Book Description

Generalized versions of the central limit theorem that lead to Gaussian distributions over one and higher dimensions, via arbitrary iterations of simple mappings, have recently been discovered by the author of this publication and his collaborators. Treasures Inside the Bell: Hidden Order in Chance reveals how these new constructions result in infinite exotic kaleidoscopic decompositions of two-dimensional circular bells in terms of beautiful deterministic patterns possessing arbitrary n-fold symmetries. These are patterns that, while reminding us of the infinite structure previously found in the celebrated Mandelbrot set, turn out to contain natural shapes such as snow crystals and biochemical rosettes, and even the DNA structure of life. ... Read more

Book Description

By looking at the processes of change over time - by carrying out longitudinal studies - researchers answer questions about learning, development, educational growth, social change and medical outcomes.

However, longitudinal research has many faces and no one approach answers all the questions about changes, event occurrences and stability over time. Longitudinal Data Analysis covers all the main approaches (such as analysis of variance and log-linear approaches) as well as newer approaches (such as structural equation modelling and multilevel modelling) to enable the reader to get a thorough understanding of the approach and make appropriate decisions about which technique can be applied to the research problem. Each method is accessibly presented with the following features;

- Conceptual explanations are used to keep complex technical and statistical terms to a minimum.

- Examples are used for each approach to show how the various models and methods can be applied to particular classes of problems.

- Issues of design, measurement and significance are intregrated into the presentation of each method.

- A standard notation is used throughout.

Book Description

Hardbound. Graph Theory has proved to be an extremely useful tool for solving combinatorial problems in such diverse areas as Geometry, Algebra, Number Theory, Topology, Operations Research and Optimization. It is natural to attempt to generalise the concept of a graph, in order to attack additional combinatorial problems. The idea of looking at a family of sets from this standpoint took shape around 1960. In regarding each set as a ``generalised edge'' and in calling the family itself a ``hypergraph'', the initial idea was to try to extend certain classical results of Graph Theory such as the theorems of Turán and König. It was noticed that this generalisation often led to simplification; moreover, one single statement, sometimes remarkably simple, could unify several theorems on graphs. This book presents what seems to be the most significant work on hypergraphs. ... Read more

Reviews (1)

The bible of hypergraphs
Not to be confused Graphs and Hypergraphs (another of his books), Claude Berge's Hypergraphs focuses solely on the structures also known as "set systems". For the curious, a hypergraph consists of a set V and a set E of subsets of S. A graph is a special case of a hypergraph where each element of E has cardinality two.

Published in 1989, this book has become, by default, the authoritative text on hypergraphs. It does not delve into more advanced, technical results (e.g.: asymptotics, etc...) but instead covers all the fundamental material related to hypergraphs (e.g.: Helly property, Konig property, Kruskal-Katona, etc...). Since hypergraphs are usually not part of standard curricula, this book has definitely carved out its own niche. Practically every paper which mentions hypergraphs (written since 1989) references it.

This book appears to be written for practicing mathematicians (or sufficiently sophisticated students) who have stumbled upon a combinatorial problem and are in need of some basic (though non-obvious) results. Thus, in many cases, results are presented somewhat tersely and with little context or motivation with the implicit assumption that the reader already knows what hypergraphs are good for and is skillful enough to navigate the densely packed theorems. ... Read more

Book Description

William Tutte, one of the founders of modern graph theory, provides a unique and personal introduction to the field. Instead of a typical survey, the author looks back at the areas which interested him most, discussing why he pursued certain problems and how he and his colleagues solved them. The book's extensive references make it a useful starting point for research as well as an important document for anyone interested in the history of graph theory. The author begins with the problems he worked on as an undergraduate at Cambridge and goes on to cover subjects such as combinatorial problems in chess, algebra in graph theory, reconstruction of graphs, symmetry in graphs, and the chromatic eigenvalues.In each case he mixes fascinating historical and biographical information with engaging descriptions of important results. ... Read more

Reviews (2)

An introduction to some advanced theorems on graphs
The author has spent most of his professional life pondering some of the more substantial problems in graph theory. This book is not a comprehensive treatise on the subject but an organized collection of a series of lectures that he delivered in 1984. The lectures were just as much an attempt to provide insight into the process that led to some advanced theorems as about the theorems themselves. For this reason, the book is best suited for the beginning graduate student with some experience in the field.
Some of the problems covered in the book are: the knight's tour problem as an exercise in graph theory, subgraphs and Hamiltonian circuits; algebra in graph theory, symmetry in graphs and graphs on spheres. Throughout the explanations of the problems and the solution strategies, it is impossible not to appreciate the effort that was put forward to solve them. Tutte is clearly one of the leading authorities in graph theory and good at explaining what graph theory is all about.
This is not an easy book to read, yet it is readable. It would be ideal as the material for a graduate seminar in graph theory or a text in advanced topics.

