Related papers: The basic principles and the structure and algorit…
This lecture aims at providing a user's perspective on the main concepts used nowadays for the implementation of numerical algorithm on common computing architecture. In particular, the concepts and applications of Central Processing Units…
The described works have been carried out in the framework of a mid-term study initiated by the Centre Electronique de l'Armement and led by ADERSA, a French company of research under contract. The aim was to study the techniques of regular…
In this text we develop the formalism of products and powers of linear codes under componentwise multiplication. As an expanded version of the author's talk at AGCT-14, focus is put mostly on basic properties and descriptive statements that…
We describe a cognitive architecture intended to solve a wide range of problems based on the five identified principles of brain activity, with their implementation in three subsystems: logical-probabilistic inference, probabilistic formal…
Here we address the challenge of profiling causal properties and tracking the transformation of chemical compounds from an algorithmic perspective. We explore the potential of applying a computational interventional calculus based on the…
This article provides a survey of circuit complexity bounds for basic boolean transforms exploited in digital circuit design and efficient methods for synthesizing such circuits. The exposition covers structurally simple functions and…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
We expose (without proofs) a unified computational approach to integrable structures (including recursion, Hamiltonian, and symplectic operators) based on geometrical theory of partial differential equations. We adopt a coordinate based…
This article covers the problem of processing of Big Data that describe process of complex networks and network systems operation. It also introduces the notion of hierarchical network systems combination into associations and conglomerates…
The paper discusses fundamental problems in mathematical description of social systems based on physical concepts, with so-called statistical social systems being the main subject of consideration. Basic properties of human beings and human…
This book is a graduate-level introduction to probabilistic programming. It not only provides a thorough background for anyone wishing to use a probabilistic programming system, but also introduces the techniques needed to design and build…
This paper establishes a general framework for describing hybrid dynamical systems which is particularly suitable for numerical simulation. In this context, the data structures used to describe the sets and functions which comprise the…
We investigate the computational properties of basic mathematical notions pertaining to $\mathbb{R}\rightarrow \mathbb{R}$-functions and subsets of $\mathbb{R}$, like finiteness, countability, (absolute) continuity, bounded variation,…
A simple algorithm with quasi-linear time complexity and linear space complexity for the evaluation of the hypergeometric series with rational coefficients is constructed. It is shown that this algorithm is suitable in practical informatics…
High Performance Distributed Computing is essential to boost scientific progress in many areas of science and to efficiently deploy a number of complex scientific applications. These applications have different characteristics that require…
We discuss a formal system of mathematics. We use it to construct the natural numbers.
They run our lives, if you believe the hype in the news, but there is no precise definition of "algorithms" which is generally accepted by the mathematicians, logicians and computer scientists who create and study them. My main aims here…
The problem of "what is 'system'?" is in the very foundations of modern quantum mechanics. Here, we point out the interest in this topic in the information-theoretic context. E.g., we point out the possibility to manipulate a pair of…
The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…
The main goal of this research is to develop the concepts of a revolutionary processor system called Functional Processor System. The fairly novel work carried out in this proposal concentrates on decoding of function pipelines and…