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Methods in Brain Connectivity Inference through Multivariate Time Series Analysis (Frontiers in Neuroengineering Series)
by Koichi Sameshima Luiz Antonio BaccaláInterest in brain connectivity inference has become ubiquitous and is now increasingly adopted in experimental investigations of clinical, behavioral, and experimental neurosciences. Methods in Brain Connectivity Inference through Multivariate Time Series Analysis gathers the contributions of leading international authors who discuss different time series analysis approaches, providing a thorough survey of information on how brain areas effectively interact. Incorporating multidisciplinary work in applied mathematics, statistics, and animal and human experiments at the forefront of the field, the book addresses the use of time series data in brain connectivity interference studies. Contributors present codes and data examples to back up their methodological descriptions, exploring the details of each proposed method as well as an appreciation of their merits and limitations. Supplemental material for the book, including code, data, practical examples, and color figures is supplied in the form of downloadable resources with directories organized by chapter and instruction files that provide additional detail.The field of brain connectivity inference is growing at a fast pace with new data/signal processing proposals emerging so often as to make it difficult to be fully up to date. This consolidated panorama of data-driven methods includes theoretical bases allied to computational tools, offering readers immediate hands-on experience in this dynamic arena.
Methods in Comparative Effectiveness Research (Chapman & Hall/CRC Biostatistics Series)
by Sally C. Morton Constantine GatsonisComparative effectiveness research (CER) is the generation and synthesis of evidence that compares the benefits and harms of alternative methods to prevent, diagnose, treat, and monitor a clinical condition or to improve the delivery of care (IOM 2009). CER is conducted to develop evidence that will aid patients, clinicians, purchasers, and health policy makers in making informed decisions at both the individual and population levels. CER encompasses a very broad range of types of studies—experimental, observational, prospective, retrospective, and research synthesis. This volume covers the main areas of quantitative methodology for the design and analysis of CER studies. The volume has four major sections—causal inference; clinical trials; research synthesis; and specialized topics. The audience includes CER methodologists, quantitative-trained researchers interested in CER, and graduate students in statistics, epidemiology, and health services and outcomes research. The book assumes a masters-level course in regression analysis and familiarity with clinical research.
Methods in Epidemiology: Population Size Estimation (Advances in Experimental Medicine and Biology #1333)
by George RutherfordThis book describes the variety of direct and indirect population size estimation (PSE) methods available along with their strengths and weaknesses. Direct estimation methods, such as enumeration and mapping, involve contact with members of hard-to-reach groups. Indirect methods have practical appeal because they require no contact with members of hard-to-reach groups. One indirect method in particular, network scale-up (NSU), has several strengths over other PSE methods: It can be applied at a province/country level, it can estimate size of several hard-to-reach population in a single study, and it is implemented with members of the general population rather than members of hard-to-reach groups.The book discusses methods to collect, analyze, and adjust results and presents methods to triangulate and finalize PSEs.
Methods in Experimental Economics: An Introduction (Springer Texts in Business and Economics)
by Joachim Weimann Jeannette Brosig-KochThis textbook provides a hands-on and intuitive overview of the methodological foundations of experimental economics. Experimental economic research has been an integral part of economic science for quite some time and is gaining more and more attention in related disciplines. The book addresses the design and execution of experiments, the evaluation of experimental data and the equipment of an experimental laboratory. It illustrates the challenges involved in designing and conducting experiments and helps the reader to address them in practice.
Methods in Medical Informatics: Fundamentals of Healthcare Programming in Perl, Python, and Ruby (Chapman & Hall/CRC Computational Biology Series)
by Jules J. BermanToo often, healthcare workers are led to believe that medical informatics is a complex field that can only be mastered by teams of professional programmers. This is simply not the case. With just a few dozen simple algorithms, easily implemented with open source programming languages, you can fully utilize the medical information contained in clini
Methods in Microarray Normalization (Drug Discovery Series)
by Phillip StaffordThis organized text compiles, for the first time, the most useful normalization methods developed for interpreting microarray data. Experts examine the mathematical processes that are important in normalizing data and avoiding inherent systematic biases. They also review modern software, including discussions on key algorithms, comparative data, and download locations. The book contains the latest microarray innovations from companies such as Agilent, Affymetrix, and GeneGo as well as new, readily adaptable normalization methods for expression and CGH arrays. It also lists of open-source molecular profiling normalization algorithms available and where to access them.
