Related papers: Hilbert++ Manual
This is brief and hopefully friendly, with basic notions, a few different perspectives, and references with more information in various directions.
This is a short tutorial about different software design methodologies.
This article is a semitutorial-style survey of computability logic. An extended online version of it is maintained at http://www.csc.villanova.edu/~japaridz/CL/ .
This is a preliminary version of the Chapter 1 of a book "Computable Integrability"
\noindent Model building in $\mathsf{SO(10)}$, which is the leading grand unification framework, often involves large Higgs representations and their couplings. Explicit calculations of such couplings is a multi-step process that involves…
As the field of Quantum Computing continues to grow, so too has the general public's interest in testing some of the publicly available quantum computers. However, many might find learning all of the supplementary information that goes into…
Software engineering education and training have obstacles caused by a lack of basic knowledge about a process of program execution. The article is devoted to the development of special tools that help to visualize the process. We analyze…
Writing complex computer programs to study scientific problems requires careful planning and an in-depth knowledge of programming languages and tools. In this chapter the importance of using the right tool for the right problem is…
In this paper, we will introduce the concept of biframes for Hilbert $ C^{\ast}- $modules produced by a pair of sequences, and we present various examples of biframes. Then, we examine the characteristics of biframes from the viewpoint of…
The present report, has been inspired by the need of the author and its colleagues to understand the underlying theory of Wirtinger's Calculus and to further extend it to include the kernel case. The aim of the present manuscript is…
These notes outline a formal method for program verification of numerical computation. It forms the basis of the software package VPC in its initial phase of development. Much of the style of presentation is in the form of notes that…
This document aims to be a self-contained, mathematically precise overview of transformer architectures and algorithms (*not* results). It covers what transformers are, how they are trained, what they are used for, their key architectural…
A remarkable new definition of a self-delimiting universal Turing machine is presented that is easy to program and runs very quickly. This provides a new foundation for algorithmic information theory. This new universal Turing machine is…
A very elementary introduction to quantum algebras is presented and a few examples of their physical applications are mentioned.
These are general notes on tensor calculus which can be used as a reference for an introductory course on tensor algebra and calculus. A basic knowledge of calculus and linear algebra with some commonly used mathematical terminology is…
The Lean mathematical library mathlib is developed by a community of users with very different backgrounds and levels of experience. To lower the barrier of entry for contributors and to lessen the burden of reviewing contributions, we have…
We introduce an open-source toolkit for neural machine translation (NMT) to support research into model architectures, feature representations, and source modalities, while maintaining competitive performance, modularity and reasonable…
We provide a simple and efficient algorithm for computing the Euclidean projection of a point onto the capped simplex---a simplex with an additional uniform bound on each coordinate---together with an elementary proof. Both the MATLAB and…
In article the basic principles put in a basis of algorithmicallysoftware of hypercomplex number calculations, structure of a software, structure of functional subsystems are considered. The most important procedures included in subsystems…
We present the Flowgen tool, which generates flowcharts from annotated C++ source code. The tool generates a set of interconnected high-level UML activity diagrams, one for each function or method in the C++ sources. It provides a simple…