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Sequential Experimentation in Clinical Trials
by Mei-Chiung Shih Tze Leung Lai Jay BartroffSequential Experimentation in Clinical Trials: Design and Analysis is developed from decades of work in research groups, statistical pedagogy, and workshop participation. Different parts of the book can be used for short courses on clinical trials, translational medical research, and sequential experimentation. The authors have successfully used the book to teach innovative clinical trial designs and statistical methods for Statistics Ph.D. students at Stanford University. There are additional online supplements for the book that include chapter-specific exercises and information. Sequential Experimentation in Clinical Trials: Design and Analysis covers the much broader subject of sequential experimentation that includes group sequential and adaptive designs of Phase II and III clinical trials, which have attracted much attention in the past three decades. In particular, the broad scope of design and analysis problems in sequential experimentation clearly requires a wide range of statistical methods and models from nonlinear regression analysis, experimental design, dynamic programming, survival analysis, resampling, and likelihood and Bayesian inference. The background material in these building blocks is summarized in Chapter 2 and Chapter 3 and certain sections in Chapter 6 and Chapter 7. Besides group sequential tests and adaptive designs, the book also introduces sequential change-point detection methods in Chapter 5 in connection with pharmacovigilance and public health surveillance. Together with dynamic programming and approximate dynamic programming in Chapter 3, the book therefore covers all basic topics for a graduate course in sequential analysis designs.
Sequential Experiments with Primes
by Mihai CaragiuWith a specific focus on the mathematical life in small undergraduate colleges, this book presents a variety of elementary number theory insights involving sequences largely built from prime numbers and contingent number-theoretic functions. Chapters include new mathematical ideas and open problems, some of which are proved in the text. Vector valued MGPF sequences, extensions of Conway's Subprime Fibonacci sequences, and linear complexity of bit streams derived from GPF sequences are among the topics covered in this book. This book is perfect for the pure-mathematics-minded educator in a small undergraduate college as well as graduate students and advanced undergraduate students looking for a significant high-impact learning experience in mathematics.
Sequential Learning and Decision-Making in Wireless Resource Management
by Rong Zheng Cunqing HuaThis book lays out the theoretical foundation of the so-called multi-armed bandit (MAB) problems and puts it in the context of resource management in wireless networks. Part I of the book presents the formulations, algorithms and performance of three forms of MAB problems, namely, stochastic, Markov and adversarial. Covering all three forms of MAB problems makes this book unique in the field. Part II of the book provides detailed discussions of representative applications of the sequential learning framework in cognitive radio networks, wireless LANs and wireless mesh networks. Both individuals in industry and those in the wireless research community will benefit from this comprehensive and timely treatment of these topics. Advanced-level students studying communications engineering and networks will also find the content valuable and accessible.
