Bifurcations and state changes in the human alpha rhythm: Theory and experiment

Despite many decades investigating scalp recordable 8–13-Hz (alpha) electroencephalographic activity, no consensus has yet emerged regarding its physiological origins nor its functional role in cognition. Here we outline a detailed, physiologically meaningful, theory for the genesis of this rhythm that may provide important clues to its functional role. In particular we find that electroencephalographically plausible model dynamics, obtained with physiological admissible parameterisations, reveals a cortex perched on the brink of stability, which when perturbed gives rise to a range of unanticipated complex dynamics that include 40-Hz (gamma) activity. Preliminary experimental evidence, involving the detection of weak nonlinearity in resting EEG using an extension of the well-known surrogate data method, suggests that nonlinear (deterministic) dynamics are more likely to be associated with weakly damped alpha activity. Thus rather than the “alpha rhythm” being an idling rhythm it may be more profitable to conceive it as a readiness rhythm.

The evolution of mobile DNAs: when will transposons create phylogenies that look as if there is a master gene?

Some families of mammalian interspersed repetitive DNA, such as the Alu SINE sequence, appear to have evolved by the serial replacement of one active sequence with another, consistent with there being a single source of transposition: the "master gene." Alternative models, in which multiple source sequences are simultaneously active, have been called "transposon models." Transposon models differ in the proportion of elements that are active and in whether inactivation occurs at the moment of transposition or later. Here we examine the predictions of various types of transposon model regarding the patterns of sequence variation expected at an equilibrium between transposition, inactivation, and deletion. Under the master gene model, all bifurcations in the true tree of elements occur in a single lineage. We show that this property will also hold approximately for transposon models in which most elements are inactive and where at least some of the inactivation events occur after transposition. Such tree shapes are therefore not conclusive evidence for a single source of transposition.

Computer generation and quantitative morphometric analysis of virtual neurons

An important goal in computational neuroanatomy is the complete and accurate simulation of neuronal morphology. We are developing computational tools to model three-dimensional dendritic structures based on sets of stochastic rules. This paper reports an extensive, quantitative anatomical characterization of simulated motoneurons and Purkinje cells. We used several local and global algorithms implemented in the L-Neuron and ArborVitae programs to generate sets of virtual neurons. Parameters statistics for all algorithms were measured from experimental data, thus providing a compact and consistent description of these morphological classes. We compared the emergent anatomical features of each group of virtual neurons with those of the experimental database in order to gain insights on the plausibility of the model assumptions, potential improvements to the algorithms, and non-trivial relations among morphological parameters. Algorithms mainly based on local constraints (e.g., branch diameter) were successful in reproducing many morphological properties of both motoneurons and Purkinje cells (e.g. total length, asymmetry, number of bifurcations). The addition of global constraints (e.g., trophic factors) improved the angle-dependent emergent characteristics (average Euclidean distance from the soma to the dendritic terminations, dendritic spread). Virtual neurons systematically displayed greater anatomical variability than real cells, suggesting the need for additional constraints in the models. For several emergent anatomical properties, a specific algorithm reproduced the experimental statistics better than the others did. However, relative performances were often reversed for different anatomical properties and/or morphological classes. Thus, combining the strengths of alternative generative models could lead to comprehensive algorithms for the complete and accurate simulation of dendritic morphology.

Competing edge networks

We introduce a model for a pair of nonlinear evolving networks, defined over a common set of vertices, sub ject to edgewise competition. Each network may grow new edges spontaneously or through triad closure. Both networks inhibit the other’s growth and encourage the other’s demise. These nonlinear stochastic competition equations yield to a mean field analysis resulting in a nonlinear deterministic system. There may be multiple equilibria; and bifurcations of different types are shown to occur within a reduced parameter space. This situation models competitive peer-to-peer communication networks such as BlackBerry Messenger displacing SMS; or instant messaging displacing emails.