1 Applications of Global Optimization and Dynamical Systems to Prediction of Epileptic Seizures -- 1.1 Introduction -- 1.2 Background -- 1.3 Method and Results -- 1.4 Quadratic 0-1 Programming -- 1.5 Conclusions and Discussion -- 2 Nonlinear Neurodynamical Features in an Animal Model of Generalized Epilepsy -- 2.1 Introduction -- 2.2 Materials and Methods -- 2.3 Results -- 2.4 Discussion -- 3 Optimization Techniques for Independent Component Analysis with Applications to EEG Data -- 3.1 Introduction -- 3.2 Extraction via maximization of the absolute value of the cumulants -- 3.3 A generalization of the fixed point algorithm -- 3.4 Examples and remarks for practical implementation -- 3.5 Combining second and fourth order statistics -- 3.6 Experiment with EEG data for detection of eye movements -- 3.7 Results -- 3.8 Conclusion -- 4 On a New Quantization in Complex Systems -- 4.1 Introduction -- 4.2 A Nonlocal Correlation between Sequences -- 4.3 The Formations of Integer Relations: Processes with Integer Particles -- 4.4 Geometrization of the Integer Relations Formations -- 4.5 Quantization of States of a Complex System as the Formations of Integer Relations -- 4.6 Conclusions -- 5 The Seizure Prediction Characteristic -- 5.1 Introduction -- 5.2 The Seizure Prediction Characteristic -- 5.3 Conclusion -- 6 Seizure Prediction Methods -- 6.1 Introduction -- 6.2 EEG data and patients characteristics -- 6.3 Seizure Prediction Methods -- 6.4 Calculation of the seizure prediction characteristic -- 6.5 Results and Discussion -- 6.6 Conclusion -- 7 Controlling Neurological Disease at the Edge of Instability -- 7.1 Introduction -- 7.2 Mathematical background and outline -- 7.3 Changes in neural synchrony -- 7.4 Multistability in delayed recurrent loops -- 7.5 Noise-induced switching between attractors -- 7.6 On-off intermittency: Parametric, or state-dependent, noise -- 7.7 Self-organized criticality -- 7.8 Discussion -- 8 Anatomical Connectivity in the Central Nervous System Revealed by Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) -- 8.1 Fundamentals of Diffusion Weighted Magnetic Resonance Imaging -- 8.2 Diffusion Tensor Magnetic Resonance Imaging -- 8.3 Scalar Measures Derived From DT-MRI -- 8.4 Fiber-Tract Mapping in Neural Tissue -- 8.5 Problems of DT-MRI Based Fiber Tracking -- Appendix: Diffusion Tensor and Displacement Profile -- 9 Epileptic Seizure Detection Using Dynamical Preprocessing (STLmax) -- 9.1 Introduction -- 9.2 Nonlinear Dynamic Preprocessing -- 9.3 Detection Methods -- 9.4 Results and Discussion -- 9.5 Conclusion and Directions for Future Work -- 10 Role Of The Dorsocentral Striatum In Contralateral Neglect And Recovery From Neglect In Rats -- 10.1. The Rodent Model of Neglect and Recovery -- 10.2 Role of the Dorsocentral Striatum in Neglect -- 10.3 Role of induced plasticity in DCS in Recovery from AGm-induced Neglect -- 10.4 Clinical Significance -- 11 Binary and Sparse Checkerboard Visual Stimuli in Multiple Sclerosis Patients -- 11.1 Methods -- 11.2 Data Analysis -- 11.3 Results -- 11.4 Discussion -- 12 Spatiotemporal Transitions in Temporal Lobe Epilepsy -- 12.1 Introduction -- 12.2 Nonlinear Dynamical and Statistical Measures -- 12.3 Results -- 12.4 Discussion -- 13 Nonlinear Dynamical and Statistical Approaches to Investigate Dynamical Transitions Before Epileptic Seizures -- 13.1 Introduction -- 13.2 Measures and Methods -- 13.3 Results -- 13.4 Discussions -- 14 Testing Whether a Prediction Scheme is Better than Guess -- 14.1 Introduction and Modeling -- 14.2 Naive Prediction Schemes -- 14.3 Testing the Hypothesis that the New Method is Better -- 14.4 An Example -- 14.5 Power Analysis -- 14.6 Concluding Remarks -- Appendix: Optimal Prediction Strategy for the Next Event.