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 flame is a very unusual environment for the development of a gas discharge, since it presents strong gradients in temperature, composition, and pre-ionization. In this paper we examine how such an environment impacts the development of the plasma when using repetitive pulsed nanosecond discharges, one of the main strategies used in the field of plasma assisted combustion. Experiments were performed in a counterflow nonpremixed burner with parallel electrodes at the nozzle exits and nanosecond-resolved photography of the plasma emission is presented. It was shown that the discharge development in stratified media may take place in the form of a dielectric barrier discharge with a localized energy deposition. In the experiments presented the discharge energy was coupled to the flame front because of the high rate of chemi-ionization and the gas density decrease in the flame.

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Localized pulsed nanosecond discharges in a counterflow nonpremixed flame environment

A nonperturbative treatment of stimulated resonance Raman (SRR) pumping is developed. This theory is based upon the derivation of an effective Hamiltonian for the interaction of the electric field with the molecular electronic–vibrational–rotational states. The resulting reduction in the number of coupled differential equations describing the SRR effect allows for a convenient numerical solution, which is important in intense laser fields. In addition, when the spectral transitions are resonant or sufficiently power broadened, the solutions become analytic. An application of the theory to the I2 system shows the possibility of selectively populating high vibrational levels (v′?10) in the ground electronic state. Most importantly, it is possible to selectively populate all the vibrational levels by suitable variations in the frequencies and proper selection of the intensities and durations of the applied laser fields.

The selective preparation of excited vibrational states using the stimulated resonance Raman effect

Influence of Upstream Pulsed Energy Addition on Shock-Wave Structure in Supersonic Flow

A new filtering technique for Raman spectroscopy utilizes atomic vapor to suppress strong elastic and Rayleigh scattering while simultaneously resolving individual rotational Raman lines. Filtered images capture high-resolution spectral information in one dimension and spatial resolution in the other dimension. The filter is based on resonance enhanced dispersion, where the index of refraction varies dramatically. In a simple prism geometry the vapor disperses incident radiation according to frequency. A mercury-vapor-based dispersion filter has been fabricated, modeled, and demonstrated to capture pure rotational Raman scattering from CO2.

Richard B. Miles

Papers

Localized pulsed nanosecond discharges in a counterflow nonpremixed flame environment

The selective preparation of excited vibrational states using the stimulated resonance Raman effect

Influence of Upstream Pulsed Energy Addition on Shock-Wave Structure in Supersonic Flow

Dispersion filter for spectral and spatial resolution of pure rotational Raman scattering.

Picosecond resonance Raman spectrum of the oxyhemoglobin photoproduct. Evidence for an electronically excited state