The book is fairly self-contained. While it requires some broader mathematical physics background, all the basic concepts are properly explained and proofs of most theorems are given in detail, so there is no need for additional sources. Without a parallel in the literature, the monograph by Exner and Kovarik guides the reader through this new and exciting field.
The book contains close to150 figures produced with lattice. Many of the examples emphasize principles of good graphical design; almost all use real data sets that are publicly available in various R packages. All code and figures in the book are also available online, along with supplementary material covering more advanced topics.
This book describes existing and advanced methods to reduce the dimensionality of numerical databases. For each method, the description starts from intuitive ideas, develops the necessary mathematical details, and ends by outlining the algorithmic implementation. Methods are compared with each other with the help of different illustrative examples.
The purpose of the book is to summarize clear facts and ideas about well-known methods as well as recent developments in the topic of nonlinear dimensionality reduction. With this goal in mind, methods are all described from a unifying point of view, in order to highlight their respective strengths and shortcomings.
The book is primarily intended for statisticians, computer scientists and data analysts. It is also accessible to other practitioners having a basic background in statistics and/or computational learning, like psychologists (in psychometry) and economists.
Fixed Point Theory and Graph Theoryprovides an intersection between the theories of fixed point theorems that give the conditions under which maps (single or multivalued) have solutions and graph theory which uses mathematical structures to illustrate the relationship between ordered pairs of objects in terms of their vertices and directed edges.
This edited reference work is perhaps the first to provide a link between the two theories, describing not only their foundational aspects, but also the most recent advances and the fascinating intersection of the domains.
The authors provide solution methods for fixed points in different settings, with two chapters devoted to the solutions method for critically important non-linear problems in engineering, namely, variational inequalities, fixed point, split feasibility, and hierarchical variational inequality problems. The last two chapters are devoted to integrating fixed point theory in spaces with the graph and the use of retractions in the fixed point theory for ordered sets.Introduces both metric fixed point and graph theory in terms of their disparate foundations and common application environmentsProvides a unique integration of otherwise disparate domains that aids both students seeking to understand either area and researchers interested in establishing an integrated research approachEmphasizes solution methods for fixed points in non-linear problems such as variational inequalities, split feasibility, and hierarchical variational inequality problems that is particularly appropriate for engineering and core science applications
The text is primarily intended for use in a one-semester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory. Prerequisites include a basic knowledge of linear algebra over a field, existence of finite fields, and group theory. The topics in each chapter build on one another and include extensive problem sets as well as hints to selected exercises. Key topics include walks on graphs, cubes and the Radon transform, the Matrix–Tree Theorem, and the Sperner property. There are also three appendices on purely enumerative aspects of combinatorics related to the chapter material: the RSK algorithm, plane partitions, and the enumeration of labeled trees.
Richard Stanley is currently professor of Applied Mathematics at the Massachusetts Institute of Technology. Stanley has received several awards including the George Polya Prize in applied combinatorics, the Guggenheim Fellowship, and the Leroy P. Steele Prize for mathematical exposition. Also by the author: Combinatorics and Commutative Algebra, Second Edition, © Birkhauser.
This monograph follows the Greek tradition in seeking beautiful shapes such as regular convex polyhedra. The primary aim is to convey to the reader how algebraic topology is effectively used to explore the rich world of crystal structures. Graph theory, homology theory, and the theory of covering maps are employed to introduce the notion of the topological crystal which retains, in the abstract, all the information on the connectivity of atoms in the crystal. For that reason the title Topological Crystallography has been chosen.
Topological crystals can be described as “living in the logical world, not in space,” leading to the question of how to place or realize them “canonically” in space. Proposed here is the notion of standard realizations of topological crystals in space, including as typical examples the crystal structures of diamond and lonsdaleite. A mathematical view ofthe standard realizations is also provided by relating them to asymptotic behaviors of random walks and harmonic maps. Furthermore, it can be seen that a discrete analogue of algebraic geometry is linked to the standard realizations.
Applications of the discussions in this volume include not only a systematic enumeration of crystal structures, an area of considerable scientific interest for many years, but also the architectural design of lightweight rigid structures. The reader therefore can see the agreement of theory and practice.
Incorporating both established and new ideas, Background Modeling and Foreground Detection for Video Surveillance provides a complete overview of the concepts, algorithms, and applications related to background modeling and foreground detection. Leaders in the field address a wide range of challenges, including camera jitter and background subtraction.
The book presents the top methods and algorithms for detecting moving objects in video surveillance. It covers statistical models, clustering models, neural networks, and fuzzy models. It also addresses sensors, hardware, and implementation issues and discusses the resources and datasets required for evaluating and comparing background subtraction algorithms. The datasets and codes used in the text, along with links to software demonstrations, are available on the book’s website.
