Related papers: Presenting LiteRed: a tool for the Loop InTEgrals …
It is a brief review on composing and solving Infrared Evolution Equations. They can be used in order to calculate amplitudes of high-energy reactions in different kinematic regions in the double-logarithmic approximation.
The systematic approach to solving the recurrence relations for multi-loop integrals is described. In particular, the criteria of their reducibility is suggested.
Recent research suggests that tree search algorithms (e.g. Monte Carlo Tree Search) can dramatically boost LLM performance on complex mathematical reasoning tasks. However, they often require more than 10 times the computational resources…
Developing intuition about quantum information theory problems is difficult, as is verifying or ruling-out of hypothesis. We present a Matlab package intended to provide the QIT community with a new and powerful tool-set for quantum…
The logic embedding tool provides a procedural encoding for non-classical reasoning problems into classical higher-order logic. It is extensible and can support an increasing number of different non-classical logics as reasoning targets.…
In this paper, we present an implementation of the harmonic polylogarithm of Remiddi and Vermaseren for Mathematica. It contains an implementation of the product algebra, the derivative properties, series expansion and numerical evaluation.…
Models on logarithmic lattices have recently been proposed as an alternative approach to the study of multi-scale nonlinear physics. Here, we introduce LogLatt, an efficient MATLAB library for the calculus between functions on…
We present a new package, VEST (Vector Einstein Summation Tools), that performs abstract vector calculus computations in Mathematica. Through the use of index notation, VEST is able to reduce three-dimensional scalar and vector expressions…
This paper deals with exploiting symmetry for solving linear and integer programming problems. Basic properties of linear representations of finite groups can be used to reduce symmetric linear programming to solving linear programs of…
The rapid advancement of large language models has unlocked remarkable capabilities across a diverse array of natural language processing tasks. However, the considerable differences among available LLMs-in terms of cost, performance, and…
In this article we introduce PINGSoft, a set of IDL routines designed to visualise and manipulate, in an interactive and friendly way, Integral Field Spectroscopic data. The package is optimised for large databases and a fast visualisation…
Loop transformations are semantics-preserving optimization techniques, widely used to maximize objectives such as parallelism. Despite decades of research, applying the optimal composition of loop transformations remains challenging due to…
We describe three algorithms for computer-aided symbolic multi-loop calculations that facilitated some recent novel results. First, we discuss an algorithm to derive the canonical form of an arbitrary Feynman integral in order to facilitate…
The Information Dynamics Toolkit xl (IDTxl) is a comprehensive software package for efficient inference of networks and their node dynamics from multivariate time series data using information theory. IDTxl provides functionality to…
Matrix Lie groups provide a language for describing motion in such fields as robotics, computer vision, and graphics. When using these tools, we are often faced with turning infinite-series expressions into more compact finite series (e.g.,…
Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all…
Trace slicing is a widely used technique for execution trace analysis that is effectively used in program debugging, analysis and comprehension. In this paper, we present a backward trace slicing technique that can be used for the analysis…
Retrograde analysis reads programs from the end to the beginning: treat statements as constraints on prior states, propagate sets of states backward, and compare the reachable inputs with the intended specification. This tutorial condenses…
Loop acceleration can be used to prove safety, reachability, runtime bounds, and (non-)termination of programs operating on integers. To this end, a variety of acceleration techniques has been proposed. However, all of them are monolithic:…
This article describes the latest versions of the Mathematica packages FeynArts, FormCalc, and LoopTools for the generation and evaluation of one-loop diagrams.