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Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…
With recent dramatic increases in AI system capabilities, there has been growing interest in utilizing machine learning for reasoning-heavy, quantitative tasks, particularly mathematics. While there are many resources capturing mathematics…
Computers are a very important part of our lives and the major reason why they have been such a success is because of the excellent graphical operating systems that run on these powerful machines. As the computer hardware is becoming more…
The geometry of atomic arrangement underpins the structural understanding of molecules in many fields. However, no general framework of mathematical/computational theory for the geometry of atomic arrangement exists. Here we present…
Multi-access edge computing (MEC) is capable of meeting the challenging requirements of next-generation networks, e.g., 6G, as a benefit of providing computing and caching capabilities in the close proximity of the users. However, the…
The main purpose of this book is to propose an introduction to the modern tools of algebraic complexity. To remain as simple as possible while providing meaningful examples, we chose to focus on effective linear algebra; this is certainly…
The declared goal of this paper is to fill this gap: "... cognitive systems research needs questions or challenges that define progress. The challenges are not (yet more) predictions of the future, but a guideline to what are the aims and…
Open Science aims to foster openness and collaboration in research, leading to more significant scientific and social impact. However, practicing Open Science comes with several challenges and is currently not properly rewarded. In this…
We give an account of the current state of the approch to quantum field theory via Hopf algebras and Hochschild cohomology. We emphasize the versatility and mathematical foundation of this algebraic structure, and collect algebraic…
Graph database systems are increasingly adapted for storing and processing heterogeneous network-like datasets. However, due to the novelty of such systems, no standard data model or query language has yet emerged. Consequently, migrating…
Compositionality is a key property for dealing with complexity, which has been studied from many points of view in diverse fields. Particularly, the composition of individual computations (or programs) has been widely studied almost since…
Applied research in graph algorithms and combinatorial structures needs comprehensive and versatile software libraries. However, the design and the implementation of flexible libraries are challenging activities. Among the other problems…
The engineering of machine learning systems is still a nascent field; relying on a seemingly daunting collection of quickly evolving tools and best practices. It is our hope that this guidebook will serve as a useful resource for machine…
We describe our ongoing project of formalization of algebraic methods for geometry theorem proving (Wu's method and the Groebner bases method), their implementation and integration in educational tools. The project includes formal…
In computer graphics (CG) education, the challenge of finding modern, versatile tools is significant, particularly when integrating both legacy and advanced technologies. Traditional frameworks, often reliant on solid, yet outdated APIs…
This PhD deals with the notion of pseudo algebraically closed (PAC) extensions of fields. It develops a group-theoretic machinery, based on a generalization of embedding problems, to study these extensions. Perhaps the main result is that…
Computer algebra systems are a great help for mathematical research but sometimes unexpected errors in the software can also badly affect it. As an example, we show how we have detected an error of Mathematica computing determinants of…
We report on our experiences exploring state of the art Groebner basis computation. We investigate signature based algorithms in detail. We also introduce new practical data structures and computational techniques for use in both signature…
Geometric programming (GP) provides a power tool for solving a variety of optimization problems. In the real world, many applications of geometric programming (GP) are engineering design problems in which some of the problem parameters are…
This volume contains the proceedings of the Second International Workshop on Developments in Implicit Computational complExity (DICE 2011), which took place on April 2-3 2011 in Saarbruecken, Germany, as a satellite event of the Joint…