Related papers: ForeignFunctions package for Macaulay2
Symbolic powers are a classical commutative algebra topic that relates to primary decomposition, consisting, in some circumstances, of the functions that vanish up to a certain order on a given variety. However, these are notoriously…
The Macaulay2 package DecomposableSparseSystems implements methods for studying and numerically solving decomposable sparse polynomial systems. We describe the structure of decomposable sparse systems and explain how the methods in this…
The nonuniform fast Fourier transform (NUFFT) generalizes the FFT to off-grid data. Its many applications include image reconstruction, data analysis, and the numerical solution of differential equations. We present FINUFFT, an efficient…
Given a time series vector, how can we efficiently compute a specified part of Fourier coefficients? Fast Fourier transform (FFT) is a widely used algorithm that computes the discrete Fourier transform in many machine learning applications.…
In this paper, the authors propose the utilization of Fibonacci Neural Networks (FNN) for solving arbitrary order differential equations. The FNN architecture comprises input, middle, and output layers, with various degrees of Fibonacci…
We present the open-source $\texttt{C++}$ library $\texttt{FireFly}$ for the reconstruction of multivariate rational functions over finite fields. We discuss the involved algorithms and their implementation. As an application, we use…
The development of software applications using multiple programming languages has increased in recent years, as it allows the selection of the most suitable language and runtime for each component of the system and the integration of…
We give two algebro-geometric inspired approaches to fast algorithms for Fourier transforms in algebraic signal processing theory based on polynomial algebras in several variables. One is based on module induction and one is based on a…
We derive results about geometric means of the Fourier modulus of filters and functions related to refinable distributions with arbitrary dilations and translations. Then we develop multi-scale constructions for dilations by…
This paper presents an interactive fuzzy goal programming (FGP) approach for solving multiobjective nonlinear programming problems (MONLPP) with interval type 2 fuzzy numbers (IT2 FNs). The cost and time of the objective functions, the…
Multi-dimensional Fourier transforms are key mathematical building blocks that appear in a wide range of applications from materials science, physics, chemistry and even machine learning. Over the past years, a multitude of software…
We present the main improvements and new features in version $\texttt{2.0}$ of the open-source $\texttt{C++}$ library $\texttt{FireFly}$ for the interpolation of rational functions. This includes algorithmic improvements, e.g. a hybrid…
The Frank Wolfe algorithm (FW) is a popular projection-free alternative for solving large-scale constrained optimization problems. However, the FW algorithm suffers from a sublinear convergence rate when minimizing a smooth convex function…
High-dimensional nonlinear optimization problems subject to nonlinear constraints can appear in several contexts including constrained physical and dynamical systems, statistical estimation, and other numerical models. Feasible optimization…
We consider the problem of training machine learning models over multi-relational data. The mainstream approach is to first construct the training dataset using a feature extraction query over input database and then use a statistical…
We present a FFT-based algorithm for the computation of a polynomial's coefficients from its roots, and apply it to obtain the coefficients of interpolation polynomials, to invert Vandermondians and to evaluate the symmetric functions of a…
This article highlights the ToricHigherDirectImages package in Macaulay2. The central feature is a method for computing (higher) direct images of line bundles under surjective toric morphisms.
Algebraic methods have a long history in statistics. The most prominent manifestation of modern algebra in statistics can be seen in the field of algebraic statistics, which brings tools from commutative algebra and algebraic geometry to…
Enhancing the adaptive capabilities of large language models is a critical pursuit in both research and application. Traditional fine-tuning methods require substantial data and computational resources, especially for enhancing specific…
Numerical Algebraic Geometry uses numerical data to describe algebraic varieties. It is based on the methods of numerical polynomial homotopy continuation, an alternative to the classical symbolic approaches of computational algebraic…