Related papers: Libra: a package for transformation of differentia…
Local Fisher discriminant analysis is a localized variant of Fisher discriminant analysis and it is popular for supervised dimensionality reduction method. lfda is an R package for performing local Fisher discriminant analysis, including…
A program package for MATLAB is introduced that helps calculations in quantum information science and quantum optics. It has commands for the following operations: (i) Reordering the qudits of a quantum register, computing the reduced state…
A MATLAB toolbox is presented, with the goal of checking occurrences of design errors typically found in fixed-point digital systems, considering finite word-length effects. In particular, the present toolbox works as a front-end to a…
We present a new release of the QCDLoop library based on a modern object-oriented framework. We discuss the available new features such as the extension to the complex masses, the possibility to perform computations in double and quadruple…
"GRAMA" is a Mathematica package for doing symbolic tensor computations and complicated algebraic manipulations in 10-dimensional (D=10) simple (N=1) supergravity. The main new ingredients of this package inside the general Mathematica…
In this paper we describe by a number of examples how to deduce one single characterizing higher order differential equation for output quantities of an analog circuit. In the linear case, we apply basic "symbolic" methods from linear…
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 methods for the numerical evaluation of the master integrals that appear in the calculation of scattering amplitudes at higher order in perturbative quantum field theory. We follow the general strategy of solving first-order…
We present a new program package for calculating one-loop Feynman integrals, based on a new method avoiding Feynman parametrization and the contraction due to Passarino and Veltman. The package is calculating one-, two- and three-point…
DiffEqFlux.jl is a library for fusing neural networks and differential equations. In this work we describe differential equations from the viewpoint of data science and discuss the complementary nature between machine learning models and…
We present the Julia package SagbiHomotopy.jl for solving systems of polynomial equations using numerical homotopy continuation. The package introduces an optimal choice of a start system based on SAGBI homotopies. For square horizontally…
In this report we introduce a \texttt{Matlab} toolbox for the regularization of descriptor systems. We apply it, in particular, for systems resulting from the generalized realization procedure of \cite{MayA07}, which generates, via rational…
We report on the calculation of multi-loop Feynman integrals for single-scale problems by means of difference equations in Mellin space. The solution to these difference equations in terms of harmonic sums can be constructed algorithmically…
This article is about the formalization of synthetic differential geometry with the Lean proof assistant and the mathematical library mathlib. The main result we prove and formalize is a Taylor theorem for functions of several variables,…
This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…
We present Llemma, a large language model for mathematics. We continue pretraining Code Llama on the Proof-Pile-2, a mixture of scientific papers, web data containing mathematics, and mathematical code, yielding Llemma. On the MATH…
Loop calculations involve the evaluation of divergent integrals. Usually [1] one computes them in a number of dimensions different than four where the integral is convergent and then one performs the analytical continuation and considers…
We implement a user-extensible ad hoc connection between the Lean proof assistant and the computer algebra system Mathematica. By reflecting the syntax of each system in the other and providing a flexible interface for extending…
Mixed Integer Linear Programming (MILP) is a fundamental tool for modeling combinatorial optimization problems. Recently, a growing body of research has used machine learning to accelerate MILP solving. Despite the increasing popularity of…
This thesis proposes an advanced, generic and high-level code rewriting and analysis system in the Julia programming language, providing applied equality saturation in the presence of multiple dispatch and metaprogramming. We show how our…