A one-stop resource on up-to-date models, algorithms, implementations, and benchmarking techniques, this book helps researchers and industry developers understand how to apply background models and foreground detection methods to video surveillance and related areas, such as optical motion capture, multimedia applications, teleconferencing, video editing, and human–computer interfaces. It can also be used in graduate courses on computer vision, image processing, real-time architecture, machine learning, or data mining.
The textbook covers topics such as fair division, graph coloring problems, evasiveness of graph properties, and embedding problems from discrete geometry. The text contains a large number of figures that support the understanding of concepts and proofs. In many cases several alternative proofs for the same result are given, and each chapter ends with a series of exercises. The extensive appendix makes the book completely self-contained.
The textbook is well suited for advanced undergraduate or beginning graduate mathematics students. Previous knowledge in topology or graph theory is helpful but not necessary. The text may be used as a basis for a one- or two-semester course as well as a supplementary text for a topology or combinatorics class.
This book will be useful to everyone who has struggled with displaying data in an informative and attractive way. Some basic knowledge of R is necessary (e.g., importing data into R). ggplot2 is a mini-language specifically tailored for producing graphics, and you'll learn everything you need in the book. After reading this book you'll be able to produce graphics customized precisely for your problems, and you'll find it easy to get graphics out of your head and on to the screen or page.
"Refreshingly different . . . an ideal training ground for the mathematical process of investigation, generalization, and conjecture leading to the discovery of proofs and counterexamples." — American Mathematical Monthly
" . . . An excellent textbook for an undergraduate course." — Australian Computer Journal
A stimulating view of mathematics that appeals to students as well as teachers, this undergraduate-level text is written in an informal style that does not sacrifice depth or challenge. Based on 20 years of teaching by the leading researcher in graph theory, it offers a solid foundation on the subject. This revised and augmented edition features new exercises, simplifications, and other improvements suggested by classroom users and reviewers. Topics include basic graph theory, colorings of graphs, circuits and cycles, labeling graphs, drawings of graphs, measurements of closeness to planarity, graphs on surfaces, and applications and algorithms. 1994 edition.
The book's three sections look at foundations, multiagent networks, and networks as systems. The authors give an overview of important ideas from graph theory, followed by a detailed account of the agreement protocol and its various extensions, including the behavior of the protocol over undirected, directed, switching, and random networks. They cover topics such as formation control, coverage, distributed estimation, social networks, and games over networks. And they explore intriguing aspects of viewing networks as systems, by making these networks amenable to control-theoretic analysis and automatic synthesis, by monitoring their dynamic evolution, and by examining higher-order interaction models in terms of simplicial complexes and their applications.
The book will interest graduate students working in systems and control, as well as in computer science and robotics. It will be a standard reference for researchers seeking a self-contained account of system-theoretic aspects of multiagent networks and their wide-ranging applications.
This book has been adopted as a textbook at the following universities:
University of Stuttgart, Germany
Royal Institute of Technology, Sweden
Johannes Kepler University, Austria
Georgia Tech, USA
University of Washington, USA
Ohio University, USA
Within these sections,each chapter includes a comprehensive introduction and step-by-step implementation summaries to accompany the explanations of key methods. The new edition includes updated coverage and existing topics as well as new topics such as adaptive MCMC and bootstrapping for correlated data. The book website now includes comprehensive R code for the entire book. There are extensive exercises, real examples, and helpful insights about how to use the methods in practice.
A Computational Introduction to Digital Image Processing, Second Edition explores the nature and use of digital images and shows how they can be obtained, stored, and displayed. Taking a strictly elementary perspective, the book only covers topics that involve simple mathematics yet offer a very broad and deep introduction to the discipline.
New to the Second Edition
This second edition provides users with three different computing options. Along with MATLAB®, this edition now includes GNU Octave and Python. Users can choose the best software to fit their needs or migrate from one system to another. Programs are written as modular as possible, allowing for greater flexibility, code reuse, and conciseness. This edition also contains new images, redrawn diagrams, and new discussions of edge-preserving blurring filters, ISODATA thresholding, Radon transform, corner detection, retinex algorithm, LZW compression, and other topics.
Principles, Practices, and Programming
Based on the author’s successful image processing courses, this bestseller is suitable for classroom use or self-study. In a straightforward way, the text illustrates how to implement imaging techniques in MATLAB, GNU Octave, and Python. It includes numerous examples and exercises to give students hands-on practice with the material.
