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Handbook of Mathematical Induction: Theory and Applications (Discrete Mathematics and Its Applications)
by David S. GundersonHandbook of Mathematical Induction: Theory and Applications shows how to find and write proofs via mathematical induction. This comprehensive book covers the theory, the structure of the written proof, all standard exercises, and hundreds of application examples from nearly every area of mathematics.In the first part of the book, the author discuss
Handbook of Mathematical Methods in Imaging
by Otmar ScherzerThe Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.
Handbook of Mathematical Science
by William H. BeyerNumerical tables of mathematical and statistical functions are in continual demand by professional scientists, by those in the teaching profession, and by students of mathematics and related sciences. This handbook contains the most up-to-date, authoritative, logically arranged and readily usable collection of reference material available
Handbook of Mathematical Techniques for Wave/Structure Interactions
by C.M. Linton P. McIverAlthough a wide range of mathematical techniques can apply to solving problems involving the interaction of waves with structures, few texts discuss those techniques within that context-most often they are presented without reference to any applications. Handbook of Mathematical Techniques for Wave/Structure Interactions brings together some of the
Handbook of Mathematics and Statistics for the Environment
by Frank R. Spellman Nancy E. WhitingA thorough revision of the previous "Environmental Engineer's Mathematics Handbook," this book offers readers an unusual approach to presenting environmental math concepts, emphasizing the relationship between the principles in natural processes and environmental processes. It integrates the fundamental math operations performed by environmental pr
Handbook of Mathematics for Engineers and Scientists (ISSN)
by Andrei D. Polyanin Alexander V. ManzhirovCovering the main fields of mathematics, this handbook focuses on the methods used for obtaining solutions of various classes of mathematical equations that underlie the mathematical modeling of numerous phenomena and processes in science and technology. The authors describe formulas, methods, equations, and solutions that are frequently used in scientific and engineering applications and present classical as well as newer solution methods for various mathematical equations. The book supplies numerous examples, graphs, figures, and diagrams and contains many results in tabular form, including finite sums and series and exact solutions of differential, integral, and functional equations.
Handbook of Measurement Error Models (Chapman & Hall/CRC Handbooks of Modern Statistical Methods)
by Grace Y. YiMeasurement error arises ubiquitously in applications and has been of long-standing concern in a variety of fields, including medical research, epidemiological studies, economics, environmental studies, and survey research. While several research monographs are available to summarize methods and strategies of handling different measurement error problems, research in this area continues to attract extensive attention. The Handbook of Measurement Error Models provides overviews of various topics on measurement error problems. It collects carefully edited chapters concerning issues of measurement error and evolving statistical methods, with a good balance of methodology and applications. It is prepared for readers who wish to start research and gain insights into challenges, methods, and applications related to error-prone data. It also serves as a reference text on statistical methods and applications pertinent to measurement error models, for researchers and data analysts alike. Features: Provides an account of past development and modern advancement concerning measurement error problems Highlights the challenges induced by error-contaminated data Introduces off-the-shelf methods for mitigating deleterious impacts of measurement error Describes state-of-the-art strategies for conducting in-depth research
Handbook of Mellin Transforms (Advances in Applied Mathematics)
by Yu. Brychkov O. Marichev N. SavischenkoThe Mellin transformation is widely used in various problems of pure and applied mathematics, in particular, in the theory of differential and integral equations and the theory of Dirichlet series. It is found in extensive applications in mathematical physics, number theory, mathematical statistics, theory of asymptotic expansions, and especially, in the theory of special functions and integral transformations. It is essentially used in algorithms of integration in computer algebra systems. <P><P>Since the majority of integrals encountered in applications can be reduced to the form of the corresponding Mellin transforms with specific parameters, this handbook can also be used for definite and indefinite integrals. By changes in variables, the Mellin transform can be turned into the Fourier and Laplace transforms. <P><P>The appendices contain formulas of connection with other integral transformations, and an algorithm for determining regions of convergence of integrals. <P><P>The Handbook of Mellin Transforms will be of interest and useful to all researchers and engineers who use mathematical methods. It will become the main source of formulas of Mellin transforms, as well as indefinite and definite integrals.
