Diskret matematik

"A rich, narrative explanation of the mathematics that has brought us machine learning and the ongoing explosion of artificial intelligence"--

The mathematical theory of tangles, the centrepiece of the celebrated Robertson-Seymour theory of graph minors, finds precise structure in imprecise data. Assuming only basic undergraduate mathematics, this book shows how tangles can identify, relate, and structure types in data: of behaviour, political views, texts, or proteins.

Petri nets model concurrent and distributed systems where active components communicate through the production and absorption of various kinds of resources. Although the dynamic properties of such systems may be very complex, they may sometimes be connected to the static structure of a Petri net. Many properties are decidable, but their complexity may be huge. It is often opportune to restrict oneself to classes of systems, to partial algorithms, and to similar but simpler properties. Instead of analysing a given system, it is also possible to search for a system satisfying some desired properties by construction. This comprehensive textbook/reference presents and discusses these issues in-depth in the context of one of the most fundamental Petri net models, called place/transition nets. The presentation is fortified by means of many examples and worked exercises. Among topics addressed: ¿ In which order may actions may be generated and scheduled? ¿ What states and configurations may be reached in a concurrent system? ¿ Which interesting classes of systems can be analysed relatively efficiently? ¿ Is it possible to synthesise a system of some class from its behaviour? ¿ How can systems be represented algebraically, compositionally, and concisely? This unique text, based on introductory as well as on advanced courses on distributed systems, will serve as an invaluable guide for students and (future) researchers interested in theoretical¿as well as in practical¿aspects of Petri nets and related system models. Eike Best has been a full professor (now retired) affiliated to Carl von Ossietzky Universität Oldenburg, Germany. Raymond Devillers has been a full professor (now retired) affiliated to Université Libre de Bruxelles, Belgium. The authors have a long record as collaborators in the fields of Petri nets and the semantics of concurrency.

API Design for C++, Second Edition?provides a comprehensive discussion of Application Programming Interface (API) development, from initial design through implementation, testing, documentation, release, versioning, maintenance, and deprecation. It is the only book that teaches the strategies of C++ API development, including interface design, versioning, scripting, and plug-in extensibility. Drawing from the author's experience on large scale, collaborative software projects, the text offers practical techniques of API design that produce robust code for the long-term. It presents patterns and practices that provide real value to individual developers as well as organizations. The Second Edition includes all new material fully updated for the latest versions of C++, including a new chapter on concurrency and multithreading, as well as a new chapter discussing how Objective C++ and C++ code can co-exist and how a C++ API can be accessed from Swift programs. In addition, it explores often overlooked issues, both technical and non-technical, contributing to successful design decisions that produce high quality, robust, and long-lived APIs. It focuses on various API styles and patterns that will allow you to produce elegant and durable libraries. A discussion on testing strategies concentrates on automated API testing techniques rather than attempting to include end-user application testing techniques such as GUI testing, system testing, or manual testing. Each concept is illustrated with extensive C++ code examples. Fully functional examples and working source code for experimentation are available online.

This book constitutes the refereed proceedings of the 21st International Workshop on Approximation and Online Algorithms, WAOA 2023, held in Amsterdam, The Netherlands, during September 7¿8, 2023The 16 full papers included in this book are carefully reviewed and selected from 43 submissions. The topics of WAOA 2023 were algorithmic game theory, algorithmic trading, coloring and partitioning, competitive analysis, computational advertising, computational finance, cuts and connectivity, FPT-approximation algorithms, geometric problems, graph algorithms, inapproximability results, mechanism design, network design, packing and covering, paradigms for the design and analysis of approximation and online algorithms, resource augmentation, and scheduling problems

One of the central highlights of this work is the exploration of the Yoneda lemma and its profound implications, during which intuitive explanations are provided, as well as detailed proofs, and specific examples. This book covers aspects of category theory often considered advanced in a clear and intuitive way, with rigorous mathematical proofs. It investigates universal properties, coherence, the relationship between categories and graphs, and treats monads and comonads on an equal footing, providing theorems, interpretations and concrete examples. Finally, this text contains an introduction to monoidal categories and to strong and commutative monads, which are essential tools in current research but seldom found in other textbooks.Starting Category Theory serves as an accessible and comprehensive introduction to the fundamental concepts of category theory. Originally crafted as lecture notes for an undergraduate course, it has been developed to be equally well-suited for individuals pursuing self-study. Most crucially, it deliberately caters to those who are new to category theory, not requiring readers to have a background in pure mathematics, but only a basic understanding of linear algebra.

