- Table View
- List View
Discrete Calculus
by Leo J. Grady Jonathan R. PolimeniThe field of discrete calculus, also known as "discrete exterior calculus", focuses on finding a proper set of definitions and differential operators that make it possible to operate the machinery of multivariate calculus on a finite, discrete space. In contrast to traditional goals of finding an accurate discretization of conventional multivariate calculus, discrete calculus establishes a separate, equivalent calculus that operates purely in the discrete space without any reference to an underlying continuous process. This unique text brings together into a single framework current research in the three areas of discrete calculus, complex networks, and algorithmic content extraction. Although there have been a few intersections in the literature between these disciplines, they have developed largely independently of one another, yet researchers working in any one of these three areas can strongly benefit from the tools and techniques being used in the others. Many example applications from several fields of computational science are provided to demonstrate the usefulness of this framework to a broad range of problems. Readers are assumed to be familiar with the basics of vector calculus, graph theory, and linear algebra. Topics and features: presents a thorough review of discrete calculus, with a focus on key concepts required for successful application; unifies many standard image processing algorithms into a common framework for viewing a wide variety of standard algorithms in filtering, clustering, and manifold learning that may be applied to processing data associated with a graph or network; explains how discrete calculus provides a natural definition of "low-frequency" on a graph, which then yields filtering and denoising algorithms; discusses how filtering algorithms can give rise to clustering algorithms, which can be used to develop manifold learning and data discovery methods; examines ranking algorithms, as well as algorithms for analyzing the structure of a network. Graduate students and researchers interested in discrete calculus, complex networks, image processing and computer graphics will find this text/reference a clear introduction to the foundations of discrete calculus as well as a useful guide to have readily available for their work. Dr. Leo J. Grady is a Senior Research Scientist with Siemens Corporate Research in Princeton, New Jersey, USA. Dr. Jonathan R. Polimeni is a Research Fellow at the Massachusetts General Hospital in Boston, Massachusetts, USA, and Instructor in Radiology at Harvard Medical School, Boston, Massachusetts, USA.
The Discrete Charm of the Machine: Why the World Became Digital
by Kenneth SteiglitzThe genesis of the digital idea and why it transformed civilizationA few short decades ago, we were informed by the smooth signals of analog television and radio; we communicated using our analog telephones; and we even computed with analog computers. Today our world is digital, built with zeros and ones. Why did this revolution occur? The Discrete Charm of the Machine explains, in an engaging and accessible manner, the varied physical and logical reasons behind this radical transformation.The spark of individual genius shines through this story of innovation: the stored program of Jacquard’s loom; Charles Babbage’s logical branching; Alan Turing’s brilliant abstraction of the discrete machine; Harry Nyquist’s foundation for digital signal processing; Claude Shannon’s breakthrough insights into the meaning of information and bandwidth; and Richard Feynman’s prescient proposals for nanotechnology and quantum computing. Ken Steiglitz follows the progression of these ideas in the building of our digital world, from the internet and artificial intelligence to the edge of the unknown. Are questions like the famous traveling salesman problem truly beyond the reach of ordinary digital computers? Can quantum computers transcend these barriers? Does a mysterious magical power reside in the analog mechanisms of the brain? Steiglitz concludes by confronting the moral and aesthetic questions raised by the development of artificial intelligence and autonomous robots.The Discrete Charm of the Machine examines why our information technology, the lifeblood of our civilization, became digital, and challenges us to think about where its future trajectory may lead.
Discrete Cuckoo Search for Combinatorial Optimization (Springer Tracts in Nature-Inspired Computing)
by Aziz OuaarabThis book provides a literature review of techniques used to pass from continuous to combinatorial space, before discussing a detailed example with individual steps of how cuckoo search (CS) can be adapted to solve combinatorial optimization problems. It demonstrates the application of CS to three different problems and describes their source code. The content is divided into five chapters, the first of which provides a technical description, together with examples of combinatorial search spaces. The second chapter summarizes a diverse range of methods used to solve combinatorial optimization problems. In turn, the third chapter presents a description of CS, its formulation and characteristics. In the fourth chapter, the application of discrete cuckoo search (DCS) to solve three POCs (the traveling salesman problem, quadratic assignment problem and job shop scheduling problem) is explained, focusing mainly on a reinterpretation of the terminology used in CS and its source of inspiration. In closing, the fifth chapter discusses random-key cuckoo search (RKCS) using random keys to represent positions found by cuckoo search in the TSP and QAP solution space.
