Quantitative Neuroscience

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-offintermittency: 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