Handbook of Metaheuristics (International Series In Operations Research And Management Science #146)
by Michel Gendreau Jean-Yves PotvinThe third edition of this handbook is designed to provide a broad coverage of the concepts, implementations, and applications in metaheuristics. The book’s chapters serve as stand-alone presentations giving both the necessary underpinnings as well as practical guides for implementation. The nature of metaheuristics invites an analyst to modify basic methods in response to problem characteristics, past experiences, and personal preferences, and the chapters in this handbook are designed to facilitate this process as well. This new edition has been fully revised and features new chapters on swarm intelligence and automated design of metaheuristics from flexible algorithm frameworks. The authors who have contributed to this volume represent leading figures from the metaheuristic community and are responsible for pioneering contributions to the fields they write about. Their collective work has significantly enriched the field of optimization in general and combinatorial optimization in particular.Metaheuristics are solution methods that orchestrate an interaction between local improvement procedures and higher level strategies to create a process capable of escaping from local optima and performing a robust search of a solution space. In addition, many new and exciting developments and extensions have been observed in the last few years. Hybrids of metaheuristics with other optimization techniques, like branch-and-bound, mathematical programming or constraint programming are also increasingly popular. On the front of applications, metaheuristics are now used to find high-quality solutions to an ever-growing number of complex, ill-defined real-world problems, in particular combinatorial ones. This handbook should continue to be a great reference for researchers, graduate students, as well as practitioners interested in metaheuristics.
Handbook of Methods for Designing, Monitoring, and Analyzing Dose-Finding Trials
by Alexia Iasonos Björn Bornkamp John O'QuigleyHandbook of Methods for Designing, Monitoring, and Analyzing Dose-Finding Trials gives a thorough presentation of state-of-the-art methods for early phase clinical trials. The methodology of clinical trials has advanced greatly over the last 20 years and, arguably, nowhere greater than that of early phase studies. The need to accelerate drug development in a rapidly evolving context of targeted therapies, immunotherapy, combination treatments and complex group structures has provided the stimulus to these advances. Typically, we deal with very small samples, sequential methods that need to be efficient, while, at the same time adhering to ethical principles due to the involvement of human subjects. Statistical inference is difficult since the standard techniques of maximum likelihood do not usually apply as a result of model misspecification and parameter estimates lying on the boundary of the parameter space. Bayesian methods play an important part in overcoming these difficulties, but nonetheless, require special consideration in this particular context. The purpose of this handbook is to provide an expanded summary of the field as it stands and also, through discussion, provide insights into the thinking of leaders in the field as to the potential developments of the years ahead. With this goal in mind we present: An introduction to the field for graduate students and novices A basis for more established researchers from which to build A collection of material for an advanced course in early phase clinical trials A comprehensive guide to available methodology for practicing statisticians on the design and analysis of dose-finding experiments An extensive guide for the multiple comparison and modeling (MCP-Mod) dose-finding approach, adaptive two-stage designs for dose finding, as well as dose–time–response models and multiple testing in the context of confirmatory dose-finding studies.? John O’Quigley is a professor of mathematics and research director at the French National Institute for Health and Medical Research based at the Faculty of Mathematics, University Pierre and Marie Curie in Paris, France. He is author of Proportional Hazards Regression and has published extensively in the field of dose finding. Alexia Iasonos is an associate attending biostatistician at the Memorial Sloan Kettering Cancer Center in New York. She has over one hundred publications in the leading statistical and clinical journals on the methodology and design of early phase clinical trials. Dr. Iasonos has wide experience in the actual implementation of model based early phase trials and has given courses in scientific meetings internationally. Björn Bornkamp is a statistical methodologist at Novartis in Basel, Switzerland, researching and implementing dose-finding designs in Phase II clinical trials. He is one of the co-developers of the MCP-Mod methodology for dose finding and main author of the DoseFinding R package. He has published numerous papers on dose finding, nonlinear models and Bayesian statistics, and in 2013 won the Royal Statistical Society award for statistical excellence in the pharmaceutical industry. ? ?
