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• Press Start.- Foundations.- Reality.- Meaning.- Play.- Balancing.- Game Over?- Solutions.- Workshop.- Worksheets.- Index.
• (source: Nielsen Book Data)

Many designers, policy makers, teachers, and other practitioners are beginning to understand the usefulness of using digital games beyond entertainment. Games have been developed for teaching, recruiting and to collect data to improve search engines. This book examines the fundamentals of designing any game with a serious purpose and provides a way of thinking on how to design one successfully. The reader will be introduced to a design philosophy called 'Triadic Game Design'; a theory that all games involve three worlds - the worlds of Reality, Meaning, and Play. Each world is affiliated with aspects. A balance needs to be found within and between the three worlds. Such a balance is difficult to achieve, during the design many tensions will arise, forcing designers to make trade-offs. To deal with these tensions and to ensure that the right decisions are made to create a harmonic game, a frame of reference is needed. This is what "Triadic Game Design" offers.
(source: Nielsen Book Data)

• The children of Democritus (prediction in science)-- The laws of chaos (the theory of probability)-- Gaussian deviations (the theory of physical measurements)-- Maxwell, or probabilities as a matter of ignorance-- Boltzmann, or probabilities as a matter of conviction (statistical physics)-- Poincare, or deterministic chaos (sensitivity to initial conditions)-- Bohr, or chance unavoidable (quantum mechanics)-- Inseparable photons (the EPR paradox).
• (source: Nielsen Book Data)

This is an introduction to the ideas of indeterminacy that are central to much of modern physics and have overthrown the "clockwork universe" conceptions of earlier centuries.
(source: Nielsen Book Data)
This is an introduction to the ideas of randomness that are central to much of modern physics and have overthrown the "clock-work universe" conceptions of earlier centuries. The author shows how the laws of probability and statistics were developed by such mathematicians as Fermat, Pascal, and Gauss, and how they received their first major application in physics in the kinetic theory of gases developed by Maxwell and Boltzmann. Here the use of statistics is necessary because the number of particles involved is too great for a deterministic calculation. But soon the mathematician and physicist Poincare demonstrated the unpredictability if certain systems containing only a small number of bodies, because of extreme sensitivity to initial conditions. He thus became a founder of chaos theory. Finally, with the advent of quantum theory, physics seemed to be based on an essential randomness, whose reality was debated by Bohr and Einstein till the end of their lives. Only recently, in the experiments of Alain Aspect, has a convincing demonstration been given the inescapable randomness of quantum theory is a fact of nature. Professor Ruhla guides the reader skilfully through all these developments and provides mathematical details in appendices. The book provides an accessible introduction to the modern physicist's conception of the world of cause and chance.
(source: Nielsen Book Data)

• The beautiful game
• An introduction to the physics and mathematics of soccer
• Follow the bouncing ball
• How about a banana split?
• Cracking the whip
• Putting it all together.

Soccer is the most popular sport in the world. It is also an endless scientific panorama. Every movement by the players and each interaction with the ball involves physics, fluid mechanics, biology, and physiology, to name just a few of the scientific disciplines. In a book that targets middle and high school players, Taylor begins with a history of soccer and its physical and mathematical aspects. He then addresses important questions such as how and why a ball bounces, how the ball spins, and what these dynamics mean for the game. He introduces readers to the science of kicking, heading, and trapping and looks at the sources of the energy required to run, jump, and kick for an entire game. Taylor then puts it all together by following a sequence of plays and describing the science behind tactical manoeuvres. Sidebars and appendices allow those with a more mathematical bent to follow the physics and perform experiments to see the effects of phenomena like drag, bounce, and spin. In addition, key terminology is highlighted, explained in the text, and summarized in the glossary.
(source: Nielsen Book Data)

• The beautiful game
• An introduction to the physics and mathematics of soccer
• Follow the bouncing ball
• How about a banana split?
• Cracking the whip
• Putting it all together.

