The Mathematics Of Finite Networks
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The Mathematics Of Finite Networks
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Author : Michael Rudolph
language : en
Publisher:
Release Date : 2022
The Mathematics Of Finite Networks written by Michael Rudolph and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with COMPUTERS categories.
"Since the early eighteenth century, the theory of networks and graphs has matured into an indispensable tool for describing countless real-world phenomena. However, the study of large-scale features of a network often requires unrealistic limits, such as taking the network size to infinity or assuming a continuum. These asymptotic and analytic approaches can significantly diverge from real or simulated networks when applied at the finite scales of real-world applications. This book offers an approach to overcoming these limitations by introducing operator graph theory, an exact, non-asymptotic set of tools combining graph theory with operator calculus. The book is intended for mathematicians, physicists, and other scientists interested in discrete finite systems and their graph-theoretical description, and in delineating the abstract algebraic structures that characterise such systems. All the necessary background on graph theory and operator calculus is included for readers to understand the potential applications of operator graph theory"--
Network Algebra
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Author : Gheorghe Stefanescu
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-04-12
Network Algebra written by Gheorghe Stefanescu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-12 with Computers categories.
Network algebra considers the algebraic study of networks and their behavior. It approaches the models in a sharp and simple manner. This book takes an integrated view of a broad range of applications, varying from concrete hardware-oriented models to high-level software-oriented models.
Finite Graphs And Networks
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Author : Robert G. Busacker
language : en
Publisher:
Release Date : 1965
Finite Graphs And Networks written by Robert G. Busacker and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Mathematics categories.
The Mathematics Of Networks
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Author : Stefan Andrus Burr
language : en
Publisher: American Mathematical Soc.
Release Date : 1982
The Mathematics Of Networks written by Stefan Andrus Burr and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Mathematics categories.
The theory of networks is a very lively one, both in terms of developments in the theory itself and of the variety of its applications. This book, based on the 1981 AMS Short Course on the Mathematics of Networks, introduces most of the basic ideas of network theory and develops some of these ideas considerably.
Mathematical Foundations Of Computer Networking
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Author : Srinivasan Keshav
language : en
Publisher: Addison-Wesley
Release Date : 2012-04-20
Mathematical Foundations Of Computer Networking written by Srinivasan Keshav and has been published by Addison-Wesley this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-20 with Computers categories.
“To design future networks that are worthy of society’s trust, we must put the ‘discipline’ of computer networking on a much stronger foundation. This book rises above the considerable minutiae of today’s networking technologies to emphasize the long-standing mathematical underpinnings of the field.” –Professor Jennifer Rexford, Department of Computer Science, Princeton University “This book is exactly the one I have been waiting for the last couple of years. Recently, I decided most students were already very familiar with the way the net works but were not being taught the fundamentals–the math. This book contains the knowledge for people who will create and understand future communications systems." –Professor Jon Crowcroft, The Computer Laboratory, University of Cambridge The Essential Mathematical Principles Required to Design, Implement, or Evaluate Advanced Computer Networks Students, researchers, and professionals in computer networking require a firm conceptual understanding of its foundations. Mathematical Foundations of Computer Networking provides an intuitive yet rigorous introduction to these essential mathematical principles and techniques. Assuming a basic grasp of calculus, this book offers sufficient detail to serve as the only reference many readers will need. Each concept is described in four ways: intuitively; using appropriate mathematical notation; with a numerical example carefully chosen for its relevance to networking; and with a numerical exercise for the reader. The first part of the text presents basic concepts, and the second part introduces four theories in a progression that has been designed to gradually deepen readers’ understanding. Within each part, chapters are as self-contained as possible. The first part covers probability; statistics; linear algebra; optimization; and signals, systems, and transforms. Topics range from Bayesian networks to hypothesis testing, and eigenvalue computation to Fourier transforms. These preliminary chapters establish a basis for the four theories covered in the second part of the book: queueing theory, game theory, control theory, and information theory. The second part also demonstrates how mathematical concepts can be applied to issues such as contention for limited resources, and the optimization of network responsiveness, stability, and throughput.
The Mathematics Of Networks Of Linear Systems
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Author : Paul A. Fuhrmann
language : en
Publisher: Springer
Release Date : 2015-05-26
The Mathematics Of Networks Of Linear Systems written by Paul A. Fuhrmann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-26 with Mathematics categories.
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.
Discrete Mathematics Of Neural Networks
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Author : Martin Anthony
language : en
Publisher: SIAM
Release Date : 2001-01-01
Discrete Mathematics Of Neural Networks written by Martin Anthony and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Computers categories.
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.
Theoretical Numerical Analysis
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Author : Kendall Atkinson
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-18
Theoretical Numerical Analysis written by Kendall Atkinson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-18 with Mathematics categories.
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the clas 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). The development of new courses is a natural consequence of a high level of 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 text book series is to meet the current and future needs of these advances and 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 Math ematical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs.
Inverse Problems Regularization Methods And Related Topics
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Author : Sergei V. Pereverzyev
language : en
Publisher: Springer Nature
Release Date : 2025-03-31
Inverse Problems Regularization Methods And Related Topics written by Sergei V. Pereverzyev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-31 with Mathematics categories.
This book features a thoughtfully curated collection of research contributions spanning regularization theory, integral equations, learning theory, and matrix and operator theory. These contributions were presented in honor of Prof. M. Thamban Nair on his 65th birthday during the International Conference on Analysis, Inverse Problems, and Applications, which took place at the IIT Madras in Chennai, India, from July 18–21, 2022. The book is a valuable resource for graduate students, engineers, scientists, and researchers looking to advance their work in the development of innovative regularization algorithms. It comprises 14 chapters contributed by esteemed experts and emerging researchers.
Graphs And Networks
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Author : Armen H. Zemanian
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Graphs And Networks written by Armen H. Zemanian and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Scientia Gratiii Scientiae It is now thirteen years since the first book that discusses transfinite graphs and elec trical networks appeared [50]. This was followed by two more books [51] and [54] which compiled results from an ongoing research effort on that subject. Why then is a fourth book, this one, being offered? Simply because still more has been achieved beyond that appearing in those prior books. An exposition of these more recent re sults is the purpose of this book. The idea of transfiniteness for graphs and networks appeared as virgin research territory about seventeen years ago. Notwithstanding the progress that has since been achieved, much more remains to be done-or so it appears. Many conclusions con cerning conventionally infinite graphs and networks can be reformulated as open problems for transfinite graphs and networks. Furthermore, questions peculiar to transfinite concepts for graphs and networks can be suggested. Indeed, these two considerations have inspired the new results displayed herein.