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Most classical results in circuit complexity theory concern circuits over the Boolean domain. Besides their simplicity and the ease of comparing different languages, the actual architecture of computers is also an important motivating…
The purpose of this paper is to explore the question "to what extent could we produce formal, machine-verifiable, proofs in real algebraic geometry?" The question has been asked before but as yet the leading algorithms for answering such…
Computation nowadays is becoming inherently concurrent, either because of characteristics of the hardware (with multicore processors becoming omnipresent) or due to the ubiquitous presence of distributed systems (incarnated in the…
Software architecture related issues are important for robotic systems. Architecture centric development and evolution of software for robotic systems has been attracting researchers attention for more than two decades. The objective of…
The increasingly concurrent and parallel landscape of hardware and software infrastructures demands the exploration and understanding of a wide variety of foundational and practical ideas. The International Workshop on Programming Language…
This paper provides an overview of the main ideas driving the bootstrap algebraic multigrid methodology, including compatible relaxation and algebraic distances for defining effective coarsening strategies, the least squares method for…
To synthesize Maxwell optics systems, the mathematical apparatus of tensor and vector analysis is generally employed. This mathematical apparatus implies executing a great number of simple stereotyped operations, which are adequately…
We survey results in algebraic complexity theory, focusing on matrix multiplication. Our goals are (i.) to show how open questions in algebraic complexity theory are naturally posed as questions in geometry and representation theory, (ii.)…
I discuss a seemingly unlikely confluence of topics in algebra, numerical computation, and computer vision. The motivating problem is that of solving multiples instances of a parametric family of systems of algebraic (polynomial or rational…
This is a survey article, based on the author's lectures in the 2015 Current developments in Mathematics meeting; published in "Current developments in Mathematics". Version 2, references corrected and added.
The report is devoted to the current state of the MathPartner computer algebra web project. We discuss the main directions of development of the project and give several examples of using it to solve selected problems.
The paper provides an overview of core functionalities that digital democracy software needs to provide in order to support democratic deliberative processes at scale. Developing these functionalities poses novel computational challenges…
With the announcement that the Aurora Supercomputer will be composed of general purpose Intel CPUs complemented by discrete high performance Intel GPUs, and the deployment of the oneAPI ecosystem, Intel has committed to enter the arena of…
The paper presents AMGCL -- an opensource C++ library implementing the algebraic multigrid method (AMG) for solution of large sparse linear systems of equations, usually arising from discretization of partial differential equations on an…
We present a new open source C library \texttt{msolve} dedicated to solving multivariate polynomial systems of dimension zero through computer algebra methods. The core algorithmic framework of \texttt{msolve} relies on Gr\''obner bases and…
Today's distributed and pervasive computing addresses large-scale cyber-physical ecosystems, characterised by dense and large networks of devices capable of computation, communication and interaction with the environment and people. While…
We analyze a dataset of 51 current (2019-2020) Distributed Systems syllabi from top Computer Science programs, focusing on finding the prevalence and context in which topics related to performance are being taught in these courses. We also…
The theme of this book chapter is to discuss algorithms for identifying and reconstructing groups and clusters of galaxies out of the general galaxy distribution. I review the progress of detection techniques through time, from the very…
These are expanded lecture notes of a series of expository talks surveying basic aspects of group cohomology and homology. They were written for someone who has had a first course in graduate algebra but no background in cohomology. You…
In this book, there are five chapters: Systems of Linear Equations, Vector Spaces, Homogeneous Systems, Characteristic Equation of Matrix, and Matrix Dot Product. It has also exercises at the end of each chapter above to let students…