Methods in Statistical Mechanics: A Modern View (Lecture Notes in Physics #974)
by Osvaldo Civitarese Manuel GadellaThis book presents a variety of techniques for tackling phenomena that are not amenable to the conventional approach based on the concept of probabilities. The methods described rely on the use of path integration, thermal Green functions, time-temperature propagators, Liouville operators, second quantization, and field correlators at finite density and temperature. Also exploring the statistical mechanics of unstable quantum systems, the book is intended as a supplementary or reference text for use in one-semester graduate courses on Quantum Mechanics, Thermodynamics, Electromagnetism, and Mathematical Methods in Physics.
Methods in Urban Analysis (Cities Research Series)
by Scott BaumThis book highlights major quantitative and qualitative methods and approaches used in the field of urban analysis. The respective chapters cover the background and relevance of various approaches to urban studies and offer guidance on implementing specific methodologies. Each chapter also provides links to real-world examples. The book is unique in its focus on Australian examples and subject matter, presented by recognized experts in the field.
Methods of Applied Mathematics (Dover Books on Mathematics)
by Francis B. HildebrandThis invaluable book offers engineers and physicists working knowledge of a number of mathematical facts and techniques not commonly treated in courses in advanced calculus, but nevertheless extremely useful when applied to typical problems in many different fields. It deals principally with linear algebraic equations, quadratic and Hermitian forms, operations with vectors and matrices, the calculus of variations, and the formulations and theory of linear integral equations. Annotated problems and exercises accompany each chapter.
Methods of Applied Mathematics with a Software Overview
by Jon H. DavisBroadly organized around the applications of Fourier analysis, "Methods of Applied Mathematics with a MATLAB Overview" covers both classical applications in partial differential equations and boundary value problems, as well as the concepts and methods associated to the Laplace, Fourier, and discrete transforms. Transform inversion problems are also examined, along with the necessary background in complex variables. A final chapter treats wavelets, short-time Fourier analysis, and geometrically-based transforms. The computer program MATLAB is emphasized throughout, and an introduction to MATLAB is provided in an appendix. Rich in examples, illustrations, and exercises of varying difficulty, this text can be used for a one- or two-semester course and is ideal for students in pure and applied mathematics, physics, and engineering.
Methods of Cut-Elimination
by Matthias Baaz Alexander LeitschThis is the first book on cut-elimination in first-order predicate logic from an algorithmic point of view. Instead of just proving the existence of cut-free proofs, it focuses on the algorithmic methods transforming proofs with arbitrary cuts to proofs with only atomic cuts (atomic cut normal forms, so-called ACNFs). The first part investigates traditional reductive methods from the point of view of proof rewriting. Within this general framework, generalizations of Gentzen's and Sch\"utte-Tait's cut-elimination methods are defined and shown terminating with ACNFs of the original proof. Moreover, a complexity theoretic comparison of Gentzen's and Tait's methods is given. The core of the book centers around the cut-elimination method CERES (cut elimination by resolution) developed by the authors. CERES is based on the resolution calculus and radically differs from the reductive cut-elimination methods. The book shows that CERES asymptotically outperforms all reductive methods based on Gentzen's cut-reduction rules. It obtains this result by heavy use of subsumption theorems in clause logic. Moreover, several applications of CERES are given (to interpolation, complexity analysis of cut-elimination, generalization of proofs, and to the analysis of real mathematical proofs). Lastly, the book demonstrates that CERES can be extended to nonclassical logics, in particular to finitely-valued logics and to G\"odel logic.
Methods of Demographic Analysis
by David A. Swanson Farhat Yusuf Jo. M. MartinsThis book provides an up-to-date overview of demographic analysis and methods, including recent developments in demography. Concepts and methods, from the nature of demographic information through data collection and the basics of statistical measures and on to demographic analysis itself are succinctly explained. Measures and analyses of fertility, mortality, life tables, migration and demographic events such as marriage, education and labour force are described while later chapters cover multiple decrement tables, population projections, the importance of testing and smoothing demographic data, the stable population model and demographic software. An emphasis on practical aspects and the use of real-life examples based on data from around the globe make this book accessible, whilst comprehensive references and links to data and other resources on the internet help readers to explore further. The text is concise and well written, making it ideally suited to a wider audience from students to academics and teachers. Students of demography, geography, sociology, economics, as well as professionals, academics and students of marketing, human resource management, and public health who have an interest in population issues will all find this book useful.