Discrete Diversity and Dispersion Maximization: A Tutorial on Metaheuristic Optimization (Springer Optimization and Its Applications #204)
by Rafael Martí Anna Martínez-GavaraThis book demonstrates the metaheuristic methodologies that apply to maximum diversity problems to solve them. Maximum diversity problems arise in many practical settings from facility location to social network analysis and constitute an important class of NP-hard problems in combinatorial optimization. In fact, this volume presents a “missing link” in the combinatorial optimization-related literature. In providing the basic principles and fundamental ideas of the most successful methodologies for discrete optimization, this book allows readers to create their own applications for other discrete optimization problems. Additionally, the book is designed to be useful and accessible to researchers and practitioners in management science, industrial engineering, economics, and computer science, while also extending value to non-experts in combinatorial optimization. Owed to the tutorials presented in each chapter, this book may be used in a master course, a doctoral seminar, or as supplementary to a primary text in upper undergraduate courses.The chapters are divided into three main sections. The first section describes a metaheuristic methodology in a tutorial style, offering generic descriptions that, when applied, create an implementation of the methodology for any optimization problem. The second section presents the customization of the methodology to a given diversity problem, showing how to go from theory to application in creating a heuristic. The final part of the chapters is devoted to experimentation, describing the results obtained with the heuristic when solving the diversity problem. Experiments in the book target the so-called MDPLIB set of instances as a benchmark to evaluate the performance of the methods.
Discrete Encounters (Chapman & Hall/CRC Cryptography and Network Security Series)
by Craig BauerEschewing the standard dry and static writing style of traditional textbooks, Discrete Explorations provides a refreshing approach to discrete mathematics. The author combines traditional course topics with popular culture, applications, and various historical examples. This book focuses on the historical development of the subject and provides details on the people behind mathematics and their motivations, which will deepen readers’ appreciation of mathematics. With its unique style, the book covers many of the same topics found in other texts but done in an alternative, entertaining style that better captures readers’ attention. Defining discrete mathematics, the author also covers many different topics. These include combinatorics, fractals, permutations, difference equations, graph theory, trees and financial mathematics. Not only will readers gain a greater impression of mathematics, but they’ll be encouraged to further explore the subject. Highlights: Features fascinating historical references to motivate readers Text includes numerous pop culture references throughout to provide a more engaging reading experience Its unique topic structure presents a fresh approach The text’s narrative style reads more like a popular book instead of a dry textbook Covers many topics from combinatorics, as well as discrete mathematics
Discrete-Event Modeling and Simulation: Theory and Applications (Computational Analysis, Synthesis, and Design of Dynamic Systems)
by Pieter J. Mosterman Gabriel A. WainerCollecting the work of the foremost scientists in the field, Discrete-Event Modeling and Simulation: Theory and Applications presents the state of the art in modeling discrete-event systems using the discrete-event system specification (DEVS) approach. It introduces the latest advances, recent extensions of formal techniques, and real-world examples of various applications. The book covers many topics that pertain to several layers of the modeling and simulation architecture. It discusses DEVS model development support and the interaction of DEVS with other methodologies. It describes different forms of simulation supported by DEVS, the use of real-time DEVS simulation, the relationship between DEVS and graph transformation, the influence of DEVS variants on simulation performance, and interoperability and composability with emphasis on DEVS standardization. The text also examines extensions to DEVS, new formalisms, and abstractions of DEVS models as well as the theory and analysis behind real-world system identification and control. To support the generation and search of optimal models of a system, a framework is developed based on the system entity structure and its transformation to DEVS simulation models. In addition, the book explores numerous interesting examples that illustrate the use of DEVS to build successful applications, including optical network-on-chip, construction/building design, process control, workflow systems, and environmental models. A one-stop resource on advances in DEVS theory, applications, and methodology, this volume offers a sampling of the best research in the area, a broad picture of the DEVS landscape, and trend-setting applications enabled by the DEVS approach. It provides the basis for future research discoveries and encourages the development of new applications.