Inside the mind of a great mathematician
It is unquestionably that W. T. Tutte is today one the greatest mathematicians in the world. I read this book with great enthusiasm because the author explains, with the work that made his fame, the most difficult part of the discovery of mathematics: The creativity involved.

The students will find in this book a great motivation to thinking in mathematics. For the experimented mathematician this book will make clear the born procces of some classic results in graph theory.

This is an excellent book, is just the story of a life of work and fun. ... Read more

Book Description

This adaptation of an earlier work by the authors is a graduate text and professional reference on the fundamentals of graph theory. It covers the theory of graphs, its applications to computer networks and the theory of graph algorithms. Also includes exercises and an updated bibliography. ... Read more

Reviews (1)

good book for graph theory and algoritms
this book has all the fundamental algorithms on graph problems and is written in a easy to understand manner ... Read more

Book Description

Steiner's Problem concerns finding a shortest interconnecting network for a finite set of points in a metric space. A solution must be a tree, which is called a Steiner Minimal Tree (SMT), and may contain vertices different from the points which are to be connected. Steiner's Problem is one of the most famous combinatorial--geometrical problems, but unfortunately it is very difficult in terms of combinatorial structure as well as computational complexity. However, if only a Minimum Spanning Tree (MST) without additional vertices in the interconnecting network is sought, then it is simple to solve. So it is of interest to know what the error is if an MST is constructed instead of an SMT. The worst case for this ratio running over all finite sets is called the Steiner ratio of the space.The book concentrates on investigating the Steiner ratio. The goal is to determine, or at least estimate, the Steiner ratio for many different metric spaces. The author shows that the description of the Steiner ratio contains many questions from geometry, optimization, and graph theory.Audience: Researchers in network design, applied optimization, and design of algorithms. ... Read more

Book Description

"Compartmental Modeling with Networks" provides a thorough and comprehensive guide for compartmental models, model construction and interdisciplinary applications.

Compartmental models, or flow models, are used when there is a flow of information or materials, such as fluids, money, energy, and resources between the components of a given system or network. They are widely used in biomedicine and ecology yet have great utility in other disciplines i.e. input-output analysis, competition models, epidemiology, networks, and genetics.

In order to provide a balanced presentation, the book is divided into four parts. Part One is devoted to the structure of the models as represented by directed graphs; part two addresses Markov Chains; part three is devoted to diverse applications; while part four covers the theoretical aspects of compartmental models. All topics, models, and methods are presented in a clear, accessible style with many helpful examples and background information.

Topics and Features:

Self contained introduction to graph theory;
Includes coverage of both discrete and continuous models applications;
Selected examples using computational program, MAPLE, in graph theory and matrix algebra problems;
Use of wide variety of interdisciplinary applications and realistic models.
This book is an essential text/reference for all advanced students, practitioners and professionals in applied mathematics and sciences that are in need of greater understanding and skills in using compartmental models in their work and research.

Series: Modeling and Simulation in Science, Engineering and Technology ... Read more

Book Description

This volume covers the principal branches of graph theory in more than a thousand exercises of varying complexity. Each section starts with the main definitions and a brief theoretical discussion, which will serve as a reminder when solving the problems. Answers and hints are supplied separately. Topics include trees, independence and coverings, matchings, tours, planarity, colourings, degree sequences, connectivity, digraphs and hypergraphs.Audience: This work will be valuable to researchers, lecturers and graduate students in graph theory, combinatorics, VLSI design, circuits and systems, and mathematical programming and optimization. ... Read more

Book Description

This book contains volumes 1-3 of the Journal of Graph Algorithms and Applications (JGAA). Topics of interest include design and analysis of graph algorithms, experiences with graph algorithms, and applications of graph algorithms. JGAA is supported by distinguished advisory and editorial boards, has high scientific standards, and takes advantage of current electronic document technology.

Contents: Volume 1: 2-Layer Straightline Crossing Minimization: Performance of Exact and Heuristic Algorithms (M Jünger & P Mutzel); Optimal Algorithms to Embed Trees in a Point Set (P Bose et al.); Low-degree Graph Partitioning via Local Search with Applications to Constraint Satisfaction, Max Cut, and Coloring (M M Halldórsson & H C Lau); Volume 2: Algorithms for Cluster Busting in Anchored Graph Drawing (K A Lyons et al.); A Broadcasting Algorithm with Time and Message Optimum on Arrangement Graphs (L Bai et al.); A Visibility Representation for Graphs in Three Dimensions (P Bose et al.); Scheduled Hot-Potato Routing (J Naor et al.); Treewidth and Minimum Fill-in on d-trapezoid Graphs (H L Bodlaender et al.); Memory Paging for Connectivity and Path Problems in Graphs (E Feuerstein & A Marchetti-Spaccamela); New Lower Bounds for Orthogonal Drawings (T C Biedl); Rectangle-visibility Layouts of Unions and Products of Trees (A M Dean & J P Hutchinson); Volume 3: Edge-Coloring and f-Coloring for Various Classes of Graphs (X Zhou & T Nishizeki); Experimental Comparison of Graph Drawing Algorithms for Cubic Graphs (T Calamoneri et al.); Subgraph Isomorphism in Planar Graphs and Related Problems (D Eppstein); Guest Editors' Introduction (G Di Battista & P Mutzel); Drawing Clustered Graphs on an Orthogonal Grid (P Eades et al.); A Linear Algorithm for Bend-Optimal Orthogonal Drawings of Triconnected Cubic Plane Graphs (M S Rahman et al.); Bounds for Orthogonal 3-D Graph Drawing (T Biedl et al.); Algorithms for Incremental Orthogonal Graph Drawing in Three Dimensions (A Papakostas & I G Tollis). ... Read more