Handbook of Military and Defense Operations Research (Chapman & Hall/CRC Series in Operations Research)
by James P. Howard Natalie M. ScalaTracing its roots back to World War II, operations research (OR) has become a vital tool in military and defense strategy. The second edition of the Handbook of Military and Defense Operations Research highlights this evolution, showcasing how OR integrates with cutting-edge areas like artificial intelligence, cybersecurity, and big data analytics.This volume is more than a historical account; it is a practical guide. The volume features expert voices and offers insights into OR applications in modern security challenges. Readers will discover a blend of theory and real-world case studies, making it an essential resource for both newcomers and seasoned defense analysis professionals.Dive into this handbook to explore the rich, dynamic field of military and defense operations research, a discipline at the heart of global security and strategic decision-making.New to the second edition: Reorganized into a three-part structure Extensive revisions throughout Numerous new exercises, examples, and case studies Several new chapters
Handbook of Military and Defense Operations Research (Chapman & Hall/CRC Series in Operations Research)
by Natalie M. Scala James P. Howard IiOperations research (OR) is a core discipline in military and defense management. Coming to the forefront initially during World War II, OR provided critical contributions to logistics, supply chains, and strategic simulation, while enabling superior decision-making for Allied forces. OR has grown to include analytics and many applications, including artificial intelligence, cybersecurity, and big data, and is the cornerstone of management science in manufacturing, marketing, telecommunications, and many other fields. The Handbook of Military and Defense Operations Research presents the voices leading OR and analytics to new heights in security through research, practical applications, case studies, and lessons learned in the field. Features Applies the experiences of educators and practitioners working in the field Employs the latest technology developments in case studies and applications Identifies best practices unique to the military, security, and national defense problem space Highlights similarities and dichotomies between analyses and trends that are unique to military, security, and defense problems
Handbook of Missing Data Methodology (Chapman & Hall/CRC Handbooks of Modern Statistical Methods)
by Geert Molenberghs Garrett Fitzmaurice Michael G. Kenward Anastasios Tsiatis Geert VerbekeMissing data affect nearly every discipline by complicating the statistical analysis of collected data. But since the 1990s, there have been important developments in the statistical methodology for handling missing data. Written by renowned statisticians in this area, Handbook of Missing Data Methodology presents many methodological advances and t
Handbook of Mixed Membership Models and Their Applications (ISSN)
by Stephen E. Fienberg Edoardo M. Airoldi Elena A. Erosheva David M. BleiIn response to scientific needs for more diverse and structured explanations of statistical data, researchers have discovered how to model individual data points as belonging to multiple groups. Handbook of Mixed Membership Models and Their Applications shows you how to use these flexible modeling tools to uncover hidden patterns in modern high-dim
Handbook of Mixture Analysis (ISSN)
by Sylvia Frühwirth-Schnatter, Gilles Celeux and Christian P. RobertMixture models have been around for over 150 years, and they are found in many branches of statistical modelling, as a versatile and multifaceted tool. They can be applied to a wide range of data: univariate or multivariate, continuous or categorical, cross-sectional, time series, networks, and much more. Mixture analysis is a very active research topic in statistics and machine learning, with new developments in methodology and applications taking place all the time. The Handbook of Mixture Analysis is a very timely publication, presenting a broad overview of the methods and applications of this important field of research. It covers a wide array of topics, including the EM algorithm, Bayesian mixture models, model-based clustering, high-dimensional data, hidden Markov models, and applications in finance, genomics, and astronomy.Features: Provides a comprehensive overview of the methods and applications of mixture modelling and analysis Divided into three parts: Foundations and Methods; Mixture Modelling and Extensions; and Selected Applications Contains many worked examples using real data, together with computational implementation, to illustrate the methods described Includes contributions from the leading researchers in the field The Handbook of Mixture Analysis is targeted at graduate students and young researchers new to the field. It will also be an important reference for anyone working in this field, whether they are developing new methodology, or applying the models to real scientific problems.