Sequential Methods and Their Applications
by Nitis Mukhopadhyay Basil M. de SilvaInteractively Run Simulations and Experiment with Real or Simulated Data to Make Sequential Analysis Come AliveTaking an accessible, nonmathematical approach to this field, Sequential Methods and Their Applications illustrates the efficiency of sequential methodologies when dealing with contemporary statistical challenges in many areas.The book fir
Sequential Models of Mathematical Physics
by Simon SerovajskyThe equations of mathematical physics are the mathematical models of the large class of phenomenon of physics, chemistry, biology, economics, etc. In Sequential Models of Mathematical Physics, the author considers the justification of the process of constructing mathematical models. The book seeks to determine the classic, generalized and sequential solutions, the relationship between these solutions, its direct physical sense, the methods of its practical finding, and its existence. Features Describes a sequential method based on the construction of space completion, as well as its applications in number theory, the theory of distributions, the theory of extremum, and mathematical physics Presentation of the material is carried out on the simplest example of a one-dimensional stationary heat transfer process; all necessary concepts and constructions are introduced and illustrated with elementary examples, which makes the material accessible to a wide area of readers The solution of a specific mathematical problem is obtained as a result of the joint application of methods and concepts from completely different mathematical directions
The Sequential Quadratic Hamiltonian Method: Solving Optimal Control Problems (Chapman & Hall/CRC Numerical Analysis and Scientific Computing Series)
by Alfio BorzìThe sequential quadratic hamiltonian (SQH) method is a novel numerical optimization procedure for solving optimal control problems governed by differential models. It is based on the characterisation of optimal controls in the framework of the Pontryagin maximum principle (PMP).The SQH method is a powerful computational methodology that is capable of development in many directions. The Sequential Quadratic Hamiltonian Method: Solving Optimal Control Problems discusses its analysis and use in solving nonsmooth ODE control problems, relaxed ODE control problems, stochastic control problems, mixed-integer control problems, PDE control problems, inverse PDE problems, differential Nash game problems, and problems related to residual neural networks. This book may serve as a textbook for undergraduate and graduate students, and as an introduction for researchers in sciences and engineering who intend to further develop the SQH method or wish to use it as a numerical tool for solving challenging optimal control problems and for investigating the Pontryagin maximum principle on new optimisation problems. Features Provides insight into mathematical and computational issues concerning optimal control problems, while discussing many differential models of interest in different disciplines. Suitable for undergraduate and graduate students and as an introduction for researchers in sciences and engineering. Accompanied by codes which allow the reader to apply the SQH method to solve many different optimal control and optimisation problems.
Sequents and Trees: An Introduction to the Theory and Applications of Propositional Sequent Calculi (Studies in Universal Logic)
by Andrzej IndrzejczakThis textbook offers a detailed introduction to the methodology and applications of sequent calculi in propositional logic. Unlike other texts concerned with proof theory, emphasis is placed on illustrating how to use sequent calculi to prove a wide range of metatheoretical results. The presentation is elementary and self-contained, with all technical details both formally stated and also informally explained. Numerous proofs are worked through to demonstrate methods of proving important results, such as the cut-elimination theorem, completeness, decidability, and interpolation. Other proofs are presented with portions left as exercises for readers, allowing them to practice techniques of sequent calculus.After a brief introduction to classical propositional logic, the text explores three variants of sequent calculus and their features and applications. The remaining chapters then show how sequent calculi can be extended, modified, and applied to non-classical logics, including modal, intuitionistic, substructural, and many-valued logics.Sequents and Trees is suitable for graduate and advanced undergraduate students in logic taking courses on proof theory and its application to non-classical logics. It will also be of interest to researchers in computer science and philosophers.
Series of Bessel and Kummer-Type Functions (Lecture Notes in Mathematics #2207)
by Tibor K. Pogány Dragana Jankov Maširević Árpád BariczThis book is devoted to the study of certain integral representations for Neumann, Kapteyn, Schlömilch, Dini and Fourier series of Bessel and other special functions, such as Struve and von Lommel functions. The aim is also to find the coefficients of the Neumann and Kapteyn series, as well as closed-form expressions and summation formulas for the series of Bessel functions considered. Some integral representations are deduced using techniques from the theory of differential equations. The text is aimed at a mathematical audience, including graduate students and those in the scientific community who are interested in a new perspective on Fourier–Bessel series, and their manifold and polyvalent applications, mainly in general classical analysis, applied mathematics and mathematical physics.