Discrete-Event Modeling and Simulation: A Practitioner's Approach (Computational Analysis, Synthesis, and Design of Dynamic Systems)
by Gabriel A. WainerComplex artificial dynamic systems require advanced modeling techniques that can accommodate their asynchronous, concurrent, and highly non-linear nature. Discrete Event systems Specification (DEVS) provides a formal framework for hierarchical construction of discrete-event models in a modular manner, allowing for model re-use and reduced development time. Discrete Event Modeling and Simulation presents a practical approach focused on the creation of discrete-event applications. The book introduces the CD++ tool, an open-source framework that enables the simulation of discrete-event models. After setting up the basic theory of DEVS and Cell-DEVS, the author focuses on how to use the CD++ tool to define a variety of models in biology, physics, chemistry, and artificial systems. They also demonstrate how to map different modeling techniques, such as Finite State Machines and VHDL, to DEVS. The in-depth coverage elaborates on the creation of simulation software for DEVS models and the 3D visualization environments associated with these tools. A much-needed practical approach to creating discrete-event applications, this book offers world-class instruction on the field’s most useful modeling tools.
Discrete Fuzzy Measures: Computational Aspects (Studies in Fuzziness and Soft Computing #382)
by Gleb Beliakov Simon James Jian-Zhang WuThis book addresses computer scientists, IT specialists, mathematicians, knowledge engineers and programmers, who are engaged in research and practice of multicriteria decision making. Fuzzy measures, also known as capacities, allow one to combine degrees of preferences, support or fuzzy memberships into one representative value, taking into account interactions between the inputs. The notions of mutual reinforcement or redundancy are modeled explicitly through coefficients of fuzzy measures, and fuzzy integrals, such as the Choquet and Sugeno integrals combine the inputs. Building on previous monographs published by the authors and dealing with different aspects of aggregation, this book especially focuses on the Choquet and Sugeno integrals. It presents a number of new findings concerning computation of fuzzy measures, learning them from data and modeling interactions. The book does not require substantial mathematical background, as all the relevant notions are explained. It is intended as concise, timely and self-contained guide to the use of fuzzy measures in the field of multicriteria decision making.
Discrete Geometry and Mathematical Morphology: Second International Joint Conference, DGMM 2022, Strasbourg, France, October 24–27, 2022, Proceedings (Lecture Notes in Computer Science #13493)
by Étienne Baudrier Benoît Naegel Adrien Krähenbühl Mohamed TajineThis book constitutes the proceedings of the Second IAPR International Conference on Discrete Geometry and Mathematical Morphology, DGMM 2022, which was held during October 24-27, 2022, in Strasbourg, France.The 33 papers included in this volume were carefully reviewed and selected from 45 submissions. They were organized in topical sections as follows: discrete and combinatorial topology; discrete tomography and inverse problems; multivariate and PDE-based mathematical morphology, morphological filtering; hierarchical and Graph-Based Models, Analysis and Segmentation; discrete geometry - models, transforms, and visualization; learning based morphology to Mathematical Morphology; and distance transform. The book also contains 3 invited keynote papers.
Discrete Geometry and Mathematical Morphology: Third International Joint Conference, DGMM 2024, Florence, Italy, April 15–18, 2024, Proceedings (Lecture Notes in Computer Science #14605)
by Sara Brunetti Andrea Frosini Simone RinaldiThis book constitutes the refereed proceedings of the Third International Joint Conference on Discrete Geometry and Mathematical Morphology, DGMM 2024, held in Florence, Italy during April 15–18, 2024. The 34 full papers included in this book were carefully reviewed and selected from 51 submissions. They were organized in topical sections as follows: Digital Geometry - Models, Transforms, and Visualization; Computational Aspects of Discrete Structures and Tilings; Learning Based Morphology; Hierarchical and Graph-Based Models, Analysis and Segmentation; Discrete and Combinatorial Topology; and Mathematical Morphology and Digital Geometry for Applications.
