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

A model of dynamic shock interaction predicts that pulsed energy addition upstream of a bow shock can be used to weaken the time-averaged shock strength. To explore these shock interactions, tests have been conducted in a small-scale, blowdown facility with off-body energy addition upstream of an oblique shock wave that was generated by a wedge in a Mach 2.4 flow. The off-body energy addition was simulated by laser-induced breakdown (350 mJ/pulse with 10-ns pulse duration). The dynamics of the interactions were captured in both schlieren and shadowgraph images taken at 250,000 and 500,000 frames per second and compared with the computational model

Shock-Wave Mitigation Through an Off-Body Pulsed Energy Deposition

Many of the so-called simple flows, including flat-plate boundary layers, two-dimensional compressible flows, and axisymrnetric rotating flows, still represent some of the most difficult, ill-understood fundamental problems in fluid mechanics today. Often, such flows contain structures that, though organized, represent a multitude of interacting scales. Inherent nonsteadiness and spacial complexity are rapidly compounded when one extends consideration to full three dimensional, high Reynolds/Mach number flows. Our success in developing a proper understanding of these complex flows depends largely on our ability to fully characterize them. Such an understanding is a critical step to the design of structures which can operate in unsteady flow regimes and to the control of unsteady phenomena including turbulence and mixing. The challenge facing experimentalists is to augment classical single-point measurements, such as those from hot wires and laser Doppler velocimeters (LDV), with three-dimensional measurements in order to generate a correlated picture of the flow field where all the structure is recorded.

Three-Dimensional Quantitative Flow Diagnostics

We consider some possible mechanisms for producing gain in the 10-nm spectral region. They involve the creation of a population inversion in a confined plasma column by selective excitation of multiply charged ions through absorption of many (>10) ultraviolet photons. Calculations of the energy-level structure of ions in the Kr isoelectronic sequence show singly and multiply excited states that provide suitable strong radiative transitions in the region of 10 nm. The potential for achieving x-ray lasing action in Kr-like ions pumped by a KrF excimer laser is most favorable at high Z.

Possibilities for achieving x-ray lasing action by use of high-order multiphoton processes

Velocimetry by femtosecond laser electronic excitation tagging (FLEET) of air and nitrogen

We report the development of ultraviolet filtered Rayleigh scattering as a diagnostic tool for measurements of gas properties. A frequency-tripled narrow-linewidth Ti:sapphire laser illuminates a sample, and Rayleigh scattered light is imaged through a mercury-vapor absorption filter. Working in the ultraviolet improves the signal-to-noise ratio compared with that previously obtained in the visible as the result of an enhanced scattering cross section as well as the nearly ideal properties of the mercury filter. Tuning the laser through the absorption notch of the filter is a means of probing the scattering line shape, which contains temperature information. Temperature measurements of air are shown to have uncertainties of less than 3%.

Richard B. Miles

Papers

Shock-Wave Mitigation Through an Off-Body Pulsed Energy Deposition

Three-Dimensional Quantitative Flow Diagnostics

Possibilities for achieving x-ray lasing action by use of high-order multiphoton processes

Velocimetry by femtosecond laser electronic excitation tagging (FLEET) of air and nitrogen

Ultraviolet filtered Rayleigh scattering temperature measurements with a mercury filter