The Science of Deep Learning emerged from courses taught by the author that have provided thousands of students with training and experience for their academic studies, and prepared them for careers in deep learning, machine learning, and artificial intelligence in top companies in industry and academia. The book begins by covering the foundations of deep learning, followed by key deep learning architectures. Subsequent parts on generative models and reinforcement learning may be used as part of a deep learning course or as part of a course on each topic. The book includes state-of-the-art topics such as Transformers, graph neural networks, variational autoencoders, and deep reinforcement learning, with a broad range of applications. The appendices provide equations for computing gradients in backpropagation and optimization, and best practices in scientific writing and reviewing. The text presents an up-to-date guide to the field built upon clear visualizations using a unified notation and equations, lowering the barrier to entry for the reader. The accompanying website provides complementary code and hundreds of exercises with solutions.

This second edition of Lessons in Play reorganizes the presentation of the popular original text in combinatorial game theory to make it even more widely accessible. Starting with a focus on the essential concepts and applications, it then moves on to more technical material. Still written in a textbook style with supporting evidence and proofs, the authors add many more exercises and examples and implement a two-step approach for some aspects of the material involving an initial introduction, examples, and basic results to be followed later by more detail and abstract results. Features Employs a widely accessible style to the explanation of combinatorial game theory Contains multiple case studies Expands further directions and applications of the field Includes a complete rewrite of CGSuite material

The rise of game theory has made bargaining one of the core issues in economic theory. Written at a theoretical and conceptual level, this book develops a framework for the analysis of bargaining processes. The framework focuses on the dynamic of the bargaining process, which is in contrast to much previous theoretical work on the subject, and most notably to the approaches stemming from game theory. Chapters include: decision-making and expectations in theories of bargaining; decision-making and expectations in a game theory model; limitations of the environment concept; game theory as a basis for a theory of bargaining; the decision/expectation/adjustment approach; the adjustment process; direct interdependence and the consistency of decisions.

Game theory now provides the theoretical underpinning for a multitude of courses in economics worldwide. The speed of these developments has been remarkable and they have constituted something of a revolution. Indeed, the basic tenets of game theory have now begun to colonize other social sciences and its proponents have been unified in claiming its natural basis as a rational theory of society.
But the technical demands of the subject and the lack of clarity of many commentators' explanations have been a problem for many. This second edition of Shaun Hargreaves-Heap and Yanis Varoufakis's classic text strips away the mystique and lets the student make his or her own mind up. This new edition:
* lays bear the philosophy behind game theory and explains all its major concepts
* conducts a clear explanation and careful analysis of all the main 'games', such as repeated games and the prisoner's dilemma, as well as less well-trodden topics such as experimental games and issues of rationality
* introduces and analyses new areas of game theory such as "evolutionary games" and "Psychological games"
Retaining the most popular features from the original edition, this latest version offers improved pedagogy, new questions for discussion, new chapters on the latest developments as well as a host of new examples. A new generation of students of game theory will grow to appreciate this superb text whilst fans of the first edition will eagerly devour this long-awaited update.

Game theory is rapidly becoming one of the cornerstones of the social sciences. The articles gathered here chart the intellectual history of game theory from its place in the Enlightenment tradition, through the explosion of literature in the late 1970s, to issues of current and emerging debates. This extensively indexed set will be a valuable reference tool to researchers in sociology and politics, as well as economics.

Congruences are ubiquitous in computer science, engineering, mathematics, and related areas. Developing techniques for finding (the number of) solutions of congruences is an important problem. But there are many scenarios in which we are interested in only a subset of the solutions; in other words, there are some restrictions. What do we know about these restricted congruences, their solutions, and applications? This book introduces the tools that are needed when working on restricted congruences and then systematically studies a variety of restricted congruences. Restricted Congruences in Computing defines several types of restricted congruence, obtains explicit formulae for the number of their solutions using a wide range of tools and techniques, and discusses their applications in cryptography, information security, information theory, coding theory, string theory, quantum field theory, parallel computing, artificial intelligence, computational biology, discrete mathematics, number theory, and more. This is the first book devoted to restricted congruences and their applications. It will be of interest to graduate students and researchers across computer science, electrical engineering, and mathematics.