Serious Cryptography, 2nd Edition: A Practical Introduction to Modern Encryption
by Jean-Philippe AumassonCrypto can be cryptic. Serious Cryptography, 2nd Edition arms you with the tools you need to pave the way to understanding modern crypto.This thoroughly revised and updated edition of the bestselling introduction to modern cryptography breaks down fundamental mathematical concepts without shying away from meaty discussions of how they work. In this practical guide, you&’ll gain immeasurable insight into topics like authenticated encryption, secure randomness, hash functions, block ciphers, and public-key techniques such as RSA and elliptic curve cryptography.You&’ll find coverage of topics like:The basics of computational security, attacker models, and forward secrecyThe strengths and limitations of the TLS protocol behind HTTPS secure websitesQuantum computation and post-quantum cryptographyHow algorithms like AES, ECDSA, Ed25519, Salsa20, and SHA-3 workAdvanced techniques like multisignatures, threshold signing, and zero-knowledge proofsEach chapter includes a discussion of common implementation mistakes using real-world examples and details what could go wrong and how to avoid these pitfalls. And, true to form, you&’ll get just enough math to show you how the algorithms work so that you can understand what makes a particular solution effective—and how they break. NEW TO THIS EDITION: This second edition has been thoroughly updated to reflect the latest developments in cryptography. You&’ll also find a completely new chapter covering the cryptographic protocols in cryptocurrency and blockchain systems.Whether you&’re a seasoned practitioner or a beginner looking to dive into the field, Serious Cryptography will demystify this often intimidating topic. You&’ll grow to understand modern encryption and its applications so that you can make better decisions about what to implement, when, and how.
Serious Fun with Flexagons
by L. P. PookA flexagon is a motion structure that has the appearance of a ring of hinged polygons. It can be flexed to display different pairs of faces, usually in cyclic order. Flexagons can be appreciated as toys or puzzles, as a recreational mathematics topic, and as the subject of serious mathematical study. Workable paper models of flexagons are easy to make and entertaining to manipulate. The mathematics of flexagons is complex, and how a flexagon works is not immediately obvious on examination of a paper model. Recent geometric analysis, included in the book, has improved theoretical understanding of flexagons, especially relationships between different types. This profusely illustrated book is arranged in a logical order appropriate for a textbook on the geometry of flexagons. It is written so that it can be enjoyed at both the recreational mathematics level, and at the serious mathematics level. The only prerequisite is some knowledge of elementary geometry, including properties of polygons. A feature of the book is a compendium of over 100 nets for making paper models of some of the more interesting flexagons, chosen to complement the text. These are accurately drawn and reproduced at half full size. Many of the nets have not previously been published. Instructions for assembling and manipulating the flexagons are included.
Serious Games and Innovation Gains: Think Innovation through Games (ISTE Invoiced)
by St Phane GoriaOver the past thirty years or so, serious games, gaming and playful activities have come to occupy an important place in organizations. While this phenomenon is an ancient one, the use of games for serious purposes has become widespread over the last two centuries, and their development has been exponential, stimulated by that of information technologies. As a result, it has become necessary to understand the specificities of these games and play activities in order to innovate and create value within organizations. For this reason, this book aims to enlighten the reader on their variety, their specific features and what they can bring to an organization. Serious Games and Innovation Gains first uncovers the history of these kinds of games and play, their main characteristics and what they can bring in terms of a vision of the future. Above all, this book explores how these games and forms of play can be implemented, especially in areas such as progressive development, education, agility support, academic research, as well as military thinking, cyber defense or knowledge base building contexts.
Serious Games for Enhancing Law Enforcement Agencies: From Virtual Reality to Augmented Reality (Security Informatics and Law Enforcement)
by Babak AkhgarThis book provides a comprehensive and practically minded introduction into serious games for law enforcement agencies. Serious games offer wide ranging benefits for law enforcement with applications from professional trainings to command-level decision making to the preparation for crises events. This book explains the conceptual foundations of virtual and augmented reality, gamification and simulation. It further offers practical guidance on the process of serious games development from user requirements elicitation to evaluation. The chapters are intended to provide principles, as well as hands-on knowledge to plan, design, test and apply serious games successfully in a law enforcement environment. A diverse set of case studies showcases the enormous variety that is possible in serious game designs and application areas and offers insights into concrete design decisions, design processes, benefits and challenges. The book is meant for law enforcement professionals interested in commissioning their own serious games as well as game designers interested in collaborative pedagogy and serious games for the law enforcement and security sector.
