Numerical simulations of type-III solar radio bursts

The first numerical simulations are presented for type-III solar radio bursts in the inhomogeneous solar corona and interplanetary space, that include microscale quasilinear and nonlinear processes, intermediate-scale driven ambient density fluctuations, and large scale evolution of electron beams, Langmuir and ion sound waves, and fundamental and harmonic electromagnetic emission. Bidirectional coronal emission is asymmetric between the upward and downward directions, and harmonic emission dominates fundamental emission. In interplanetary space, fundamental and/or harmonic emission can be important. Langmuir and ion sound waves are bursty and the statistics of Langmuir wave energy agree well with the predictions of stochastic growth theory.

Patchy propagators, brain dynamics, and the generation of spatially structured gamma oscillations

Propagator theory of brain dynamics is generalized to incorporate a new class of patchy propagators that enable treatment of approximately periodic structures such as are seen in the visual cortex. Complex response fields are also incorporated to allow for features such as orientation preference and wave-number selectivity. The results are applied to the corticothalamic system associated with the primary visual cortex. It is found that this system can generate gamma ( > or = 30 Hz) oscillations during stimulation, whose properties are consistent with experimental findings on gamma frequency and bandwidth, and existence of fine-scale spatial structure. It is found that a potential resonance is associated with each reciprocal lattice vector corresponding to periodic modulations of the propagators. It is found that the lowest resonances are the most likely to give rise to noticeable spectral peaks and increases of correlation amplitude, length, and time, and that these aspects are prominent only if the system is close to marginal stability, in accord with previous measurements and discussions of cortical stability. These features also enable gamma resonances to be stimulus-evoked, with substantial resonance sharpening for relatively small changes in mean neural firing rate. The results also imply dependence of gamma frequency on stimulus features.

BOLD responses to stimuli: dependence on frequency, stimulus form, amplitude, and repetition rate

A quantitative theory is developed for the relationship between stimulus and the resulting blood oxygen level-dependent (BOLD) functional MRI signal. The relationship of stimuli to neuronal activity during evoked responses is inferred from recent physiology-based quantitative modeling of evoked response potentials (ERPs). A hemodynamic model is then used to calculate the BOLD response to neuronal activity having the form of an impulse, a sinusoid, or an ERP-like damped sinusoid. Using the resulting equations, the BOLD response is analyzed for different forms, frequencies, and amplitudes of stimuli, in contrast with previous research, which has mostly concentrated on sustained stimuli. The BOLD frequency response is found to be closely linear in the parameter ranges of interest, with the form of a low-pass filter with a weak resonance at approximately 0.07 Hz. An improved BOLD impulse response is systematically obtained which includes initial dip and post-stimulus undershoot for some parameter ranges. It is found that the BOLD response depends strongly on the precise temporal course of the evoked neuronal activity, not just its peak value or typical amplitude. Indeed, for short stimuli, the linear BOLD response is closely proportional to the time-integrated activity change evoked by the stimulus, regardless of amplitude. It is concluded that there can be widely differing proportionalities between BOLD and peak activity, that this is the likely reason for the low level of correspondence seen experimentally between ERP sources and BOLD measurements and that non-BOLD measurements, such as ERPs, can be used to correct for this effect to obtain improved activity estimates. Finally, stimulus sequences that optimize the signal-to-noise ratio in event-related BOLD fMRI (efMRI) experiments are derived using the hemodynamic transfer function.