Book Description

This volume presents the lectures given during the second French--Uzbek Colloquium on Algebra and Operator Theory which took place in Tashkent in 1997, at the Mathematical Institute of the Uzbekistan Academy of Sciences. Among the algebraic topics discussed here are deformation of Lie algebras, cohomology theory, the algebraic variety of the laws of Lie algebras, Euler equations on Lie algebras, Leibniz algebras, and real K-theory. Some contributions have a geometrical aspect, such as supermanifolds. The papers on operator theory deal with the study of certain types of operator algebras. This volume also contains a detailed introduction to the theory of quantum groups.Audience: This book is intended for graduate students specialising in algebra, differential geometry, operator theory, and theoretical physics, and for researchers in mathematics and theoretical physics. ... Read more

Book Description

Finally there is a book that presents real applications of graph theory in a unified format. This book is the only source for an extended, concentrated focus on the theory and techniques common to various types of intersection graphs. It is a concise treatment of the aspects of intersection graphs that interconnect many standard concepts and form the foundation of a surprising array of applications to biology, computing, psychology, matrices, and statistics.

The authors emphasize the underlying tools and techniques and demonstrate how this approach constitutes a definite theory within graph theory. Some of the applications are not widely known or available in the graph theoretic literature and are presented here for the first time. The book also includes a detailed literature guide for many specialized and related areas, a current bibliography, and more than 100 exercises.

Audience:

This book is written for students who have completed a basic graph theory course and for mathematicians seeking a guide for graph theory and graph modeling.Anyone working in applications of intersection graphs stands to gain a better understanding of the larger context of the field by reading this book. ... Read more

Book Description

The study of directed graphs has developed enormously over recent decades, yet no book covers more than a tiny fraction of the results from more than 3000 research articles on the topic. Digraphs is the first book to present a unified and comprehensive survey of the subject. In addition to covering the theoretical aspects, including detailed proofs of many important results, the authors present a number of algorithms and applications. The applications of digraphs and their generalizations include among other things recent developments in the Travelling Salesman Problem, genetics and network connectivity. More than 700 exercises and 180 figures will help readers to study the topic while open problems and conjectures will inspire further research. This book will be essential reading and reference for all graduate students, researchers and professionals in mathematics, operational research, computer science and other areas who are interested in graph theory and its applications. ... Read more

Reviews (1)

Directed graphs are more general than undirected graphs
This book reflects the main achievements of the last three decades in the directed graphs theory as well as many applications including combinatorial optimization, operations research and the fascinating area of mathematics and computer science called discrete mathematics. Since the monograph contents are given, I do not wish to go into details of material presented there. Instead I'd like to discuss the aims of the book as well as who could be its readers.

The text strives to accomplish the following objectives:

1. To give a great deal of information on both results and proof techniques for specialists in graph theory. No other book covers even 10\% of material provided in Digraphs, and thus before this monograph has been published even specialists in graph theory very often needed to search for a specific result or proof technique through the ocean of literature on digraphs. Now the situation has drastically improved.

2. To introduce researchers and practitioners from various other fields in mathematics, computer science, operations research, biology, etc. to basic and more advanced results in digraph theory and algorithms and some carefully selected applications. It offers much more than merely a pure bibliography and provides the ideal starting point for any researcher who needs to become familiar either with theory oriented aspects of this interesting area or with some application in a relatively short time.

3. To provide enough material for intermediate and final year BSc or MSc courses for students in mathematics, computer science and operations research. The large number of exercises (more than 700) of various difficulty is of great help to instructors and lecturers. The applications provided in the book will help to provide enough motivation for the students to study digraph theory and algorithms.

4. To provide a large variety of topics for final year student projects in mathematics, computer science, operations research and other fields. The monograph can be used as a source for the projects because because several areas of digraph theory are covered there in real depth and they vary from relatively simple to reasonably complicated ones.

To summarize, I'd like to notice that the monograph is aimed to a wide range of readers including specialists in mathematics, operations research, computer science, biology, etc. as well as students of second year and higher.

Boris Goldengorin, Department of Econometrics and Operations Research, University of Groningen, The Netherlands ... Read more