Quantitative Neuroscience

1. Front Matter

   Pages i-xi

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2. Applications of Global Optimization and Dynamical Systems to Prediction of Epileptic Seizures

   • W. Chaovalitwongse, P. M. Pardalos, L. D. Iasemidis, D.-S. Shiau, J. C. Sackellares

   Pages 1-35

3. Nonlinear Neurodynamical Features in an Animal Model of Generalized Epilepsy

   • P. R. Carney, D.-S. Shiau, P. M. Pardalos, L. D. Iasemidis, W. Chaovalitwongse, J. C. Sackellares

   Pages 37-51

4. Optimization Techniques for Independent Component Analysis with Applications to EEG Data

   • Pando Georgiev, Andrzej Cichocki, Hovagim Bakardjian

   Pages 53-68

5. On a New Quantization in Complex Systems

   • Victor Korotkikh, Galina Korotkikh

   Pages 69-89

6. The Seizure Prediction Characteristic

   • T. Maiwald, M. Winterhalder, H. U. Voss, R. Aschenbrenner-Scheibe, A. Schulze-Bonhage, J. Timmer

   Pages 91-101

7. Seizure Prediction Methods

   • M. Winterhalder, T. Maiwald, H. U. Voss, R. Aschenbrenner-Scheibe, A. Schulze-Bonhage, J. Timmer

   Pages 103-116

8. Controlling Neurological Disease at the Edge of Instability

   • John G. Milton, Jennifer Foss, John D. Hunter, Juan Luis Cabrera

   Pages 117-143

9. Anatomical Connectivity in the Central Nervous System Revealed by Diffusion Tensor Magnetic Resonance Imaging (DT-MRI)

   • Evren Özarslan, Thomas H. Mareci

   Pages 145-169

10. Epileptic Seizure Detection Using Dynamical Preprocessing (STLmax)

    • G. Ramachandran, J. C. Principe, J. C. Sackellares

    Pages 171-189

11. Role of the Dorsocentral Striatum in Contralateral Neglect and Recovery from Neglect in Rats

    • Roger L. Reep, J. L. Cheatwood, J. V. Corwin

    Pages 191-211

12. Binary and Sparse Checkerboard Visual Stimuli in Multiple Sclerosis Patients

    • Rasa Ruseckaite, Teddy Maddess, Andrew Charles James

    Pages 213-221

13. Spatiotemporal Transitions in Temporal Lobe Epilepsy

    • J. C. Sackellares, L. D. Iasemidis, D.-S. Shiau, P. M. Pardalos, P. R. Carney

    Pages 223-237

14. Nonlinear Dynamical and Statistical Approaches to Investigate State Transitions before Epileptic Seizures

    • D.-S. Shiau, W. Chaovalitwongse, L. D. Iasemidis, P. M. Pardalos, P. R. Carney, J. C. Sackellares

    Pages 239-249

15. Testing Whether a Prediction Scheme is Better than Guess

    • Mark C. K. Yang, D.-S. Shiau, J. C. Sackellares

    Pages 251-262

Advances in the field of signal processing, nonlinear dynamics, statistics, and optimization theory, combined with marked improvement in instrumenta­ tion and development of computers systems, have made it possible to apply the power of mathematics to the task of understanding the human brain. This verita­ ble revolution already has resulted in widespread availability of high resolution neuroimaging devices in clinical as well as research settings. Breakthroughs in functional imaging are not far behind. Mathematical tech­ niques developed for the study of complex nonlinear systems and chaos already are being used to explore the complex nonlinear dynamics of human brain phys­ iology. Global optimization is being applied to data mining expeditions in an effort to find knowledge in the vast amount of information being generated by neuroimaging and neurophysiological investigations. These breakthroughs in the ability to obtain, store and analyze large datasets offer, for the first time, exciting opportunities to explore the mechanisms underlying normal brain func­ tion as well as the affects of diseases such as epilepsy, sleep disorders, movement disorders, and cognitive disorders that affect millions of people every year. Ap­ plication of these powerful tools to the study of the human brain requires, by necessity, collaboration among scientists, engineers, neurobiologists and clini­ cians. Each discipline brings to the table unique knowledge, unique approaches to problem solving, and a unique language.

• algorithms
• complex system
• data mining
• diagnostics
• dynamical systems
• magnetic resonance
• magnetic resonance imaging (MRI)
• Mathematica
• mathematics
• modeling
• optimization
• programming
• statistics
• tissue

• Departments of Industrial and Systems Engineering, Biomedical Engineering, and McKnight Brain Institute, University of Florida, USA

  P. M. Pardalos

• Departments of Neuroscience, Neurology, Pediatrics, and Biomedical Engineering, University of Florida; VA Medical Center, USA

  J. C. Sackellares

• Departments of Pediatrics, Neurology, and Neuroscience, University of Florida, USA

  P. R. Carney

• Department of Biomedical Engineering, Arizona State University, USA

  L. D. Iasemidis

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