Soccer is the most popular sport in the world. It is also an endless scientific panorama. Every movement by the players and each interaction with the ball involves physics, fluid mechanics, biology, and physiology, to name just a few of the scientific disciplines. In a book that targets middle and high school players, Taylor begins with a history of soccer and its physical and mathematical aspects. He then addresses important questions such as how and why a ball bounces, how the ball spins, and what these dynamics mean for the game. He introduces readers to the science of kicking, heading, and trapping and looks at the sources of the energy required to run, jump, and kick for an entire game. Taylor then puts it all together by following a sequence of plays and describing the science behind tactical manoeuvres. Sidebars and appendices allow those with a more mathematical bent to follow the physics and perform experiments to see the effects of phenomena like drag, bounce, and spin. In addition, key terminology is highlighted, explained in the text, and summarized in the glossary.
(source: Nielsen Book Data)

Essential reading for all outdoor enthusiasts who venture into mountainous terrain where avalanches are common.In spite of the increasing sophistication of avalanche hazard forecasting, an alarming number of people die every year in backcountry avalanche accidents. This updated edition of Backcountry Avalanche Safety contains the latest information on avalanche risk and focuses on the following vital topics:• Mountain Weather• Snow and Snowpack• Types of Avalanches• Avalanche Terrain• Trip Planning• Avalanche Gear• Travel in Avalanche Terrain• Riding Steep Slopes• Companion RescueUsing colour photographs along with detailed charts, graphs and diagrams, the author clearly explains the importance of managing risk while enjoying backcountry adventure during the winter months.

• A table of contents is not available for this title.
• (source: Nielsen Book Data)

*Shows how to create realistic action games without assuming college-level Physics (which the majority of gamers won't have); includes necessary physics and mathematics *Ideal for all budding games programmers, with example code in Java, C#, and C *Complements Apress's platform-specific gaming books, like Advanced Java Games Programming and Beginning .NET Games Programming with C#, and the forthcoming Beginning .NET Games Programming in VB.NET *Palmer has strong contacts in the Microsoft Games Division and Electronic Arts, a major gaming producer.
(source: Nielsen Book Data)

• Introduction.- General Presentation of Mean Field Control Problems.- Discussion of the Mean Field game.- Discussion of the Mean Field Type Control.- Approximation of Nash Games with a large number of players.- Linear Quadratic Models.- Stationary Problems- Different Populations.- Nash differential games with Mean Field effect.
• (source: Nielsen Book Data)

Mean field games and Mean field type control introduce new problems in Control Theory. The terminology "games" may be confusing. In fact they are control problems, in the sense that one is interested in a single decision maker, whom we can call the representative agent. However, these problems are not standard, since both the evolution of the state and the objective functional is influenced but terms which are not directly related to the state or the control of the decision maker. They are however, indirectly related to him, in the sense that they model a very large community of agents similar to the representative agent. All the agents behave similarly and impact the representative agent. However, because of the large number an aggregation effect takes place. The interesting consequence is that the impact of the community can be modeled by a mean field term, but when this is done, the problem is reduced to a control problem.
(source: Nielsen Book Data)

• Preface; Book Outline; Thanks; Bibliographical Notes; Acknowledgments; Contents; 1 Introduction; 1.1 Derivation of MFG Models; 1.1.1 Optimal Control and Hamilton-Jacobi Equations; 1.1.2 Transport Equation; 1.1.3 Mean-Field Models; 1.1.4 Extensions and Additional Problems; 1.1.5 Uniqueness; 2 Explicit Solutions, Special Transformations, and Further Examples; 2.1 Explicit Solutions; 2.2 The Hopf-Cole Transform; 2.3 Gaussian-Quadratic Solutions; 2.4 Interface Formation; 2.5 Bibliographical Notes; 3 Estimates for the Hamilton-Jacobi Equation; 3.1 Comparison Principle; 3.2 Control Theory Bounds.

• 3.2.1 Optimal Trajectories3.2.2 Dynamic Programming Principle; 3.2.3 Subdifferentials and Superdifferentials of the Value Function; 3.2.4 Regularity of the Value Function; 3.3 Integral Bernstein Estimate; 3.4 Integral Estimates for HJ Equations; 3.5 Gagliardo-Nirenberg Estimates; 3.6 Bibliographical Notes; 4 Estimates for the Transport and Fokker-Planck Equations; 4.1 Mass Conservation and Positivity of Solutions; 4.2 Regularizing Effects of the Fokker-Planck Equation; 4.3 Fokker-Planck Equation with Singular Initial Conditions; 4.4 Iterative Estimates for the Fokker-Planck Equation.

