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E-grāmata: Multiscale Analysis and Nonlinear Dynamics: From Genes to the Brain

Edited by (California Institute of Technology, Pasadena, USA), Series edited by
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Multiscale Analysis and Nonlinear Dynamics: From Genes to the BrainPalielināt
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Complex biological systems capable of effective information processing are often governed by mechanisms operating simultaneously on multiple spatial/temporal scales. The book focuses on multiresolution analysis and modeling multiscale phenomena in systems biology and neuroscience.

Modeling multiscale phenomena in systems biology and neuroscience is a very interdisciplinary task, so the editor of the book invited experts in bio-engineering, chemistry, cardiology, neuroscience, computer science, and applied mathematics, to provide their perspectives. Multiscale analysis is the major integrating theme of the book, as indicated by its title. The subtitle does not call for bridging the scales all the way from genes to behavior, but rather stresses the unifying perspective provided by the concepts referred to in the title. Each chapter provides a window into the current state of the art in the areas of research discussed. The book is thus intended for advanced researchers interested in recent developments in these fields. It is believed that the interdisciplinary perspective adopted here will be beneficial for all the above-mentioned fields. The roads between different sciences, "while often the quickest shortcut to another part of our own science, are not visible from the viewpoint of one science alone."

List of Contributors
xiii
Preface xv
1 Introduction: Multiscale Analysis - Modeling, Data, Networks, and Nonlinear Dynamics
1(18)
Misha (Meyer) Z. Pesenson
1.1 Multiscale Modeling
5(5)
1.1.1 Domain-Specific Modeling
6(1)
1.1.2 Analysis
7(2)
1.1.3 Model Interpretation and Verification: Experimental/Simulation Data
9(1)
1.2 Multiresolution Analysis and Processing of High-Dimensional Information/Data
10(1)
1.3 Multiscale Analysis, Networks, and Nonlinear Dynamics
11(3)
1.4 Conclusions
14(5)
References
14(5)
Part One Multiscale Analysis
19(64)
2 Modeling Across Scales: Discrete Geometric Structures in Homogenization and Inverse Homogenization
21(44)
Mathieu Desbrun
Roger D. Donaldson
Houman Owhadi
2.1 Introduction
21(2)
2.2 Homogenization of Conductivity Space
23(1)
22.1 Homogenization as a Nonlinear Operator
24(7)
2.2.2 Parameterization of the Conductivity Space
26(5)
2.3 Discrete Geometric Homogenization
31(8)
2.3.1 Homogenization by Volume Averaging
32(1)
2.3.2 Homogenization by Linear Interpolation
33(4)
2.3.3 Semigroup Properties in Geometric Homogenization
37(2)
2.4 Optimal Weighted Delaunay Triangulations
39(8)
2.4.1 Construction of Positive Dirichlet Weights
40(3)
2.4.2 Weighted Delaunay and Q-Adapted Triangulations
43(1)
2.4.3 Computing Optimal Weighted Delaunay Meshes
44(3)
2.5 Relationship to Inverse Homogenization
47(2)
2.6 Electrical Impedance Tomography
49(16)
2.6.1 Numerical Tests
52(1)
2.6.1.1 Harmonic Coordinate Iteration
53(2)
2.6.1.2 Divergence-Free Parameterization Recovery
55(6)
References
61(4)
3 Multiresolution Analysis on Compact Riemannian Manifolds
65(18)
Isaac Z. Pesenson
3.1 Introduction
65(1)
3.2 Compact Manifolds and Operators
66(3)
3.2.1 Manifolds without Boundary
66(1)
3.2.2 Compact Homogeneous Manifolds
67(1)
3.2.3 Bounded Domains with Smooth Boundaries
68(1)
3.3 Hilbert Frames
69(1)
3.4 Multiresolution and Sampling
70(2)