This book offers an up-to-date, comprehensive account of determinantal rings and varieties, presenting a multitude of methods used in their study, with tools from combinatorics, algebra, representation theory and geometry.After a concise introduction to Grobner and Sagbi bases, determinantal ideals are studied via the standard monomial theory and the straightening law. This opens the door for representation theoretic methods, such as the Robinson-Schensted-Knuth correspondence, which provide a description of the Grobner bases of determinantal ideals, yielding homological and enumerative theorems on determinantal rings. Sagbi bases then lead to the introduction of toric methods. In positive characteristic, the Frobenius functor is used to study properties of singularities, such as F-regularity and F-rationality. Castelnuovo-Mumford regularity, an important complexity measure in commutative algebra and algebraic geometry, is introduced in the general setting of a Noetherian base ring and then applied to powers and products of ideals. The remainder of the book focuses on algebraic geometry, where general vanishing results for the cohomology of line bundles on flag varieties are presented and used to obtain asymptotic values of the regularity of symbolic powers of determinantal ideals. In characteristic zero, the Borel-Weil-Bott theorem provides sharper results for GL-invariant ideals. The book concludes with a computation of cohomology with support in determinantal ideals and a survey of their free resolutions.Determinants, Grobner Bases and Cohomology provides a unique reference for the theory of determinantal ideals and varieties, as well as an introduction to the beautiful mathematics developed in their study. Accessible to graduate students with basic grounding in commutative algebra and algebraic geometry, it can be used alongside general texts to illustrate the theory with a particularly interesting and important class of varieties.

Information Modeling and Relational Databases provides an introduction to ORM (Object Role Modeling)-and much more. In fact, it's the only book to go beyond introductory coverage and provide all of the in-depth instruction you need to transform knowledge from domain experts into a sound database design. Inside, ORM authority Terry Halpin blends conceptual information with practical instruction that will let you begin using ORM effectively as soon as possible. Supported by examples, exercises, and useful background information, his step-by-step approach teaches you to develop a natural-language-based ORM model and then, where needed, abstract ER and UML models from it. This book will quickly make you proficient in the modeling technique that is proving vital to the development of accurate and efficient databases that best meet real business objectives.The most in-depth coverage of Object Role Modeling available anywhere-written by a pioneer in the development of ORM.Provides additional coverage of Entity Relationship (ER) modeling and the Unified Modeling Language-all from an ORM perspective.Intended for anyone with a stake in the accuracy and efficacy of databases: systems analysts, information modelers, database designers and administrators, instructors, managers, and programmers.Explains and illustrates required concepts from mathematics and set theory.

The Role of Blockchain in Disaster Management explores the architecture and implementation of existing blockchain-based IoT frameworks for the detection and prevention of disasters, along with the management of relative supply chains to protect against mismanagement of essential materials. The distributed nature of Blockchain helps to protect data from internal or external attacks, especially in disaster areas or times of crisis when database systems become overloaded and vulnerable to unauthorized access, manipulation, and disruption of critical services. This book can be used as a reference by graduate students, researchers, professors, and professionals in computer science, software design, and disaster management.