The game of Dots-and-Boxes, the popular game in which two players take turns connecting an array of dots to form squares, or "boxes" has long been considered merely a child's game. In this book, however, the author reveals the surprising complexity of the game, along with advanced strategies that will allow the reader to win at any level of gameplay desired. This book is an essential guide to the game of Dots-and-Boxes and its mathematical underpinnings. Chapters of strategy are interspersed with dozens of sample problems and their solutions. Furthermore, the strategies can be applied to several other games, such as Strings-and-Coins and Nimstring.

A PRACTICAL GUIDE TO OPTIMIZATION PROBLEMS WITH DISCRETE OR INTEGER VARIABLES, REVISED AND UPDATED The revised second edition of Integer Programming explains in clear and simple terms how to construct custom-made algorithms or use existing commercial software to obtain optimal or near-optimal solutions for a variety of real-world problems. The second edition also includes information on the remarkable progress in the development of mixed integer programming solvers in the 22 years since the first edition of the book appeared. The updated text includes information on the most recent developments in the field such as the much improved preprocessing/presolving and the many new ideas for primal heuristics included in the solvers. The result has been a speed-up of several orders of magnitude. The other major change reflected in the text is the widespread use of decomposition algorithms, in particular column generation (branch-(cut)-and-price) and Benders' decomposition. The revised second edition: Contains new developments on column generation Offers a new chapter on Benders' algorithm Includes expanded information on preprocessing, heuristics, and branch-and-cut Presents several basic and extended formulations, for example for fixed cost network flows Also touches on and briefly introduces topics such as non-bipartite matching, the complexity of extended formulations or a good linear program for the implementation of lift-and-project Written for students of integer/mathematical programming in operations research, mathematics, engineering, or computer science, Integer Programming offers an updated edition of the basic text that reflects the most recent developments in the field.

Problems in network optimization arise in all areas of technology and industrial management. The topic of network flows has applications in diverse fields such as chemistry, engineering, management science, scheduling and transportation, to name a few.

Many experiments have shown the human brain generally has very serious problems dealing with probability and chance. A greater understanding of probability can help develop the intuition necessary to approach risk with the ability to make more informed (and better) decisions. The first four chapters offer the standard content for an introductory probability course, albeit presented in a much different way and order. The chapters afterward include some discussion of different games, different "ideas" that relate to the law of large numbers, and many more mathematical topics not typically seen in such a book. The use of games is meant to make the book (and course) feel like fun! Since many of the early games discussed are casino games, the study of those games, along with an understanding of the material in later chapters, should remind you that gambling is a bad idea; you should think of placing bets in a casino as paying for entertainment. Winning can, obviously, be a fun reward, but should not ever be expected. Changes for the Second Edition: New chapter on Game Theory New chapter on Sports Mathematics The chapter on Blackjack, which was Chapter 4 in the first edition, appears later in the book. Reorganization has been done to improve the flow of topics and learning. New sections on Arkham Horror, Uno, and Scrabble have been added. Even more exercises were added! The goal for this textbook is to complement the inquiry-based learning movement. In my mind, concepts and ideas will stick with the reader more when they are motivated in an interesting way. Here, we use questions about various games (not just casino games) to motivate the mathematics, and I would say that the writing emphasizes a "just-in-time" mathematics approach. Topics are presented mathematically as questions about the games themselves are posed. Table of Contents Preface 1. Mathematics and Probability 2. Roulette and Craps: Expected Value 3. Counting: Poker Hands 4. More Dice: Counting and Combinations, and Statistics 5. Game Theory: Poker Bluffing and Other Games 6. Probability/Stochastic Matrices: Board Game Movement 7. Sports Mathematics: Probability Meets Athletics 8. Blackjack: Previous Methods Revisited 9. A Mix of Other Games 10. Betting Systems: Can You Beat the System? 11. Potpourri: Assorted Adventures in Probability Appendices Tables Answers and Selected Solutions Bibliography Biography Dr. David G. Taylor is a professor of mathematics and an associate dean for academic affairs at Roanoke College in southwest Virginia. He attended Lebanon Valley College for his B.S. in computer science and mathematics and went to the University of Virginia for his Ph.D. While his graduate school focus was on studying infinite dimensional Lie algebras, he started studying the mathematics of various games in order to have a more undergraduate-friendly research agenda. Work done with two Roanoke College students, Heather Cook and Jonathan Marino, appears in this book! Currently he owns over 100 different board games and enjoys using probability in his decision-making while playing most of those games. In his spare time, he enjoys reading, cooking, coding, playing his board games, and spending time with his six-year-old dog Lilly.