• 4.4.1 Regularity by Estimates on the Divergence of the Drift4.4.2 Polynomial Estimates for the Fokker-Planck Equation, p<∞; 4.4.3 Polynomial Estimates for the Fokker-Planck Equation, p=∞; 4.5 Relative Entropy; 4.6 Weak Solutions; 4.7 Bibliographical Notes; 5 The Nonlinear Adjoint Method; 5.1 Representation of Solutions and Lipschitz Bounds; 5.2 Conserved Quantities; 5.3 The Vanishing Viscosity Convergence Rate; 5.4 Semiconcavity Estimates; 5.5 Lipschitz Regularity for the Heat Equation; 5.6 Irregular Potentials; 5.7 The Hopf-Cole Transform; 5.8 Bibliographical Notes; 6 Estimates for MFGs

• 6.1 Maximum Principle Bounds6.2 First-Order Estimates; 6.3 Additional Estimates for Solutions of the Fokker-Plank Equation; 6.4 Second-Order Estimates; 6.4.1 Stationary Problems; 6.4.2 Time-Dependent Problems; 6.5 Some Consequences of Second-Order Estimates; 6.6 The Evans Method for the Evans-Aronsson Problem; 6.7 An Energy Conservation Principle; 6.8 Porreta's Cross Estimates; 6.9 Bibliographical Notes; 7 A Priori Bounds for Stationary Models; 7.1 The Bernstein Method; 7.2 A MFG with Congestion; 7.3 Logarithmic Nonlinearity; 7.4 Bibliographical Notes.

• 8 A Priori Bounds for Time-Dependent Models8.1 Subquadratic Hamiltonians; 8.2 Quadratic Hamiltonians; 8.3 Bibliographical Notes; 9 A Priori Bounds for Models with Singularities; 9.1 Logarithmic Nonlinearities; 9.2 Congestion Models: Local Existence; 9.2.1 Estimates for Arbitrary Terminal Time; 9.2.2 Short-Time Estimates; 9.3 Bibliographical Notes; 10 Non-local Mean-Field Games: Existence; 10.1 First-Order, Non-local Mean-Field Games; 10.2 Second-Order, Non-local Mean-Field Games; 10.3 Bibliographical Notes; 11 Local Mean-Field Games: Existence; 11.1 Bootstrapping Regularity.

Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.

• Preface to Volume I.- Part I: The Probabilistic Approach to Mean Field Games.- Learning by Examples: What is a Mean Field Game?.- Probabilistic Approach to Stochastic Differential Games.- Stochastic Differential Mean Field Games.- FBSDEs and the Solution of MFGs without Common Noise.- Part II: Analysis on Wasserstein Space and Mean Field Control.- Spaces of Measures and Related Differential Calculus.- Optimal Control of SDEs of McKean-Vlasov Type.- Epologue to Volume I.- Extensions for Volume I. References.- Indices.
• (source: Nielsen Book Data)

This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions. Volume I of the book is entirely devoted to the theory of mean field games without a common noise. The first half of the volume provides a self-contained introduction to mean field games, starting from concrete illustrations of games with a finite number of players, and ending with ready-for-use solvability results. Readers are provided with the tools necessary for the solution of forward-backward stochastic differential equations of the McKean-Vlasov type at the core of the probabilistic approach. The second half of this volume focuses on the main principles of analysis on the Wasserstein space. It includes Lions' approach to the Wasserstein differential calculus, and the applications of its results to the analysis of stochastic mean field control problems. Together, both Volume I and Volume II will greatly benefit mathematical graduate students and researchers interested in mean field games. The authors provide a detailed road map through the book allowing different access points for different readers and building up the level of technical detail. The accessible approach and overview will allow interested researchers in the applied sciences to obtain a clear overview of the state of the art in mean field games.
(source: Nielsen Book Data)

• Foreword.- Preface to Volume II.- Part I: MFGs with a Common Noise.- Optimization in a Random Environment.- MFGs with a Common Noise: Strong and Weak Solutions.- Solving MFGs with a Common Noise.- Part II: The Master Equation, Convergence, and Approximation Problems.- The Master Field and the Master Equation.- Classical Solutions to the Master Equation.- Convergence and Approximations.- Epilogue to Volume II.- Extensions for Volume II.- References.- Indices.
• (source: Nielsen Book Data)

This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions. Volume II tackles the analysis of mean field games in which the players are affected by a common source of noise. The first part of the volume introduces and studies the concepts of weak and strong equilibria, and establishes general solvability results. The second part is devoted to the study of the master equation, a partial differential equation satisfied by the value function of the game over the space of probability measures. Existence of viscosity and classical solutions are proven and used to study asymptotics of games with finitely many players. Together, both Volume I and Volume II will greatly benefit mathematical graduate students and researchers interested in mean field games. The authors provide a detailed road map through the book allowing different access points for different readers and building up the level of technical detail. The accessible approach and overview will allow interested researchers in the applied sciences to obtain a clear overview of the state of the art in mean field games.
(source: Nielsen Book Data)

• pt.
• 1. Equilibrium Statistical Physics
• Microscopic Dynamics of a Physical System
• Statistical Description of an Isolated System at Equilibrium
• Equilibrium System in Contact with its Environment
• Phase Transitions
• Disordered Systems and Glass Transition
• pt.
• 2. Non-Stationary Dynamics and Stochastic Formalism
• Markovian Stochastic Processes and Master Equation
• Langevin and Fokker-Planck Equations
• Anomalous Diffusion and Physical Aging
• pt.
• 3. Statistical Physics of Interacting Macroscopic "Entities"
• Dynamics of Residential Moves
• Condensation Transition
• Synchronization Transition
• Collective Motion of Active Particles.

