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Hamilton-Jacobi Equations: Paola Loreti, Nicoletta Anna Tchou
by Yves Achdou Paola Loreti Nicoletta Tchou Guy Barles Grigory L. Litvinov Hitoshi IshiiThese Lecture Notes contain the material relative to the courses given at the CIME summer school held in Cetraro, Italy from August 29 to September 3, 2011. The topic was "Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications". The courses dealt mostly with the following subjects: first order and second order Hamilton-Jacobi-Bellman equations, properties of viscosity solutions, asymptotic behaviors, mean field games, approximation and numerical methods, idempotent analysis. The content of the courses ranged from an introduction to viscosity solutions to quite advanced topics, at the cutting edge of research in the field. We believe that they opened perspectives on new and delicate issues. These lecture notes contain four contributions by Yves Achdou (Finite Difference Methods for Mean Field Games), Guy Barles (An Introduction to the Theory of Viscosity Solutions for First-order Hamilton-Jacobi Equations and Applications), Hitoshi Ishii (A Short Introduction to Viscosity Solutions and the Large Time Behavior of Solutions of Hamilton-Jacobi Equations) and Grigory Litvinov (Idempotent/Tropical Analysis, the Hamilton-Jacobi and Bellman Equations).
Hamiltonian Dynamical Systems: A REPRINT SELECTION
by R S MacKay; J D MeissClassical mechanics is a subject that is teeming with life. However, most of the interesting results are scattered around in the specialist literature, which means that potential readers may be somewhat discouraged by the effort required to obtain them. Addressing this situation, Hamiltonian Dynamical Systems includes some of the most significant papers in Hamiltonian dynamics published during the last 60 years. The book covers bifurcation of periodic orbits, the break-up of invariant tori, chaotic behavior in hyperbolic systems, and the intricacies of real systems that contain coexisting order and chaos. It begins with an introductory survey of the subjects to help readers appreciate the underlying themes that unite an apparently diverse collection of articles. The book concludes with a selection of papers on applications, including in celestial mechanics, plasma physics, chemistry, accelerator physics, fluid mechanics, and solid state mechanics, and contains an extensive bibliography. The book provides a worthy introduction to the subject for anyone with an undergraduate background in physics or mathematics, and an indispensable reference work for researchers and graduate students interested in any aspect of classical mechanics.
Hamiltonian Group Actions and Equivariant Cohomology (SpringerBriefs in Mathematics)
by Shubham Dwivedi Jonathan Herman Lisa C. Jeffrey Theo van den HurkThis monograph could be used for a graduate course on symplectic geometry as well as for independent study.The monograph starts with an introduction of symplectic vector spaces, followed by symplectic manifolds and then Hamiltonian group actions and the Darboux theorem. After discussing moment maps and orbits of the coadjoint action, symplectic quotients are studied. The convexity theorem and toric manifolds come next and we give a comprehensive treatment of Equivariant cohomology. The monograph also contains detailed treatment of the Duistermaat-Heckman Theorem, geometric quantization, and flat connections on 2-manifolds. Finally, there is an appendix which provides background material on Lie groups. A course on differential topology is an essential prerequisite for this course. Some of the later material will be more accessible to readers who have had a basic course on algebraic topology. For some of the later chapters, it would be helpful to have some background on representation theory and complex geometry.
Hamiltonian Mechanics of Gauge Systems
by Lev V. Prokhorov Sergei V. ShabanovThis highly acclaimed series of monographs provides introductory accounts of specialized topics in mathematical physics for graduate students and research workers. The monographs in this series are of outstanding scholarship and are written by those at the very frontiers of research, Subject areas covered include cosmology, astrophysics, relativity theory, particle physics, quantum theory, nuclear physics, statistical mechanics, condensed matter physics, plasma physics, and the theory of chaos.
Hamiltonian Partial Differential Equations and Applications
by Philippe Guyenne David Nicholls Catherine SulemThis book is a unique selection of work by world-class experts exploring the latest developments in Hamiltonian partial differential equations and their applications. Topics covered within are representative of the field's wide scope, including KAM and normal form theories, perturbation and variational methods, integrable systems, stability of nonlinear solutions as well as applications to cosmology, fluid mechanics and water waves. The volume contains both surveys and original research papers and gives a concise overview of the above topics, with results ranging from mathematical modeling to rigorous analysis and numerical simulation. It will be of particular interest to graduate students as well as researchers in mathematics and physics, who wish to learn more about the powerful and elegant analytical techniques for Hamiltonian partial differential equations.