Key environmental issues, such as biodiversity and climate change, have in recent years become more pressing than ever. Where the critical papers in the early 1990s explained the difficulties of cooperation in tackling transboundary environmental problems, later works have analyzed the various alternatives, and increased our understanding of various institutional designs and negotiation protocols' impact on the success of cooperation. This collection brings together the most important articles on the game theoretic analysis of international environmental cooperation to both confront the cooperative and non-cooperative approaches to this, and demonstrate the diversity of methods used to analyze international environmental agreements.

Features Provides a uniquely historical perspective on the mathematical underpinnings of a comprehensive list of games Suitable for a broad audience of differing mathematical levels. Anyone with a passion for games, game theory, and mathematics will enjoy this book, whether they be students, academics, or game enthusiasts Covers a wide selection of topics at a level that can be appreciated on a historical, recreational, and mathematical level.

This book offers a unique and insightful econometric evaluation of the policies used to fight transnational terrorism between 1990 and 2014. It uses the tools of modern economics, game theory and structural econometrics to analyze the roles of foreign aid, educational capital, and military intervention. Jean-Paul Azam and Veronique Thelen analyze panel data over 25 years across 124 countries. They prove that foreign aid plays a key role in inducing recipient governments to protect the donors' political and economic interests within their sphere of influence. Demonstrating that countries endowed with better educational capital export fewer terrorist attacks, they also illustrate that, in contrast, military intervention is counter-productive in abating terrorism. Recognizing the strides taken by the Obama administration to increase the role of foreign aid and reduce the use of military interventions, this book shows the significant impact this has had in reducing the number of transnational terrorist attacks per source country, and suggests further developments in this vein. Practical and timely, this book will be of particular interest to students and scholars of economics and political science, as well as those working on the wider issue of terrorism. Presenting a series of new findings, the book will also appeal to international policy makers and government officials.

This book is for those interested in number systems, abstract algebra, and analysis. It provides an understanding of negative and fractional numbers with theoretical background and explains rationale of irrational and complex numbers in an easy to understand format. This book covers the fundamentals, proof of theorems, examples, definitions, and concepts. It explains the theory in an easy and understandable manner and offers problems for understanding and extensions of concept are included. The book provides concepts in other fields and includes an understanding of handling of numbers by computers. Research scholars and students working in the fields of engineering, science, and different branches of mathematics will find this book of interest, as it provides the subject in a clear and concise way.

Congruences are ubiquitous in computer science, engineering, mathematics, and related areas. Developing techniques for finding (the number of) solutions of congruences is an important problem. But there are many scenarios in which we are interested in only a subset of the solutions; in other words, there are some restrictions. What do we know about these restricted congruences, their solutions, and applications? This book introduces the tools that are needed when working on restricted congruences and then systematically studies a variety of restricted congruences. Restricted Congruences in Computing defines several types of restricted congruence, obtains explicit formulae for the number of their solutions using a wide range of tools and techniques, and discusses their applications in cryptography, information security, information theory, coding theory, string theory, quantum field theory, parallel computing, artificial intelligence, computational biology, discrete mathematics, number theory, and more. This is the first book devoted to restricted congruences and their applications. It will be of interest to graduate students and researchers across computer science, electrical engineering, and mathematics.

Many systems architecture optimization problems are characterized by a variable number of optimization variables. Many classical optimization algorithms are not suitable for such problems. The book presents recently developed optimization concepts that are designed to solve such problems. These new concepts are implemented using genetic algorithms and differential evolution. The examples and applications presented show the effectiveness of the use of these new algorithms in optimizing systems architectures. The book focuses on systems architecture optimization. It covers new algorithms and its applications, besides reviewing fundamental mathematical concepts and classical optimization methods. It also provides detailed modeling of sample engineering problems. The book is suitable for graduate engineering students and engineers. The second part of the book includes numerical examples on classical optimization algorithms, which are useful for undergraduate engineering students. While focusing on the algorithms and their implementation, the applications in this book cover the space trajectory optimization problem, the optimization of earth orbiting satellites orbits, and the optimization of the wave energy converter dynamic system: architecture and control. These applications are illustrated in the starting of the book, and are used as case studies in later chapters for the optimization methods presented in the book.