A refresher for more experienced readers, the first part of the book presents an introduction to Python, Python modules, reading and writing images using Python, and an introduction to images. The second part discusses the basics of image processing, including pre/post processing using filters, segmentation, morphological operations, and measurements. The last part describes image acquisition using various modalities, such as x-ray, CT, MRI, light microscopy, and electron microscopy. These modalities encompass most of the common image acquisition methods currently used by researchers in academia and industry.
This guide to writing mathematical expressions covers both simple notations used in general texts and professional formulas and equations used in natural sciences, mathematics, and other fields. It is an essential handbook for people who write, edit, or typeset of texts where mathematical notations may be needed. The book presents notations defined in the modern international standard ISO 80000-2 but also describes other common practices.
After a preview of configurations in Chapter 1, a concise introduction to graph theory is presented in Chapter 2, followed by a geometric introduction to groups in Chapter 3. Maps and surfaces are combinatorially treated in Chapter 4. Chapter 5 introduces the concept of incidence structure through vertex colored graphs, and the combinatorial aspects of classical configurations are studied. Geometric aspects, some historical remarks, references, and applications of classical configurations appear in the last chapter.
With over two hundred illustrations, challenging exercises at the end of each chapter, a comprehensive bibliography, and a set of open problems, Configurations from a Graphical Viewpoint is well suited for a graduate graph theory course, an advanced undergraduate seminar, or a self-contained reference for mathematicians and researchers.
The book presents state-of-the-art image processing methodology, including current industrial practices for image compression, image de-noising methods based on partial differential equations (PDEs), and new image compression methods, such as fractal image compression and wavelet compression. It begins with coverage of representation, and then moves on to communications and processing. It concludes with discussions of processing techniques based on image representations and transformations developed in earlier chapters. The accompanying CD-ROM contains code for all algorithms.
Suitable as a text for any course on image processing, the book can also be used as a self-study resource for researchers who need a concise and clear view of current image processing methods and coding examples. The authors introduce mathematical concepts with rigor suitable for readers with some background in calculus, algebra, geometry, and PDEs. All algorithms described are illustrated with code implementation and many images compare the results of different methods. The inclusion of C++ implementation code for each algorithm described enables students and practitioners to build up their own analysis tool.
From the review:
".... This carefully written textbook, the third English edition, contains substantial new developments on the numerical solution of differential equations. It is typeset in a two-color design and is written in a style suited for readers who have mathematics, natural sciences, computer sciences or economics as a background and who are interested in a well-organized introduction to the subject." Roberto Plato (Siegen), Zentralblatt MATH 1205.65002.
New approaches to graphics are needed to visualize the information in large datasets and most of the innovations described in this book are developments of standard graphics. There are considerable advantages in extending displays which are well-known and well-tried, both in understanding how best to make use of them in your work and in presenting results to others. It should also make the book readily accessible for readers who already have a little experience of drawing statistical graphics. All ideas are illustrated with displays from analyses of real datasets and the authors emphasize the importance of interpreting displays effectively. Graphics should be drawn to convey information and the book includes many insightful examples.
From the reviews:
"Anyone interested in modern techniques for visualizing data will be well rewarded by reading this book. There is a wealth of important plotting types and techniques." Paul Murrell for the Journal of Statistical Software, December 2006
"This fascinating book looks at the question of visualizing large datasets from many different perspectives. Different authors are responsible for different chapters and this approach works well in giving the reader alternative viewpoints of the same problem. Interestingly the authors have cleverly chosen a definition of 'large dataset'. Essentially they focus on datasets with the order of a million cases. As the authors point out there are now many examples of much larger datasets but by limiting to ones that can be loaded in their entirety in standard statistical software they end up with a book that has great utility to the practitioner rather than just the theorist. Another very attractive feature of the book is the many colour plates, showing clearly what can now routinely be seen on the computer screen. The interactive nature of data analysis with large datasets is hard to reproduce in a book but the authors make an excellent attempt to do just this." P. Marriott for the Short Book Reviews of the ISI
This book examines all aspects essential for a successful application of geometric algebra: the theoretical foundations, the representation of geometric constraints, and the numerical estimation from uncertain data. Formally, the book consists of two parts: theoretical foundations and applications. The first part includes chapters on random variables in geometric algebra, linear estimation methods that incorporate the uncertainty of algebraic elements, and the representation of geometry in Euclidean, projective, conformal and conic space. The second part is dedicated to applications of geometric algebra, which include uncertain geometry and transformations, a generalized camera model, and pose estimation.
Graduate students, scientists, researchers and practitioners will benefit from this book. The examples given in the text are mostly recent research results, so practitioners can see how to apply geometric algebra to real tasks, while researchers note starting points for future investigations. Students will profit from the detailed introduction to geometric algebra, while the text is supported by the author's visualization software, CLUCalc, freely available online, and a website that includes downloadable exercises, slides and tutorials.