Prelude. Cycle 1. Introduction. Cycle 2. Structure defines function. Cycle 3. Diversity of cortical functions is provided by inhibition. Cycle 4. Windows on the brain. Cycle 5. A system of rhythms: from simple to complex dynamics. Cycle 6. Synchronization by oscillation. Cycle 7. The brain's default state: self-organized oscillations in rest and sleep. Cycle 8. Perturbation of the default patterns by experience. Cycle 9. The gamma buzz: gluing by oscillations in the waking brain. Cycle 10. Perceptions and actions are brain state-dependent. Cycle 11. Oscillations in the "other cortex:" navigation in real and memory space. Cycle 12. Coupling of systems by oscillations. Cycle 13. The tough problem. References.

Rhythms of the brain

This book explains the relationship of electrophysiology, nonlinear dynamics, and the computational properties of neurons, with each concept presented in terms of both neuroscience and mathematics and illustrated using geometrical intuition In order to model neuronal behavior or to interpret the results of modeling studies, neuroscientists must call upon methods of nonlinear dynamics This book offers an introduction to nonlinear dynamical systems theory for researchers and graduate students in neuroscience It also provides an overview of neuroscience for mathematicians who want to learn the basic facts of electrophysiology "Dynamical Systems in Neuroscience" presents a systematic study of the relationship of electrophysiology, nonlinear dynamics, and computational properties of neurons It emphasizes that information processing in the brain depends not only on the electrophysiological properties of neurons but also on their dynamical properties The book introduces dynamical systems starting with one- and two-dimensional Hodgkin-Huxley-type models and continuing to a description of bursting systems Each chapter proceeds from the simple to the complex, and provides sample problems at the end The book explains all necessary mathematical concepts using geometrical intuition; it includes many figures and few equations, making it especially suitable for non-mathematicians Each concept is presented in terms of both neuroscience and mathematics, providing a link between the two disciplines Nonlinear dynamical systems theory is at the core of computational neuroscience research, but it is not a standard part of the graduate neuroscience curriculum - or taught by math or physics department in a way that is suitable for students of biology This book offers neuroscience students and researchers a comprehensive account of concepts and methods increasingly used in computational neuroscience

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Dynamical Systems in Neuroscience

Neuronal activity in the brain gives rise to transmembrane currents that can be measured in the extracellular medium. Although the major contributor of the extracellular signal is the synaptic transmembrane current, other sources — including Na+ and Ca2+ spikes, ionic fluxes through voltage- and ligand-gated channels, and intrinsic membrane oscillations — can substantially shape the extracellular field. High-density recordings of field activity in animals and subdural grid recordings in humans, combined with recently developed data processing tools and computational modelling, can provide insight into the cooperative behaviour of neurons, their average synaptic input and their spiking output, and can increase our understanding of how these processes contribute to the extracellular signal.

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The origin of extracellular fields and currents — EEG, ECoG, LFP and spikes

Interneurons of the hippocampus

EEG alpha oscillations: The inhibition–timing hypothesis

Magnetic steering of the thrust vector for laser-ablated plasma was experimentally studied in vacuum using a uniform 1.0 Tesla magnetic field permanent magnet assembly whose field lines passed directly through the ablation surface. In this study, an aluminum plasma was formed by ablating a solid target surface with a single pulse of 20 mJ from a 1064 nm Nd:YAG laser. A 1-MHz-frame-rate camera captured continuous sequential images of the ejected plasma plume. This work demonstrates that a 1.0 Tesla applied magnetic field collimates the plasma plume and deflects the plasma along the magnetic field lines. It was also determined that the plume collimation increases with multiple laser pulses in the same spot. These results indicate that thrust vectoring can be achieved using permanent magnets.

Thrust vectoring of laser-ablated aluminum plasma using permanent magnets

Comparison of RELIEF flow tagging and hot-wire velocimetry for fundamental studies of turbulent free jets

Spatial and temporal variations of air density due to atmospheric turbulence lead to wavefront distortions and irradiance fluctuations in free-space laser propagation. Many factors, including the specific structure of the refractive index fluctuations, determine the amplitude and spectrum of fluctuations imprinted on the beam. In this investigation, we report on the development and characterization of a controlled aerodynamic environment used to create a repeatable and consistent turbulent field. The enclosed 80-ft long test range, known as the Sub-scale Atmospheric Facility (SAF), consists of 8 pipe sections which are 10 ft long and 2 ft in diameter; each of those 10 ft sections is outfitted with a heated wire rope. Initial scintillation experiments were carried out with a 4 in diameter, collimated 532 nm laser beam as a function of propagation distance and turbulent intensity in order to determine scaling parameters and quantify the capabilities and characteristics of the facility. Log-amplitude variances were observed to follow a scaling law of L^{2.69} - L^{2.86}, which did not vary significantly with power dissipation and is slightly below the L^{3} scaling expected for the geometric optics regime. C_n^2 dependency on heat rope power was found by fitting scintillation data to theoretical models. As the heat rope power increased, C_n^2 varied from approximately 5*10^{-12} to 1.5*10^{-11}. 

Laser Scintillation Measurement in a Controlled Turbulent Environment

A microfabricated optically-interrogated wall shear stress sensor has been developed which allows for quantitative measurement of the shear stress distribution present on aerodynamic surfaces. The sensor employs a close-packed array of elastomeric cylindrical pillars having a aspect ratio of 4 to 1 and a typical diameters from 20-60 m. The pillar array is partially reflective, and the application of a shear stress results in a change in the reflectivity of the surface of the array which provides a direct measurement of local shear stress distribution. The operation of the sensor has been experimentally verified in both subsonic and supersonic flow regimes. The experimental set-up used to validate its performance is described and a computational model used to provide a quantitative estimate of shear stress as a function of the experimentally determined sensor response is presented.

An Optically Interrogated, Microfabricated Pillar Array for Wall Shear Stress Sensing

Three techniques for the visualization of species and/or velocity in unseeded H2/air flames and heated air jets are described and preliminary image data are presented. The techniques described are: (1) simultaneous ArF laser imaging of H2, O2, and Rayleigh cross-section weighted density in an H2, O2, and Rayleigh cross-section weighted density in an H2/air flame; (2) ultraviolet flashlamp imaging of O2, OH, and Rayleigh cross-section weighted density in an H2/air flame; and (3) Raman Excitation plus Laser Induced Electronic Fluorescence velocimetry in heater air flows, up to static temperatures of 700 K. Application of these techniques, individually or in combination, should provide useful insight into mixing and reacting flows containing H2, O2, N2 and reaction intermediates such as OH.

Richard B. Miles

Papers

Thrust vectoring of laser-ablated aluminum plasma using permanent magnets

Comparison of RELIEF flow tagging and hot-wire velocimetry for fundamental studies of turbulent free jets

Laser Scintillation Measurement in a Controlled Turbulent Environment

An Optically Interrogated, Microfabricated Pillar Array for Wall Shear Stress Sensing

Species and velocity visualization of unseeded heated air and combusting hydrogen jets using laser and flashlamp sources