Four and a half LIM protein 1 binds myosin-binding protein C and regulates myosin filament formation and sarcomere assembly

Four and a half LIM protein 1 (FHL1/SLIM1) is highly expressed in skeletal and cardiac muscle; however, the function of FHL1 remains unknown. Yeast two-hybrid screening identified slow type skeletal myosin-binding protein C as an FHL1 binding partner. Myosin-binding protein C is the major myosin-associated protein in striated muscle that enhances the lateral association and stabilization of myosin thick filaments and regulates actomyosin interactions. The interaction between FHL1 and myosin-binding protein C was confirmed using co-immunoprecipitation of recombinant and endogenous proteins. Recombinant FHL2 and FHL3 also bound myosin-binding protein C. FHL1 impaired co-sedimentation of myosin-binding protein C with reconstituted myosin filaments, suggesting FHL1 may compete with myosin for binding to myosin-binding protein C. In intact skeletal muscle and isolated myofibrils, FHL1 localized to the I-band, M-line, and sarcolemma, co-localizing with myosin-binding protein C at the sarcolemma in intact skeletal muscle. Furthermore, in isolated myofibrils FHL1 staining at the M-line appeared to extend partially into the C-zone of the A-band, where it co-localized with myosin-binding protein C. Overexpression of FHL1 in differentiating C2C12 cells induced "sac-like" myotube formation (myosac), associated with impaired Z-line and myosin thick filament assembly. This phenotype was rescued by co-expression of myosin-binding protein C. FHL1 knockdown using RNAi resulted in impaired myosin thick filament formation associated with reduced incorporation of myosin-binding protein C into the sarcomere. This study identified FHL1 as a novel regulator of myosin-binding protein C activity and indicates a role for FHL1 in sarcomere assembly.

A unifying explanation of primary generalized seizures through nonlinear brain modeling and bifurcation analysis

The aim of this paper is to explain critical features of the human primary generalized epilepsies by investigating the dynamical bifurcations of a nonlinear model of the brain's mean field dynamics. The model treats the cortex as a medium for the propagation of waves of electrical activity, incorporating key physiological processes such as propagation delays, membrane physiology, and corticothalamic feedback. Previous analyses have demonstrated its descriptive validity in a wide range of healthy states and yielded specific predictions with regards to seizure phenomena. We show that mapping the structure of the nonlinear bifurcation set predicts a number of crucial dynamic processes, including the onset of periodic and chaotic dynamics as well as multistability. Quantitative study of electrophysiological data supports the validity of these predictions. Hence, we argue that the core electrophysiological and cognitive differences between tonic-clonic and absence seizures are predicted and interrelated by the global bifurcation diagram of the model's dynamics. The present study is the first to present a unifying explanation of these generalized seizures using the bifurcation analysis of a dynamical model of the brain.

Multiscale brain modelling

A central difficulty of brain modelling is to span the range of spatio-temporal scales from synapses to the whole brain. This paper overviews results from a recent model of the generation of brain electrical activity that incorporates both basic microscopic neurophysiology and large-scale brain anatomy to predict brain electrical activity at scales from a few tenths of a millimetre to the whole brain. This model incorporates synaptic and dendritic dynamics, nonlinearity of the firing response, axonal propagation and corticocortical and corticothalamic pathways. Its relatively few parameters measure quantities such as synaptic strengths, corticothalamic delays, synaptic and dendritic time constants, and axonal ranges, and are all constrained by independent physiological measurements. It reproduces quantitative forms of electroencephalograms seen in various states of arousal, evoked response potentials, coherence functions, seizure dynamics and other phenomena. Fitting model predictions to experimental data enables underlying physiological parameters to be inferred, giving a new non-invasive window into brain function that complements slower, but finer-resolution, techniques such as fMRI. Because the parameters measure physiological quantities relating to multiple scales, and probe deep structures such as the thalamus, this will permit the testing of a range of hypotheses about vigilance, cognition, drug action and brain function. In addition, referencing to a standardized database of subjects adds strength and specificity to characterizations obtained.