Hamilton’s Principle in Continuum Mechanics
by Anthony BedfordThis revised, updated edition provides a comprehensive and rigorous description of the application of Hamilton’s principle to continuous media. To introduce terminology and initial concepts, it begins with what is called the first problem of the calculus of variations. For both historical and pedagogical reasons, it first discusses the application of the principle to systems of particles, including conservative and non-conservative systems and systems with constraints. The foundations of mechanics of continua are introduced in the context of inner product spaces. With this basis, the application of Hamilton’s principle to the classical theories of fluid and solid mechanics are covered. Then recent developments are described, including materials with microstructure, mixtures, and continua with singular surfaces.
Handbook and Atlas of Curves
by null Eugene V. ShikinThe Handbook and Atlas of Curves describes available analytic and visual properties of plane and spatial curves. Information is presented in a unique format, with one half of the book detailing investigation tools and the other devoted to the Atlas of Plane Curves. Main definitions, formulas, and facts from curve theory (plane and spatial) are discussed.
Handbook for Applied Modeling: Non-Gaussian and Correlated Data
by Jamie D. Riggs Trent L. LalondeDesigned for the applied practitioner, this book is a compact, entry-level guide to modeling and analyzing non-Gaussian and correlated data. Many practitioners work with data that fail the assumptions of the common linear regression models, necessitating more advanced modeling techniques. This Handbook presents clearly explained modeling options for such situations, along with extensive example data analyses. The book explains core models such as logistic regression, count regression, longitudinal regression, survival analysis, and structural equation modelling without relying on mathematical derivations. All data analyses are performed on real and publicly available data sets, which are revisited multiple times to show differing results using various modeling options. Common pitfalls, data issues, and interpretation of model results are also addressed. Programs in both R and SAS are made available for all results presented in the text so that readers can emulate and adapt analyses for their own data analysis needs.
Handbook for Management of Threats: Security and Defense, Resilience and Optimal Strategies (Springer Optimization and Its Applications #205)
by Konstantinos P. Balomenos Antonios Fytopoulos Panos M. PardalosIn answer to the unprecedented challenges and threats that face today’s globalized world, the primary goal of this Handbook is to identify the most probable threats that have affected humanity in recent years and our world in years to come. The Handbook comprises mostly expository chapters that discuss tested methods/algorithms, case studies, as well as policy decision-making techniques surrounding threats and unnatural disasters, to evaluate their effects on people and to propose ways to mitigate these effects. In several chapters, new approaches and suggested policies supplement algorithms that are already in practice. The curated content brings together key experts from the academic and policy worlds to formulate a guide of principal techniques employed to gain better control over selected types of threats.This Handbook explores a wide range of technologies and theories and their impact on countering threats. These include artificial intelligence, machine learning, variational inequality theory, game theory, data envelopment analysis, and data-driven risk analysis. These tools play a vital role in decision-making processes and aid in finding optimal solutions. Additionally, a variety of optimization techniques are employed. These include (mixed) integer linear programming models for identifying critical nodes in complex systems, heuristics, approximation algorithms, and bilevel mixed integer programming for determining the most impactful links in dynamic networks. Furthermore, simulation tools are described that enable the quantification of societal resilience. These techniques collectively provide a mathematical framework capable of quantifying fundamental aspects of threats. They equip policymakers with the necessary tools and knowledge to minimize the impact of unnatural threats. The expected readership is wide and includes officials working in technical and policy roles in various ministries such as the Ministry of Defense, Civil Protection, Ministry of Public Order and Citizen Protection, United Nations, European Institutions for Threat Management, NATO, Intelligence Agencies, Centers of Excellence for Countering Threats, Think Tanks, Centers for Policy Studies, Political Leaders, the European Commission, National Institutes, International Organizations, Strategic Consulting Experts, Policymakers, and Foreign Affairs personnel. Some of these national or international organizations employ algorithms to measure resilience and enhance security. Quantification is challenging but crucial in the scenarios discussed in the book. This Handbook will also prove valuable to various universities (non-practitioners), studying systems engineering, leadership, management, strategy, foreign affairs, politics, and related disciplines.