Handbook of Model Predictive Control (Control Engineering)
by Saša V. Raković William S. LevineRecent developments in model-predictive control promise remarkable opportunities for designing multi-input, multi-output control systems and improving the control of single-input, single-output systems. This volume provides a definitive survey of the latest model-predictive control methods available to engineers and scientists today. The initial set of chapters present various methods for managing uncertainty in systems, including stochastic model-predictive control. With the advent of affordable and fast computation, control engineers now need to think about using “computationally intensive controls,” so the second part of this book addresses the solution of optimization problems in “real” time for model-predictive control. The theory and applications of control theory often influence each other, so the last section of Handbook of Model Predictive Control rounds out the book with representative applications to automobiles, healthcare, robotics, and finance. The chapters in this volume will be useful to working engineers, scientists, and mathematicians, as well as students and faculty interested in the progression of control theory. Future developments in MPC will no doubt build from concepts demonstrated in this book and anyone with an interest in MPC will find fruitful information and suggestions for additional reading.
Handbook of Monte Carlo Methods
by Dirk P. Kroese Thomas Taimre Zdravko I. BotevA comprehensive overview of Monte Carlo simulation that explores the latest topics, techniques, and real-world applications More and more of today's numerical problems found in engineering and finance are solved through Monte Carlo methods. The heightened popularity of these methods and their continuing development makes it important for researchers to have a comprehensive understanding of the Monte Carlo approach. Handbook of Monte Carlo Methods provides the theory, algorithms, and applications that helps provide a thorough understanding of the emerging dynamics of this rapidly-growing field. The authors begin with a discussion of fundamentals such as how to generate random numbers on a computer. Subsequent chapters discuss key Monte Carlo topics and methods, including: Random variable and stochastic process generation Markov chain Monte Carlo, featuring key algorithms such as the Metropolis-Hastings method, the Gibbs sampler, and hit-and-run Discrete-event simulation Techniques for the statistical analysis of simulation data including the delta method, steady-state estimation, and kernel density estimation Variance reduction, including importance sampling, latin hypercube sampling, and conditional Monte Carlo Estimation of derivatives and sensitivity analysis Advanced topics including cross-entropy, rare events, kernel density estimation, quasi Monte Carlo, particle systems, and randomized optimization The presented theoretical concepts are illustrated with worked examples that use MATLAB®, a related Web site houses the MATLAB® code, allowing readers to work hands-on with the material and also features the author's own lecture notes on Monte Carlo methods. Detailed appendices provide background material on probability theory, stochastic processes, and mathematical statistics as well as the key optimization concepts and techniques that are relevant to Monte Carlo simulation. Handbook of Monte Carlo Methods is an excellent reference for applied statisticians and practitioners working in the fields of engineering and finance who use or would like to learn how to use Monte Carlo in their research. It is also a suitable supplement for courses on Monte Carlo methods and computational statistics at the upper-undergraduate and graduate levels.
Handbook of Moth-Flame Optimization Algorithm: Variants, Hybrids, Improvements, and Applications (Advances in Metaheuristics)
by Seyedali MirjaliliMoth-Flame Optimization algorithm is an emerging meta-heuristic and has been widely used in both science and industry. Solving optimization problem using this algorithm requires addressing a number of challenges, including multiple objectives, constraints, binary decision variables, large-scale search space, dynamic objective function, and noisy parameters. Handbook of Moth-Flame Optimization Algorithm: Variants, Hybrids, Improvements, and Applications provides an in-depth analysis of this algorithm and the existing methods in the literature to cope with such challenges. Key Features: • 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 This handbook will interest researchers in evolutionary computation and meta-heuristics and those who are interested in applying Moth-Flame Optimization algorithm and swarm intelligence methods overall to different application areas.