This book is devoted to the study of multivariate discrete q-distributions, which is greatly facilitated by existing multivariate q-sequences and q-functions. Classical multivariate discrete distributions are defined on a sequence of independent and identically distributed Bernoulli trials, with either being a success of a certain rank (level) or a failure. The author relaxes the assumption that the probability of success of a trial is constant by assuming that it varies geometrically with the number of trials and/or the number of successes. The latter is advantageous in the sense that it permits incorporating the experience gained from the previous trials and/or successes, which leads to multivariate discrete q-distributions. Furthermore, q-multinomial and negative q-multinomial formulae are obtained. Next, the book addresses q-multinomial and negative q-multinomial distributions of the first and second kind. The author also examines multiple q-Polya urn model, multivariate q-Polya and inverse q-Polya distributions. Presents definitions and theorems that highlight key concepts and worked examples to illustrate the various applicationsContains numerous exercises at varying levels of difficulty that consolidate the presented concepts and resultsIncludes hints and answers to all exercises via the appendix and is supplemented with an Instructor's Solution Manual

This book treats the elements of discrete mathematics that have important applications in computer science, thus providing the necessary tools for the reader to come to a competent mathematical judgement of modern developments in the age of information. Almost all assertions are shown with full proofs. Exercises are provided, with solutions presented in full detail.

This book studies 1-D and 2-D solutions of discrete and continuous analogue dynamical systems and identifies their intrinsic differences. It starts by introducing discrete dynamical systems before comparing them to continuous analogue ones. It studies in some depth periodic and chaotic-type solutions of quadratic and cubic equations and the harvesting/fishing effect on non-periodic and periodic solutions of populations models based on them. Considerations about the stability of the solutions are critical in their study. It contains examples of applications to accounting, pharmacology, harvesting/fishing strategies, economic and population models and historical battles.

Die 3., ergänzte Auflage stellt auf breiter fachlicher Ebene einfache elementare zahlentheoretische Inhalte vor sowie Stoffkomplexe aus der analytischen und algebraischen Zahlentheorie. Das Lehrbuch bietet auf überschaubaren mathematischen Niveau einen leicht verständlichen Einstieg in ausgewählte Themen der Zahlentheorie und beschreibt aktuelle Forschungsergebnisse zum RSA-Algorithmus. Sämtliche Kapitel enthalten umfassende Beispiele, Übungsaufgaben mit Lösungen und ausführlich durchgerechnete Beweise, so dass es sich sehr gut zur Prüfungsvorbereitung eignet.

Securing Next-Generation Connected Healthcare Systems: Artificial Intelligence Technologies focuses on the crucial aspects of IoT security in a connected environment, which will not only benefit from cutting-edge methodological approaches but also assist in the rapid scalability and improvement of these systems. This book shows how to utilize technologies like blockchain and its integration with IoT for communication, data security, and trust management. It introduces the security aspect of next generation technologies for healthcare, covering a wide range of security and computing methodologies.Researchers, data scientists, students, and professionals interested in the application of artificial intelligence in healthcare management, data security of connected healthcare systems and related fields, specifically on data intensive secured systems and computing environments, will finds this to be a welcomed resource.

This book provides essential information on Petri net theory and Petri net-based model checking methods. As for the Petri net theory, it involves the interleaving semantics and concurrency semantics of elementary net systems, some important net structures (e.g., invariant, repetitive vector, siphon, and trap), some classical net subclasses with special structures (e.g., state machine, marked graph, free-choice net,asymmetric-choice net, normal net, and weakly persistent net), and some basic properties (e.g., reachability, liveness, deadlock, and soundness). It also involves four high-level Petri nets: knowledge-oriented Petri nets, Petri nets with insecure places, time Petri nets, and plain time Petri nets with priorities, focusing on different fields of application. As for the model checking methods, this book introduces readers to computation tree logic (CTL), computation tree logic of knowledge (CTLK), and timed computation tree logic (TCTL), as well as Petri net-based methods for checking them. The basic principle of the reduced ordered binary decision diagram (ROBDD) is employed to compress the state space used in these model checking procedures. The book also covers time-soundness for time Petri nets and secure bisimulation for Petri nets with insecure places, both of which are based on the bisimulation theory. As such, it offers an introduction to basic information on bisimulation theory.