Discrete Geometry and Mathematical Morphology: First International Joint Conference, DGMM 2021, Uppsala, Sweden, May 24–27, 2021, Proceedings (Lecture Notes in Computer Science #12708)
by Joakim Lindblad Filip Malmberg Nataša SladojeThis book constitutes the proceedings of the First IAPR International Conference on Discrete Geometry and Mathematical Morphology, DGMM 2021, which was held during May 24-27, 2021, in Uppsala, Sweden.The conference was created by joining the International Conference on Discrete Geometry for computer Imagery, DGCI, with the International Symposium on Mathematical Morphology, ISMM. The 36 papers included in this volume were carefully reviewed and selected from 59 submissions. They were organized in topical sections as follows: applications in image processing, computer vision, and pattern recognition; discrete and combinatorial topology; discrete geometry - models, transforms, visualization; discrete tomography and inverse problems; hierarchical and graph-based models, analysis and segmentation; learning-based approaches to mathematical morphology; multivariate and PDE-based mathematical morphology, morphological filtering. The book also contains 3 invited keynote papers.
Discrete Geometry for Computer Imagery: 21st IAPR International Conference, DGCI 2019, Marne-la-Vallée, France, March 26–28, 2019, Proceedings (Lecture Notes in Computer Science #11414)
by Michel Couprie Jean Cousty Yukiko Kenmochi Nabil MustafaThis book constitutes the thoroughly refereed proceedings of the 21st IAPR International Conference on Discrete Geometry for Computer Imagery, DGCI 2019, held in Marne-la-Vallée, France, in March 2019. The 38 full papers were carefully selected from 50 submissions. The papers are organized in topical sections on discrete geometric models and transforms; discrete topology; graph-based models, analysis and segmentation; mathematical morphology; shape representation, recognition and analysis; and geometric computation.
Discrete Geometry for Computer Imagery
by Nicolas Normand Jeanpierre Guédon Florent AutrusseauThisbook constitutes the refereed proceedings of the 19th IAPR InternationalConference on Discrete Geometry for Computer Imagery, DGCI 2016, held in Nantes,France, in April 2016. The 32 revised full papers presented together with 2invited talks were carefully selected from 51 submissions. The papers areorganized in topical sections on combinatorial tools; discretization; discretetomography; discrete and combinatorial topology; shape descriptors; models fordiscrete geometry; circle drawing; morphological analysis; geometrictransforms; and discrete shape representation, recognition and analysis.
The Discrete Math Workbook: A Companion Manual for Practical Study (Texts in Computer Science)
by Sergei Kurgalin Sergei BorzunovThis practically-oriented textbook presents an accessible introduction to discrete mathematics through a substantial collection of classroom-tested exercises. Each chapter opens with concise coverage of the theory underlying the topic, reviewing the basic concepts and establishing the terminology, as well as providing the key formulae and instructions on their use. This is then followed by a detailed account of the most common problems in the area, before the reader is invited to practice solving such problems for themselves through a varied series of questions and assignments.Topics and features: provides an extensive set of exercises and examples of varying levels of complexity, suitable for both laboratory practical training and self-study; offers detailed solutions to many problems, applying commonly-used methods and computational schemes; introduces the fundamentals of mathematical logic, the theory of algorithms, Boolean algebra, graph theory, sets, relations, functions, and combinatorics; presents more advanced material on the design and analysis of algorithms, including asymptotic analysis, and parallel algorithms; includes reference lists of trigonometric and finite summation formulae in an appendix, together with basic rules for differential and integral calculus.This hands-on study guide is designed to address the core needs of undergraduate students training in computer science, informatics, and electronic engineering, emphasizing the skills required to develop and implement an algorithm in a specific programming language.
The Discrete Math Workbook: A Companion Manual Using Python (Texts in Computer Science)
by Sergei Kurgalin Sergei BorzunovThis practically-focused study guide introduces the fundamentals of discrete mathematics through an extensive set of classroom-tested problems. Each chapter presents a concise introduction to the relevant theory, followed by a detailed account of common challenges and methods for overcoming these. The reader is then encouraged to practice solving such problems for themselves, by tackling a varied selection of questions and assignments of different levels of complexity.This updated second edition now covers the design and analysis of algorithms using Python, and features more than 50 new problems, complete with solutions.Topics and features: provides a substantial collection of problems and examples of varying levels of difficulty, suitable for both laboratory practical training and self-study; offers detailed solutions to each problem, applying commonly-used methods and computational schemes; introduces the fundamentals of mathematical logic, the theory of algorithms, Boolean algebra, graph theory, sets, relations, functions, and combinatorics; presents more advanced material on the design and analysis of algorithms, including Turing machines, asymptotic analysis, and parallel algorithms; includes reference lists of trigonometric and finite summation formulae in an appendix, together with basic rules for differential and integral calculus.This hands-on workbook is an invaluable resource for undergraduate students of computer science, informatics, and electronic engineering. Suitable for use in a one- or two-semester course on discrete mathematics, the text emphasizes the skills required to develop and implement an algorithm in a specific programming language.
