Dynamic mean-field and cavity methods for diluted Ising systems

We compare dynamic mean-field and dynamic cavity as methods to describe the stationary states of dilute kinetic Ising models. We compute dynamic mean-field theory by expanding in interaction strength to third order, and compare to the exact dynamic mean-field theory for fully asymmetric networks. We show that in diluted networks the dynamic cavity method generally predicts magnetizations of individual spins better than both first order ("naive") and second order ("TAP") dynamic mean field theory

Eclipse Timings of the Transient Low Mass X-ray Binary EXO0748-676. IV. The Rossi X-Ray Timing Explorer Eclipses

We report our complete database of X-ray eclipse timings of the low mass X-ray binary EXO0748-676 observed by the Rossi X-Ray Timing Explorer (RXTE) satellite. As of this writing we have accumulated 443 full X-ray eclipses, 392 of which have been observed with the Proportional Counter Array on RXTE. These include both observations where an eclipse was specifically targeted and those eclipses found in the RXTE data archive. Eclipse cycle count has been maintained since the discovery of the EXO0748-676 system in February 1985. We describe our observing and analysis techniques for each eclipse and describe improvements we have made since the last compilation by Wolff et al. (2002). The principal result of this paper is the database containing the timing results from a seven-parameter fit to the X-ray light curve for each observed eclipse along with the associated errors in the fitted parameters. Based on the standard O-C analysis, EXO0748-676 has undergone four distinct orbital period epochs since its discovery. In addition, EXO0748-676 shows small-scale events in the O-C curve that are likely due to short-lived changes in the secondary star.Comment: Accepted for publication in The Astrophysical Journal Supplement Series, 5 figures. Analysis revised. Tables 1 & 3 update

Response variability in balanced cortical networks

We study the spike statistics of neurons in a network with dynamically balanced excitation and inhibition. Our model, intended to represent a generic cortical column, comprises randomly connected excitatory and inhibitory leaky integrate-and-fire neurons, driven by excitatory input from an external population. The high connectivity permits a mean-field description in which synaptic currents can be treated as Gaussian noise, the mean and autocorrelation function of which are calculated self-consistently from the firing statistics of single model neurons. Within this description, we find that the irregularity of spike trains is controlled mainly by the strength of the synapses relative to the difference between the firing threshold and the post-firing reset level of the membrane potential. For moderately strong synapses we find spike statistics very similar to those observed in primary visual cortex.Comment: 22 pages, 7 figures, submitted to Neural Computatio

State Concentration Exponent as a Measure of Quickness in Kauffman-type Networks

We study the dynamics of randomly connected networks composed of binary Boolean elements and those composed of binary majority vote elements. We elucidate their differences in both sparsely and densely connected cases. The quickness of large network dynamics is usually quantified by the length of transient paths, an analytically intractable measure. For discrete-time dynamics of networks of binary elements, we address this dilemma with an alternative unified framework by using a concept termed state concentration, defined as the exponent of the average number of t-step ancestors in state transition graphs. The state transition graph is defined by nodes corresponding to network states and directed links corresponding to transitions. Using this exponent, we interrogate the dynamics of random Boolean and majority vote networks. We find that extremely sparse Boolean networks and majority vote networks with arbitrary density achieve quickness, owing in part to long-tailed in-degree distributions. As a corollary, only relatively dense majority vote networks can achieve both quickness and robustness.Comment: 6 figure

Field-free two-direction alignment alternation of linear molecules by elliptic laser pulses

We show that a linear molecule subjected to a short specific elliptically polarized laser field yields postpulse revivals exhibiting alignment alternatively located along the orthogonal axis and the major axis of the ellipse. The effect is experimentally demonstrated by measuring the optical Kerr effect along two different axes. The conditions ensuring an optimal field-free alternation of high alignments along both directions are derived.Comment: 5 pages, 4 color figure

Brecht v. Abrahamson: Harmful Error in Habeas Corpus Law

For the past two and one-half decades, the Supreme Court and the lower federal courts have applied the same rule for assessing the harmlessness of constitutional error in habeas corpus proceedings as they have applied on direct appeal of both state and federal convictions. Under that rule, which applied to all constitutional errors except those deemed per se prejudicial or per se reversible, the state could avoid reversal upon a finding of error only by proving that the error was harmless beyond a reasonable doubt. The Supreme Court adopted this stringent standard in Chapman v. California to fulfill the federal courts\u27 responsibility to protect people from infractions by the States of federally guaranteed rights. Although Chapman itself arose on direct appeal, the Court understood the decision\u27s harmless error rule to be of constitutional magnitude and, consistent with the principle of parity between direct and habeas corpus consideration of constitutional issues in the federal courts, the Court repeatedly and routinely applied the same standard in habeas corpus proceedings. So did the lower federal courts

Coefficient of Restitution for Viscoelastic Spheres: The Effect of Delayed Recovery

The coefficient of normal restitution of colliding viscoelastic spheres is computed as a function of the material properties and the impact velocity. From simple arguments it becomes clear that in a collision of purely repulsively interacting particles, the particles loose contact slightly before the distance of the centers of the spheres reaches the sum of the radii, that is, the particles recover their shape only after they lose contact with their collision partner. This effect was neglected in earlier calculations which leads erroneously to attractive forces and, thus, to an underestimation of the coefficient of restitution. As a result we find a novel dependence of the coefficient of restitution on the impact rate.Comment: 11 pages, 2 figure