Nonlinear dynamics in physiology : a state-space approach /

Nonlinear dynamics in physiology : a state-space approach /

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Bibliographic Details
Author / Creator:Shelhamer, Mark.
Imprint:Singapore ; Hackensack, NJ : World Scientific, c2007.
Description:xx, 345 p. : ill. ; 24 cm.
Language:English
Subject:
Physiology -- Mathematical models.
Nonlinear systems.
State-space methods.
Nonlinear systems.
Physiology -- Mathematical models.
State-space methods.
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/6270387
Hidden Bibliographic Details
ISBN:9812700293
9789812700292
Notes:Includes bibliographical references and index.
Table of Contents:
  • Preface
  • 1. The mathematical analysis of physiological systems: goals and approaches
  • 1.1. The goals of mathematical analysis in physiology
  • 1.2. Outline of dynamic systems
  • 1.3. Types of dynamic systems - random, deterministic, linear, nonlinear
  • 1.4. Types of dynamic behaviors - random, fixed point, periodic, quasi-periodic, chaotic
  • 1.5. Follow the "noise"
  • 1.6. Chaos and physiology
  • General Bibliography
  • References for Chapter 1
  • 2. Fundamental signal processing and analysis concepts and measures
  • 2.1. Sampled data and continuous distributions
  • 2.2. Basic statistics
  • 2.3. Correlation coefficient
  • 2.4. Linear regression, least-squares, squared-error
  • 2.5. Random processes, white noise, correlated noise
  • 2.6. Autocorrelation
  • 2.7. Concluding remarks
  • References for Chapter 2
  • 3. Analysis approaches based on linear systems
  • 3.1. Definition and properties of linear systems
  • 3.2. Autocorrelation, cross-correlation, stationarity
  • 3.3. Fourier transforms and spectral analysis
  • 3.4. Examples of autocorrelations and frequency spectra
  • 3.5. Transfer functions of linear systems, Gaussian statistics
  • References for Chapter 3
  • 4. State-space reconstruction
  • 4.1. State variables, state space
  • 4.2. Time-delay reconstruction
  • 4.3. A digression on topology
  • 4.4. How to do the reconstruction correctly
  • 4.5. Example: detection of fast-phase eye movements
  • 4.6. Historical notes, examples from the literature
  • 4.7. Points for further consideration
  • References for Chapter 4
  • 5. Dimensions
  • 5.1. Euclidean dimension and topological dimension
  • 5.2. Dimension as a scaling process - coastline length, Mandelbrot, fractals, Cantor, Koch
  • 5.3. Box-counting dimension and correlation dimension
  • 5.4. Correlation dimension - how to measure it correctly
  • 5.5. Error bars on dimension estimates
  • 5.6. Interpretation of the dimension
  • 5.7. Tracking dimension over time
  • 5.8. Examples
  • 5.9. Points for further consideration
  • References for Chapter 5
  • 6. Surrogate data
  • 6.1. The need for surrogates
  • 6.2. Statistical hypothesis testing
  • 6.3. Statistical randomization and its implementation
  • 6.4. Random surrogates
  • 6.5. Phase-randomization surrogate
  • 6.6. AAFT surrogate
  • 6.7. Pseudo-periodic surrogate
  • 6.8. First differences and surrogates
  • 6.9. Multivariate surrogates
  • 6.10. Surrogates tailored to specific physiological hypotheses
  • 6.11. Examples of different surrogates
  • 6.12. Physiological examples
  • References for Chapter 6
  • 7. Nonlinear forecasting
  • 7.1. Predictability of prototypical systems
  • 7.2. Methodology
  • 7.3. Variations
  • 7.4. Surrogates, global linear forecasting
  • 7.5. Time-reversal and amplitude-reversal for detection of nonlinearity
  • 7.6. Chaos versus colored noise
  • 7.7. Forecasting of neural spike trains and other discrete events
  • 7.8. Examples
  • References for Chapter 7
