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This article makes the key observation that when using cylindrical algebraic decomposition (CAD) to solve a problem with respect to a set of polynomials, it is not always the signs of those polynomials that are of paramount importance but…
Resampling algorithms are a useful approach to deal with imbalanced learning in multilabel scenarios. These methods have to deal with singularities in the multilabel data, such as the occurrence of frequent and infrequent labels in the same…
Multimodal Large Language Models (MLLMs) excel in solving text-based mathematical problems, but they struggle with mathematical diagrams since they are primarily trained on natural scene images. For humans, visual aids generally enhance…
MulAtoLEG (Multi-Atom Liouville Equation Generator) is an open-source Mathematica package for generating Liouville superoperators and Liouville equations, specialized for multilevel atomic systems comprising an arbitrary number of atoms.…
Routines for computation of Weber's parabolic cylinder functions and their derivatives are implemented in Matlab for both moderate and great values of the argument. Standard, real solutions are considered. Tables of values are included.
In this research paper, structured bi-matrix variate, matrix quadratic equations are considered. Some lemmas related to determining the eigenvalues of unknown matrices are proved. Also, a method of determining the diagonalizabe unknown…
Despite data's crucial role in machine learning, most existing tools and research tend to focus on systems on top of existing data rather than how to interpret and manipulate data. In this paper, we propose DataLab, a unified data-oriented…
Pattern recognition and machine learning are becoming integral parts of algorithms in a wide range of applications. Different algorithms and approaches for machine learning include different tradeoffs between performance and computation, so…
A suitable piece of software is presented to connect Abaqus, a sophisticated finite element package, with Matlab, the most comprehensive program for mathematical analysis. This interface between these well-known codes not only benefits from…
In the past two decades, some major efforts have been made to reduce exact (e.g. integer, rational, polynomial) linear algebra problems to matrix multiplication in order to provide algorithms with optimal asymptotic complexity. To provide…
Loop invariants are properties of a program loop that hold before and after each iteration of the loop. They are often employed to verify programs and ensure that algorithms consistently produce correct results during execution.…
We present a MATLAB toolbox for five different classes of exponential integrators for solving (mildly) stiff ordinary differential equations or time-dependent partial differential equations. For the efficiency of such exponential…
Numerical algebraic geometry provides a number of efficient tools for approximating the solutions of polynomial systems. One such tool is the parameter homotopy, which can be an extremely efficient method to solve numerous polynomial…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
Multiple polylogarithms appear in analytic calculations of higher order corrections in quantum field theory. In this article we study the numerical evaluation of multiple polylogarithms. We provide algorithms, which allow the evaluation for…
This work aims to accelerate the convergence of proximal gradient methods used to solve regularized linear inverse problems. This is achieved by designing a polynomial-based preconditioner that targets the eigenvalue spectrum of the normal…
GlobalBioIm is an open-source MATLAB library for solving inverse problems. The library capitalizes on the strong commonalities between forward models to standardize the resolution of a wide range of imaging inverse problems. Endowed with an…
Many nonlinear differential equations arising from practical problems may permit nontrivial multiple solutions relevant to applications, and these multiple solutions are helpful to deeply understand these practical problems and to improve…
In this article we show how to compute a matrix representation and the implicit equation by means of the method developed in [Botbol: arXiv:1007.3437], using the computer algebra system Macaulay2 \cite{M2}. As it is probably the most…
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…