Related papers: Semi-Centennial REDUCE
We describe the architecture of an evolving algebra partial evaluator, a program which specializes an evolving algebra with respect to a portion of its input. We discuss the particular analysis, specialization, and optimization techniques…
We propose a functional description of rewriting systems where reduction rules are represented by linear maps called reduction operators. We show that reduction operators admit a lattice structure. Using this structure we define the notion…
We study vertex algebras and their modules associated with possibly degenerate even lattices, using an approach somewhat different from others. Several known results are recovered and a number of new results are obtained. We also study…
There have been several modifications of how basic calculus has been taught, but very few of these modifications have considered the computational tools available at our disposal. Here, we present a few tools that are easy to develop and…
Owing to the computational complexity of electronic structure algorithms running on classical digital computers, the range of molecular systems amenable to simulation remains tightly circumscribed even after many decades of work. Quantum…
In this paper we study the lattice of restricted subalgebras of a restricted Lie algebra. In particular, we consider those algebras in which this lattice is dually atomistic, lower or upper semimodular, or in which every restricted…
For a reduced one-dimensional complete local $k$-algebra $R$, Huneke et al. (Res. Math. Sci., 8(4), paper no. 60, 2021) introduced an important invariant, the reduced type. In this article, we study the extremal behavior of reduced type of…
Deep Learning models enjoy considerable success in Natural Language Processing. While deep architectures produce useful representations that lead to improvements in various tasks, they are often difficult to interpret. This makes the…
A method of prediction is presented to aid compression of sequences of complex-valued samples. The focus is on using prediction to reduce the average magnitude of residual values after prediction (not on the subsequent compression of the…
We consider cylindrical algebraic decompositions (CADs) as a tool for representing semi-algebraic subsets of $\mathbb{R}^n$. In this framework, a CAD $\mathscr{C}$ is adapted to a given set $S$ if $S$ is a union of cells of $\mathscr{C}$.…
Degradation data are considered for assessing reliability in highly reliable systems. The usual assumption is that degradation units come from a homogeneous population. But in presence of high variability in the manufacturing process, this…
In this paper we describe an algorithm to determine the vectors normal to a space-time V4 embedded in a pseudo-Euclidean manifold M4+n. An application of this algorithm is given considering the Schwarzchild space-time geometry embedded in a…
This set of notes re-proves known results on weighted automata (over a field, also known as multiplicity automata). The text offers a unified view on theorems and proofs that have appeared in the literature over decades and were written in…
I describe a method, particularly suitable to implementation by computer algebra, for the derivation of low-dimensional models of dynamical systems. The method is systematic and is based upon centre manifold theory. Computer code for the…
Symmetries and reductions of some algebraic equations are considered. Transformations that preserve the form of several algebraic equations, as well as transformations that reduce the degree of these equations, are described. Illustrative…
The Reduced Basis (RB) method is a well established method for the model order reduction of problems formulated as parametrized partial differential equations. One crucial requirement for the application of RB schemes is the availability of…
A wardian calculus of sequences started almost seventy years ago constitutes the general scheme for extensions of the classical umbral operator calculus considered by many afterwards . At the same time this calculus is an example of the…
In the last decades, great achievements have been made in the development of computing machines. However, due to exponential growth of transistor density and in particular due to tremendously increasing power consumption, researchers expect…
This book chapter describes a novel approach to training machine learning systems by means of a hybrid computer setup i.e. a digital computer tightly coupled with an analog computer. As an example a reinforcement learning system is trained…
We give another proof that a reductive algebraic group is geometrically reductive. We show that a quotient of the semi-stable locus (by a linear action of a reductive algebraic group on a projective scheme) exists, and from this Haboush's…