Many constraints on structural and functional cortical network connectivity have been suggested, based on ideas as diverse as minimization of axonal wiring length or volume, minimization of information processing steps, and maximization of complexity. This paper discusses recently suggested roles for static and dynamic
network stability in providing further constraints on connectivity. A variety of network types and constraints will be covered, including ones involving purely excitatory, mixed excitatory-inhibitory, and small-world features. Dynamical implications for adaptability of networks and dynamically changing patterns of activity are discussed,
with implications for what classes of brain structures are available to be selected by evolution.
A low-dimensional, compact brain model has recently been developed
based on physiologically based mean-field continuum formulation of
electric activity of the brain.
The essential feature of the new compact model is
a second order time-delayed differential equation
that has physiologically plausible terms, such as rapid corticocortical
feedback and delayed feedback via extracortical pathways.
Due to its compact form, the model facilitates insight into
complex brain dynamics via standard linear and nonlinear techniques.
The model successfully reproduces many features of previous models and
For example, experimentally observed typical rhythms of
electroencephalogram (EEG) signals are reproduced in
a physiologically plausible parameter region.
In the nonlinear regime, onsets of seizures, which often develop
into limit cycles, are illustrated by modulating model parameters.
It is also shown that a hysteresis can occur
when the system has multiple attractors.
As a further illustration of this approach, power spectra of the model
are fitted to those of sleep EEGs of two subjects
(one with apnea, the other with narcolepsy).
The model parameters obtained from the fittings show good matches
with previous literature.
Our results suggest that the compact model can provide a theoretical
basis for analyzing complex EEG signals.
The electrical activity of the brain has been observed for over a
century and is widely used to probe brain function and disorders,
chiefly through the electroencephalogram (EEG) recorded by
electrodes on the scalp. However, the connections between
physiology and EEGs have been chiefly qualitative until recently, and most
uses of the EEG have been based on phenomenological correlations.
A quantitative mean-field model of brain electrical activity is described
that spans the range of
physiological and anatomical scales from microscopic synapses to the whole brain.
Its parameters measure quantities such as synaptic
strengths, signal delays, cellular time constants, and neural
ranges, and are all constrained by independent physiological measurements.
Application of standard techniques from wave physics allows successful
predictions to be made of a wide range of EEG phenomena, including time series and
spectra, evoked responses to stimuli, dependence on arousal state, seizure dynamics, and
relationships to functional magnetic resonance imaging (fMRI).
Fitting to experimental data also enables physiological parameters to be infered,
giving a new noninvasive window into brain function, especially when referenced to a
standardized database of subjects.
Modifications of the core model to treat mm-scale
patchy interconnections in the visual cortex are also described, and it is shown that
resulting waves obey the Schroedinger equation. This
opens the possibility of classical cortical analogs of quantum phenomena.
In solid core Microstructured Optical Fibers (MOFs), guidance of light is due to a finite number of layers of holes surrounding a solid core. Because the potential barrier is finite, all modes are leaky, blurring the distinction between guided and non-guided modes. Through simulations using a multipole formulation, we clarify the definition of modal cutoff in MOFs. We establish that the fundamental mode of MOFs undergoes a transition between modal confinement and non-confinement similar to modal cutoff. An asymptotic analysis gives us a better understanding of mode properties on each side of the cutoff but also near cutoff and leads us to define a cutoff point and a cutoff region for the fundamental mode. Three operation regimes with very different mode properties can be distinguished. Only two of these are of practical interest, one with strong mode confinement and another with broader field distributions. The former is of interest for single-mode guidance with strong confinement, whereas the latter, the cutoff region, is where highly adjustable chromatic dispersion can be achieved. We provide a map of the parameter space (MOF "phase diagram") summarizing the operating regimes of MOFs, and show for a few examples how this map can be used for deterministic MOF design.