Biophysical modeling of tonic cortical electrical activity in attention deficit hyperactivity disorder

Psychophysiological theories characterize Attention Deficit Hyperactivity Disorder (ADHD) in terms of cortical hypoarousal and a lack of inhibition of irrelevant sensory input, drawing on evidence of abnormal electroencephalographic (EEG) delta-theta activity. To investigate the mechanisms underlying this disorder a biophysical model of the cortex was used to fit and replicate the EEGs from 54 ADHD adolescents and their control subjects. The EEG abnormalities in ADHD were accounted for by the model's neurophysiological parameters as follows: (i) dendritic response times were increased, (ii) intrathalamic activity involving the thalamic reticular nucleus (TRN) was increased, consistent with enhanced delta-theta activity, and (iii) intracortical activity was increased, consistent with slow wave (<1 Hz) abnormalities. The longer dendritic response time is consistent with the increase in the activity of inhibitory cells types, particularly in the TRN, and therefore reduced arousal. The increase in intracortical activity may also reflect an increase in background activity or cortical noise within neocortical circuits. In terms of neurochemistry, these findings may be accounted for by disturbances in the cholinergic and/or noradrenergic systems. To the knowledge of the authors, this is the first study to use a detailed biophysical model of the brain to elucidate the neurophysiological mechanisms underlying tonic abnormalities in ADHD.

Protection against Helicobacter pylori infection in the Mongolian gerbil after prophylactic vaccination

Vaccines against Helicobacter pylori could circumvent the problem of increasing antibiotic resistance. They would be particularly useful in developing countries, where re-infection rates are high following standard eradication regimes. The Mongolian gerbil is a good model for H. pylori infection, as the gastric pathology induced by infection is similar to that in humans. The H. pylori-induced inflammatory response in gerbils is considerably greater than in murine models. The aim of this study was to determine if gerbils could be vaccinated against H. pylori. Mongolian gerbils were vaccinated orally with an H. pylori whole cell sonicate preparation and cholera toxin adjuvant. Vaccinated gerbils and controls were challenged with the autologous H. pylori strain 42GX. All infection, and cholera toxin, control gerbils were H. pylori positive 6 weeks post-challenge. By contrast, a significant degree of protection was demonstrated in vaccinated gerbils. Only two of 10 of gerbils were H. pylori positive (P<0.001). Protection was associated with increased serum H. pylori IgG antibodies. Protected gerbils had histologically normal gastric mucosa and, in contrast to mice, no post-immunisation gastritis was evident. In the control groups, the degree of inflammation was variable, with some of the animals having corpus gastritis and corpus mucous metaplasia. The levels of gastric IL-12p40 and IFNgamma transcripts were significantly decreased in vaccinated animals compared to infection and cholera toxin controls (P<0.01). Gastric IL-10 and TGFbeta transcripts were found only at relatively low levels. These results demonstrate that Mongolian gerbils can be successfully vaccinated against H. pylori and protected from H. pylori-induced pathology.

Propagator theory of brain dynamics

A physiologically based continuum model of brain dynamics is extended to incorporate arbitrary numbers of structures and neural populations, multiple outgoing fields of activity from a single population of neurons to various targets, improved treatment of converging or diverging projections and mesoscopic structure, and generalized connections to quantities observable via electroencephalography and other methods. The results are applied to study the corticothalamic system, predicting an intracortical resonance that leads to enhancements of electroencephalographic activity in the gamma (>30 Hz) range. This resonance involves feedback loops incorporating slow, short-range inhibitory fibers.

Criticality in a Vlasov-Poisson system: a fermioniclike universality class

A model Vlasov-Poisson system is simulated close to the point of marginal stability, thus assuming only the wave-particle resonant interactions are responsible for saturation, and shown to obey the power-law scaling of a second-order phase transition. The set of critical exponents analogous to those of the Ising universality class is calculated and shown to obey the Widom and Rushbrooke scaling and Josephson's hyperscaling relations at the formal dimensionality d=5 below the critical point at nonzero order parameter. However, the two-point correlation function does not correspond to the propagator of Euclidean quantum field theory, which is the Gaussian model for the Ising universality class. Instead, it corresponds to the propagator for the fermionic vector field and to the upper critical dimensionality d(c) = 2. This suggests criticality of collisionless Vlasov-Poisson systems corresponds to a universality class analogous to that of critical phenomena of a fermionic quantum field description.

