A Dynamic Neural Field Model of Mesoscopic Cortical Activity Captured with Voltage-Sensitive Dye Imaging

A neural field model is presented that captures the essential non-linear characteristics of activity dynamics across several millimeters of visual cortex in response to local flashed and moving stimuli. We account for physiological data obtained by voltage-sensitive dye (VSD) imaging which reports mesoscopic population activity at high spatio-temporal resolution. Stimulation included a single flashed square, a single flashed bar, the line-motion paradigm – for which psychophysical studies showed that flashing a square briefly before a bar produces sensation of illusory motion within the bar – and moving squares controls. We consider a two-layer neural field (NF) model describing an excitatory and an inhibitory layer of neurons as a coupled system of non-linear integro-differential equations. Under the assumption that the aggregated activity of both layers is reflected by VSD imaging, our phenomenological model quantitatively accounts for the observed spatio-temporal activity patterns. Moreover, the model generalizes to novel similar stimuli as it matches activity evoked by moving squares of different speeds. Our results indicate that feedback from higher brain areas is not required to produce motion patterns in the case of the illusory line-motion paradigm. Physiological interpretation of the model suggests that a considerable fraction of the VSD signal may be due to inhibitory activity, supporting the notion that balanced intra-layer cortical interactions between inhibitory and excitatory populations play a major role in shaping dynamic stimulus representations in the early visual cortex

Planetary Rings

Planetary rings are the only nearby astrophysical disks, and the only disks that have been investigated by spacecraft. Although there are significant differences between rings and other disks, chiefly the large planet/ring mass ratio that greatly enhances the flatness of rings (aspect ratios as small as 1e-7), understanding of disks in general can be enhanced by understanding the dynamical processes observed at close-range and in real-time in planetary rings. We review the known ring systems of the four giant planets, as well as the prospects for ring systems yet to be discovered. We then review planetary rings by type. The main rings of Saturn comprise our system's only dense broad disk and host many phenomena of general application to disks including spiral waves, gap formation, self-gravity wakes, viscous overstability and normal modes, impact clouds, and orbital evolution of embedded moons. Dense narrow rings are the primary natural laboratory for understanding shepherding and self-stability. Narrow dusty rings, likely generated by embedded source bodies, are surprisingly found to sport azimuthally-confined arcs. Finally, every known ring system includes a substantial component of diffuse dusty rings. Planetary rings have shown themselves to be useful as detectors of planetary processes around them, including the planetary magnetic field and interplanetary impactors as well as the gravity of nearby perturbing moons. Experimental rings science has made great progress in recent decades, especially numerical simulations of self-gravity wakes and other processes but also laboratory investigations of coefficient of restitution and spectroscopic ground truth. The age of self-sustained ring systems is a matter of debate; formation scenarios are most plausible in the context of the early solar system, while signs of youthfulness indicate at least that rings have never been static phenomena.Comment: 82 pages, 34 figures. Final revision of general review to be published in "Planets, Stars and Stellar Systems", P. Kalas and L. French (eds.), Springer (http://refworks.springer.com/sss

Waves, bumps, and patterns in neural field theories

Neural field models of firing rate activity have had a major impact in helping to develop an understanding of the dynamics seen in brain slice preparations. These models typically take the form of integro-differential equations. Their non-local nature has led to the development of a set of analytical and numerical tools for the study of waves, bumps and patterns, based around natural extensions of those used for local differential equation models. In this paper we present a review of such techniques and show how recent advances have opened the way for future studies of neural fields in both one and two dimensions that can incorporate realistic forms of axo-dendritic interactions and the slow intrinsic currents that underlie bursting behaviour in single neurons