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Constraint satisfaction problems are computational problems that naturally appear in many areas of theoretical computer science. One of the central themes is their computational complexity, and in particular the border between…
Fully automatic worst-case complexity analysis has a number of applications in computer-assisted program manipulation. A classical and powerful approach to complexity analysis consists in formally deriving, from the program syntax, a set of…
The words ``Programming is the second literacy'' were coined more than 40 years ago but never came to life. This paper is one in the series of papers aimed at the analysis of mathematical requirements for a merge of school mathematics with…
This paper presents the computational challenge on differential geometry and topology that happened within the ICLR 2021 workshop "Geometric and Topological Representation Learning". The competition asked participants to provide creative…
Correctly applying distributed systems concepts is important for software that seeks to be scalable, reliable and fast. For this reason, Distributed Systems is a course included in many Computer Science programs. To both describe current…
The development of Internet wide resources for general purpose parallel computing poses the challenging task of matching computation and communication complexity. A number of parallel computing models exist that address this for traditional…
The concept of a universal algorithm is discussed. Examples of this kind of algorithms are presented. Software implementations of such algorithms in C++ type languages are discussed together with means that provide for computations with an…
This report records a large number of open problems in Affine Algebraic Geometry that were proposed by participants in a Conference on Open Algebraic Varieties at the Centre de Recherches en Mathematiques in Montreal at December 1994.
Symbolic integration is an important module of a typical Computer Algebra System. As for now, Mathematica, Matlab, Maple and Sage are all mainstream CAS. They share the same framework for symbolic integration at some points. In this book…
The integration of machine learning techniques in materials discovery has become prominent in materials science research and has been accompanied by an increasing trend towards open-source data and tools to propel the field. Despite the…
This chapter is a tutorial on techniques and results in free convex algebraic geometry and free real algebraic geometry (RAG). The term free refers to the central role played by algebras of noncommutative polynomials R<x> in free (freely…
Our title challenges the reader to venture beyond linear algebra in designing models and in thinking about numerical algorithms for identifying solutions. This article accompanies the author's lecture at the International Congress of…
Nowadays, AI-based systems have achieved outstanding results and have outperformed humans in different domains. However, the processes of training AI models and inferring from them require high computational resources, which pose a…
Research software has become a central asset in academic research. It optimizes existing and enables new research methods, implements and embeds research knowledge, and constitutes an essential research product in itself. Research software…
Processors with large numbers of cores are becoming commonplace. In order to take advantage of the available resources in these systems, the programming paradigm has to move towards increased parallelism. However, increasing the level of…
In this chapter we first outline some of the popular computing environments used for analysing neural data, followed by a brief discussion of 'software carpentry', basic tools and skills from software engineering that can be of great use to…
The Distance Geometry Problem (DGP) seeks to find positions for a set of points in geometric space when some distances between pairs of these points are known. The so-called discretization assumptions allow to discretize the search space of…
This is a review devoted to some results of Algebraic Programming (Computer Algebra) used in treating several problems of general relativity, based mainly on already published articles. The article contains the talk given by the author at…
Numerical software in computational science and engineering often relies on highly-optimized building blocks from libraries such as BLAS and LAPACK, and while such libraries provide portable performance for a wide range of computing…
Let $\mathbb{R}$ be the field of real numbers. We consider the problem of computing the real isolated points of a real algebraic set in $\mathbb{R}^n$ given as the vanishing set of a polynomial system. This problem plays an important role…