Stimulant drug action in attention deficit hyperactivity disorder (ADHD): inference of neurophysiological mechanisms via quantitative modelling

OBJECTIVE

To infer the neural mechanisms underlying tonic transitions in the electroencephalogram (EEG) in 11 adolescents diagnosed with attention deficit hyperactivity disorder (ADHD) before and after treatment with stimulant medication.

METHODS

A biophysical model was used to analyse electroencephalographic (EEG) measures of tonic brain activity at multiple scalp sites before and after treatment with medication.

RESULTS

It was observed that stimulants had the affect of significantly reducing the parameter controlling activation in the intrathalamic pathway involving the thalamic reticular nucleus (TRN) and the parameter controlling excitatory cortical activity. The effect of stimulant medication was also found to be preferentially localized within subcortical nuclei projecting towards frontal and central scalp sites.

CONCLUSIONS

It is suggested that the action of stimulant medication occurs via suppression of the locus coeruleus, which in turn reduces stimulation of the TRN, and improves cortical arousal. The effects localized to frontal and central sites are consistent with the occurrence of frontal delta-theta EEG abnormalities in ADHD, and existing theories of hypoarousal.

SIGNIFICANCE

To our knowledge, this is the first study where a detailed biophysical model of the brain has been used to estimate changes in neurophysiological parameters underlying the effects of stimulant medication in ADHD.

Conductance of photons in disordered photonic crystals

The conductance of photons in two-dimensional disordered photonic crystals is calculated using an exact multipole-plane wave method that includes all multiple scattering processes. Conductance fluctuations, the universal nature of which has been established for electrons in the diffusive regime, are studied for photons, in both principal polarizations and for varying disorder. Our simulations show that universal conductance fluctuations can be observed in H(||) (TE) polarization for weak and intermediate disorder while, for E(||) (TM) polarization, we show that the conductance variance is essentially independent of sample size but strongly dependent on disorder. The probability distribution of the conductance is also calculated in the diffusive and localized regimes, and also at their transition, for which the distributions for both polarizations are seen to be very similar.

New regimes of stochastic wave growth

Stochastic-growth theory (SGT) of bursty waves is generalized and it is shown that the previously separate theory of "elementary bursts" is a limiting case. New regimes of SG are found and elucidated, and results are compared with the first relevant simulations via quasilinear theory and a reduced-parameter model. Both display stochastic behavior with the expected properties--the first simulations to demonstrate SGT behavior explicitly. Reexamination of data and simulations previously analyzed using SGT or elementary burst theory also shows good agreement with the new predictions.

Analysis of the electroencephalographic activity associated with thalamic tumors

A physiologically based model of corticothalamic dynamics is used to investigate the electroencephalographic (EEG) activity associated with tumors of the thalamus. Tumor activity is modeled by introducing localized two-dimensional spatial non-uniformities into the model parameters, and calculating the resulting activity via the coupling of spatial eigenmodes. The model is able to reproduce various qualitative features typical of waking eyes-closed EEGs in the presence of a thalamic tumor, such as the appearance of abnormal peaks at theta ( approximately 3Hz) and spindle ( approximately 12Hz) frequencies, the attenuation of normal eyes-closed background rhythms, and the onset of epileptic activity, as well as the relatively normal EEGs often observed. The results indicate that the abnormal activity at theta and spindle frequencies arises when a small portion of the brain is forced into an over-inhibited state due to the tumor, in which there is an increase in the firing of (inhibitory) thalamic reticular neurons. The effect is heightened when there is a concurrent decrease in the firing of (excitatory) thalamic relay neurons, which are in any case inhibited by the reticular ones. This is likely due to a decrease in the responsiveness of the peritumoral region to cholinergic inputs from the brainstem, and a corresponding depolarization of thalamic reticular neurons, and hyperpolarization of thalamic relay neurons, similar to the mechanism active during slow-wave sleep. The results indicate that disruption of normal thalamic activity is essential to generate these spectral peaks. Furthermore, the present work indicates that high-voltage and epileptiform EEGs are caused by a tumor-induced local over-excitation of the thalamus, which propagates to the cortex. Experimental findings relating to local over-inhibition and over-excitation are discussed. It is also confirmed that increasing the size of the tumor leads to greater abnormalities in the observable EEG. The usefulness of EEG for localizing the tumor is investigated.

