Related papers: On the use of algebraic programming in the general…
Categories and categorical structures are increasingly recognized as useful abstractions for modeling in science and engineering. To uniformly implement category-theoretic mathematical models in software, we introduce GATlab, a…
There are many complementary approaches to the construction of solutions to the field equations of general relativity. Among these, numerical approximation offers the only possibility to compute a variety of dynamical spacetimes, and so has…
This note is based on the plenary talk given by the second author at MACIS 2015, the Sixth International Conference on Mathematical Aspects of Computer and Information Sciences. Motivated by some of the work done within the Priority…
These notes are for the author's lectures, "Integral Reduction and Applied Algebraic Geometry Techniques" in the School and Workshop on Amplitudes in Beijing 2016. I introduce the applications of algebraic geometry methods on multi-loop…
This review is an up-to-date account of the use of numerical relativity to study dynamical, strong-gravity environments in a cosmological context. First, we provide a gentle introduction into the use of numerical relativity in solving…
In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…
This review presents an overview of various kinds of models -- physical, abstract, mathematical, visual -- that can be used to present the concepts and applications of Einstein's general theory of relativity at the level of undergraduate…
Numerical relativity is an essential tool for solving Einstein's equations of general relativity for dynamical systems characterized by high velocities and strong gravitational fields. The implementation of new algorithms that can solve…
This is an English translation of the Italian version of an encyclopedia chapter that appeared in the Italian Encyclopedia of the Physical Sciences, edited by Bruno Bertotti (1994). Following requests from colleagues we have decided to make…
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…
The universal object oriented languages made programming more simple and efficient. In the article is considered possibilities of using similar methods in computer algebra. A clear and powerful universal language is useful if particular…
Computer Algebra systems are widely spread because of some of their remarkable features such as their ease of use and performance. Nonetheless, this focus on performance sometimes leads to unwanted consequences: algorithms and computations…
The purpose of this article is to draw attention to some fundamental issues in General Relativity. It is argued that these deep issues cannot be resolved within the standard approach to general relativity that considers {\em every} solution…
I summarize here the logic that leads us to a program for the Theory of the Total Field in Einstein's sense. The purpose is to show that this theory is a logical culmination of the developments of (fundamental) physical concepts and, hence,…
Algebraic quantum field theory is an approach to relativistic quantum physics, notably the theory of elementary particles, which complements other modern developments in this field. It is particularly powerful for structural analysis but…
10 years ago or so Bill Helton introduced me to some mathematical problems arising from semidefinite programming. This paper is a partial account of what was and what is happening with one of these problems, including many open questions…
We will follow the growth of gravitational theory in Germany from 1915 to the 1990s, i.e., relativistic theories of gravitation, mainly Einstein's, as a branch of physics in the sense of social, more precisely institutional history. As…
This paper presents an algebraic theory of instruction sequences with instructions for Turing tapes as basic instructions, the behaviours produced by the instruction sequences concerned under execution, and the interaction between such…
The subject of this work is quantum predicative programming -- the study of developing of programs intended for execution on a quantum computer. We look at programming in the context of formal methods of program development, or programming…
In this Book we argue that the fruitful interaction of computer vision and belief calculus is capable of stimulating significant advances in both fields. From a methodological point of view, novel theoretical results concerning the…