"Constructive Computation in Stochastic Models with Applications: The RG-Factorizations" provides a unified, constructive and algorithmic framework for numerical computation of many practical stochastic systems. It summarizes recent important advances in computational study of stochastic models from several crucial directions, such as stationary computation, transient solution, asymptotic analysis, reward processes, decision processes, sensitivity analysis as well as game theory. Graduate students, researchers and practicing engineers in the field of operations research, management sciences, applied probability, computer networks, manufacturing systems, transportation systems, insurance and finance, risk management and biological sciences will find this book valuable.

Dr. Quan-Lin Li is an Associate Professor at the Department of Industrial Engineering of Tsinghua University, China.

Reviews the literature of the Moth-Flame Optimization algorithm; Provides an in-depth analysis of equations, mathematical models, and mechanisms of the Moth-Flame Optimization algorithm; Proposes different variants of the Moth-Flame Optimization algorithm to solve binary, multi-objective, noisy, dynamic, and combinatorial optimization problems; Demonstrates how to design, develop, and test different hybrids of Moth-Flame Optimization algorithm; Introduces several applications areas of the Moth-Flame Optimization algorithm focusing in sustainability.

This book describes the fundamental and theoretical concepts of optimization algorithms in a systematic manner, along with their potential applications and implementation strategies in mining engineering. It explains basics of systems engineering, linear programming, and integer linear programming, transportation and assignment algorithms, network analysis, dynamic programming, queuing theory and their applications to mine systems. Reliability analysis of mine systems, inventory management in mines, and applications of non-linear optimization in mines are discussed as well. All the optimization algorithms are explained with suitable examples and numerical problems in each of the chapters. Features include: * Integrates operations research, reliability, and novel computerized technologies in single volume, with a modern vision of continuous improvement of mining systems. * Systematically reviews optimization methods and algorithms applied to mining systems including reliability analysis. * Gives out software-based solutions such as MATLAB (R), AMPL, LINDO for the optimization problems. * All discussed algorithms are supported by examples in each chapter. * Includes case studies for performance improvement of the mine systems. This book is aimed primarily at professionals, graduate students, and researchers in mining engineering.

Economic Games and Strategic Behaviour is a seminal volume which introduces a model providing solutions to economic games subject to repeated play. It develops a link between strategic bargaining and the theory of self-enforcing contracts to give insights into the long-term relationships between two parties, such as firms or governments, who meet in a negotiating situation. The author provides an original approach to strategic bargaining to find a solution to economic games in which cooperation cannot be enforced by a third party. He then applies this approach to a wide range of real life situations including international environmental agreements, bilateral trade agreements, collusion between firms in industry and bargaining between buyers and sellers in the market place. The author also discusses important policy implications as well as setting an agenda for future research. Economic Games and Strategic Behaviour is an original contribution to the existing literature which will be welcomed for providing accurate outcomes for situations in which conventional theories produce ambiguous results. It will be of great interest to students and scholars of microeconomics, game theory and industrial economics.

This book discusses an important area of numerical optimization, called interior-point method. This topic has been popular since the 1980s when people gradually realized that all simplex algorithms were not convergent in polynomial time and many interior-point algorithms could be proved to converge in polynomial time. However, for a long time, there was a noticeable gap between theoretical polynomial bounds of the interior-point algorithms and efficiency of these algorithms. Strategies that were important to the computational efficiency became barriers in the proof of good polynomial bounds. The more the strategies were used in algorithms, the worse the polynomial bounds became. To further exacerbate the problem, Mehrotra's predictor-corrector (MPC) algorithm (the most popular and efficient interior-point algorithm until recently) uses all good strategies and fails to prove the convergence. Therefore, MPC does not have polynomiality, a critical issue with the simplex method. This book discusses recent developments that resolves the dilemma. It has three major parts. The first, including Chapters 1, 2, 3, and 4, presents some of the most important algorithms during the development of the interior-point method around the 1990s, most of them are widely known. The main purpose of this part is to explain the dilemma described above by analyzing these algorithms' polynomial bounds and summarizing the computational experience associated with them. The second part, including Chapters 5, 6, 7, and 8, describes how to solve the dilemma step-by-step using arc-search techniques. At the end of this part, a very efficient algorithm with the lowest polynomial bound is presented. The last part, including Chapters 9, 10, 11, and 12, extends arc-search techniques to some more general problems, such as convex quadratic programming, linear complementarity problem, and semi-definite programming.