Discrete Mathematical Structures: A Succinct Foundation (Mathematics and its Applications)
by B. V. Kumar Hemen DuttaThis book contains fundamental concepts on discrete mathematical structures in an easy to understand style so that the reader can grasp the contents and explanation easily. The concepts of discrete mathematical structures have application to computer science, engineering and information technology including in coding techniques, switching circuits, pointers and linked allocation, error corrections, as well as in data networking, Chemistry, Biology and many other scientific areas. The book is for undergraduate and graduate levels learners and educators associated with various courses and progammes in Mathematics, Computer Science, Engineering and Information Technology. The book should serve as a text and reference guide to many undergraduate and graduate programmes offered by many institutions including colleges and universities. Readers will find solved examples and end of chapter exercises to enhance reader comprehension. Features Offers comprehensive coverage of basic ideas of Logic, Mathematical Induction, Graph Theory, Algebraic Structures and Lattices and Boolean Algebra Provides end of chapter solved examples and practice problems Delivers materials on valid arguments and rules of inference with illustrations Focuses on algebraic structures to enable the reader to work with discrete structures
Discrete Mathematics: A Concise Introduction (Synthesis Lectures on Mathematics & Statistics)
by George TourlakisThis book is ideal for a first or second year discrete mathematics course for mathematics, engineering, and computer science majors. The author has extensively class-tested early conceptions of the book over the years and supplements mathematical arguments with informal discussions to aid readers in understanding the presented topics. “Safe” – that is, paradox-free – informal set theory is introduced following on the heels of Russell’s Paradox as well as the topics of finite, countable, and uncountable sets with an exposition and use of Cantor’s diagonalisation technique. Predicate logic “for the user” is introduced along with axioms and rules and extensive examples. Partial orders and the minimal condition are studied in detail with the latter shown to be equivalent to the induction principle. Mathematical induction is illustrated with several examples and is followed by a thorough exposition of inductive definitions of functions and sets. Techniques for solving recurrence relations including generating functions, the O- and o-notations, and trees are provided. Over 200 end of chapter exercises are included to further aid in the understanding and applications of discrete mathematics.
Discrete Mathematics and Applications (Springer Optimization and Its Applications #165)
by Andrei M. Raigorodskii Michael Th. RassiasAdvances in discrete mathematics are presented in this book with applications in theoretical mathematics and interdisciplinary research. Each chapter presents new methods and techniques by leading experts. Unifying interdisciplinary applications, problems, and approaches of discrete mathematics, this book connects topics in graph theory, combinatorics, number theory, cryptography, dynamical systems, finance, optimization, and game theory. Graduate students and researchers in optimization, mathematics, computer science, economics, and physics will find the wide range of interdisciplinary topics, methods, and applications covered in this book engaging and useful.
Discrete Mathematics and Applications, Second Edition (Textbooks in Mathematics)
by Kevin FerlandThis book is intended for a one-semester course in discrete mathematics. Such a course is typically taken by mathematics, mathematics education, and computer science majors, usually in their sophomore year. Calculus is not a prerequisite to use this book. Part one focuses on how to write proofs, then moves on to topics in number theory, employing set theory in the process. Part two focuses on computations, combinatorics, graph theory, trees, and algorithms.
Discrete Mathematics and Graph Theory: A Concise Study Companion and Guide (Undergraduate Topics in Computer Science)
by K. ErciyesThis textbook can serve as a comprehensive manual of discrete mathematics and graph theory for non-Computer Science majors; as a reference and study aid for professionals and researchers who have not taken any discrete math course before. It can also be used as a reference book for a course on Discrete Mathematics in Computer Science or Mathematics curricula. The study of discrete mathematics is one of the first courses on curricula in various disciplines such as Computer Science, Mathematics and Engineering education practices. Graphs are key data structures used to represent networks, chemical structures, games etc. and are increasingly used more in various applications such as bioinformatics and the Internet. Graph theory has gone through an unprecedented growth in the last few decades both in terms of theory and implementations; hence it deserves a thorough treatment which is not adequately found in any other contemporary books on discrete mathematics, whereas about 40% of this textbook is devoted to graph theory. The text follows an algorithmic approach for discrete mathematics and graph problems where applicable, to reinforce learning and to show how to implement the concepts in real-world applications.