Unifying and interpreting the spectral wavenumber content of EEGs, ECoGs, and ERPs

A biological model of corticothalamic dynamics is used to investigate the spatial power spectrum (wavenumber spectrum) of electrical activity in the brain. The model provides a single framework for unifying different aspects of activity. Comparisons of the predicted spectra with published electrocorticographic, electroencephalographic, and evoked response potential data enable physiology and anatomy to be inferred, producing results which are complementary to those obtained from comparisons in the frequency domain; the inferred quantities are consistent with, and complementary to, direct physiological and anatomical measurements. We also use the model to quantify the interdependence of the wavenumber and frequency domains, and deduce that further experiments that cover large wavenumber and frequency ranges simultaneously would greatly increase our knowledge of brain function. We conclude that both the frequency and wavenumber domains should be studied in order to build the fullest picture of brain dynamics: the two domains are both complementary and interdependent.

Lévy walks in random scattering and growth of waves

Random spatial wave scattering and stochastic wave growth are studied where one or both of the random processes can be described by a Lévy walk. This analysis extends previous work on randomly growing and scattering waves where both the random processes are modeled by Gaussian diffusive statistics. Both random spatial scattering and stochastic wave growth modeled by Lévy walks are studied separately, together, and in combination with Gaussian processes. Transmission coefficients, lasing thresholds, and energy densities in the medium are obtained for the different permutations.

Estimation of multiscale neurophysiologic parameters by electroencephalographic means

It is shown that new model-based electroencephalographic (EEG) methods can quantify neurophysiologic parameters that underlie EEG generation in ways that are complementary to and consistent with standard physiologic techniques. This is done by isolating parameter ranges that give good matches between model predictions and a variety of experimental EEG-related phenomena simultaneously. Resulting constraints range from the submicrometer synaptic level to length scales of tens of centimeters, and from timescales of around 1 ms to 1 s or more, and are found to be consistent with independent physiologic and anatomic measures. In the process, a new method of obtaining model parameters from the data is developed, including a Monte Carlo implementation for use when not all input data are available. Overall, the approaches used are complementary to other methods, constraining allowable parameter ranges in different ways and leading to much tighter constraints overall. EEG methods often provide the most restrictive individual constraints. This approach opens a new, noninvasive window on quantitative brain analysis, with the ability to monitor temporal changes, and the potential to map spatial variations. Unlike traditional phenomenologic quantitative EEG measures, the methods proposed here are based explicitly on physiology and anatomy.

Statistics of polarization and Stokes parameters of stochastic waves

Several theories now exist to describe the probability distribution functions (PDFs) for the electric field strength, intensity, and power of signals. In this work, a model is developed for the PDFs of the polarization properties of the superposition of multiple transverse wave populations. The polarization of each transverse wave population is described by a polarization ellipse with fixed axial ratio and polarization angle, and PDFs for the field strength and phase. Wave populations are vectorially added, and expressions found for the Stokes parameters I , U , Q , and V , as well as the degrees of linear and circular polarization, and integral expressions for their statistics. In this work, lognormal distributions are chosen for the electric field, corresponding to stochastic growth, and polarization PDFs are numerically calculated for the superposition of orthonormal mode populations, which might represent the natural modes emitted by a source. Examples are provided of the superposition of linear, circular, and elliptically polarized wave populations in cases where the component field strength PDFs are the same, and where one field strength PDF is dominant.

