Related papers: Fundamentals of Computing
The field of computational statistics refers to statistical methods or tools that are computationally intensive. Due to the recent advances in computing power some of these methods have become prominent and central to modern data analysis.…
These lecture notes, suitable for a two-semester introductory course or self-study, offer an elementary and self-contained exposition of the basic tools and concepts that are encountered in practical computations in perturbative thermal…
Quantum computing is a new computational paradigm with the potential to solve certain computationally challenging problems much faster than traditional approaches. Civil engineering encompasses many computationally challenging problems,…
As quantum computers become available to the general public, the need has arisen to train a cohort of quantum programmers, many of whom have been developing classical computer programs for most of their careers. While currently available…
The article is devoted to introduce and investigation of new numeral systems. These representations are generalizations of classical representations of real numbers. The main properties of investigating representations are described. The…
This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…
People are witnessing quantum computing revolutions nowadays. Progress in the number of qubits, coherence times and gate fidelities are happening. Although quantum error correction era has not arrived, the research and development of…
Quantum mechanics, the fundamental theory that governs the behaviour of matter and energy at microscopic scales, forms the foundation of quantum computing and quantum information science. As quantum technologies progress, software engineers…
These notes were compiled as lecture notes for a course developed and taught at the University of the Southern California. They should be accessible to a typical engineering graduate student with a strong background in Applied Mathematics.…
This paper shows that, even at the most basic level, the parallel, countable branching and uncountable branching recurrences of Computability Logic (see http://www.cis.upenn.edu/~giorgi/cl.html) validate different principles.
Functionals are an important research subject in Mathematics and Computer Science as well as a challenge in Information Technologies where the current programming paradigm states that only symbolic computations are possible on higher order…
The fields of computing and biology have begun to cross paths in new ways. In this paper a review of the current research in biological computing is presented. Fundamental concepts are introduced and these foundational elements are explored…
Graphs are common mathematical structures that are visual and intuitive. They constitute a natural and seamless way for system modelling in science, engineering and beyond, including computer science, biology, business process modelling,…
Can AI solve all math? What do we actually mean by doing mathematics? How do we communicate mathematics? What is mathematics beyond problem solving? This essay is my attempt to answer these questions.
Quantum computation offers a promising new kind of information processing, where the non-classical features of quantum mechanics can be harnessed and exploited. A number of models of quantum computation exist, including the now well-studied…
We present numerical techniques based on generalized functions adapted to nonlinear calculations. They concern main numerical engineering problems ruled by-or issued from-nonlinear equations of continuum mechanics. The aim of this text is…
One of the fundamental results in computability is the existence of well-defined functions that cannot be computed. In this paper we study the effects of data representation on computability; we show that, while for each possible way of…
Here practical aspects of conducting research via computer simulations are discussed. The following issues are addressed: software engineering, object-oriented software development, programming style, macros, make files, scripts, libraries,…
Neural network-based machine learning is capable of approximating functions in very high dimension with unprecedented efficiency and accuracy. This has opened up many exciting new possibilities, not just in traditional areas of artificial…
The paper provides an overview of core functionalities that digital democracy software needs to provide in order to support democratic deliberative processes at scale. Developing these functionalities poses novel computational challenges…