This book details cutting-edge research into human-like driving technology, utilising game theory to better suit a human and machine hybrid driving environment. Covering feature identification and modelling of human driving behaviours, the book explains how to design an algorithm for decision making and control of autonomous vehicles in complex scenarios. Beginning with a review of current research in the field, the book uses this as a springboard from which to present a new theory of human-like driving framework for autonomous vehicles. Chapters cover system models of decision making and control, driving safety, riding comfort and travel efficiency. Throughout the book, game theory is applied to human-like decision making, enabling the autonomous vehicle and the human driver interaction to be modelled using noncooperative game theory approach. It also uses game theory to model collaborative decision making between connected autonomous vehicles. This framework enables human-like decision making and control of autonomous vehicles, which leads to safer and more efficient driving in complicated traffic scenarios. The book will be of interest to students and professionals alike, in the field of automotive engineering, computer engineering and control engineering.

There are thousands of books relating to poker, blackjack, roulette and baccarat, including strategy guides, statistical analysis, psychological studies, and much more. However, there are no books on Pell, Rouleno, Street Dice, and many other games that have had a short life in casinos! While this is understandable - most casino gamblers have not heard of these games, and no one is currently playing them - their absence from published works means that some interesting mathematics and gaming history are at risk of being lost forever. Table games other than baccarat, blackjack, craps, and roulette are called carnival games, as a nod to their origin in actual traveling or seasonal carnivals. Mathematics of Casino Carnival Games is a focused look at these games and the mathematics at their foundation. Features * Exercises, with solutions, are included for readers who wish to practice the ideas presented * Suitable for a general audience with an interest in the mathematics of gambling and games * Goes beyond providing practical 'tips' for gamblers, and explores the mathematical principles that underpin gambling games

The detailed survey on constraint handling techniques specifically penalty function approach is presented in the book; presents the Cohort Intelligence (CI) algorithm incorporated with a novel self-adaptive penalty function (SAPF) approach which helped in avoiding preliminary trials of selecting penalty parameter. The approach is referred to as CI-SAPF; CI-SAPF is further hybridized with Colliding Bodies Optimization (CBO) algorithm to promote a parameter less metaheuristic algorithm; presents solutions to several problems from discrete truss structure domain, mixed variable design engineering domain, and linear & nonlinear domain validating the CI-SAPF and CI-SAPF-CBO; behavior of SAPF approach on pseudo objective function, constraint violations, penalty function and penalty parameter have been analyzed and discussed in very detail; presents the in-depth analysis and comparison of the CI-SAPF, CI-SAPF-CBO and CBO algorithms with other contemporary techniques; provides the solution to real-world manufacturing problems of optimizing multi pass milling and turning processes using CI-SPF, CI-SAPF and CI-SAPF-CBO approaches.

This book synthesizes the game-theoretic modeling of decision-making processes and an ancient moral requirement called the Golden Rule of ethics (GR). This rule states "Behave to others as you would like them to behave to you." The GR is one of the oldest, most widespread, and specific moral requirements that appear in Christianity, Islam, Judaism, Buddhism, and Confucianism. This book constructs and justifies mathematical models of dynamic socio-economic processes and phenomena that reveal the mechanism of the GR and are based on the concept of Berge equilibrium. The GR can be naturally used for resolving or balancing conflicts, and its "altruistic character" obviously excludes wars, blood-letting, and armed clashes. The previous book by the authors, The Berge Equilibrium: A Game-Theoretic Framework for the Golden Rule of Ethics, covers the static case of the GR. In this book, the dynamic case of the GR is investigated using the altruistic concept of Berge equilibrium and three factors as follows: 1) a modification of N.N. Krasovskii's mathematical formalization of differential positional games (DPGs), in view of the counterexamples given by A.I. Subbotin and A.F. Kononenko; 2) the method of guiding control, proposed by N.N. Krasovskii; and 3) the Germier convolution of the payoff functions of different players. Additionally, this book features exercises, problems, and solution tips collected together in Appendix 1, as well as new approaches to conflict resolution as presented in Appendices 2 to 4. This book will be of use to undergraduate and graduate students and experts in the field of decision-making in complex control and management systems, as well as anyone interested in game theory and applications.