Spherical harmonic decomposition applied to spatial-temporal analysis of human high-density EEG

We demonstrate an application of spherical harmonic decomposition to analysis of the human electroencephalogram (EEG). We implement two methods and discuss issues specific to analysis of hemispherical, irregularly sampled data. Performance of the methods and spatial sampling requirements are quantified using simulated data. The analysis is applied to experimental EEG data, confirming earlier reports of an approximate frequency-wavenumber relationship in some bands.Comment: 12 pages, 8 figures, submitted to Phys. Rev. E, uses APS RevTeX style

Cell calcium oscillations: the origin of their variability

Oscillation in calcium levels in the cytoplasm of individual cells has been observed experimentally to consist of a series of spikes and plateaux of differing amplitudes and inter-peak intervals. On the other hand, mathematical models based on known biochemical reaction kinetic behaviours predict, in the main, limit cycle behaviour. Chaotic solutions do not mimic the observed variability, and so another solution was sought by the introduction of filtered noise into some of the kinetic coefficients. Some of the variability can be predicted from this mechanism, but it is likely that other sources contribute to this as well

A simple, low-cost demonstration of wavelength division multiplexing

Optics and photonics can be used to motivate students in physics courses at the high school, college, or university level. Many fundamental ideas and concepts can be taught by exploring wavelength division multiplexing as used in optical fiber communication systems. We describe a safe, simple, low-cost experimental apparatus that can be used to demonstrate the key concepts of wavelength division multiplexing. The apparatus can form the basis of several hands-on, active-learning activitie

Robust chaos in a model of the electroencephalogram: implications for brain dynamics

Various techniques designed to extract nonlinear characteristics from experimental time series have provided no clear evidence as to whether the electroencephalogram (EEG) is chaotic. Compounding the lack of firm experimental evidence is the paucity of physiologically plausible theories of EEG that are capable of supporting nonlinear and chaotic dynamics. Here we provide evidence for the existence of chaotic dynamics in a neurophysiologically plausible continuum theory of electrocortical activity and show that the set of parameter values supporting chaos within parameter space has positive measure and exhibits fat fractal scaling

On the variability of cell calcium oscillations

Abstract not available

Is collecting anonymous but code-identified intervention assessment data worth the effort? Reflections on a recent study in electronics

Often the effectiveness of an educational intervention for a large lecture group is assessed by testing the cohort before and after the intervention and measuring any improvement in the aggregated data from pre- to post-testing. A limitation of this method is that not all students may attend the pre-test, post-test or the lectures where the intervention is administered, diluting the significance of the results. An alternative approach is for students to use a unique but anonymous research code that allows researchers to 'tag' each individual student and hence identify those students who participate in all intervention activities and tests ('complete responders'). This paper argues that tagged data can increase the statistical significance of an intervention hypothesis when compared to untagged data even when the statistical sample is small. In a recent study that tested the efficacy of interactive lecture demonstrations (ILDs) in improving students' conceptual understanding for an advanced topic in electronics (AC resonance), the 'complete responders' formed a relatively small subgroup (N=21) of the full group (N=86) that participated in all or only some of the activities or tests ('all responders'). The learning gains for the 'complete responders' were more significant than those of 'all responders'. The reasons for the increased significance are discussed in this paper

A spatially continuous mean field theory of electrocortical activity

A set of nonlinear continuum field equations is presented which describes the dynamics of neural activity in cortex. These take into account the most pertinent anatomical and physiological features found in cortex with all parameter values obtainable from independent experiment. Derivation of a white noise fluctuation spectrum from a linearized set of equations shows the presence of strong resonances that correspond to electroencephalographically observed 0.3-4 Hz (mammalian delta), 4-8 Hz (mammalian theta), 8-13 Hz (mammalian alpha) and >13 Hz (mammalian beta) activity. Numerical solutions of a full set of one-dimensional nonlinear equations include properties analogous to cortical evoked potentials, travelling waves at experimentally observed velocities, threshold type spike activity and limit cycle, chaotic and noise driven oscillations at the frequency of the mammalian alpha rhythm. All these types of behaviour are generated with parameters that are within ranges reported experimentally. The strong dependence of the phenomena observed on inhibitory-inhibitory interactions is demonstrated. These results suggest that the classically described alpha may be instantiated in a number of qualitatively distinct dynamical regimes, all of which depend on the integrity of inhibitory-inhibitory population interactions

Erratum: a spatially continuous mean field theory of electrocortical activity

Corrects an error in: Liley, D. T. J., Cadusch, P. J., Dafilis, M. P. (2002). A spatially continuous mean field theory of electrocortical activity. Network: Computation Neural System, 13 (1), 67-113. For the original article see: http://hdl.handle.net/1959.3/191

Specific predictions of a physiologically detailed theory of alpha electrorhythmogenesis

Abstract not available.200

Chaos and generalised multistability in a mesoscopic model of the electroencephalogram

We present evidence for chaos and generalised multistability in a mesoscopic model of the electroencephalogram (EEG). Two limit cycle attractors and one chaotic attractor were found to coexist in a two-dimensional plane of the ten-dimensional volume of initial conditions. The chaotic attractor was found to have a moderate value of the largest Lyapunov exponent (3.4 s-1 base e) with an associated Kaplan-Yorke (Lyapunov) dimension of 2.086. There are two different limit cycles appearing in conjunction with this particular chaotic attractor: one multiperiodic low amplitude limit cycle whose largest spectral peak is within the alpha band (8-13 Hz) of the EEG; and another multiperiodic large-amplitude limit cycle which may correspond to epilepsy. The cause of the coexistence of these structures is explained with a one-parameter bifurcation analysis. Each attractor has a basin of differing complexity: the large-amplitude limit cycle has a basin relatively uncomplicated in its structure while the small-amplitude limit cycle and chaotic attractor each have much more finely structured basins of attraction, but none of the basin boundaries appear to be fractal. The basins of attraction for the chaotic and small-amplitude limit cycle dynamics apparently reside within each other. We briefly discuss the implications of these findings in the context of theoretical attempts to understand the dynamics of brain function and behaviour