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Nonlinear dynamics in physiology [[electronic resource] ] : a state-space approach / / Mark Shelhamer
| Nonlinear dynamics in physiology [[electronic resource] ] : a state-space approach / / Mark Shelhamer |
| Autore | Shelhamer Mark |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, NJ, : World Scientific, c2007 |
| Descrizione fisica | 1 online resource (367 p.) |
| Disciplina |
515.252
571.01/5118 571.015118 |
| Soggetto topico |
Physiology - Mathematical models
Nonlinear systems State-space methods |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-92446-6
9786611924461 981-277-279-0 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 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 coefficient2.4 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 space4.2 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 estimates5.6 Interpretation of the dimension; 5.7 Tracking dimension overtime; 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 examplesReferences 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 |
| Record Nr. | UNINA-9910453180103321 |
Shelhamer Mark
|
||
| Singapore ; ; Hackensack, NJ, : World Scientific, c2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Nonlinear dynamics in physiology [[electronic resource] ] : a state-space approach / / Mark Shelhamer
| Nonlinear dynamics in physiology [[electronic resource] ] : a state-space approach / / Mark Shelhamer |
| Autore | Shelhamer Mark |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, NJ, : World Scientific, c2007 |
| Descrizione fisica | 1 online resource (367 p.) |
| Disciplina |
515.252
571.01/5118 571.015118 |
| Soggetto topico |
Physiology - Mathematical models
Nonlinear systems State-space methods |
| ISBN |
1-281-92446-6
9786611924461 981-277-279-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 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 coefficient2.4 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 space4.2 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 estimates5.6 Interpretation of the dimension; 5.7 Tracking dimension overtime; 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 examplesReferences 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 |
| Record Nr. | UNINA-9910782346103321 |
|
Shelhamer Mark
|
||
| Singapore ; ; Hackensack, NJ, : World Scientific, c2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Nonlinear dynamics in physiology [[electronic resource] ] : a state-space approach / / Mark Shelhamer
| Nonlinear dynamics in physiology [[electronic resource] ] : a state-space approach / / Mark Shelhamer |
| Autore | Shelhamer Mark |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, NJ, : World Scientific, c2007 |
| Descrizione fisica | 1 online resource (367 p.) |
| Disciplina |
515.252
571.01/5118 571.015118 |
| Soggetto topico |
Physiology - Mathematical models
Nonlinear systems State-space methods |
| ISBN |
1-281-92446-6
9786611924461 981-277-279-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 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 coefficient2.4 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 space4.2 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 estimates5.6 Interpretation of the dimension; 5.7 Tracking dimension overtime; 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 examplesReferences 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 |
| Record Nr. | UNINA-9910828029503321 |
|
Shelhamer Mark
|
||
| Singapore ; ; Hackensack, NJ, : World Scientific, c2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||