic, but their…

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…

RIPE is a novel deterministic and easily understandable prediction algorithm developed for continuous and discrete ordered data. It infers a model, from a sample, to predict and to explain a real variable $Y$ given an input variable $X \in…

Reduze is a computer program for reducing Feynman Integrals to master integrals employing a Laporta algorithm. The program is written in C++ and uses classes provided by the GiNaC library to perform the simplifications of the algebraic…

A MapReduce algorithm can be described by a mapping schema, which assigns inputs to a set of reducers, such that for each required output there exists a reducer that receives all the inputs that participate in the computation of this…

In this paper, we propose an incremental algorithm for computing cylindrical algebraic decompositions. The algorithm consists of two parts: computing a complex cylindrical tree and refining this complex tree into a cylindrical tree in real…

We propose a new method for low-rank approximation of Moore-Penrose pseudoinverses (MPPs) of large-scale matrices using tensor networks. The computed pseudoinverses can be useful for solving or preconditioning of large-scale overdetermined…

An integral equation is a way to encapsulate the relationships between a function and its integrals. We develop a systematic way of describing Volterra integral equations -- specifically an algorithm that reduces any separable Volterra…

This paper discusses an efficient implementation of the generation of order conditions for the construction of exponential integrators like exponential splitting and Magnus-type methods in the computer algebra system Maple. At the core of…

In this article, we present a new implementation of the Laporta algorithm to reduce scalar multi-loop integrals---appearing in quantum field theoretic calculations---to a set of master integrals. We extend existing approaches by using an…

These lectures give a brief introduction to the Computer Algebra systems Reduce and Maple. The aim is to provide a systematic survey of most important commands and concepts. In particular, this includes a discussion of simplification…

In this paper we study a worst case to average case reduction for the problem of matrix multiplication over finite fields. Suppose we have an efficient average case algorithm, that given two random matrices $A,B$ outputs a matrix that has a…