Handbook in Monte Carlo Simulation
by Paolo BrandimarteAn accessible treatment of Monte Carlo methods, techniques, and applications in the field of finance and economicsProviding readers with an in-depth and comprehensive guide, the Handbook in Monte Carlo Simulation: Applications in Financial Engineering, Risk Management, and Economics presents a timely account of the applicationsof Monte Carlo methods in financial engineering and economics. Written by an international leading expert in thefield, the handbook illustrates the challenges confronting present-day financial practitioners and provides various applicationsof Monte Carlo techniques to answer these issues. The book is organized into five parts: introduction andmotivation; input analysis, modeling, and estimation; random variate and sample path generation; output analysisand variance reduction; and applications ranging from option pricing and risk management to optimization.The Handbook in Monte Carlo Simulation features:An introductory section for basic material on stochastic modeling and estimation aimed at readers who may need a summary or review of the essentialsCarefully crafted examples in order to spot potential pitfalls and drawbacks of each approachAn accessible treatment of advanced topics such as low-discrepancy sequences, stochastic optimization, dynamic programming, risk measures, and Markov chain Monte Carlo methodsNumerous pieces of R code used to illustrate fundamental ideas in concrete terms and encourage experimentationThe Handbook in Monte Carlo Simulation: Applications in Financial Engineering, Risk Management, and Economics is a complete reference for practitioners in the fields of finance, business, applied statistics, econometrics, and engineering, as well as a supplement for MBA and graduate-level courses on Monte Carlo methods and simulation.
Handbook of Abductive Cognition
by Lorenzo MagnaniThis Handbook offers the first comprehensive reference guide to the interdisciplinary field of abductive cognition, providing readers with extensive information on the process of reasoning to hypotheses in humans, animals, and in computational machines. It highlights the role of abduction in both theory practice: in generating and testing hypotheses and explanatory functions for various purposes and as an educational device. It merges logical, cognitive, epistemological and philosophical perspectives with more practical needs relating to the application of abduction across various disciplines and practices, such as in diagnosis, creative reasoning, scientific discovery, diagrammatic and ignorance-based cognition, and adversarial strategies. It also discusses the inferential role of models in hypothetical reasoning, abduction and creativity, including the process of development, implementation and manipulation for different scientific and technological purposes. Written by a group of internationally renowned experts in philosophy, logic, general epistemology, mathematics, cognitive, and computer science, as well as life sciences, engineering, architecture, and economics, the Handbook of Abductive Cognition offers a unique reference guide for readers approaching the process of reasoning to hypotheses from different perspectives and for various theoretical and practical purposes. Numerous diagrams, schemes and other visual representations are included to promote a better understanding of the relevant concepts and to make concepts highly accessible to an audience of scholars and students with different scientific backgrounds.
Handbook of Adaptive Designs in Pharmaceutical and Clinical Development
by Annpey Pong Shein-Chung ChowIn response to the US FDA's Critical Path Initiative, innovative adaptive designs are being used more and more in clinical trials due to their flexibility and efficiency, especially during early phase development. Handbook of Adaptive Designs in Pharmaceutical and Clinical Development provides a comprehensive and unified presentation of the princip
Handbook of Advanced Multilevel Analysis (European Association of Methodology Series)
by Joop J. HoxThis new handbook is the definitive resource on advanced topics related to multilevel analysis. The editors assembled the top minds in the field to address the latest applications of multilevel modeling as well as the specific difficulties and methodological problems that are becoming more common as more complicated models are developed. Each chapter features examples that use actual datasets. These datasets, as well as the code to run the models, are available on the book’s website http://www.hlm-online.com . Each chapter includes an introduction that sets the stage for the material to come and a conclusion. Divided into five sections, the first provides a broad introduction to the field that serves as a framework for understanding the latter chapters. Part 2 focuses on multilevel latent variable modeling including item response theory and mixture modeling. Section 3 addresses models used for longitudinal data including growth curve and structural equation modeling. Special estimation problems are examined in section 4 including the difficulties involved in estimating survival analysis, Bayesian estimation, bootstrapping, multiple imputation, and complicated models, including generalized linear models, optimal design in multilevel models, and more. The book’s concluding section focuses on statistical design issues encountered when doing multilevel modeling including nested designs, analyzing cross-classified models, and dyadic data analysis. Intended for methodologists, statisticians, and researchers in a variety of fields including psychology, education, and the social and health sciences, this handbook also serves as an excellent text for graduate and PhD level courses in multilevel modeling. A basic knowledge of multilevel modeling is assumed.
