Multiscale Analysis and Nonlinear Dynamics

Since modeling multiscale phenomena in systems biology and neuroscience is a highly interdisciplinary task, the editor of the book invited experts in bio-engineering, chemistry, cardiology, neuroscience, computer science, and applied mathematics, to provide their perspectives. Each chapter is a window into the current state of the art in the areas of research discussed and the book is intended for advanced researchers interested in recent developments in these fi elds. While multiscale analysis is the major integrating theme of the book, its subtitle does not call for bridging the scales from genes to behavior, but rather stresses the unifying perspective offered by the concepts referred to in the title. It is believed that the interdisciplinary approach adopted here will be beneficial for all the above mentioned fi elds. Indeed, the roads between different sciences, while often the quickest shortcut to another part of our own science, are not visible from the viewpoint of one science alone (P.W. Anderson, More is Different). From the contents: MULTIRESOLUTION ANALYSIS _ Discrete Geometric Structures in Homogenization and Inverse Homogenization _ Multiresolution Analysis on Compact Riemannian Manifolds NONLINEAR DYNAMICS IN SYNTHETIC BIOCHEMICAL CIRCUITS _ Dynamics of Synthetic Transcription Networks _ Synthetic Biochemical Dynamic Circuits NONLINEAR DYNAMICS: THE HEART AND THE BRAIN _ Theoretical and Experimental Electrophysiology in Human Neocortex: Multiscale Dynamic Correlates of Conscious Experience _ Multiscale Network Organization in the Human Brain _ Neuronal Oscillations Scale up and Scale Down the Brain Dynamics _ Linking Nonlinear Neural Dynamics to Single-trial Human Behavior _ Brain Dynamics at Rest: How Structure Shapes Dynamics _ Adaptive Multiscale Encoding - a Computational Function of Neuronal Synchronization _ Multiscale Nonlinear Dynamics in Cardiac Electrophysiology: From Sparks to Sudden Death _ Measures of Spike Train Synchrony: From Single Neurons to Populations