Spatially uniform and nonuniform analyses of electroencephalographic dynamics,with application to the topography of the alpha rhythm

Corticothalamic dynamics are investigated using a model in which spatial nonuniformities are incorporated via the coupling of spatial eigenmodes. Comparison of spectra generated using the nonuniform analysis with those generated using a uniform one demonstrates that, for most frequencies, local activity is only weakly dependent on activity elsewhere in the cortex; however, dispersion of low-wave-number activity ensures that distant dynamics influence local dynamics at low frequencies (below approximately 2 Hz ), and at the alpha frequency (approximately 10 Hz ), where propagating signals are inherently weakly damped, and wavelengths are large. When certain model parameters have similar spatial profiles, as is expected from physiology, the low-frequency discrepancies tend to cancel, and the uniform analysis with local parameter values is an adequate approximation to the full nonuniform one across the whole spectrum, at least for large-scale nonuniformities. After comparing the uniform and nonuniform analyses, we consider one possible application of the nonuniform analysis: studying the phenomenon of occipital alpha dominance, whereby the alpha frequency and power are greater at the back of the head (occipitally) than at the front. In order to infer realistic nonuniformities in the model parameters, the uniform version of the model is first fitted to data recorded from 98 normal subjects in a waking, eyes-closed state. This yields a set of parameters at each of five electrode sites along the midline. The inferred parameter nonuniformities are consistent with anatomical and physiological constraints. Introducing these spatial profiles into the full nonuniform model then quantitatively reproduces observed site-dependent variations in the alpha power and frequency. The results confirm that the frequency shift is mainly due to a decrease in the corticothalamic propagation delay, but indicate that the delay nonuniformity cannot account for the observed occipital increase in alpha power; the occipital alpha dominance is due to decreased cortical gains and increased thalamic gains in occipital regions compared to frontal ones.

Skeletal muscle LIM protein 1 (SLIM1/FHL1) induces alpha 5 beta 1-integrin-dependent myocyte elongation

Skeletal muscle LIM protein 1 (SLIM1/FHL1) contains four and a half LIM domains and is highly expressed in skeletal and cardiac muscle. Elevated SLIM1 mRNA expression has been associated with postnatal skeletal muscle growth and stretch-induced muscle hypertrophy in mice. Conversely, SLIM1 mRNA levels decrease during muscle atrophy. Together, these observations suggest a link between skeletal muscle growth and increased SLIM1 expression. However, the precise function of SLIM1 in skeletal muscle, specifically the role of SLIM1 during skeletal muscle differentiation, is not known. This study investigated the effect of increased SLIM1 expression during skeletal muscle differentiation. Western blot analysis showed an initial decrease followed by an increase in SLIM1 expression during differentiation. Overexpression of SLIM1 in Sol8 or C2C12 skeletal muscle cell lines, at levels observed during hypertrophy, induced distinct effects in differentiating myocytes and undifferentiated reserve cells, which were distinguished by differential staining for two markers of differentiation, MyoD and myogenin. In differentiating skeletal myocytes, SLIM1 overexpression induced hyperelongation, which, by either plating cells on poly-l-lysine or using a series of peptide blockade experiments, was shown to be specifically dependent on ligand binding to the alpha5beta1-integrin, whereas in reserve cells, SLIM1 overexpression induced the formation of multiple cytoplasmic protrusions (branching), which was also integrin mediated. These results suggest that SLIM1 may play an important role during the early stages of skeletal muscle differentiation, specifically in alpha5beta1-integrin-mediated signaling pathways.