Handbook of AI and Data Sciences for Sleep Disorders (Springer Optimization and Its Applications #216)
by Richard B. Berry Panos M. Pardalos Xiaochen XianThe rise of lifestyle changes resulting from constant connectivity, irregular work schedules, heightened stress, and disruptive sleep patterns, have contributed to increasing insomnia rates. Exacerbated by the COVID-19 pandemic, sleep disorders are more prevalent than ever. This handbook offers a comprehensive exploration of the fusion of Artificial Intelligence (AI) and data science within the realm of sleep disorders, presenting innovative approaches to diagnosis, treatment, and personalized care. The interdisciplinary nature of this handbook fosters collaboration between experts from diverse fields, including computer science, engineering, neuroscience, medicine, public health, AI, data science, and sleep medicine. Each chapter delves into specific aspects of sleep disorder analysis, innovative methodologies, novel insights, and real-world applications that showcase the transformative potential of AI and data science in sleep medicine, from analyzing sleep patterns and predicting disorder risk factors to utilizing big data analytics for large-scale epidemiological studies. This handbook hopes to offer a comprehensive resource for researchers, clinicians, and policymakers striving to address the challenges in sleep medicine.
Handbook of AI-based Metaheuristics (Advances in Metaheuristics)
by Anand J. KulkarniAt the heart of the optimization domain are mathematical modeling of the problem and the solution methodologies. The problems are becoming larger and with growing complexity. Such problems are becoming cumbersome when handled by traditional optimization methods. This has motivated researchers to resort to artificial intelligence (AI)-based, nature-inspired solution methodologies or algorithms. The Handbook of AI-based Metaheuristics provides a wide-ranging reference to the theoretical and mathematical formulations of metaheuristics, including bio-inspired, swarm-based, socio-cultural, and physics-based methods or algorithms; their testing and validation, along with detailed illustrative solutions and applications; and newly devised metaheuristic algorithms. This will be a valuable reference for researchers in industry and academia, as well as for all Master’s and PhD students working in the metaheuristics and applications domains.
Handbook of Algorithms for Wireless Networking and Mobile Computing (Chapman & Hall/CRC Computer and Information Science Series)
by Azzedine BoukercheThe Handbook of Algorithms for Wireless Networking and Mobile Computing focuses on several aspects of mobile computing, particularly algorithmic methods and distributed computing with mobile communications capability. It provides the topics that are crucial for building the foundation for the design and construction of future generations of mobile and wireless networks, including cellular, wireless ad hoc, sensor, and ubiquitous networks. Following an analysis of fundamental algorithms and protocols, the book offers a basic overview of wireless technologies and networks. Other topics include issues related to mobility, aspects of QoS provisioning in wireless networks, future applications, and much more.
