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Author: Shouchuan Hu
Publisher: Springer Nature
ISBN: 3031178378
Category : Mathematics
Languages : en
Pages : 544
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Book Description
This book, which is the first of two volumes, presents, in a unique way, some of the most relevant research tools of modern analysis. This work empowers young researchers with all the necessary techniques to explore the various subfields of this broad subject, and introduces relevant frameworks where these tools can be immediately deployed. Volume I starts with the foundations of modern analysis. The first three chapters are devoted to topology, measure theory, and functional analysis. Chapter 4 offers a comprehensive analysis of the main function spaces, while Chapter 5 covers more concrete subjects, like multivariate analysis, which are closely related to applications and more difficult to find in compact form. Chapter 6 deals with smooth and non-smooth calculus of functions; Chapter 7 introduces certain important classes of nonlinear operators; and Chapter 8 complements the previous three chapters with topics of variational analysis. Each chapter of this volume finishes with a list of problems – handy for understanding and self-study – and historical notes that give the reader a more vivid picture of how the theory developed. Volume II consists of various applications using the tools and techniques developed in this volume. By offering a clear and wide picture of the tools and applications of modern analysis, this work can be of great benefit not only to mature graduate students seeking topics for research, but also to experienced researchers with an interest in this vast and rich field of mathematics.
Author: Shouchuan Hu
Publisher: Springer Nature
ISBN: 3031178378
Category : Mathematics
Languages : en
Pages : 544
Get Book
Book Description
This book, which is the first of two volumes, presents, in a unique way, some of the most relevant research tools of modern analysis. This work empowers young researchers with all the necessary techniques to explore the various subfields of this broad subject, and introduces relevant frameworks where these tools can be immediately deployed. Volume I starts with the foundations of modern analysis. The first three chapters are devoted to topology, measure theory, and functional analysis. Chapter 4 offers a comprehensive analysis of the main function spaces, while Chapter 5 covers more concrete subjects, like multivariate analysis, which are closely related to applications and more difficult to find in compact form. Chapter 6 deals with smooth and non-smooth calculus of functions; Chapter 7 introduces certain important classes of nonlinear operators; and Chapter 8 complements the previous three chapters with topics of variational analysis. Each chapter of this volume finishes with a list of problems – handy for understanding and self-study – and historical notes that give the reader a more vivid picture of how the theory developed. Volume II consists of various applications using the tools and techniques developed in this volume. By offering a clear and wide picture of the tools and applications of modern analysis, this work can be of great benefit not only to mature graduate students seeking topics for research, but also to experienced researchers with an interest in this vast and rich field of mathematics.
Author: Lixin Cheng
Publisher: Frontiers Media SA
ISBN: 283253175X
Category : Science
Languages : en
Pages : 757
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Book Description
This Research Topic is part of a series with, "Bioinformatics Analysis of Omics Data for Biomarker Identification in Clinical Research - Volume I" (https://www.frontiersin.org/research-topics/13816/bioinformatics-analysis-of-omics-data-for-biomarker-identification-in-clinical-research) The advances and the decreasing cost of omics data enable profiling of disease molecular features at different levels, including bulk tissues, animal models, and single cells. Large volumes of omics data enhance the ability to search for information for preclinical study and provide the opportunity to leverage them to understand disease mechanisms, identify molecular targets for therapy, and detect biomarkers of treatment response. Identification of stable, predictive, and interpretable biomarkers is a significant step towards personalized medicine and therapy. Omics data from genomics, transcriptomics, proteomics, epigenomics, metagenomics, and metabolomics help to determine biomarkers for prognostic and diagnostic applications. Preprocessing of omics data is of vital importance as it aims to eliminate systematic experimental bias and technical variation while preserving biological variation. Dozens of normalization methods for correcting experimental variation and bias in omics data have been developed during the last two decades, while only a few consider the skewness between different sample states, such as the extensive over-repression of genes in cancers. The choice of normalization methods determines the fate of identified biomarkers or molecular signatures. From these considerations, the development of appropriate normalization methods or preprocessing strategies may promote biomarker identification and facilitate clinical decision-making.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 484
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Book Description
Author: Helena Chmura Kraemer
Publisher: SAGE
ISBN: 9780803929494
Category : Mathematics
Languages : en
Pages : 128
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Book Description
How Many Subjects? is a practical guide to sample size calculations and general principles of cost-effective research. It introduces a simple technique of statistical power analysis which allows researchers to compute approximate sample sizes and power for a wide variety of research designs. Because the same technique is used with only slight modifications for different statistical tests, researchers can easily compare the sample sizes required by different designs and tests to make cost-effective decisions in planning a study. These comparisons, emphasized throughout the book, demonstrate important principles of design, measurement and analysis that are rarely discussed in courses or textbooks.