Handbook of Multiple Comparisons (Chapman & Hall/CRC Handbooks of Modern Statistical Methods)
by Xinping Cui, Thorsten Dickhaus, Ying Ding, Jason C. HsuWritten by experts that include originators of some key ideas, chapters in the Handbook of Multiple Testing cover multiple comparison problems big and small, with guidance toward error rate control and insights on how principles developed earlier can be applied to current and emerging problems. Some highlights of the coverages are as follows. Error rate control is useful for controlling the incorrect decision rate. Chapter 1 introduces Tukey's original multiple comparison error rates and point to how they have been applied and adapted to modern multiple comparison problems as discussed in the later chapters. Principles endure. While the closed testing principle is more familiar, Chapter 4 shows the partitioning principle can derive confidence sets for multiple tests, which may become important as the profession goes beyond making decisions based on p-values. Multiple comparisons of treatment efficacy often involve multiple doses and endpoints. Chapter 12 on multiple endpoints explains how different choices of endpoint types lead to different multiplicity adjustment strategies, while Chapter 11 on the MCP-Mod approach is particularly useful for dose-finding. To assess efficacy in clinical trials with multiple doses and multiple endpoints, the reader can see the traditional approach in Chapter 2, the Graphical approach in Chapter 5, and the multivariate approach in Chapter 3. Personalized/precision medicine based on targeted therapies, already a reality, naturally leads to analysis of efficacy in subgroups. Chapter 13 draws attention to subtle logical issues in inferences on subgroups and their mixtures, with a principled solution that resolves these issues. This chapter has implication toward meeting the ICHE9R1 Estimands requirement. Besides the mere multiple testing methodology itself, the handbook also covers related topics like the statistical task of model selection in Chapter 7 or the estimation of the proportion of true null hypotheses (or, in other words, the signal prevalence) in Chapter 8. It also contains decision-theoretic considerations regarding the admissibility of multiple tests in Chapter 6. The issue of selected inference is addressed in Chapter 9. Comparison of responses can involve millions of voxels in medical imaging or SNPs in genome-wide association studies (GWAS). Chapter 14 and Chapter 15 provide state of the art methods for large scale simultaneous inference in these settings.
Handbook of Multivariate Process Capability Indices
by Ashis Kumar Chakraborty Moutushi ChatterjeeProviding a single-valued assessment of the performance of a process is often one of the greatest challenges for a quality professional. Process Capability Indices (PCIs) precisely do this job. For processes having a single measurable quality characteristic, there is an ample number of PCIs, defined in literature. The situation worsens for multivariate processes, i.e., where there is more than one correlated quality characteristic. Since in most situations quality professionals face multiple quality characteristics to be controlled through a process, Multivariate Process Capability Indices (MPCIs) become the order of the day. However, there is no book which addresses and explains different MPCIs and their properties. The literature of Multivariate Process Capability Indices (MPCIs) is not well organized, in the sense that a thorough and systematic discussion on the various MPCIs is hardly available in the literature. Handbook of Multivariate Process Capability Indices provides an extensive study of the MPCIs defined for various types of specification regions. This book is intended to help quality professionals to understand which MPCI should be used and in what situation. For researchers in this field, the book provides a thorough discussion about each of the MPCIs developed to date, along with their statistical and analytical properties. Also, real life examples are provided for almost all the MPCIs discussed in the book. This helps both the researchers and the quality professionals alike to have a better understanding of the MPCIs, which otherwise become difficult to understand, since there is more than one quality characteristic to be controlled at a time. Features: A complete guide for quality professionals on the usage of different MPCIs. A step by step discussion on multivariate process capability analysis, starting from a brief discussion on univariate indices. A single source for all kinds of MPCIs developed so far. Comprehensive analysis of the MPCIs, including analysis of real-life data. References provided at the end of each chapter encompass the entire literature available on the respective topic. Interpretation of the MPCIs and development of threshold values of many MPCIs are also included. This reference book is aimed at the post graduate students in Industrial Statistics. It will also serve researchers working in the field of Industrial Statistics, as well as practitioners requiring thorough guidance regarding selection of an appropriate MPCI suitable for the problem at hand.