Handbook of Alternative Data in Finance, Volume I (CRC Press/OptiRisk Series in Finance)
by Gautam Mitra Christina Erlwein-Sayer Kieu Thi Hoang Diana Roman Zryan SadikHandbook of Alternative Data in Finance, Volume I motivates and challenges the reader to explore and apply Alternative Data in finance. The book provides a robust and in-depth overview of Alternative Data, including its definition, characteristics, difference from conventional data, categories of Alternative Data, Alternative Data providers, and more. The book also offers a rigorous and detailed exploration of process, application and delivery that should be practically useful to researchers and practitioners alike. Features Includes cutting edge applications in machine learning, fintech, and more Suitable for professional quantitative analysts, and as a resource for postgraduates and researchers in financial mathematics Features chapters from many leading researchers and practitioners
Handbook of Analytic Computational Methods in Applied Mathematics
by George AnastassiouWorking computationally in applied mathematics is the very essence of dealing with real-world problems in science and engineering. Approximation theory-on the borderline between pure and applied mathematics- has always supplied some of the most innovative ideas, computational methods, and original approaches to many types of problems. The f
Handbook of Analytic Operator Theory (CRC Press/Chapman and Hall Handbooks in Mathematics Series)
by Kehe ZhuHandbook of Analytic Operator Theory thoroughly covers the subject of holomorphic function spaces and operators acting on them. The spaces covered include Bergman spaces, Hardy spaces, Fock spaces and the Drury-Averson space. Operators discussed in the book include Toeplitz operators, Hankel operators, composition operators, and Cowen-Douglas class operators. <P><P>The volume consists of eleven articles in the general area of analytic function spaces and operators on them. Each contributor focuses on one particular topic, for example, operator theory on the Drury-Aversson space, and presents the material in the form of a survey paper which contains all the major results in the area and includes all relevant references. The overalp between this volume and existing books in the area is minimal. The material on two-variable weighted shifts by Curto, the Drury-Averson space by Fang and Xia, the Cowen-Douglas class by Misra, and operator theory on the bi-disk by Yang has never appeared in book form before. <P><P>Features: <li>The editor of the handbook is a widely known and published researcher on this topic <li>The handbook's contributors are a who's=who of top researchers in the area <li>The first contributed volume on these diverse topics
Handbook of Applications of Chaos Theory
by CHRISTOS H. SKIADAS AND CHARILAOS SKIADASIn addition to explaining and modeling unexplored phenomena in nature and society, chaos uses vital parts of nonlinear dynamical systems theory and established chaotic theory to open new frontiers and fields of study. Handbook of Applications of Chaos Theory covers the main parts of chaos theory along with various applications to diverse areas. Expert contributors from around the world show how chaos theory is used to model unexplored cases and stimulate new applications. Accessible to scientists, engineers, and practitioners in a variety of fields, the book discusses the intermittency route to chaos, evolutionary dynamics and deterministic chaos, and the transition to phase synchronization chaos. It presents important contributions on strange attractors, self-exciting and hidden attractors, stability theory, Lyapunov exponents, and chaotic analysis. It explores the state of the art of chaos in plasma physics, plasma harmonics, and overtone coupling. It also describes flows and turbulence, chaotic interference versus decoherence, and an application of microwave networks to the simulation of quantum graphs. The book proceeds to give a detailed presentation of the chaotic, rogue, and noisy optical dissipative solitons; parhelic-like circle and chaotic light scattering; and interesting forms of the hyperbolic prism, the Poincaré disc, and foams. It also covers numerous application areas, from the analysis of blood pressure data and clinical digital pathology to chaotic pattern recognition to economics to musical arts and research.
Handbook of Applied Cryptography (Discrete Mathematics and Its Applications)
by Alfred J. Menezes Paul C. van Oorschot Scott A. VanstoneCryptography, in particular public-key cryptography, has emerged in the last 20 years as an important discipline that is not only the subject of an enormous amount of research, but provides the foundation for information security in many applications. Standards are emerging to meet the demands for cryptographic protection in most areas of data communications. Public-key cryptographic techniques are now in widespread use, especially in the financial services industry, in the public sector, and by individuals for their personal privacy, such as in electronic mail. This Handbook will serve as a valuable reference for the novice as well as for the expert who needs a wider scope of coverage within the area of cryptography. It is a necessary and timely guide for professionals who practice the art of cryptography. The Handbook of Applied Cryptography provides a treatment that is multifunctional:It serves as an introduction to the more practical aspects of both conventional and public-key cryptography It is a valuable source of the latest techniques and algorithms for the serious practitioner It provides an integrated treatment of the field, while still presenting each major topic as a self-contained unit It provides a mathematical treatment to accompany practical discussions It contains enough abstraction to be a valuable reference for theoreticians while containing enough detail to actually allow implementation of the algorithms discussedNow in its third printing, this is the definitive cryptography reference that the novice as well as experienced developers, designers, researchers, engineers, computer scientists, and mathematicians alike will use.