Discrete Mathematics and Its Applications Seventh Edition
by Kenneth H. RosenDiscrete Mathematics and Its Applications, Seventh Edition, is intended for one or two term introductory Discrete Mathematics courses taken by students from a wide variety of majors, including Computer Science, Mathematics, and Engineering.
Discrete Mathematics for Computing (3rd Edition)
by Peter Grossman<p>Palgrave Macmillan Discrete Mathematics for Computing is suitable for students taking a one-semester introductory course in discrete mathematics, particularly those studying Computing and Informations Systems. It presents the essential mathematics needed for computing in a style suitable for students with only a moderate background in the subject. <p>Material is introduced at a gentle pace and in an informal style, without compromising mathematical integrity. The text includes many examples of how the theory is applied to problems in computing. This third edition includes: a new expanded section on encryption, additional examples to illustrate key concepts, new exercises at a variety of levels. <p>Peter Grossman has worked in universities and industry as a mathematician and computing professional. As a lecturer in mathematics, he was responsible for coordinating and developing mathematics courses for computing students. He has applied his skills in areas as diverse as calculator design, irrigation systems and underground mine layouts.
Discrete Mathematics with Coding (Textbooks in Mathematics)
by Hugo D JunghennThis book, for a first undergraduate course in Discrete Mathematics, systematically exploits the relationship between discrete mathematics and computer programming. Unlike most discrete mathematics texts focusing on one of the other, the book explores the rich and important connection between these two disciplines and shows how each discipline reinforces and enhances the other. The mathematics in the book is self-contained, requiring only a good background in precalculus and some mathematical maturity. New mathematical topics are introduced as needed. The coding language used is VBA Excel. The language is easy to learn, has intuitive commands, and the reader can develop interesting programs from the outset. Additionally, the spreadsheet platform in Excel makes for convenient and transparent data input and output and provides a powerful venue for complex data manipulation. Manipulating data is greatly simplified using spreadsheet features and visualizing the data can make programming and debugging easier. The VBA language is seamlessly integrated into the spreadsheet environment with no other resources required. Furthermore, as some of the modules in the book show, intricate patterns, graphs, and animation in the form of moving cells is possible. Features Introduces coding in VBA Excel assuming no previous coding experience. Develops programs in Linear Analysis, Logic, Combinatorics, Probability, and Number Theory. Contains over 90 fully tested and debugged programs. The code for these is as well as the exercises is available on the author's website. Contains numerous examples that gradually introduce the reader to coding techniques. Includes programs that solve systems of linear equations, linear programming problems, combinatorial problems, Venn diagram problems and programs that produce truth tables from logic statements and logic statements from switching and gate circuits, encrypt and decrypt messages and simulate probability experiments.
Discrete Mathematics with Ducks (Textbooks in Mathematics)
by Sarah-Marie Belcastro<p>Discrete Mathematics with Ducks, Second Edition is a gentle introduction for students who find the proofs and abstractions of mathematics challenging. At the same time, it provides stimulating material that instructors can use for more advanced students. The first edition was widely well received, with its whimsical writing style and numerous exercises and materials that engaged students at all levels. <p>The new, expanded edition continues to facilitate effective and active learning. It is designed to help students learn about discrete mathematics through problem-based activities. These are created to inspire students to understand mathematics by actively practicing and doing, which helps students better retain what they’ve learned. As such, each chapter contains a mixture of discovery-based activities, projects, expository text, in-class exercises, and homework problems. The author’s lively and friendly writing style is appealing to both instructors and students alike and encourages readers to learn. The book’s light-hearted approach to the subject is a guiding principle and helps students learn mathematical abstraction.</p>
Discrete Problems in Nature Inspired Algorithms
by Anupam Shukla Ritu TiwariThis book includes introduction of several algorithms which are exclusively for graph based problems, namely combinatorial optimization problems, path formation problems, etc. Each chapter includes the introduction of the basic traditional nature inspired algorithm and discussion of the modified version for discrete algorithms including problems pertaining to discussed algorithms.