Big data in omics and imaging: association analysis PDF
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Big Data in Omics and Imaging: Association Analysis CHAPMAN & HALL/CRC Mathematical and Computational Biology Series Aims and Scope: This series aims to capture new developments and summarize what is known over the entire spectrum of mathematical and computational biology and medicine. It seeks to encourage the integration of mathematical, s tatistical, and computational methods into biology by publishing a broad range of textbooks, reference works, and handbooks. The titles included in the series are meant to appeal to students, researchers, and professionals in the mathematical, s tatistical and computational sciences, fundamental biology and bioengineering, as well as interdisciplinary researchers involved in the field. The inclusion of concrete examples and applications, and programming techniques and examples, is highly encouraged. Series Editors N. F. Britton Department of Mathematical Sciences University of Bath Xihong Lin Department of Biostatistics Harvard University Nicola Mulder University of Cape Town South Africa Maria Victoria Schneider European Bioinformatics Institute Mona Singh Department of Computer Science Princeton University Proposals for the series should be submitted to one of the series editors above or directly to: CRC Press, Taylor & Francis Group 3 Park Square, Milton Park Abingdon, Oxfordshire OX14 4RN UK Published Titles An Introduction to Systems Biology: Design Statistical Methods for QTL Mapping Principles of Biological Circuits Zehua Chen Uri Alon An Introduction to Physical Oncology: Glycome Informatics: Methods and How Mechanistic Mathematical Applications Modeling Can Improve Cancer Therapy Kiyoko F. Aoki-Kinoshita Outcomes Vittorio Cristini, Eugene J. Koay, and Zhihui Wang Computational Systems Biology of Cancer Normal Mode Analysis: Theory and Emmanuel Barillot, Laurence Calzone, Applications to Biological and Chemical Philippe Hupé, Jean-Philippe Vert, and Systems Andrei Zinovyev Qiang Cui and Ivet Bahar Python for Bioinformatics, Second Edition Kinetic Modelling in Systems Biology Sebastian Bassi Oleg Demin and Igor Goryanin Quantitative Biology: From Molecular to Data Analysis Tools for DNA Microarrays Cellular Systems Sorin Draghici Sebastian Bassi Statistics and Data Analysis for Methods in Medical Informatics: Microarrays Using R and Bioconductor, Fundamentals of Healthcare Second Edition Programming in Perl, Python, and Ruby Sorin Drăghici Jules J. Berman Computational Neuroscience: Chromatin: Structure, Dynamics, A Comprehensive Approach Regulation Jianfeng Feng Ralf Blossey Mathematical Models of Plant-Herbivore Computational Biology: A Statistical Interactions Mechanics Perspective Zhilan Feng and Donald L. DeAngelis Ralf Blossey Biological Sequence Analysis Using Game-Theoretical Models in Biology the SeqAn C++ Library Mark Broom and Jan Rychtář Andreas Gogol-Döring and Knut Reinert Computational and Visualization Gene Expression Studies Using Techniques for Structural Bioinformatics Affymetrix Microarrays Using Chimera Hinrich Göhlmann and Willem Talloen Forbes J. Burkowski Handbook of Hidden Markov Models Structural Bioinformatics: An Algorithmic in Bioinformatics Approach Martin Gollery Forbes J. Burkowski Meta-Analysis and Combining Spatial Ecology Information in Genetics and Genomics Stephen Cantrell, Chris Cosner, and Shigui Ruan Rudy Guerra and Darlene R. Goldstein Cell Mechanics: From Single Scale- Differential Equations and Mathematical Based Models to Multiscale Modeling Biology, Second Edition Arnaud Chauvière, Luigi Preziosi, D.S. Jones, M.J. Plank, and B.D. Sleeman and Claude Verdier Knowledge Discovery in Proteomics Bayesian Phylogenetics: Methods, Igor Jurisica and Dennis Wigle Algorithms, and Applications Introduction to Proteins: Structure, Ming-Hui Chen, Lynn Kuo, and Paul O. Lewis Function, and Motion Amit Kessel and Nir Ben-Tal Published Titles (continued) RNA-seq Data Analysis: A Practical Introduction to Bio-Ontologies Approach Peter N. Robinson and Sebastian Bauer Eija Korpelainen, Jarno Tuimala, Dynamics of Biological Systems Panu Somervuo, Mikael Huss, and Garry Wong Michael Small Introduction to Mathematical Oncology Genome Annotation Yang Kuang, John D. Nagy, and Jung Soh, Paul M.K. Gordon, and Steffen E. Eikenberry Christoph W. Sensen Biological Computation Niche Modeling: Predictions from Ehud Lamm and Ron Unger Statistical Distributions Optimal Control Applied to Biological David Stockwell Models Algorithms for Next-Generation Suzanne Lenhart and John T. Workman Sequencing Clustering in Bioinformatics and Drug Wing-Kin Sung Discovery Algorithms in Bioinformatics: A Practical John D. MacCuish and Norah E. MacCuish Introduction Spatiotemporal Patterns in Ecology Wing-Kin Sung and Epidemiology: Theory, Models, Introduction to Bioinformatics and Simulation Anna Tramontano Horst Malchow, Sergei V. Petrovskii, and Ezio Venturino The Ten Most Wanted Solutions in Protein Bioinformatics Stochastic Dynamics for Systems Biology Anna Tramontano Christian Mazza and Michel Benaïm Combinatorial Pattern Matching Statistical Modeling and Machine Algorithms in Computational Biology Learning for Molecular Biology Using Perl and R Alan M. Moses Gabriel Valiente Engineering Genetic Circuits Managing Your Biological Data Chris J. Myers with Python Allegra Via, Kristian Rother, and Pattern Discovery in Bioinformatics: Anna Tramontano Theory & Algorithms Laxmi Parida Cancer Systems Biology Edwin Wang Exactly Solvable Models of Biological Invasion Stochastic Modelling for Systems Sergei V. Petrovskii and Bai-Lian Li Biology, Second Edition Darren J. Wilkinson Computational Hydrodynamics of Capsules and Biological Cells Big Data in Omics and Imaging: C. Pozrikidis Association Analysis Momiao Xiong Modeling and Simulation of Capsules and Biological Cells Big Data Analysis for Bioinformatics and C. Pozrikidis Biomedical Discoveries Shui Qing Ye Cancer Modelling and Simulation Luigi Preziosi Bioinformatics: A Practical Approach Shui Qing Ye Computational Exome and Genome Analysis Introduction to Computational Peter N. Robinson, Rosario M. Piro, Proteomics and Marten Jäger Golan Yona Big Data in Omics and Imaging: Association Analysis Momiao Xiong CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2018 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed on acid-free paper International Standard Book Number-13: 978-1-4987-2578-1 (Hardback) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the con- sequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. 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Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com To Ping Contents Preface, xxv Author, xxxi Chapter 1 ◾ Mathematical Foundation 1 1.1 SPARSITY-INDUCING NORMS, DUAL NORMS, AND FENCHEL CONJUGATE 1 1.1.1 “Entrywise” Norms 4 1.1.1.1 L Norm 5 2 , 1 1.1.1.2 L Norm 5 p , q 1.1.2 Frobenius Norm 5 1.1.2.1 l /l Norm 5 1 2 1.1.3 Overlapping Groups 6 1.1.4 Dual Norm 8 1.1.4.1 The Norm Dual to the Group Norm 9 1.1.5 Fenchel Conjugate 10 1.1.6 Fenchel Duality 13 1.2 SUBDIFFERENTIAL 16 1.2.1 Definition of Subgradient 17 1.2.2 Subgradients of Differentiable Functions 18 1.2.3 Calculus of Subgradients 18 1.2.3.1 Nonnegative Scaling 19 1.2.3.2 Addition 19 1.2.3.3 Affine Transformation of Variables 19 1.2.3.4 Pointwise Maximum 19 1.2.3.5 Pointwise Supremum 21 1.2.3.6 Expectation 21 1.2.3.7 Chain Rule 22 ix
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