Service Network Design of Bike Sharing Systems
by Patrick VogelThis monograph presents a tactical planning approach for service network design in metropolitan areas. Designing the service network requires the suitable aggregation of demand data as well as the anticipation of operational relocation decisions. To this end, an integrated approach of data analysis and mathematical optimization is introduced. The book also includes a case study based on real-world data to demonstrate the benefit of the proposed service network design approach. The target audience comprises primarily research experts in the field of traffic engineering, but the book may also be beneficial for graduate students.
Service-Oriented Distributed Knowledge Discovery
by Paolo Trunfio Domenico TaliaA new approach to distributed large-scale data mining, service-oriented knowledge discovery extracts useful knowledge from today's often unmanageable volumes of data by exploiting data mining and machine learning distributed models and techniques in service-oriented infrastructures. Service-Oriented Distributed Knowledge Discovery presents techniqu
Service Science: The Foundations of Service Engineering and Management
by Robin G. Qiul natures Computational thinking and system modeling such as abstraction, digitalization, holistic perspectives, and analytics Plentiful examples of service organizations such as automobile after-sale services, global project management networks, and express delivery services An interdisciplinary emphasis that includes integrated approaches from the fields of mathematics, engineering, industrial engineering, business, operations research, and management science A detailed analysis of the key concepts and body of knowledge for readers to master the foundations of service management Service Science: The Foundations of Service Engineering and Management is an ideal reference for practitioners in the contemporary service engineering and management field as well as researchers in applied mathematics, statistics, business/management science, operations research, industrial engineering, and economics. The book is also appropriate as a text for upper-undergraduate and graduate-level courses in industrial engineering, operations research, and management science as well as MBA students studying service management.
Services for Aging Persons in China: Spatial Variations in Supply and Demand (Global Perspectives on Health Geography)
by Xiaoping Shen Shangyi Zhou Xiulan ZhangThis volume draws upon one of the first comprehensive studies on the regional variations of services for aging persons in China to provide an empirical and theoretical understanding of the impact of China's rapidly growing aging population on the country's socioeconomic, cultural, and political systems. In three parts, the manuscript combines case-oriented comparative methods with variable-oriented statistical and GIS analyses to examine the spatial patterns and relationships between supply and demand of affordable and accessible services for aging persons in China. Part one gives a historical review of population aging in China, including the development of services for aging persons and government policies and programs geared towards elders. Part two provides an analysis of spatial variations of supply and demand for services including food, housing, health, and community services for aging persons. Part three uses case studies to analyse the regional and local dimensions of elderly services. Suggestions are made for future planning, development, and policies. This book will appeal to policy makers, city planners, service providing businesses, and advanced undergraduate and graduate students studying economic geography, planning, and regional development.
Set Function T: An Account on F. B. Jones' Contributions to Topology (Developments in Mathematics #67)
by Sergio MacíasThis book presents, in a clear and structured way, the set function \mathcal{T} and how it evolved since its inception by Professor F. Burton Jones in the 1940s. It starts with a very solid introductory chapter, with all the prerequisite material for navigating through the rest of the book. It then gradually advances towards the main properties, Decomposition theorems, \mathcal{T}-closed sets, continuity and images, to modern applications.The set function \mathcal{T} has been used by many mathematicians as a tool to prove results about the semigroup structure of the continua, and about the existence of a metric continuum that cannot be mapped onto its cone or to characterize spheres. Nowadays, it has been used by topologists worldwide to investigate open problems in continuum theory.This book can be of interest to both advanced undergraduate and graduate students, and to experienced researchers as well. Its well-defined structure make this book suitable not only for self-study but also as support material to seminars on the subject. Its many open problems can potentially encourage mathematicians to contribute with further advancements in the field.
