Table Of ContentBig Data in Omics and Imaging:
Association Analysis
CHAPMAN & HALL/CRC
Mathematical and Computational Biology Series
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An Introduction to Systems Biology: Design Statistical Methods for QTL Mapping
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Applications Modeling Can Improve Cancer Therapy
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Computational Systems Biology of
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Handbook of Hidden Markov Models
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Forbes J. Burkowski
Meta-Analysis and Combining
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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
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RNA-seq Data Analysis: A Practical Introduction to Bio-Ontologies
Approach Peter N. Robinson and Sebastian Bauer
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and Biological Cells Big Data Analysis for Bioinformatics and
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Big Data in Omics and Imaging:
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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
