Finite-Size Scaling in the Energy-Entropy Plane for the 2D +- J Ising Spin Glass

For $L \times L$ square lattices with $L \le 20$ the 2D Ising spin glass with +1 and -1 bonds is found to have a strong correlation between the energy and the entropy of its ground states. A fit to the data gives the result that each additional broken bond in the ground state of a particular sample of random bonds increases the ground state degeneracy by approximately a factor of 10/3. For $x = 0.5$ (where $x$ is the fraction of negative bonds), over this range of $L$, the characteristic entropy defined by the energy-entropy correlation scales with size as $L^{1.78(2)}$. Anomalous scaling is not found for the characteristic energy, which essentially scales as $L^2$. When $x= 0.25$, a crossover to $L^2$ scaling of the entropy is seen near $L = 12$. The results found here suggest a natural mechanism for the unusual behavior of the low temperature specific heat of this model, and illustrate the dangers of extrapolating from small $L$.Comment: 9 pages, two-column format; to appear in J. Statistical Physic

Tree-Structured Nonlinear Adaptive Signal Processing

In communication systems, nonlinear adaptive filtering has become increasingly popular in a variety of applications such as channel equalization, echo cancellation and speech coding. However, existing nonlinear adaptive filters such as polynomial (truncated Volterra series) filters and multilayer perceptrons suffer from a number of problems. First, although high Order polynomials can approximate complex nonlinearities, they also train very slowly. Second, there is no systematic and efficient way to select their structure. As for multilayer perceptrons, they have a very complicated structure and train extremely slowly Motivated by the success of classification and regression trees on difficult nonlinear and nonparametfic problems, we propose the idea of a tree-structured piecewise linear adaptive filter. In the proposed method each node in a tree is associated with a linear filter restricted to a polygonal domain, and this is done in such a way that each pruned subtree is associated with a piecewise linear filter. A training sequence is used to adaptively update the filter coefficients and domains at each node, and to select the best pruned subtree and the corresponding piecewise linear filter. The tree structured approach offers several advantages. First, it makes use of standard linear adaptive filtering techniques at each node to find the corresponding Conditional linear filter. Second, it allows for efficient selection of the subtree and the corresponding piecewise linear filter of appropriate complexity. Overall, the approach is computationally efficient and conceptually simple. The tree-structured piecewise linear adaptive filter bears some similarity to classification and regression trees. But it is actually quite different from a classification and regression tree. Here the terminal nodes are not just assigned a region and a class label or a regression value, but rather represent: a linear filter with restricted domain, It is also different in that classification and regression trees are determined in a batch mode offline, whereas the tree-structured adaptive filter is determined recursively in real-time. We first develop the specific structure of a tree-structured piecewise linear adaptive filter and derive a stochastic gradient-based training algorithm. We then carry out a rigorous convergence analysis of the proposed training algorithm for the tree-structured filter. Here we show the mean-square convergence of the adaptively trained tree-structured piecewise linear filter to the optimal tree-structured piecewise linear filter. Same new techniques are developed for analyzing stochastic gradient algorithms with fixed gains and (nonstandard) dependent data. Finally, numerical experiments are performed to show the computational and performance advantages of the tree-structured piecewise linear filter over linear and polynomial filters for equalization of high frequency channels with severe intersymbol interference, echo cancellation in telephone networks and predictive coding of speech signals

Finite-Size Scaling of the Domain Wall Entropy Distributions for the 2D ±J\pm J Ising Spin Glass

The statistics of domain walls for ground states of the 2D Ising spin glass with +1 and -1 bonds are studied for $L \times L$ square lattices with $L \le 48$, and $p$ = 0.5, where $p$ is the fraction of negative bonds, using periodic and/or antiperiodic boundary conditions. When $L$ is even, almost all domain walls have energy $E_{dw}$ = 0 or 4. When $L$ is odd, most domain walls have $E_{dw}$ = 2. The probability distribution of the entropy, $S_{dw}$, is found to depend strongly on $E_{dw}$. When $E_{dw} = 0$, the probability distribution of $|S_{dw}|$ is approximately exponential. The variance of this distribution is proportional to $L$, in agreement with the results of Saul and Kardar. For $E_{dw} = k > 0$ the distribution of $S_{dw}$ is not symmetric about zero. In these cases the variance still appears to be linear in $L$, but the average of $S_{dw}$ grows faster than $\sqrt{L}$. This suggests a one-parameter scaling form for the $L$-dependence of the distributions of $S_{dw}$ for $k > 0$.Comment: 13 page