  • 8. Recurrence analysis
  • 8.1. Concept and methodology
  • 8.2. Recurrence plots of simple systems
  • 8.3. Recurrence quantification analysis (RQA)
  • 8.4. Extensions
  • 8.5. Examples
  • References for Chapter 8
  • 9. Tests for dynamical interdependence
  • 9.1. Concepts
  • 9.2. Mutual false nearest neighbors
  • 9.3. Mutual prediction, cross-prediction
  • 9.4. Cross-recurrence, joint recurrence
  • 9.5. Mathematical properties of mappings
  • 9.6. Multivariate surrogates and other test data
  • 9.7. Examples
  • References for Chapter 9
  • 10. Unstable periodic orbits
  • 10.1. Concepts
  • 10.2. Example
  • 10.3. Physiological examples
  • References for Chapter 10
  • 11. Other approaches based on the state space
  • 11.1. Properties of mappings
  • 11.2. Parallel flows in state space
  • 11.3. Exceptional events
  • 11.4. Lyapunov exponents
  • 11.5. Deterministic versus stochastic (DVS) analysis
  • References for Chapter 11
  • 12. Poincare sections, fixed points, and control of chaotic systems
  • 12.1. Poincare section
  • 12.2. Fixed points
  • 12.3. Chaos control
  • 12.4. Anticontrol
  • References for Chapter 12
  • 13. Stochastic measures related to nonlinear dynamical concepts
  • 13.1. Fractal time series, fractional Brownian motion
  • 13.2. fBm, correlation dimension, nonlinear forecasting
  • 13.3. Quantifying fBm: spectrum, autocorrelation, Hurst exponent, detrended fluctuation analysis
  • 13.4. Self-organized criticality
  • References for Chapter 13
  • 14. From measurements to models
  • 14.1. The nature of the problem
  • 14.2. Approaches to nonlinear system identification
  • 14.3. A reasonable compromise
  • References for Chapter 14
  • 15. Case study - oculomotor control
  • 15.1. Optokinetic nystagmus - dimension, surrogates, prediction
  • Recurrence analysis
  • Correlation dimension
  • Surrogate data
  • Filtering
  • Nonlinear forecasting
  • Mutual forecasting
  • Physiological interpretation
  • 15.2. Eye movements and reading ability
  • References for Chapter 15
  • 16. Case study - motor control
  • 16.1. Postural center of pressure
  • 16.2. Rhythmic movements
  • References for Chapter 16
  • 17. Case study - neurological tremor
  • 17.1. Physiology background
  • 17.2. Initial studies - evidence for chaos
  • 17.3. Later studies - evidence for randomness
  • References for Chapter 17
  • 18. Case study - neural dynamics and epilepsy
  • 18.1. Epilepsy background
  • 18.2. Initial dynamical studies
  • 18.3. Dimension as a seizure predictor
  • 18.4. Dynamical similarity as a seizure predictor
  • 18.5. Validation with surrogates, comparison of procedures
  • References for Chapter 18
  • 19. Case study - cardiac dynamics and fibrillation
  • 19.1. Heart-rate variability
  • 19.2. Noisy clock or chaos?
  • 19.3. Forecasting and chaos
  • 19.4. Detection of imminent fibrillation: point correlation dimension
  • References for Chapter 19
  • 20. Case study - epidemiology
  • 20.1. Background and early approaches
  • 20.2. Nonlinear forecasting of disease epidemics
  • References for Chapter 20
  • 21. Case study - psychology
  • 21.1. General concepts
  • 21.2. Psychiatric disorders
  • 21.3. Perception and action
  • References for Chapter 21
  • 22. Final remarks
  • References on climatic attractors
  • Suggested references for further study
  • Appendix
  • A.1. State-space reconstruction
  • A.2. Correlation dimension
  • A.3. Surrogate data
  • A.4. Forecasting
  • A.5. Recurrence plots
  • A.6. Periodic orbits
  • A.7. Poincare sections
  • A.8. Software packages
  • A.9. Sources of sample data sets
  • Index
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