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

Enhancement of FLEET in Argon Gas Mixtures

Towards shear flow measurements using FLEET

Enhancement of coherent anti-Stokes Raman scattering (CARS) by molecular nitrogen in a hollow planar periodically corrugated waveguide is experimentally detected. The measured dependence of CARS efficiency on the thickness of the waveguide layer indicates that CARS enhancement under these conditions is at least partially due to the decrease in the group velocity of pump pulses around the photonic band gap.

Coherent Anti-Stokes Raman Scattering of Slow Light in a Hollow Planar Periodically Corrugated Waveguide

During reentry from space, a layer of high temperature air (>3000 K) is formed extending tens of centimeters from the surface of the vehicle, well out into the high speed flow regime. Magnetohydrodynamics (MHD) can then be used to generate power by projecting magnetic fields outside the vehicle into the conducting air stream and collecting the resulting current. Here, we analyze a multifunctional MHD panel which generates the requisite magnetic fields, protects the vehicle from high temperatures, and is structurally stiff and strong. The analysis shows that a magnetic system weighing approximately 110 kg can generate 0.6 MW of power for 1000 s.

A Magnetohydrodynamic Power Panel for Space Reentry Vehicles

A zero-dimensional kinetics simulation of femtosecond laser ionization in nitrogen is proposed that includes fast gas heating effects, electron scattering (elastic and inelastic) rate coefficients from BOLSIG+, and photoionization based on filamentation theory. Key rate coefficients possessing significant uncertainty are tuned (within the range of variation found in the literature) to reproduce the time-varying signal acquired by a bandpass-filtered photomultiplier tube with good agreement up to several hundred nanoseconds. Separate spectral measurements calibrate the relative strength of signal components. Derived equations relate the model to experimental measurements in absolute units. Reactions contributing to the rate of change of important species are displayed in terms of absolute rate and relative fraction. In general, decreasing the gas density lengthens the duration of early reactions and delays the start of later reactions. The model agrees with data taken in a variable temperature and pressure free jet by an intensified camera. Results demonstrate that initial signal depends primarily on gas density and secondarily on gas temperature. The initial signal is optimized (maximized) at subatmospheric conditions. Decreases in gas density alter the evolution of excited-state populations, postponing the peak (while reducing its value) and slowing the rate of decay. For the optimal case, populations are favorably shifted in time with respect to the gate delay (and width) to boost the signal. Reductions in gas temperature generally enhance initial signal due to elevated dissociative recombination of cluster ions (along with excited-state coupling from quenching and energy pooling).

Richard B. Miles

Papers

Enhancement of FLEET in Argon Gas Mixtures

Towards shear flow measurements using FLEET

Coherent Anti-Stokes Raman Scattering of Slow Light in a Hollow Planar Periodically Corrugated Waveguide

A Magnetohydrodynamic Power Panel for Space Reentry Vehicles

Kinetics Model of Femtosecond Laser Ionization in Nitrogen and Comparison to Experiment