Set-Indexed Martingales (Chapman & Hall/CRC Monographs on Statistics and Applied Probability)
by Gail Ivanoff Ely MerzbachSet-Indexed Martingales offers a unique, comprehensive development of a general theory of Martingales indexed by a family of sets. The authors establish-for the first time-an appropriate framework that provides a suitable structure for a theory of Martingales with enough generality to include many interesting examples. Developed from first principles, the theory brings together the theories of Martingales with a directed index set and set-indexed stochastic processes. Part One presents several classical concepts extended to this setting, including: stopping, predictability, Doob-Meyer decompositions, martingale characterizations of the set-indexed Poisson process, and Brownian motion. Part Two addresses convergence of sequences of set-indexed processes and introduces functional convergence for processes whose sample paths live in a Skorokhod-type space and semi-functional convergence for processes whose sample paths may be badly behaved.Completely self-contained, the theoretical aspects of this work are rich and promising. With its many important applications-especially in the theory of spatial statistics and in stochastic geometry- Set Indexed Martingales will undoubtedly generate great interest and inspire further research and development of the theory and applications.
Set, Measure and Probability Theory (River Publishers Series in Mathematical, Statistical and Computational Modelling for Engineering)
by Marcelo S. Alencar Raphael T. AlencarThis book introduces the basic concepts of set theory, measure theory, the axiomatic theory of probability, random variables and multidimensional random variables, functions of random variables, convergence theorems, laws of large numbers, and fundamental inequalities. The idea is to present a seamless connection between the more abstract advanced set theory, the fundamental concepts from measure theory, and integration, to introduce the axiomatic theory of probability, filling in the gaps from previous books and leading to an interesting, robust and, hopefully, self-contained exposition of the theory. This book also presents an account of the historical evolution of probability theory as a mathematical discipline. Each chapter presents a short biography of the important scientists who helped develop the subject. Appendices include Fourier transforms in one and two dimensions, important formulas and inequalities and commented bibliography. Many examples, illustrations and graphics help the reader understand the theory.
Set Operads in Combinatorics and Computer Science
by Miguel A. MéndezThis monograph has two main objectives. The first one is to give a self-contained exposition of the relevant facts about set operads, in the context of combinatorial species and its operations. This approach has various advantages: one of them is that the definition of combinatorial operations on species, product, sum, substitution and derivative, are simple and natural. They were designed as the set theoretical counterparts of the homonym operations on exponential generating functions, giving an immediate insight on the combinatorial meaning of them. The second objective is more ambitious. Before formulating it, authors present a brief historic account on the sources of decomposition theory. For more than forty years decompositions of discrete structures have been studied in different branches of discrete mathematics: combinatorial optimization, network and graph theory, switching design or boolean functions, simple multi-person games and clutters, etc.
Set Optimization and Applications - The State of the Art
by Carola Schrage Birgit Rudloff Andreas Löhne Frank Heyde Andreas H. HamelThis volume presents five surveys with extensivebibliographies and six original contributions on set optimization and its applicationsin mathematical finance and game theory. The topics range from moreconventional approaches that look for minimal/maximal elements with respect tovector orders or set relations, to the new complete-lattice approach thatcomprises a coherent solution concept for set optimization problems, along withexistence results, duality theorems, optimality conditions, variationalinequalities and theoretical foundations for algorithms. Modern approaches toscalarization methods can be found as well as a fundamental contribution to conditionalanalysis. The theory is tailor-made for financial applications, in particular riskevaluation and [super-]hedging for market models with transaction costs, but italso provides a refreshing new perspective on vector optimization. There is nocomparable volume on the market, making the book an invaluable resource forresearchers working in vector optimization and multi-criteria decision-making, mathematicalfinance and economics as well as [set-valued] variational analysis.