Recent Trends in Swarm Intelligence Enabled Research for Engineering Applications focuses on recent, up-to-date technologies, combining other intelligent tools with swarm intelligence techniques to yield robust and failsafe solutions to real world problems. This book aims to provide audiences with a platform to learn and gain insights into the latest developments in hybrid swarm intelligence. It will be useful to researchers, engineers, developers, practitioners, and graduate students working in the major and interdisciplinary areas of computational intelligence, communication systems, computer networks, and soft computing. With the advent of data-intensive applications, the elimination of redundancy in disseminated information has become a serious challenge for researchers who are on the lookout for evolving metaheuristic algorithms which can explore and exploit the information feature space to derive the optimal settings for specific applications. Swarm intelligence algorithms have developed as one of the most widely used metaheuristic techniques for addressing this challenge in an effective way. Inspired by the behavior of a swarm of bees, these swarm intelligence techniques emulate the corresponding natural instincts to derive optimal solutions for data-intensive applications.

The New Mathematical Coloring Book (TNMCB) includes striking results of the past 15-year renaissance that produced new approaches, advances, and solutions to problems from the first edition. A large part of the new edition ¿Ask what your computer can do for you,¿ presents the recent breakthrough by Aubrey de Grey and works by Marijn Heule, Jaan Parts, Geoffrey Exoo, and Dan Ismailescu. TNMCB introduces new open problems and conjectures that will pave the way to the future keeping the book in the center of the field. TNMCB presents mathematics of coloring as an evolution of ideas, with biographies of their creators and historical setting of the world around them, and the world around us.A new thing in the world at the time, TMCB I is now joined by a colossal sibling containing more than twice as much of what only Alexander Soifer can deliver: an interweaving of mathematics with history and biography, well-seasoned with controversy and opinion. ¿Peter D. Johnson, Jr.Auburn UniversityLike TMCB I, TMCB II is a unique combination of Mathematics, History, and Biography written by a skilled journalist who has been intimately involved with the story for the last half-century. ¿The nature of the subject makes much of the material accessible to students, but also of interest to working Mathematicians. ¿ In addition to learning some wonderful Mathematics, students will learn to appreciate the influences of Paul Erd¿s, Ron Graham, and others.¿Geoffrey ExooIndiana State UniversityThe beautiful and unique Mathematical coloring book of Alexander Soifer is another case of ¿good mathematics¿, containing a lot of similar examples (it is not by chance that Szemerédi¿s Theorem story is included as well) and presenting mathematics as both a science and an art¿¿Peter MihókMathematical Reviews, MathSciNetA postman came to the door with a copy of the masterpiece of the century. I thank you and the mathematics community should thank you for years to come. You have set a standard for writing about mathematics and mathematicians that will be hard to match.¿ Harold W. KuhnPrinceton UniversityI have never encountered a book of this kind. The best description of it I can give is that it is a mystery novel¿ I found it hard to stop reading before I finished (in two days) the whole text. Soifer engages the reader's attention not only mathematically, but emotionally and esthetically. May you enjoy the book as much as I did!¿ Branko GrünbaumUniversity of WashingtonI am in absolute awe of your 2008 book.¿Aubrey D.N.J. de GreyLEV Foundation

Decision Making Models: A Perspective of Fuzzy Logic and Machine Learning presents the latest developments in the field of uncertain mathematics and decision science. The book aims to deliver a systematic exposure to soft computing techniques in fuzzy mathematics as well as artificial intelligence in the context of real-life problems and is designed to address recent techniques to solving uncertain problems encountered specifically in decision sciences. Researchers, professors, software engineers, and graduate students working in the fields of applied mathematics, software engineering, and artificial intelligence will find this book useful to acquire a solid foundation in fuzzy logic and fuzzy systems.Other areas of note include optimization problems and artificial intelligence practices, as well as how to analyze IoT solutions with applications and develop decision-making mechanisms realized under uncertainty.