Author: Dorothy Brown Shaffer
Publisher: American Mathematical Soc.
ISBN: 0821850377
Category : Mathematics
Languages : en
Pages : 154
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Book Description
Presents mathematical ideas based on papers given at an AMS meeting held at Fairfield University in October 1983. This work deals with the Loewner equation, classical results on coefficient bodies and modern optimal control theory. It also deals with support points for the class $S$, Loewner chains and the process of truncation.
Author: Tuomas Hytönen
Publisher: Springer
ISBN: 9783319839615
Category : Mathematics
Languages : en
Pages : 614
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Book Description
The present volume develops the theory of integration in Banach spaces, martingales and UMD spaces, and culminates in a treatment of the Hilbert transform, Littlewood-Paley theory and the vector-valued Mihlin multiplier theorem. Over the past fifteen years, motivated by regularity problems in evolution equations, there has been tremendous progress in the analysis of Banach space-valued functions and processes. The contents of this extensive and powerful toolbox have been mostly scattered around in research papers and lecture notes. Collecting this diverse body of material into a unified and accessible presentation fills a gap in the existing literature. The principal audience that we have in mind consists of researchers who need and use Analysis in Banach Spaces as a tool for studying problems in partial differential equations, harmonic analysis, and stochastic analysis. Self-contained and offering complete proofs, this work is accessible to graduate students and researchers with a background in functional analysis or related areas.
Author: Răzvan Gelca
Publisher: Springer
ISBN: 3319589881
Category : Mathematics
Languages : en
Pages : 857
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Book Description
This book takes the reader on a journey through the world of college mathematics, focusing on some of the most important concepts and results in the theories of polynomials, linear algebra, real analysis, differential equations, coordinate geometry, trigonometry, elementary number theory, combinatorics, and probability. Preliminary material provides an overview of common methods of proof: argument by contradiction, mathematical induction, pigeonhole principle, ordered sets, and invariants. Each chapter systematically presents a single subject within which problems are clustered in each section according to the specific topic. The exposition is driven by nearly 1300 problems and examples chosen from numerous sources from around the world; many original contributions come from the authors. The source, author, and historical background are cited whenever possible. Complete solutions to all problems are given at the end of the book. This second edition includes new sections on quad ratic polynomials, curves in the plane, quadratic fields, combinatorics of numbers, and graph theory, and added problems or theoretical expansion of sections on polynomials, matrices, abstract algebra, limits of sequences and functions, derivatives and their applications, Stokes' theorem, analytical geometry, combinatorial geometry, and counting strategies. Using the W.L. Putnam Mathematical Competition for undergraduates as an inspiring symbol to build an appropriate math background for graduate studies in pure or applied mathematics, the reader is eased into transitioning from problem-solving at the high school level to the university and beyond, that is, to mathematical research. This work may be used as a study guide for the Putnam exam, as a text for many different problem-solving courses, and as a source of problems for standard courses in undergraduate mathematics. Putnam and Beyond is organized for independent study by undergraduate and gradu ate students, as well as teachers and researchers in the physical sciences who wish to expand their mathematical horizons.
Author: Harris Cooper
Publisher: Russell Sage Foundation
ISBN: 1610448863
Category : Social Science
Languages : en
Pages : 567
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Book Description
Research synthesis is the practice of systematically distilling and integrating data from many studies in order to draw more reliable conclusions about a given research issue. When the first edition of The Handbook of Research Synthesis and Meta-Analysis was published in 1994, it quickly became the definitive reference for conducting meta-analyses in both the social and behavioral sciences. In the third edition, editors Harris Cooper, Larry Hedges, and Jeff Valentine present updated versions of classic chapters and add new sections that evaluate cutting-edge developments in the field. The Handbook of Research Synthesis and Meta-Analysis draws upon groundbreaking advances that have transformed research synthesis from a narrative craft into an important scientific process in its own right. The editors and leading scholars guide the reader through every stage of the research synthesis process—problem formulation, literature search and evaluation, statistical integration, and report preparation. The Handbook incorporates state-of-the-art techniques from all quantitative synthesis traditions and distills a vast literature to explain the most effective solutions to the problems of quantitative data integration. Among the statistical issues addressed are the synthesis of non-independent data sets, fixed and random effects methods, the performance of sensitivity analyses and model assessments, the development of machine-based abstract screening, the increased use of meta-regression and the problems of missing data. The Handbook also addresses the non-statistical aspects of research synthesis, including searching the literature and developing schemes for gathering information from study reports. Those engaged in research synthesis will find useful advice on how tables, graphs, and narration can foster communication of the results of research syntheses. The third edition of the Handbook provides comprehensive instruction in the skills necessary to conduct research syntheses and represents the premier text on research synthesis. Praise for the first edition: "The Handbook is a comprehensive treatment of literature synthesis and provides practical advice for anyone deep in the throes of, just teetering on the brink of, or attempting to decipher a meta-analysis. Given the expanding application and importance of literature synthesis, understanding both its strengths and weaknesses is essential for its practitioners and consumers. This volume is a good beginning for those who wish to gain that understanding." —Chance "Meta-analysis, as the statistical analysis of a large collection of results from individual studies is called, has now achieved a status of respectability in medicine. This respectability, when combined with the slight hint of mystique that sometimes surrounds meta-analysis, ensures that results of studies that use it are treated with the respect they deserve....The Handbook of Research Synthesis is one of the most important publications in this subject both as a definitive reference book and a practical manual."