Set-Theoretic Methods for the Social Sciences
by Carsten Q. Schneider Claudius WagemannQualitative Comparative Analysis (QCA) and other set-theoretic methods distinguish themselves from other approaches to the study of social phenomena by using sets and the search for set relations. In virtually all social science fields, statements about social phenomena can be framed in terms of set relations, and using set-theoretic methods to investigate these statements is therefore highly valuable. This book guides readers through the basic principles of set theory and then on to the applied practices of QCA. It provides a thorough understanding of basic and advanced issues in set-theoretic methods together with tricks of the trade, software handling and exercises. Most arguments are introduced using examples from existing research. The use of QCA is increasing rapidly and the application of set-theory is both fruitful and still widely misunderstood in current empirical comparative social research. This book provides an invaluable guide to these methods for researchers across the social sciences.
Set-Theoretic Methods in Control
by Franco Blanchini Stefano MianiThe second edition of this monograph describes the set-theoretic approach for the control and analysis of dynamic systems, both from a theoretical and practical standpoint. This approach is linked to fundamental control problems, such as Lyapunov stability analysis and stabilization, optimal control, control under constraints, persistent disturbance rejection, and uncertain systems analysis and synthesis. Completely self-contained, this book provides a solid foundation of mathematical techniques and applications, extensive references to the relevant literature, and numerous avenues for further theoretical study. All the material from the first edition has been updated to reflect the most recent developments in the field, and a new chapter on switching systems has been added. Each chapter contains examples, case studies, and exercises to allow for a better understanding of theoretical concepts by practical application. The mathematical language is kept to the minimum level necessary for the adequate formulation and statement of the main concepts, yet allowing for a detailed exposition of the numerical algorithms for the solution of the proposed problems. Set-Theoretic Methods in Control will appeal to both researchers and practitioners in control engineering and applied mathematics. It is also well-suited as a textbook for graduate students in these areas.
Set Theory: An Introduction to Axiomatic Reasoning (Textbooks in Mathematics)
by Robert AndréContemporary students of mathematics differ considerably from those of half a century ago. In spite of this, many textbooks written decades ago, and now considered to be “classics”, are still prescribed for students today. These texts are not suitable for today’s students. This text is meant for and written to today’s mathematics students. Set theory is a pure mathematics endeavor in the sense that it seems to have no immediate applications; yet the knowledge and skills developed in such a course can easily branch out to various fields of both pure mathematics and applied mathematics.Rather than transforming the reader into a practicing mathematician, this book is more designed to initiate the reader to what may be called “mathematical thinking” while developing knowledge about foundations of modern mathematics. Without this insight, becoming a practicing mathematician is much more daunting.The main objective is twofold. The students will develop some fundamental understanding of the foundations of mathematics and elements of set theory, in general. In the process, the student will develop skills in proving simple mathematical statements with “mathematical rigor”.Carefully presented detailed proofs and rigorous chains of logical arguments will guide the students from the fundamental ZFC-axioms and definitions to show why a basic mathematical statement must hold true. The student will recognize the role played by each fundamental axiom in development of modern mathematics. The student will learn to distinguish between a correct mathematical proof and an erroneous one. The subject matter is presented while bypassing the complexities encountered when using formal logic.
Set Theory: A First Course (Cambridge Mathematical Textbooks Ser.)
by Daniel W. CunninghamSet theory is a rich and beautiful subject whose fundamental concepts permeate virtually every branch of mathematics. One could say that set theory is a unifying theory for mathematics, since nearly all mathematical concepts and results can be formalized within set theory. This textbook is meant for an upper undergraduate course in set theory. In this text, the fundamentals of abstract sets, including relations, functions, the natural numbers, order, cardinality, transfinite recursion, the axiom of choice, ordinal numbers, and cardinal numbers, are developed within the framework of axiomatic set theory. The reader will need to be comfortable reading and writing mathematical proofs. The proofs in this textbook are rigorous, clear, and complete, while remaining accessible to undergraduates who are new to upper-level mathematics. Exercises are included at the end of each section in a chapter, with useful suggestions for the more challenging exercises.