3.5 Shannon Sampling of Band-limited Functions on Manifolds
72(1)
3.6 Localized Frames on Compact Manifolds
73(3)
3.7 Parseval Frames on Homogeneous Manifolds
76(3)
3.8 Variational Splines on Manifolds
79(2)
3.9 Conclusions
81(2)
References
81(2)
Part Two Nonlinear Dynamics: Cenelets and Synthetic Biochemical Circuits
83(64)
4 Transcriptional Oscillators
85(28)
Elisa Franco
Jongmin Kim
Friedrich C. Simmel
4.1 Introduction
85(1)
4.2 Synthetic Transcriptional Modules
86(3)
4.2.1 Elementary Activation and Inhibition Pathways, and Simple Loops
87(1)
4.2.2 Experimental Implementation
88(1)
4.3 Molecular Clocks
89(7)
4.3.1 A Two-Node Molecular Oscillator
90(1)
4.3.2 Analysis of the Oscillatory Regime
91(4)
4.3.3 Experimental Implementation and Data
95(1)
4.4 Scaling Up Molecular Circuits: Synchronization of Molecular Processes
96(9)
4.4.1 Analysis of the Load Dynamics
97(2)
4.4.1.1 Quasisteady State Approximation of the Load Dynamics
99(1)
4.4.1.2 Efficiency of Signal Transmission
99(1)
4.4.2 Perturbation of the Oscillator Caused by the Load
100(1)
4.4.2.1 Consumptive Coupling
100(1)
4.4.2.2 Nonconsumptive Coupling and Retroactivity
100(2)
4.4.3 Insulation
102(1)
4.4.3.1 Reduction of Perturbations on the Oscillator Dynamics
103(1)
4.4.3.2 Signal Transmission to the Insulated Load
104(1)
4.5 Oscillator Driving a Load: Experimental Implementation and Data
105(1)
4.6 Deterministic Predictive Models for Complex Reaction Networks
105(2)
4.7 Stochastic Effects
107(3)
4.8 Conclusions
110(3)
References
110(3)
5 Synthetic Biochemical Dynamic Circuits
113(34)
Raphael Plasson
Yannick Rondelez
5.1 Introduction
113(1)
5.2 Out-of-Equilibrium Chemical Systems
114(9)
5.2.1 A Short Historical Overview
114(1)
5.2.1.1 Discovery of Nonlinear Chemical Systems
114(1)
5.2.1.2 Unexpected Oscillating Chemical Systems
115(1)
5.2.2 Building Nonequilibrium Systems
116(1)
5.2.2.1 Energetic Requirements
116(1)
5.2.2.2 System Closure
116(2)
5.2.2.3 Instabilities and Dynamic Stability
118(1)
5.2.3 Design Principles
119(1)
5.2.3.1 Dynamism
119(2)
5.2.3.2 Interacting Feedbacks Processes
121(1)
5.2.3.3 Modularity
122(1)
5.3 Biological Circuits
123(7)
5.3.1 Biological Networks Modeled by Chemistry
123(1)
5.3.2 Biosystems: A Multilevel Complexity
124(1)
5.3.3 A First Example of a Biological Reaction Circuit
124(1)
5.3.4 Biological Networking Strategy
125(1)
5.3.4.1 GRNs Are Templated Networks
125(1)
5.3.4.2 Regulation and Feedback Loops
125(2)
5.3.4.3 Nonlinearities in Genetic Regulation
127(1)
5.3.4.4 Delays
128(1)
5.3.4.5 Titration Effects
129(1)
5.3.5 Higher Level Motifs and Modularity of Biochemical Networks
129(1)
5.4 Programmable In Vitro Dynamics
130(9)
5.4.1 Enzymatic Systems
130(1)
5.4.1.1 DNA-RNA Sequence Amplification
131(1)
5.4.1.2 The Genelet System
131(1)
5.4.1.3 The PEN Toolbox
132(2)
5.4.2 Nonenzymatic Networks: Strand Displacement Systems
134(1)
5.4.3 Numerical Modeling
135(1)
5.4.3.1 Mathematical Descriptions
135(2)
5.4.3.2 LSA and Bifurcation Analysis for Design
137(1)
5.4.3.3 Time Evolutions
138(1)
5.4.3.4 Robustness Analysis and In Silico Evolutions
138(1)
5.5 Perspectives
139(8)
5.5.1 DNA Computing
140(1)
5.5.2 Self Organizing Spatial Patterns
140(1)
5.5.3 Models of Biological Networks
141(1)
5.5.4 Origin of life
141(1)
References
142(5)
Part Three Nonlinear Dynamics: the Brain and the Heart
147(152)
6 Theoretical and Experimental Electrophysiology in Human Neocortex: Multiscale Dynamic Correlates of Conscious Experience
149(30)
Paul L. Nunez
Ramesh Srinivasan
Lester Ingber
6.1 Introduction to Brain Complexity
149(5)
6.1.1 Human Brains and Other Complex Adaptive Systems
149(1)