Handbook of Natural Language Processing (Chapman & Hall/CRC Machine Learning & Pattern Recognition)
by Nitin Indurkhya Fred J. DamerauThe Handbook of Natural Language Processing, Second Edition presents practical tools and techniques for implementing natural language processing in computer systems. Along with removing outdated material, this edition updates every chapter and expands the content to include emerging areas, such as sentiment analysis.New to the Second EditionGreater
Handbook of Networks in Power Systems I (Energy Systems)
by Alexey Sorokin Steffen Rebennack Panos M. Pardalos Niko A. Iliadis Mario V. F. PereiraEnergy has been an inevitable component of human lives for decades. Recent rapid developments in the area require analyzing energy systems not as independent components but rather as connected interdependent networks. The Handbook of Networks in Power Systems includes the state-of-the-art developments that occurred in the power systems networks, in particular gas, electricity, liquid fuels, freight networks, as well as their interactions. The book is separated into two volumes with three sections, where one scientific paper or more are included to cover most important areas of networks in power systems. The first volume covers topics arising in electricity network, in particular electricity markets, smart grid, network expansion, as well as risk management. The second volume presents problems arising in gas networks; such as scheduling and planning of natural gas systems, pricing, as well as optimal location of gas supply units. In addition, the second volume covers the topics of interactions between energy networks. Each subject is identified following the activity on the domain and the recognition of each subject as an area of research. The scientific papers are authored by world specialists on the domain and present either state-of-the-arts reviews or scientific developments.
Handbook of Networks in Power Systems II
by Alexey Sorokin Panos M. Pardalos Steffen Rebennack Mario V. Pereira Niko A. IliadisEnergy has been an inevitable component of human lives for decades. Recent rapid developments in the area require analyzing energy systems not as independent components but rather as connected interdependent networks. The Handbook of Networks in Power Systems includes the state-of-the-art developments that occurred in the power systems networks, in particular gas, electricity, liquid fuels, freight networks, as well as their interactions. The book is separated into two volumes with three sections, where one scientific paper or more are included to cover most important areas of networks in power systems. The first volume covers topics arising in electricity network, in particular electricity markets, smart grid, network expansion, as well as risk management. The second volume presents problems arising in gas networks; such as scheduling and planning of natural gas systems, pricing, as well as optimal location of gas supply units. In addition, the second volume covers the topics of interactions between energy networks. Each subject is identified following the activity on the domain and the recognition of each subject as an area of research. The scientific papers are authored by world specialists on the domain and present either state-of-the-arts reviews or scientific developments.
Handbook of Networks in Power Systems II (Energy Systems)
by Alexey Sorokin Steffen Rebennack Panos M. Pardalos Niko A. Iliadis Mario V. F. PereiraEnergy has been an inevitable component of human lives for decades. Recent rapid developments in the area require analyzing energy systems not as independent components but rather as connected interdependent networks. The Handbook of Networks in Power Systems includes the state-of-the-art developments that occurred in the power systems networks, in particular gas, electricity, liquid fuels, freight networks, as well as their interactions. The book is separated into two volumes with three sections, where one scientific paper or more are included to cover most important areas of networks in power systems. The first volume covers topics arising in electricity network, in particular electricity markets, smart grid, network expansion, as well as risk management. The second volume presents problems arising in gas networks; such as scheduling and planning of natural gas systems, pricing, as well as optimal location of gas supply units. In addition, the second volume covers the topics of interactions between energy networks. Each subject is identified following the activity on the domain and the recognition of each subject as an area of research. The scientific papers are authored by world specialists on the domain and present either state-of-the-arts reviews or scientific developments.
Handbook of Neural Computation: Supplement 1
by Emile Fiesler Russell BealeThe Handbook of Neural Computation is a practical, hands-on guide to the design and implementation of neural networks used by scientists and engineers to tackle difficult and/or time-consuming problems.The handbook bridges an information pathway between scientists and engineers in different disciplines who apply neural networks to similar probl