On the geometry of solutions of the quasi-geostrophic and Euler equations

We study solutions of the two-dimensional quasi-geostrophic thermal active scalar equation involving simple hyperbolic saddles. There is a naturally associated notion of simple hyperbolic saddle breakdown. It is proved that such breakdown cannot occur in finite time. At large time, these solutions may grow at most at a quadruple-exponential rate. Analogous results hold for the incompressible three-dimensional Euler equation.

Effects of the Heartbeat Wales programme over five years on behavioural risks for cardiovascular disease: quasi-experimental comparison of results from Wales and a matched reference area

Objective: To assess the net 5 year effects of intervention of a community based demonstration project, the Heartbeat Wales programme, on modifiable behavioural risks for prevention of cardiovascular disease.

Optical evidence for the unification of active galactic nuclei and quasi-stellar objects.

There is a variety of optical evidence for some unification of different types of active galactic nuclei and quasi-stellar objects (QSOs). The case is very strong for the unification of at least some Seyfert galaxies, where polarization data show that the type assigned to the Seyfert galaxy must depend on viewing direction. It has been proposed that Fanaroff-Riley type 2 (FR2) radio galaxies are quasars seen in a direction from which the quasar is obscured, and there is some limited direct evidence for this picture. The broad absorption line QSOs may be normal QSOs seen from a special direction. Some of the sources observed to have high luminosities in the far infrared could be obscured QSOs and active nuclei. Mergers and interactions are likely to play an important role in nuclear activity, and active galaxies and QSOs could change their apparent types through these encounters followed by subsequent evolution.

Cortical activity flips among quasi-stationary states.

Parallel recordings of spike trains of several single cortical neurons in behaving monkeys were analyzed as a hidden Markov process. The parallel spike trains were considered as a multivariate Poisson process whose vector firing rates change with time. As a consequence of this approach, the complete recording can be segmented into a sequence of a few statistically discriminated hidden states, whose dynamics are modeled as a first-order Markov chain. The biological validity and benefits of this approach were examined in several independent ways: (i) the statistical consistency of the segmentation and its correspondence to the behavior of the animals; (ii) direct measurement of the collective flips of activity, obtained by the model; and (iii) the relation between the segmentation and the pair-wise short-term cross-correlations between the recorded spike trains. Comparison with surrogate data was also carried out for each of the above examinations to assure their significance. Our results indicated the existence of well-separated states of activity, within which the firing rates were approximately stationary. With our present data we could reliably discriminate six to eight such states. The transitions between states were fast and were associated with concomitant changes of firing rates of several neurons. Different behavioral modes and stimuli were consistently reflected by different states of neural activity. Moreover, the pair-wise correlations between neurons varied considerably between the different states, supporting the hypothesis that these distinct states were brought about by the cooperative action of many neurons.