Information Dynamics

l Introduction. - 2 Dynamical Systems: An Overview 7. - 2. 1 Deterministic Dynamical Systems. - 2. 3 Statistical Time-Series Analysis. - 3 Statistical Structure Extraction in Dynamical Systems: Parametric Formulation. - 3. 1 Basic Concepts of Information Theory. - 3. 2 Parametric Estimation : Maximum-Likelihood Principle. - 3. 3 Linear Models. - 3. 4 Nonlinear Models. - 3. 5 Density Estimation. - 3. 6 Information-Theoretic Approach to Time-Series Modeling: Redundancy Extraction. - 4 Applications: Parametric Characterization of Time Series. - 4. 1 Feedforward Learning : Chaotic Dynamics. - 4. 2 Recurrent Learning : Chaotic Dynamics. - 4. 3 Dynamical Overtraining and Lyapunov Penalty Term. - 4. 4 Feedforward and Recurrent Learning of Biomedical Data. - 4. 5 Unsupervised Redundancy-Extraction-Based Modeling: Chaotic Dynamics. - 4. 6 Unsupervised Redundancy Extraction Modeling: Biomedical Data. - 5 Statistical Structure Extraction in Dynamical Systems: Nonparametric Formulation. - 5. 1 Nonparametric Detection ofStatistical Dependencies in Time Series. - 5. 2 Nonparametric Characterization of Dynamics: The Information Flow Concept. - 5. 3 Information Flow and Coarse Graining. - 6 Applications: Nonparametric Characterization of Time Series. - 6. 1 Detecting Nonlinear Correlations in Time Series. - 6. 2 Nonparametric Analysis of Time Series : Optimal Delay Selection. - 6. 3 Determining the Information Flow ofDynamical Systems from Continuous Probability Distributions. - 6. 4 Dynamical Characterization ofTime Signals: The Integrated Information Flow. - 6. 5 Information Flow and Coarse Graining: Numerical Experiments. - 7 Statistical Structure Extraction in Dynamical Systems: Semiparametric Formulation. - 7. 1 Markovian Characterization of Univariate Time Series. - 7. 2 Markovian Characterization of Multivariate Time Series. - 8 Applications: Semiparametric Characterization of Time Series. - 8. 1 Univariate Time Series : Artificial Data. - 8. 2 Univariate Time Series: Real-World Data. - 8. 3 Multivariate Time Series: Artificial Data. - 8. 4 Multivariate Time Series : Tumor Detection in EEG Time Series. - 9 Information Processing and Coding in Spatiotemporal Dynamical Systems: Spiking Networks. - 9. 1 Spiking Neurons. - 9. 2 Information Processing and Coding in Single Spiking Neurons. - 9. 3 Information Processing and Coding in Networks of Spiking Neurons. - 9. 4 The Processing and Coding ofDynamical Systems. - 10 Applications: Information Processing and Coding in Spatiotemporal Dynamical Systems. - 10. 1 The Binding Problem. - 10. 2 Discrimination of Stimulus by Spiking Neural Networks. - 10. 3 Numerical Experiments. - Epilogue. - Appendix A Chain Rules Inequalities and Other Useful Theorems in Information Theory. - A. 1 Chain Rules. - A. 2 Fundamental Inequalities ofInformation Theory. - Appendix B Univariate and Multivariate Cumulants. - Appendix C Information Flow of Chaotic Systems: Thermodynamical Formulation. - Appendix D Generalized Discriminability by the Spike Response Model ofa Single Spiking Neuron: Analytical Results. - References. Language: English