6.1.2 Is "Consciousness" a Four-Letter Word?
150(1)
6.1.3 Motivations and Target Audiences for this
Chapter
151(1)
6.1.4 Brain Imaging at Multiple Spatial and Temporal Scales
151(2)
6.1.5 Multiple Scales of Brain Dynamics in Consciousness
153(1)
6.2 Brief Overview of Neocortical Anatomy and Physiology
154(6)
6.2.1 The Human Brain at Large Scales
154(1)
6.2.2 Chemical Control of Brain and Behavior
155(1)
6.2.3 Electrical Transmission
156(1)
6.2.4 Neocortex
156(2)
6.2.5 The Nested Hierarchy of Neocortex: Multiple Scales of Brain Tissue
158(1)
6.2.6 Corticocortical Connections Are Nonlocal and "Small World"
159(1)
6.3 Multiscale Theory in Electrophysiology
160(6)
6.3.1 Characteristic EEG and Physiological Time Scales
160(1)
6.3.2 Local versus Global Brain Models and Spatial Scale
161(1)
6.3.3 A Large-Scale Model of EEG Standing Waves
162(2)
6.3.4 Relationships between Small, Intermediate, and Large Scales: A Simple Mechanical Analog
164(2)
6.4 Statistical Mechanics of Neocortical Interactions
166(7)
6.4.1 SMNI on Short-Term Memory and EEG
166(1)
6.4.1.1 SMNI STM
167(1)
6.4.1.2 SMNI EEG
168(1)
6.4.2 Euler-Lagrange Equations
168(1)
6.4.2.1 Columnar EL
169(1)
6.4.2.2 Strings EL
170(1)
6.4.2.3 Springs EL
171(1)
6.4.3 Smoking Gun
171(1)
6.4.3.1 Neocortical Magnetic Fields
172(1)
6.4.3.2 SMNI Vector Potential
172(1)
6.5 Concluding Remarks
173(6)
References
174(5)
7 Multiscale Network Organization in the Human Brain
179(8)
Danielle S. Bassett
Felix Siebenhuhner
7.1 Introduction
179(2)
7.2 Mathematical Concepts
181(1)
7.3 Structural Multiscale Organization
182(5)
7.4 A Functional Multiscale Organization
187(18)
7.5 Discussion
191(14)
7.5.1 Structure and Function
191(2)
7.5.2 Hierarchical Modularity
193(1)
7.5.3 Power-Law Scaling
194(1)
7.5.4 Network Models of Multiscale Structure 194 References
195(10)
8 Neuronal Oscillations Scale Up and Scale Down Brain Dynamics
205(12)
Michel Le Van Quyen
Vicente Botella-Soler
Mario Valderrama
8.1 Introduction
205(1)
8.2 The Brain Web of Cross-Scale Interactions
206(2)
8.3 Multiscale Recordings of the Human Brain
208(2)
8.4 Physiological Correlates of Cross-Level Interactions
210(2)
8.5 Level Entanglement and Cross-Scale Coupling of Neuronal Oscillations
212(1)
8.6 Conclusions
213(4)
References
214(3)
9 Linking Nonlinear Neural Dynamics to Single-Trial Human Behavior
217(16)
Michael X. Cohen
Bradley Voytek
9.1 Neural Dynamics Are Complex
217(1)
9.2 Data Analysis Techniques and Possibilities Are Expanding Rapidly
218(1)
9.3 The Importance of Linking Neural Dynamics to Behavior Dynamics
219(1)
9.4 Linear Approaches of Linking Neural and Behavior Dynamics
220(1)
9.5 Nonlinear Dynamics and Behavior Phase Modulations
221(3)
9.6 Cross-Frequency Coupling
224(2)
9.7 Linking Cross-Frequency Coupling to Behavior
226(2)
9.8 Testing for Causal Involvement of Nonlinear Dynamics in Cognition and Behavior
228(1)
9.9 Conclusions
229(4)
References
229(4)
10 Brain Dynamics at Rest: How Structure Shapes Dynamics
233(12)
Etienne Hugues
Juan R. Vidal
Jean-Philippe Lachaux
Gustavo Deco
10.1 Introduction