This concise primer (based on lectures given at summer schools on complex systems and on a masters degree course in complex systems modeling) will provide graduate students and newcomers to the field with the basic knowledge of the concepts and methods of statistical physics and its potential for application to interdisciplinary topics. Â Indeed, in recent years, statistical physics has begun to attract the interest of a broad community of researchers in the field of complex system sciences, ranging from biology to the social sciences, economics and computer science. More generally, a growing number of graduate students and researchers feel the need to learn some basic concepts and questions originating in other disciplines without necessarily having to master all of the corresponding technicalities and jargon. Generally speaking, the goals of statistical physics may be summarized as follows: on the one hand to study systems composed of a large number of interacting âentitiesâ, and on the other to predict the macroscopic (or collective) behavior of the system considered from the microscopic laws ruling the dynamics of the individual âentitiesâ. These two goals are, to some extent, also shared by what is nowadays called âcomplex systems scienceâ and for these reasons, systems studied in the framework of statistical physics may be considered as among the simplest examples of complex systemsâ"allowing in addition a rather well developed mathematical treatment.

• Introduction.- Predictability in deterministic and random dynamical systems.- Mechanical randomizers - history, type of games, how fair they are.- Dynamical models.- Simulation results.- Why are mechanical randomizers predictable?.- Why can mechanical randomizers approximate random processes?- Nature of randomness in mechanical systems.
• (source: Nielsen Book Data)

This monograph presents a concise discussion of the dynamics of mechanical randomizers (coin tossing, die throw and roulette). The authors derive the equations of motion, also describing collisions and body contacts. It is shown and emphasized that, from the dynamical point of view, outcomes are predictable, i.e. if an experienced player can reproduce initial conditions with a small finite uncertainty, there is a good chance that the desired final state will be obtained. Finally, readers learn why mechanical randomizers can approximate random processes and benefit from a discussion of the nature of randomness in mechanical systems. In summary, the book not only provides a general analysis of random effects in mechanical (engineering) systems, but addresses deep questions concerning the nature of randomness, and gives potentially useful tips for gamblers and the gaming industry.

• Introduction xv
• Chapter 1. Mathematical Prerequisites 1
• Chapter 2. The Scalar Theory of Diffraction 27
• Chapter 3. Calculating Diffraction by Fast Fourier Transform 77
• Chapter 4. Fundamentals of Holography 115
• Chapter 5. Digital Off-Axis Fresnel Holography 165
• Chapter 6. Reconstructing Wavefronts Propagated through an Optical System 237
• Chapter 7. Digital Holographic Interferometry and Its Applications 271 Appendix. Examples of Digital Hologram Reconstruction Programs 319 Bibliography 339 Index 355.
• (source: Nielsen Book Data)

This book presents a substantial description of the principles and applications of digital holography. The first part of the book deals with mathematical basics and the linear filtering theory necessary to approach the topic. The next part describes the fundamentals of diffraction theory and exhaustively details the numerical computation of diffracted fields using FFT algorithms. A thorough presentation of the principles of holography and digital holography, including digital color holography, is proposed in the third part. A special section is devoted to the algorithms and methods for the numerical reconstruction of holograms. There is also a chapter devoted to digital holographic interferometry with applications in holographic microscopy, quantitative phase contrast imaging, multidimensional deformation investigations, surface shape measurements, fluid mechanics, refractive index investigations, synthetic aperture imaging and information encrypting. Keys so as to understand the differences between digital holography and speckle interferometry and examples of software for hologram reconstructions are also treated in brief. Contents 1. Mathematical Prerequisites. 2. The Scalar Theory of Diffraction. 3. Calculating Diffraction by Fast Fourier Transform. 4. Fundamentals of Holography. 5. Digital Off-Axis Fresnel Holography. 6. Reconstructing Wavefronts Propagated through an Optical System. 7. Digital Holographic Interferometry and Its Applications. Appendix. Examples of Digital Hologram Reconstruction Programs.
(source: Nielsen Book Data)