Very high-energy neutrinos from slowly decaying, massive dark matter, as a source of explosive energy for gamma-ray bursts

We consider a speculative model for gamma-ray bursts (GRB), which predicts that the total kinetic energy in the ejected matter is less than the total energy in the gamma rays. There is also secondary energy in X-rays, which are emitted contemporaneously with the gamma rays. The model suggests that bremsstrahlung and Compton up-scattering by very energetic electrons, are important processes for producing the observed burst radiation. The dynamics naturally allows for the possibility of a moderate degree of beaming of matter and radiation in some gamma-ray bursts. GRB are predicted to have an intrinsically wide distribution in total energies, in particular, on the low side. They are predicted to occur out to large red-shifts, z~8, in local regions of dense matter.Comment: 12 pages, no figur

SubmilliJansky Transients in Archival Radio Observations

[ABRIDGED] We report the results of a 944-epoch survey for transient sources with archival data from the Very Large Array spanning 22 years with a typical epoch separation of 7 days. Observations were obtained at 5 or 8.4 GHz for a single field of view with a full-width at half-maximum of 8.6' and 5.1', respectively, and achieved a typical point-source detection threshold at the beam center of ~300 microJy per epoch. Ten transient sources were detected with a significance threshold such that only one false positive would be expected. Of these transients, eight were detected in only a single epoch. Two transients were too faint to be detected in individual epochs but were detected in two-month averages. None of the ten transients was detected in longer-term averages or associated with persistent emission in the deep image produced from the combination of all epochs. The cumulative rate for the short timescale radio transients above 370 microJy at 5 and 8.4 GHz is 0.07 < R < 40 deg^-2 yr^-1, where the uncertainty is due to the unknown duration of the transients, 20 min < t_char < 7 days. A two-epoch survey for transients will detect 1.5 +/- 0.4 transient per square degrees above a flux density of 370 microJy. Two transients are associated with galaxies at z=0.040 and z=0.249. These may be similar to the peculiar Type Ib/c radio supernova SN 1998bw associated with GRB 980428. Six transients have no counterparts in the optical or infrared (R=27, Ks=18). The hosts and progenitors of these transients are unknown.Comment: Accepted for ApJ; full quality figures available at http://astro.berkeley.edu/~gbower/ps/rt.pd

Conductance and its universal fluctuations in the directed network model at the crossover to the quasi-one-dimensional regime

The directed network model describing chiral edge states on the surface of a cylindrical 3D quantum Hall system is known to map to a one-dimensional quantum ferromagnetic spin chain. Using the spin wave expansion for this chain, we determine the universal functions for the crossovers between the 2D chiral metallic and 1D metallic regimes in the mean and variance of the conductance along the cylinder, to first nontrivial order.Comment: 10 pages, REVTeX, uses epsf, 2 .eps figures included. Newly written Introduction and small changes to other section

Clonal expansion within pneumococcal serotype 6C after use of seven-valent vaccine

Streptococcus pneumoniae causes invasive infections, primarily at the extremes of life. A seven-valent conjugate vaccine (PCV7) is used to protect against invasive pneumococcal disease in children. Within three years of PCV7 introduction, we observed a fourfold increase in serotype 6C carriage, predominantly due to a single clone. We determined the whole-genome sequences of nineteen S. pneumoniae serotype 6C isolates, from both carriage (n = 15) and disease (n = 4) states, to investigate the emergence of serotype 6C in our population, focusing on a single multi-locus sequence type (MLST) clonal complex 395 (CC395). A phylogenetic network was constructed to identify different lineages, followed by analysis of variability in gene sets and sequences. Serotype 6C isolates from this single geographical site fell into four broad phylogenetically distinct lineages. Variation was seen in the 6C capsular locus and in sequences of genes encoding surface proteins. The largest clonal complex was characterised by the presence of lantibiotic synthesis locus. In our population, the 6C capsular locus has been introduced into multiple lineages by independent capsular switching events. However, rapid clonal expansion has occurred within a single MLST clonal complex. Worryingly, plasticity exists within current and potential vaccine-associated loci, a consideration for future vaccine use, target selection and design