—British Medical Journal When the first edition of The Handbook of Research Synthesis was published in 1994, it quickly became the definitive reference for researchers conducting meta-analyses of existing research in both the social and biological sciences. In this fully revised second edition, editors Harris Cooper, Larry Hedges, and Jeff Valentine present updated versions of the Handbook's classic chapters, as well as entirely new sections reporting on the most recent, cutting-edge developments in the field. Research synthesis is the practice of systematically distilling and integrating data from a variety of sources in order to draw more reliable conclusions about a given question or topic. The Handbook of Research Synthesis and Meta-Analysis draws upon years of groundbreaking advances that have transformed research synthesis from a narrative craft into an important scientific process in its own right. Cooper, Hedges, and Valentine have assembled leading authorities in the field to guide the reader through every stage of the research synthesis process—problem formulation, literature search and evaluation, statistical integration, and report preparation. The Handbook of Research Synthesis and Meta-Analysis incorporates state-of-the-art techniques from all quantitative synthesis traditions. Distilling a vast technical literature and many informal sources, the Handbook provides a portfolio of the most effective solutions to the problems of quantitative data integration. Among the statistical issues addressed by the authors are the synthesis of non-independent data sets, fixed and random effects methods, the performance of sensitivity analyses and model assessments, and the problem of missing data. The Handbook of Research Synthesis and Meta-Analysis also provides a rich treatment of the non-statistical aspects of research synthesis. Topics include searching the literature, and developing schemes for gathering information from study reports. Those engaged in research synthesis will also find useful advice on how tables, graphs, and narration can be used to provide the most meaningful communication of the results of research synthesis. In addition, the editors address the potentials and limitations of research synthesis, and its future directions. The past decade has been a period of enormous growth in the field of research synthesis. The second edition Handbook thoroughly revises original chapters to assure that the volume remains the most authoritative source of information for researchers undertaking meta-analysis today. In response to the increasing use of research synthesis in the formation of public policy, the second edition includes a new chapter on both the strengths and limitations of research synthesis in policy debates
Author: Peter O'Donoghue
Publisher: Routledge
ISBN: 1134005350
Category : Science
Languages : en
Pages : 381
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Book Description
Modern techniques of sports performance analysis enable the sport scientist, coach and athlete to objectively assess, and therefore improve upon, sporting performance. They are an important tool for any serious practitioner in sport and, as a result, performance analysis has become a key component of degree programmes in sport science and sports coaching. Research Methods for Sports Performance Analysis explains how to undertake a research project in performance analysis including: selection and specification of a research topic the research proposal gaining ethical approval for a study developing a performance analysis system testing a system for reliability analysing and discussing data writing up results. Covering the full research cycle and clearly introducing the key themes and issues in contemporary performance analysis, this is the only book that sports students will need to support a research project in performance analysis, from undergraduate dissertation to doctoral thesis. Including case studies, examples and data throughout, this book is essential reading for any student or practitioner with an interest in performance analysis, sports coaching or applied sport science.
Author: Peter O'Donoghue
Publisher: Routledge
ISBN: 1317213025
Category : Sports & Recreation
Languages : en
Pages : 204
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Book Description
The research project or dissertation is a core component of any degree programme in the rapidly developing discipline of sport performance analysis. This highly practical and accessible book provides a complete step-by-step guide to doing a research project. Showcasing the very latest research methods, it covers the whole research process, from identifying a research question and system development to data collection, data analysis and writing up the results. Introducing the fundamentals of project planning and management, this book highlights the importance of research ethics and explains the differences between successful undergraduate and postgraduate projects. Full of expert advice and original insights that can be applied to theoretical and empirical research projects, it covers all the key aspects of conducting a degree-level research project, including: selecting a research topic and writing a research proposal working with a supervisor understanding research ethics implementing best practices for project management collecting, interpreting and presenting results. Doing a Research Project in Sport Performance Analysis is an indispensable guide for any student, lecturer or practitioner working in sport performance analysis.