Methods of Fourier Analysis and Approximation Theory
by Michael Ruzhansky Sergey TikhonovDifferent facets of interplay between harmonic analysis andapproximation theory are covered in this volume. The topics included areFourier analysis, function spaces, optimization theory, partial differentialequations, and their links to modern developments in the approximation theory. The articles of this collection were originated from two events. The first eventtook place during the 9th ISAAC Congress in Krakow, Poland, 5th-9th August2013, at the section "ApproximationTheory and Fourier Analysis". The secondevent was the conference on Fourier Analysis and Approximation Theory in theCentre de Recerca Matemàtica (CRM), Barcelona, during 4th-8th November 2013,organized by the editors of this volume. All articles selected to be part ofthis collection were carefully reviewed.
Methods of Housing Analysis: Techniques and Case Studies
by A. James GregorIn order to understand and formulate housing policy and programs, it is necessary to have a working knowledge of the internal economic operation of housing from the points of view of both the investor and the owner. James W. Hughes argues that investors' and owners' behavior and activity tend to be governed by market forces and other realities. In that regard, he begins this work by analyzing market rates of return in real estate and housing undertakings, and the variety of analytical techniques which underlie their determination.Methods of Housing Analysis is designed to provide urban planners with an introduction to the basic, quantitative techniques associated with the analysis of housing. A myriad of specific analytical methods has evolved in each of the professions concerned with this subject area. Planners, investors, developers, engineers, appraisers, social scientists, and governmental officials all tend to exhibit unique perspectives when examining housing and have developed their analytical frameworks accordingly.The work is comprised of an extensive discussion by the author, detailed case studies and examples, and a number of essays by leading experts that detail specific analytical procedures and demonstrate their use. The book is divided into four major sections: analysis of the internal operation of housing; basic cost-revenue analysis; expanded cost-revenue/benefit analysis; and government regulation of housing. The thorough nature of Hughes' discussion and of the related readings makes this volume an ideal textbook and reference source.
Methods of Mathematical Modelling
by Mark Bowen Thomas WitelskiThis book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.
Methods of Mathematical Modelling: Fractional Differential Equations (Mathematics and its Applications)
by Dumitru Baleanu Harendra Singh Devendra KumarThis book features original research articles on the topic of mathematical modelling and fractional differential equations. The contributions, written by leading researchers in the field, consist of chapters on classical and modern dynamical systems modelled by fractional differential equations in physics, engineering, signal processing, fluid mechanics, and bioengineering, manufacturing, systems engineering, and project management. The book offers theory and practical applications for the solutions of real-life problems and will be of interest to graduate level students, educators, researchers, and scientists interested in mathematical modelling and its diverse applications. Features Presents several recent developments in the theory and applications of fractional calculus Includes chapters on different analytical and numerical methods dedicated to several mathematical equations Develops methods for the mathematical models which are governed by fractional differential equations Provides methods for models in physics, engineering, signal processing, fluid mechanics, and bioengineering Discusses real-world problems, theory, and applications
Methods of Mathematical Oncology: Fusion of Mathematics and Biology, Osaka, Japan, October 26–28, 2020 (Springer Proceedings in Mathematics & Statistics #370)
by Takashi Suzuki Mark Chaplain Clair Poignard Vito QuarantaThis book presents original papers reflecting topics featured at the international symposium entitled “Fusion of Mathematics and Biology” and organized by the editor of the book. The symposium, held in October 2020 at Osaka University in Japan, was the core event for the final year of the research project entitled “Establishing International Research Networks of Mathematical Oncology.” The project had been carried out since April 2015 as part of the Core-to-Core Program of Japan Society for the Promotion of Science (JSPS). In this book, the editor presents collaborative research from prestigious organizations in France, the UK, and the USA. By utilizing their individual strengths and realizing the fusion of life science and mathematical science, the project achieved a combination of mathematical analysis, verification by biomedical experiments, and statistical analysis of chemical databases.Mathematics is sometimes regarded as a universal language. It is a valuable property that everyone can understand beyond the boundaries of culture, religion, and language. This unifying force of mathematics also applies to the various fields of science. Mathematical oncology has two aspects, i.e., data science and mathematical modeling, and definitely helps in the prediction and control of biological phenomena observed in cancer evolution.The topics addressed in this book represent several methods of applying mathematical modeling to scientific problems in the natural sciences. Furthermore, novel reviews are included that may motivate many mathematicians to become interested in biological research.