233(1)
10.2 Model
234(2)
10.3 Results
236(3)
10.3.1 Neural Dynamics
236(1)
10.3.1.1 Case of Infinite Conduction Velocity
236(2)
10.3.1.2 Case of Finite Conduction Velocity
238(1)
10.3.2 BOLD Dynamics
238(1)
10.4 Comparison with Experimental Data
239(1)
10.5 Discussion
240(5)
References
242(3)
11 Adaptive Multiscale Encoding: A Computational Function of Neuronal Synchronization
245(12)
Misha (Meyer) Z. Pesenson
11.1 Introduction
245(2)
11.2 Some Basic Mathematical Concepts
247(1)
11.3 Neural Synchronization
247(7)
11.3.1 Connections with Some Existing Approaches to MRA
253(1)
11.4 Concluding Remarks 253 References
254(3)
12 Multiscale Nonlinear Dynamics in Cardiac Electrophysiology: From Sparks to Sudden Death
257(20)
Zhilin Qu
Michael Nivala
12.1 Introduction
257(1)
12.2 Subcellular Scale: Criticality in the Transition from Ca Sparks to Ca Waves
258(2)
12.3 Cellular Scale: Action Potential and Ca Cycling Dynamics
260(6)
12.3.1 Intracellular Ca Alternans
260(2)
12.3.2 Fast Pacing-Induced Complex APD Dynamics
262(2)
12.3.3 EAD-Mediated Nonlinear Dynamics at Slow Heart Rates
264(2)
12.4 Excitation Dynamics on the Tissue and Organ Scales
266(5)
12.4.1 Spatially Discordant APD Alternans
266(1)
12.4.2 Spiral and Scroll Wave Dynamics
267(2)
12.4.3 Chaos Synchronization
269(2)
12.5 Conclusions
271(6)
References
271(6)
13 Measures of Spike Train Synchrony: From Single Neurons to Populations
277(22)
Conor Houghton
Thomas Kreuz
13.1 Introduction
277(1)
13.2 Measures of Spike Train Distance
278(8)
13.2.1 Notation
278(1)
13.2.2 The Victor-Purpura Metric
279(1)
13.2.3 The van Rossum Metric
280(2)
13.2.4 The ISI- and the SPIKE-Distance
282(2)
13.2.4.1 The ISI-Distance
284(1)
13.2.4.2 The SPIKE-Distance
285(1)
13.2.5 Entropy-Based Measure
286(1)
13.3 Comparisons
286(4)
13.3.1 The ISI- and the SPIKE-Distance
286(1)
13.3.2 The ISI-Distance and the van Rossum Metric
287(1)
13.3.3 The SPIKE-Distance and the Victor-Purpura Metric
288(1)
13.3.4 Comparison of All Distances on Birdsong Data
289(1)
13.4 Measuring the Dissimilarity within a Population
290(2)
13.5 Measuring the Dissimilarity between Populations
292(2)
13.5.1 The Population Extension of the Victor-Purpura Metric
292(1)
13.5.2 The Population Extension of the van Rossum Metric
293(1)
13.6 Discussion
294(5)
References
296(3)
Index 299
Dr. Misha (Meyer) Z. Pesenson has held positions in academia, including UCLA and Caltech, since 1990. He is currently Research Scientist at the Computing and Mathematical Sciences Dept., California Institute of Technology. Dr. Pesenson's research focuses on multiscale modeling, nonlinear dynamics, neural networks, and complex information processing.

The Series Editor Heinz Georg Schuster is Professor of Theoretical Physics at the University of Kiel in Germany. He was a visiting professor at the Weizmann-Institute of Science in Israel and at the California Institute of Technology in Pasadena, USA. He authored and edited many books on nonlinear phenomena and chaos control.
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