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Brain Network Analysis [Hardback]

4.00/5 (6 ratings by Goodreads)
(University of Wisconsin, Madison)
  • Formāts: Hardback, 338 pages, height x width x depth: 235x156x21 mm, weight: 640 g, Worked examples or Exercises; 41 Line drawings, color
  • Izdošanas datums: 27-Jun-2019
  • Izdevniecība: Cambridge University Press
  • ISBN-10: 110718486X
  • ISBN-13: 9781107184862
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  • Hardback
  • Cena: 97,63 €
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Brain Network AnalysisPalielināt
  • Formāts: Hardback, 338 pages, height x width x depth: 235x156x21 mm, weight: 640 g, Worked examples or Exercises; 41 Line drawings, color
  • Izdošanas datums: 27-Jun-2019
  • Izdevniecība: Cambridge University Press
  • ISBN-10: 110718486X
  • ISBN-13: 9781107184862
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9781107184862.html
Keywords:
This tutorial reference serves as a coherent overview of various statistical and mathematical approaches used in brain network analysis, where modeling the complex structures and functions of the human brain often poses many unique computational and statistical challenges. This book fills a gap as a textbook for graduate students while simultaneously articulating important and technically challenging topics. Whereas most available books are graph theory-centric, this text introduces techniques arising from graph theory and expands to include other different models in its discussion on network science, regression, and algebraic topology. Links are included to the sample data and codes used in generating the book's results and figures, helping to empower methodological understanding in a manner immediately usable to both researchers and students.

This tutorial reference provides a coherent overview of statistical and mathematical approaches used in brain network analysis. It goes beyond graph theory to explore different models in network science, regression, and algebraic topology, empowering methodological understanding in a manner immediately usable to both researchers and students.

Recenzijas

'This book is a must-read for students and researchers in brain network analysis. It is unique across many fronts. First, it weaves together the important background material in statistics, computational mathematics and algebraic topology. Second, it accomplishes the dual role of a research monograph and a textbook reference. The author, an expert in this field, conveys his enthusiasm for brain network analysis and lays down the most essential mathematical and statistical foundations for future advances.' Hernando Ombao, King Abdullah University of Science and Technology, Saudi Arabia

Papildus informācija

This coherent mathematical and statistical approach aimed at graduate students incorporates regression and topology as well as graph theory.
Preface xi
1 Statistical Preliminary
1(26)
1.1 General Linear Models
1(5)
1.2 Logistic Regression
6(3)
1.3 Random Fields
9(7)
1.4 Statistical Inference on Fields
16(11)
2 Brain Network Nodes and Edges
27(34)
2.1 Brain Templates
27(1)
2.2 Brain Parcellations
28(6)
2.3 Deterministic Connectivity
34(12)
2.4 Probabilistic Connectivity
46(4)
2.5 Parcellation-Free Brain Network
50(5)
2.6 Structural Covariates
55(6)
3 Graph Theory
61(15)
3.1 Trees and Graphs
61(1)
3.2 Minimum Spanning Trees
62(3)
3.3 Node Degree
65(5)
3.4 Shortest Path Length
70(1)
3.5 Clustering Coefficient
71(1)
3.6 Small-Worldness
72(1)
3.7 Fractal Dimension
73(3)
4 Correlation Networks
76(32)
4.1 Pearson Correlations
76(2)
4.2 Partial Correlations
78(1)
4.3 Averaging Correlations
79(6)
4.4 Correlation as Metric
85(2)
4.5 Statistical Inference on Correlations
87(2)
4.6 Cosine Series Representation
89(14)
4.7 Correlating Functional Signals
103(3)
4.8 Thresholding Correlation Networks
106(2)
5 Big Brain Network Data
108(21)
5.1 Big Data
108(4)
5.2 Sparsity
112(2)
5.3 Hierarchy
114(6)
5.4 Computing Large Correlation Matrices
120(3)
5.5 Online Algorithms
123(6)
6 Network Simulations
129(27)
6.1 Multivariate Normal Distributions
129(7)
6.2 Multivariate Linear Models
136(7)
6.3 Mixed Effects Models
143(6)
6.4 Simulating Dependent Images
149(3)
6.5 Dependent Correlation Networks
152(4)
7 Persistent Homology
156(24)
7.1 Simplicial Homology
157(6)
7.2 Morse Filtrations
163(5)
7.3 Graph Filtrations
168(5)
7.4 Betti Plots
173(7)
8 Diffusions on Graphs
180(27)
8.1 Diffusion as a Cauchy Problem
180(4)
8.2 Finite Difference Method
184(4)
8.3 Laplacian on Planner Graphs
188(1)
8.4 Graph Laplacian
189(4)
8.5 Fiedler Vectors
193(3)
8.6 Heat Kernel Smoothing on Graphs
196(8)
8.7 Laplace Equation
204(3)
9 Sparse Networks
207(19)
9.1 Why Sparse Models?
207(3)
9.2 Sparse Likelihood
210(3)
9.3 Sparse Correlation Network
213(9)
9.4 Partial Correlation Network
222(4)
10 Brain Network Distances
226(20)
10.1 Matrix Norms
227(2)
10.2 Bottleneck Distance
229(2)
10.3 Gromov-Hausdorff Distance
231(2)
10.4 Kolmogorov-Smirnov Distance
233(3)
10.5 Performance Analysis
236(2)
10.6 Comparisons on Modules
238(3)
10.7 Hypernetworks
241(5)
11 Combinatorial Inferences for Networks
246(23)
11.1 Permutation Test
246(7)
11.2 Exact Combinatorial Inference
253(10)
11.3 Bootstrap
263(6)
12 Series Expansion of Connectivity Matrices
269(23)
12.1 Spectral Decomposition
269(2)
12.2 Iterative Residual Fitting
271(7)
12.3 Spectral Decomposition with Different Bases
278(1)
12.4 Spectral Permutation
279(1)
12.5 Karhunen-Loeve Expansion
280(3)
12.6 Vandermonde Matrix Expansion
283(4)
12.7 The Space of Positive Definite Symmetric Matrices
287(5)
13 Dynamic Network Models
292(10)
13.1 Dynamic Causal Model
293(2)
13.2 Dynamic Time Series Models
295(3)
13.3 Persistent Homological Dynamic Network Model
298(4)
Bibliography 302(24)
Index 326
Moo K. Chung is an Associate Professor in the Department of Biostatistics and Medical Informatics at the University of Wisconsin, Madison and is also affiliated with the Department of Statistics and Waisman Laboratory for Brain Imaging and Behavior. He has received the Vilas Associate Award for his research in applied topology to medical imaging, the Editor's Award for best paper published in the Journal of Speech, Language, and Hearing Research for a paper that analyzed CT images, and a National Institutes of Health (NIH) Brain Initiative Award for work on persistent homological brain network analysis. He has written numerous papers in computational neuroimaging and two previous books on computation on brain image analysis.