Methods of Mathematical Physics
by Harold Jeffreys Bertha SwirlesThis well-known text and reference contains an account of those mathematical methods that have applications in at least two branches of physics. The authors give examples of the practical use of the methods taken from a wide range of physics, including dynamics, hydrodynamics, elasticity, electromagnetism, heat conduction, wave motion and quantum theory. They pay particular attention to the conditions under which theorems hold. Helpful exercises accompany each chapter.
Methods of Mathematical Physics: Classical and Modern
by Vladislav V. Kravchenko Alexey N. KarapetyantsThis textbook provides a thorough overview of mathematical physics, highlighting classical topics as well as recent developments. Readers will be introduced to a variety of methods that reflect current trends in research, including the Bergman kernel approach for solving boundary value and spectral problems for PDEs with variable coefficients. With its careful treatment of the fundamentals as well as coverage of topics not often encountered in textbooks, this will be an ideal text for both introductory and more specialized courses.The first five chapters present standard material, including the classification of PDEs, an introduction to boundary value and initial value problems, and an introduction to the Fourier method of separation of variables. More advanced material and specialized treatments follow, including practical methods for solving direct and inverse Sturm-Liouville problems; the theory of parabolic equations, harmonic functions, potential theory, integral equations and the method of non-orthogonal series.Methods of Mathematical Physics is ideal for undergraduate students and can serve as a textbook for a regular course in equations of mathematical physics as well as for more advanced courses on selected topics.
Methods of Mathematics Applied to Calculus, Probability, and Statistics (Dover Books on Mathematics)
by Richard W. HammingUnderstanding calculus is vital to the creative applications of mathematics in numerous areas. This text focuses on the most widely used applications of mathematical methods, including those related to other important fields such as probability and statistics. The four-part treatment begins with algebra and analytic geometry and proceeds to an exploration of the calculus of algebraic functions and transcendental functions and applications. In addition to three helpful appendixes, the text features answers to some of the exercises. Appropriate for advanced undergraduates and graduate students, it is also a practical reference for professionals. 1985 edition. 310 figures. 18 tables.
Methods of Multivariate Analysis
by William F. Christensen Alvin C. RencherPraise for the Second Edition"This book is a systematic, well-written, well-organized text on multivariate analysis packed with intuition and insight . . . There is much practical wisdom in this book that is hard to find elsewhere."-IIE TransactionsFilled with new and timely content, Methods of Multivariate Analysis, Third Edition provides examples and exercises based on more than sixty real data sets from a wide variety of scientific fields. It takes a "methods" approach to the subject, placing an emphasis on how students and practitioners can employ multivariate analysis in real-life situations.This Third Edition continues to explore the key descriptive and inferential procedures that result from multivariate analysis. Following a brief overview of the topic, the book goes on to review the fundamentals of matrix algebra, sampling from multivariate populations, and the extension of common univariate statistical procedures (including t-tests, analysis of variance, and multiple regression) to analogous multivariate techniques that involve several dependent variables. The latter half of the book describes statistical tools that are uniquely multivariate in nature, including procedures for discriminating among groups, characterizing low-dimensional latent structure in high-dimensional data, identifying clusters in data, and graphically illustrating relationships in low-dimensional space. In addition, the authors explore a wealth of newly added topics, including:Confirmatory Factor AnalysisClassification TreesDynamic GraphicsTransformations to NormalityPrediction for Multivariate Multiple RegressionKronecker Products and Vec NotationNew exercises have been added throughout the book, allowing readers to test their comprehension of the presented material. Detailed appendices provide partial solutions as well as supplemental tables, and an accompanying FTP site features the book's data sets and related SAS® code.Requiring only a basic background in statistics, Methods of Multivariate Analysis, Third Edition is an excellent book for courses on multivariate analysis and applied statistics at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for both statisticians and researchers across a wide variety of disciplines.
