The Mathematics Of Networks
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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.
The Mathematics Of Finite Networks
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Author : Michael Rudolph
language : en
Publisher: Cambridge University Press
Release Date : 2022-05-12
The Mathematics Of Finite Networks written by Michael Rudolph and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-12 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.
The Mathematics Of Networks Of Linear Systems
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Author : Paul A. Fuhrmann
language : en
Publisher:
Release Date : 2015
The Mathematics Of Networks Of Linear Systems written by Paul A. Fuhrmann and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with 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.
Mathematical Aspects Of Network Routing Optimization
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Author : Carlos A.S. Oliveira
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-08-26
Mathematical Aspects Of Network Routing Optimization written by Carlos A.S. Oliveira 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 2011-08-26 with Mathematics categories.
Before the appearance of broadband links and wireless systems, networks have been used to connect people in new ways. Now, the modern world is connected through large-scale, computational networked systems such as the Internet. Because of the ever-advancing technology of networking, efficient algorithms have become increasingly necessary to solve some of the problems developing in this area. "Mathematical Aspects of Network Routing Optimization" focuses on computational issues arising from the process of optimizing network routes, such as quality of the resulting links and their reliability. Algorithms are a cornerstone for the understanding of the protocols underlying multicast routing. The main objective in the text is to derive efficient algorithms, with or without guarantee of approximation. Notes have been provided for basic topics such as graph theory and linear programming to assist those who are not fully acquainted with the mathematical topics presented throughout the book. "Mathematical Aspects of Network Routing Optimization" provides a thorough introduction to the subject of algorithms for network routing, and focuses especially on multicast and wireless ad hoc systems. This book is designed for graduate students, researchers, and professionals interested in understanding the algorithmic and mathematical ideas behind routing in computer networks. It is suitable for advanced undergraduate students, graduate students, and researchers in the area of network algorithms.
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.
Discrete And Continuous Models In The Theory Of Networks
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Author : Fatihcan M. Atay
language : en
Publisher: Springer Nature
Release Date : 2020-09-03
Discrete And Continuous Models In The Theory Of Networks written by Fatihcan M. Atay and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-03 with Mathematics categories.
This book contains contributions from the participants of the research group hosted by the ZiF - Center for Interdisciplinary Research at the University of Bielefeld during the period 2013-2017 as well as from the conclusive conference organized at Bielefeld in December 2017. The contributions consist of original research papers: they mirror the scientific developments fostered by this research program or the state-of-the-art results presented during the conclusive conference. The volume covers current research in the areas of operator theory and dynamical systems on networks and their applications, indicating possible future directions. The book will be interesting to researchers focusing on the mathematical theory of networks; it is unique as, for the first time, continuous network models - a subject that has been blooming in the last twenty years - are studied alongside more classical and discrete ones. Thus, instead of two different worlds often growing independently without much intercommunication, a new path is set, breaking with the tradition. The fruitful and beneficial exchange of ideas and results of both communities is reflected in this book.
Graph Spectra For Complex Networks
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Author : Piet van Mieghem
language : en
Publisher: Cambridge University Press
Release Date : 2010-12-02
Graph Spectra For Complex Networks written by Piet van Mieghem and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-02 with Technology & Engineering categories.
Analyzing the behavior of complex networks is an important element in the design of new man-made structures such as communication systems and biologically engineered molecules. Because any complex network can be represented by a graph, and therefore in turn by a matrix, graph theory has become a powerful tool in the investigation of network performance. This self-contained 2010 book provides a concise introduction to the theory of graph spectra and its applications to the study of complex networks. Covering a range of types of graphs and topics important to the analysis of complex systems, this guide provides the mathematical foundation needed to understand and apply spectral insight to real-world systems. In particular, the general properties of both the adjacency and Laplacian spectrum of graphs are derived and applied to complex networks. An ideal resource for researchers and students in communications networking as well as in physics and mathematics.
Networks
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Author : Mark Newman
language : en
Publisher: Oxford University Press
Release Date : 2010-03-25
Networks written by Mark Newman and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-03-25 with Computers categories.
This book brings together advances in mathematics, physics, computer science, biology and social network analysis to present a comprehensive picture of the scientific study of networks. The book includes discussion of computer networks, social networks, biological networks, and others, and an introduction to the mathematics of network theory.
Spatial Networks
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Author : Marc Barthelemy
language : en
Publisher: Springer Nature
Release Date : 2022-02-20
Spatial Networks written by Marc Barthelemy and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-20 with Mathematics categories.
This book provides a complete introduction into spatial networks. It offers the mathematical tools needed to characterize these structures and how they evolve in time and presents the most important models of spatial networks. The book puts a special emphasis on analyzing complex systems which are organized under the form of networks where nodes and edges are embedded in space. In these networks, space is relevant, and topology alone does not contain all the information. Characterizing and understanding the structure and the evolution of spatial networks is thus crucial for many different fields, ranging from urbanism to epidemiology. This subject is therefore at the crossroad of many fields and is of potential interest to a broad audience comprising physicists, mathematicians, engineers, geographers or urbanists. In this book, the author has expanded his previous book ("Morphogenesis of Spatial Networks") to serve as a textbook and reference on this topic for a wide range of students and professional researchers.
The Math Of Neural Networks
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Author : Michael Taylor
language : en
Publisher: Independently Published
Release Date : 2017-10-04
The Math Of Neural Networks written by Michael Taylor and has been published by Independently Published this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-04 with Computers categories.
There are many reasons why neural networks fascinate us and have captivated headlines in recent years. They make web searches better, organize photos, and are even used in speech translation. Heck, they can even generate encryption. At the same time, they are also mysterious and mind-bending: how exactly do they accomplish these things ? What goes on inside a neural network?On a high level, a network learns just like we do, through trial and error. This is true regardless if the network is supervised, unsupervised, or semi-supervised. Once we dig a bit deeper though, we discover that a handful of mathematical functions play a major role in the trial and error process. It also becomes clear that a grasp of the underlying mathematics helps clarify how a network learns. In the following chapters we will unpack the mathematics that drive a neural network. To do this, we will use a feedforward network as our model and follow input as it moves through the network.