The effect of gender on Helicobacter felis-mediated gastritis, epithelial cell proliferation, and apoptosis in the mouse model

The murine Helicobacter felis model has been extensively used to investigate the importance of host factors in the development of chronic gastritis. The effect of gender in this murine model is unknown. Male and female C57BL/6J mice were infected with H felis for up to 1 year. At 4, 8, 19, 36, and 52 weeks post-infection, gastric histopathology, epithelial cell proliferation, and apoptosis were examined and compared with age- and gender-matched controls. In female mice, infection with H felis resulted in an earlier onset of chronic gastric inflammation, epithelial hyperplasia, and oxyntic cell loss than males. In females, there was a trend towards increased gastric pathology compared with males, with long-term-infected female mice having significantly greater (p < 0.05) chronic inflammation than male mice. The histopathological differences in male and female mice did not relate to the density of H felis infection. Female mice infected with H felis had significantly increased gastric epithelial cell proliferation in the cardia and corpus at both 8 and 52 weeks post-infection (p < 0.05). Epithelial cell apoptosis in the glandular mucosa of the corpus at 36 and 52 weeks post-infection was significantly increased (p < 0.05) in female mice compared with uninfected gender controls. In contrast, there was no significant increase in epithelial cell proliferation or apoptosis in any area of the stomach at any time point after H felis infection in male mice. These results demonstrate that there are gender differences in the gastric inflammatory and epithelial response to H felis in the murine model. The functional importance of gender should be considered in future murine studies on H felis- and H pylori-induced chronic gastritis.

Nonuniform corticothalamic continuum model of electroencephalographic spectra with application to split-alpha peaks

Recent theoretical work has successfully predicted electroencephalographic spectra from physiology using a model corticothalamic system with spatially uniform parameters. The present work incorporates parameter nonuniformities into this model via the coupling they induce between spatial eigenmodes. Splitting of the spectral alpha peak, an effect seen in a small percentage of the normal population, is investigated as an illustrative special case. It is confirmed that weak splitting can arise from mode structure if the peak is sufficiently sharp, even for uniform parameters. However, it is further demonstrated that greater splitting can result from nonuniformities, and it is argued that this mechanism for split alpha is better able to account quantitatively for this effect than previously suggested alternatives of pacemakers or purely cortical resonances. On introducing nonuniformities in corticothalamic loop time delays, we find that the alpha frequency also varies as one moves from the front to the back of the head, in accord with observations, and that analogous (but less distinct) variations are seen in the beta peak. Analysis shows realistic variations of around +/-10 ms relative to the mean loop delay of approximately 80 ms can account for observed splittings of about 1 Hz. It is also suggested that subjects who display clear alpha splitting form the tail of a distribution of magnitude of cortical inhomogeneity, rather than a separate population.

Effects of disorder in two-dimensional photonic crystal waveguides

The effects of randomness on the guiding properties of waveguides embedded in disordered two-dimensional photonic crystals composed of a finite cluster of circular cylinders of infinite length are investigated for TM-polarized radiation. Different degrees of disorder in the radius, filling fraction, refractive index, and position are considered for both straight and 90 degrees bent guides. The crystals exhibit similar sensitivity to refractive index and radius disorder, with a degree of disorder from 15%-20% yielding little substantial change in the guiding properties. A smaller range of position disorder is also considered. For strong disorder in radius and refractive index, the guide effectively closes. These results were obtained by a Monte Carlo simulation method, and the performance of this method is analyzed. The method requires at least ten realizations in some cases for convergence to commence; substantially more realizations are required for moderate and strong disorder to achieve accurate results.

Neurophysical modeling of brain dynamics

A recent neurophysical model of brain electrical activity is outlined and applied to EEG phenomena. It incorporates single-neuron physiology and the large-scale anatomy of corticocortical and corticothalamic pathways, including synaptic strengths, dendritic propagation, nonlinear firing responses, and axonal conduction. Small perturbations from steady states account for observed EEGs as functions of arousal. Evoked response potentials (ERPs), correlation, and coherence functions are also reproduced. Feedback via thalamic nuclei is critical in determining the forms of these quantities, the transition between sleep and waking, and stability against seizures. Many disorders correspond to significant changes in EEGs, which can potentially be quantified in terms of the underlying physiology using this theory. In the nonlinear regime, limit cycles are often seen, including a regime in which they have the characteristic petit mal 3 Hz spike-and-wave form.