Author : Michael Rudolph
Publisher : Cambridge University Press
Page : 355 pages
File Size : 42,92 MB
Release : 2022-05-12
Category : Computers
ISBN : 1107134439
Offers an exact, non-asymptotic approach to studying large-scale features of finite networks that arise in real applications.
Author : Dieter Jungnickel
Publisher : Springer Science & Business Media
Page : 597 pages
File Size : 31,45 MB
Release : 2013-06-29
Category : Mathematics
ISBN : 3662038226
Revised throughout Includes new chapters on the network simplex algorithm and a section on the five color theorem Recent developments are discussed
Author : Paul Slepian
Publisher : Springer Science & Business Media
Page : 205 pages
File Size : 11,2 MB
Release : 2012-12-06
Category : Science
ISBN : 364287424X
In this book we attempt to develop the fundamental results of resistive network analysis, based upon a sound mathematical structure. The axioms upon which our development is based are Ohm's Law, Kirchhoff's Voltage Law, and Kirchhoff's Current Law. In order to state these axioms precisely, and use them in the development of our network analysis, an elaborate mathematical structure is introduced, involving concepts of graph theory, linear algebra, and one dimensional algebraic topology. The graph theory and one dimensional algebraic topology used are developed from first principles; the reader needs no background in these subjects. However, we do assume that the reader has some familiarity with elementary linear algebra. It is now stylish to teach elementary linear algebra at the sophomore college level, and we feel that the require ment that the reader should be familiar with elementary linear algebra is no more demanding than the usual requirement in most electrical engineering texts that the reader should be familiar with calculus. In this book, however, no calculus is needed. Although no formal training in circuit theory is needed for an understanding of the book, such experience would certainly help the reader by presenting him with familiar examples relevant to the mathematical abstractions introduced. It is our intention in this book to exhibit the effect of the topological properties of the network upon the branch voltages and branch currents, the objects of interest in network analysis.
Author : Alan Gibbons
Publisher : Cambridge University Press
Page : 280 pages
File Size : 37,28 MB
Release : 1985-06-27
Category : Computers
ISBN : 9780521288811
An introduction to pure and applied graph theory with an emphasis on algorithms and their complexity.
Author : Paul A. Fuhrmann
Publisher : Springer
Page : 670 pages
File Size : 27,30 MB
Release : 2015-05-26
Category : Mathematics
ISBN : 3319166468
This book provides the mathematical foundations of networks of linear control systems, developed from an algebraic systems theory perspective. This includes a thorough treatment of questions of controllability, observability, realization theory, as well as feedback control and observer theory. The potential of networks for linear systems in controlling large-scale networks of interconnected dynamical systems could provide insight into a diversity of scientific and technological disciplines. The scope of the book is quite extensive, ranging from introductory material to advanced topics of current research, making it a suitable reference for graduate students and researchers in the field of networks of linear systems. Part I can be used as the basis for a first course in Algebraic System Theory, while Part II serves for a second, advanced, course on linear systems. Finally, Part III, which is largely independent of the previous parts, is ideally suited for advanced research seminars aimed at preparing graduate students for independent research. “Mathematics of Networks of Linear Systems” contains a large number of exercises and examples throughout the text making it suitable for graduate courses in the area.
Author : Bernd Heinrich
Publisher : Walter de Gruyter GmbH & Co KG
Page : 212 pages
File Size : 41,22 MB
Release : 1987-12-31
Category : Mathematics
ISBN : 311272089X
No detailed description available for "Finite Difference Methods on Irregular Networks".
Author : Pal Domosi
Publisher : SIAM
Page : 270 pages
File Size : 18,93 MB
Release : 2005-01-01
Category : Mathematics
ISBN : 9780898718492
Investigates automata networks as algebraic structures and develops their theory in line with other algebraic theories, such as those of semigroups, groups, rings, and fields. The authors also investigate automata networks as products of automata, that is, as compositions of automata obtained by cascading without feedback or with feedback of various restricted types or, most generally, with the feedback dependencies controlled by an arbitrary directed graph. They survey and extend the fundamental results in regard to automata networks, including the main decomposition theorems of Letichevsky, of Krohn and Rhodes, and of others.
Author : Kendall Atkinson
Publisher : Springer Science & Business Media
Page : 583 pages
File Size : 21,32 MB
Release : 2007-06-07
Category : Mathematics
ISBN : 0387287698
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scienti?c disciplines and a resurgence of interest in the modern as well as the cl- sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). Thedevelopmentofnewcoursesisanaturalconsequenceofahighlevelof excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Ma- ematical Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs.
Author : Stephen W. Ellacott
Publisher : Springer Science & Business Media
Page : 423 pages
File Size : 26,98 MB
Release : 2012-12-06
Category : Computers
ISBN : 1461560993
This volume of research papers comprises the proceedings of the first International Conference on Mathematics of Neural Networks and Applications (MANNA), which was held at Lady Margaret Hall, Oxford from July 3rd to 7th, 1995 and attended by 116 people. The meeting was strongly supported and, in addition to a stimulating academic programme, it featured a delightful venue, excellent food and accommo dation, a full social programme and fine weather - all of which made for a very enjoyable week. This was the first meeting with this title and it was run under the auspices of the Universities of Huddersfield and Brighton, with sponsorship from the US Air Force (European Office of Aerospace Research and Development) and the London Math ematical Society. This enabled a very interesting and wide-ranging conference pro gramme to be offered. We sincerely thank all these organisations, USAF-EOARD, LMS, and Universities of Huddersfield and Brighton for their invaluable support. The conference organisers were John Mason (Huddersfield) and Steve Ellacott (Brighton), supported by a programme committee consisting of Nigel Allinson (UMIST), Norman Biggs (London School of Economics), Chris Bishop (Aston), David Lowe (Aston), Patrick Parks (Oxford), John Taylor (King's College, Lon don) and Kevin Warwick (Reading). The local organiser from Huddersfield was Ros Hawkins, who took responsibility for much of the administration with great efficiency and energy. The Lady Margaret Hall organisation was led by their bursar, Jeanette Griffiths, who ensured that the week was very smoothly run.
Author : Martin Anthony
Publisher : SIAM
Page : 137 pages
File Size : 47,77 MB
Release : 2001-01-01
Category : Computers
ISBN : 089871480X
This concise, readable book provides a sampling of the very large, active, and expanding field of artificial neural network theory. It considers select areas of discrete mathematics linking combinatorics and the theory of the simplest types of artificial neural networks. Neural networks have emerged as a key technology in many fields of application, and an understanding of the theories concerning what such systems can and cannot do is essential. Some classical results are presented with accessible proofs, together with some more recent perspectives, such as those obtained by considering decision lists. In addition, probabilistic models of neural network learning are discussed. Graph theory, some partially ordered set theory, computational complexity, and discrete probability are among the mathematical topics involved. Pointers to further reading and an extensive bibliography make this book a good starting point for research in discrete mathematics and neural networks.