Methods of Nonsmooth Optimization in Stochastic Programming: From Conceptual Algorithms to Real-World Applications (International Series in Operations Research & Management Science #363)
by Wim Stefanus van Ackooij Welington Luis de OliveiraThis book presents a comprehensive series of methods in nonsmooth optimization, with a particular focus on their application in stochastic programming and dedicated algorithms for decision-making under uncertainty. Each method is accompanied by rigorous mathematical analysis, ensuring a deep understanding of the underlying principles. The theoretical discussions included are essential for comprehending the mechanics of various algorithms and the nature of the solutions they provide—whether they are global, local, stationary, or critical. The book begins by introducing fundamental tools from set-valued analysis, optimization, and probability theory. It then transitions from deterministic to stochastic optimization, starting with a thorough discussion of modeling, understanding uncertainty, and incorporating it into optimization problems. Following this foundation, the book explores numerical algorithms for nonsmooth optimization, covering well-known decomposition techniques and algorithms for convex optimization, mixed-integer convex programming, and nonconvex optimization. Additionally, it introduces numerical algorithms specifically for stochastic programming, focusing on stochastic programming with recourse, chance-constrained optimization, and detailed algorithms for both risk-neutral and risk-averse multistage stochastic programs. The book guides readers through the entire process, from defining optimization models for practical problems to presenting implementable algorithms that can be applied in practice. It is intended for students, practitioners, and scholars who may be unfamiliar with stochastic programming and nonsmooth optimization. The analyses provided are also valuable for practitioners who may not be interested in convergence proofs but wish to understand the nature of the solutions obtained.
Methods of Operations Research
by Dr Saul I. Gass Philip M. Morse George E. KimballOperations research originated during World War II with the military's need for a scientific method of providing executive departments with a quantitative decision-making basis. This volume — co-written by the father of operations research and one of his closest associates — originally appeared in classified form but was later made available to scientists, engineers, and other nonmilitary professionals. The authors discuss probability and the use of measures of effectiveness. They explore strategical kinematics, tactical analysis, gunnery and bombardment problems, operational experiments with equipment and tactics, and organizational and procedural problems. This new edition features an introduction by Saul I. Gass. 51 figures. 31 tables.
Methods of Optimization and Systems Analysis for Problems of Transcomputational Complexity
by Ivan V. SergienkoThis work presents lines of investigation and scientific achievements of the Ukrainian school of optimization theory and adjacent disciplines. These include the development of approaches to mathematical theories, methodologies, methods, and application systems for the solution of applied problems in economy, finances, energy saving, agriculture, biology, genetics, environmental protection, hardware and software engineering, information protection, decision making, pattern recognition, self-adapting control of complicated objects, personnel training, etc. The methods developed include sequential analysis of variants, nondifferential optimization, stochastic optimization, discrete optimization, mathematical modeling, econometric modeling, solution of extremum problems on graphs, construction of discrete images and combinatorial recognition, etc. Some of these methods became well known in the world's mathematical community and are now known as classic methods.
Methods of Solving Complex Geometry Problems
by Ellina GrigorievaThis book is a unique collection of challenging geometry problems and detailed solutions that will build students' confidence in mathematics. By proposing several methods to approach each problem and emphasizing geometry's connections with different fields of mathematics, Methods of Solving Complex Geometry Problems serves as a bridge to more advanced problem solving. Written by an accomplished female mathematician who struggled with geometry as a child, it does not intimidate, but instead fosters the reader's ability to solve math problems through the direct application of theorems. Containing over 160 complex problems with hints and detailed solutions, Methods of Solving Complex Geometry Problems can be used as a self-study guide for mathematics competitions and for improving problem-solving skills in courses on plane geometry or the history of mathematics. It contains important and sometimes overlooked topics on triangles, quadrilaterals, and circles such as the Menelaus-Ceva theorem, Simson's line, Heron's formula, and the theorems of the three altitudes and medians. It can also be used by professors as a resource to stimulate the abstract thinking required to transcend the tedious and routine, bringing forth the original thought of which their students are capable. Methods of Solving Complex Geometry Problems will interest high school and college students needing to prepare for exams and competitions, as well as anyone who enjoys an intellectual challenge and has a special love of geometry. It will also appeal to instructors of geometry, history of mathematics, and math education courses.