Smart Spaces covers the latest concepts and technologies surrounding smart spaces, providing technical personnel engaged in smart space related research and industries a more in-depth understanding of smart spaces. This book can be used as a reference for practicing this emerging discipline, but it will also be useful for researchers, scientists, developers, practitioners, and graduate students working in the fields of smart spaces and artificial intelligence. It combines the study of working or living spaces with computing, information equipment, and multimodal sensing devices, and with natural and convenient interactive interfaces to support how people can easily obtain services from computer systems. People's work and life in smart spaces use computer systems; it is a process of uninterrupted interaction between people and the computer system. In this process, the computer is no longer just an information processing tool that passively executes explicit human operation commands but a collaborator with people to complete tasks - a partner to human beings. International research on smart spaces is quite extensive, which shows the important role of smart spaces in ubiquitous computing research.

This book constitutes refereed proceedings of the 22nd International Conference on Mathematical Optimization Theory and Operations Research: Recent Trends, MOTOR 2023, held in Ekaterinburg, Russia, during July 2¿8, 2023. The 28 full papers and one invited paper presented in this volume were carefully reviewed and selected from a total of 61 submissions. The papers in the volume are organized according to the following topical headings: mathematical programming; stochastic optimization; discrete and combinatorial optimization; operations research; optimal control and mathematical economics; and optimization in machine learning.

This book systematically establishes the almost periodic theory of dynamic equations and presents applications on time scales in fuzzy mathematics and uncertainty theory. The authors introduce a new division of fuzzy vectors depending on a determinant algorithm and develop a theory of almost periodic fuzzy multidimensional dynamic systems on time scales. Several applications are studied; in particular, a new type of fuzzy dynamic systems called fuzzy q-dynamic systems (i.e. fuzzy quantum dynamic systems) is presented. The results are not only effective on classical fuzzy dynamic systems, including their continuous and discrete situations, but are also valid for other fuzzy multidimensional dynamic systems on various hybrid domains. In an effort to achieve more accurate analysis in real world applications, the authors propose a number of uncertain factors in the theory. As such, fuzzy dynamical models, interval-valued functions, differential equations, fuzzy-valued differential equations, and their applications to dynamic equations on time scales are considered.

This volume constitutes the thoroughly refereed proceedings of the 49th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2023. The 33 full papers presented in this volume were carefully reviewed and selected from a total of 116 submissions. The WG 2022 workshop aims to merge theory and practice by demonstrating how concepts from graph theory can be applied to various areas in computer science, or by extracting new graph theoretic problems from applications.

This book is intended to provide graduate students and researchers in graph theory with an overview of the elementary methods of graph Ramsey theory. It is especially targeted towards graduate students in extremal graph theory, graph Ramsey theory, and related fields, as the included contents allow the text to be used in seminars. It is structured in thirteen chapters which are application-focused and largely independent, enabling readers to target specific topics and information to focus their study. The first chapter includes a true beginner's overview of elementary examples in graph Ramsey theory mainly using combinatorial methods. The following chapters progress through topics including the probabilistic methods, algebraic construction, regularity method, but that's not all. Many related interesting topics are also included in this book, such as the disproof for a conjecture of Borsuk on geometry, intersecting hypergraphs, Turan numbers and communication channels, etc.

This proceedings volume gathers selected, revised papers presented at the 51st Southeastern International Conference on Combinatorics, Graph Theory and Computing (SEICCGTC 2020), held at Florida Atlantic University in Boca Raton, USA, on March 9-13, 2020. The SEICCGTC is broadly considered to be a trendsetter for other conferences around the world - many of the ideas and themes first discussed at it have subsequently been explored at other conferences and symposia.The conference has been held annually since 1970, in Baton Rouge, Louisiana and Boca Raton, Florida. Over the years, it has grown to become the major annual conference in its fields, and plays a major role in disseminating results and in fostering collaborative work.This volume is intended for the community of pure and applied mathematicians, in academia, industry and government, working in combinatorics and graph theory, as well as related areas of computer science and the interactions among these fields.