Handbook Of Applied Econometrics And Statistical Inference
by null Aman UllahSummarizing developments and techniques in the field, this reference covers sample surveys, nonparametric analysis, hypothesis testing, time series analysis, Bayesian inference, and distribution theory for applications in statistics, economics, medicine, biology, engineering, sociology, psychology, and information technology. It supplies a geometric proof of an extended Gauss-Markov theorem, approaches for the design and implementation of sample surveys, advances in the theory of Neyman's smooth test, and methods for pre-test and biased estimation. It includes discussions ofsample size requirements for estimation in SUR models, innovative developments in nonparametric models, and more.
Handbook of Applied Economic Statistics (Statistics: A Series of Textbooks and Monographs)
by Aman Ullah David E. A. GilesThis work examines theoretical issues, as well as practical developments in statistical inference related to econometric models and analysis. This work offers discussions on such areas as the function of statistics in aggregation, income inequality, poverty, health, spatial econometrics, panel and survey data, bootstrapping and time series.
Handbook of Approximate Bayesian Computation (Chapman & Hall/CRC Handbooks of Modern Statistical Methods)
by S. A. Sisson, Y. Fan and M. A. BeaumontAs the world becomes increasingly complex, so do the statistical models required to analyse the challenging problems ahead. For the very first time in a single volume, the Handbook of Approximate Bayesian Computation (ABC) presents an extensive overview of the theory, practice and application of ABC methods. These simple, but powerful statistical techniques, take Bayesian statistics beyond the need to specify overly simplified models, to the setting where the model is defined only as a process that generates data. This process can be arbitrarily complex, to the point where standard Bayesian techniques based on working with tractable likelihood functions would not be viable. ABC methods finesse the problem of model complexity within the Bayesian framework by exploiting modern computational power, thereby permitting approximate Bayesian analyses of models that would otherwise be impossible to implement. The Handbook of ABC provides illuminating insight into the world of Bayesian modelling for intractable models for both experts and newcomers alike. It is an essential reference book for anyone interested in learning about and implementing ABC techniques to analyse complex models in the modern world.
Handbook of Approximation Algorithms and Metaheuristics: Contemporary and Emerging Applications, Volume 2 (Chapman & Hall/CRC Computer and Information Science Series)
by Teofilo F. GonzalezHandbook of Approximation Algorithms and Metaheuristics, Second Edition reflects the tremendous growth in the field, over the past two decades. Through contributions from leading experts, this handbook provides a comprehensive introduction to the underlying theory and methodologies, as well as the various applications of approximation algorithms and metaheuristics. Volume 1 of this two-volume set deals primarily with methodologies and traditional applications. It includes restriction, relaxation, local ratio, approximation schemes, randomization, tabu search, evolutionary computation, local search, neural networks, and other metaheuristics. It also explores multi-objective optimization, reoptimization, sensitivity analysis, and stability. Traditional applications covered include: bin packing, multi-dimensional packing, Steiner trees, traveling salesperson, scheduling, and related problems. Volume 2 focuses on the contemporary and emerging applications of methodologies to problems in combinatorial optimization, computational geometry and graphs problems, as well as in large-scale and emerging application areas. It includes approximation algorithms and heuristics for clustering, networks (sensor and wireless), communication, bioinformatics search, streams, virtual communities, and more. About the Editor Teofilo F. Gonzalez is a professor emeritus of computer science at the University of California, Santa Barbara. He completed his Ph.D. in 1975 from the University of Minnesota. He taught at the University of Oklahoma, the Pennsylvania State University, and the University of Texas at Dallas, before joining the UCSB computer science faculty in 1984. He spent sabbatical leaves at the Monterrey Institute of Technology and Higher Education and Utrecht University. He is known for his highly cited pioneering research in the hardness of approximation; for his sublinear and best possible approximation algorithm for k-tMM clustering; for introducing the open-shop scheduling problem as well as algorithms for its solution that have found applications in numerous research areas; as well as for his research on problems in the areas of job scheduling, graph algorithms, computational geometry, message communication, wire routing, etc.