Fractional Quantum Hall Effect from Anomalies in WZNW Model

An approach to understand Fractional Quantum Hall Effect (FQHE) using anomalies is studied in this paper. More specifically, this is done by looking at the anomaly in the current conservation equation of a WZNW theory describing fields living at the edge of the two dimensional Hall sample. This WZNW theory itself comes from the non-Abelian bosonisation of fermions living at the edge. It is shown that this model can describe both integer and fractional quantization of conductivities in a unified manner.Comment: 14 pages, SU-4240-56

The Connection Between X-ray Binaries and Star Clusters in NGC 4449

We present 23 candidate X-ray binaries with luminosities down to 1.8x10^36 erg/s, in the nearby starburst galaxy NGC 4449, from observations totaling 105 ksec taken with the ACIS-S instrument on the Chandra Space Telescope. We determine count rates, luminosities, and colors for each source, and perform spectral fits for sources with sufficient counts. We also compile a new catalog of 129 compact star clusters in NGC 4449 from high resolution, multi-band optical images taken with the Hubble Space Telescope, doubling the number of clusters known in this galaxy. The UBVI,Ha luminosities of each cluster are compared with predictions from stellar evolution models to estimate their ages and masses. We find strong evidence for a population of very young massive, black-hole binaries, which comprise nearly 50% of the detected X-ray binaries in NGC 4449. Approximately a third of these remain within their parent star clusters, which formed t < 6-8 Myr ago, while others have likely been ejected from their parent clusters. We also find evidence for a population of somewhat older X-ray binaries, including both supergiant and Be-binaries, which appear to be associated with somewhat older t ~ 100-400 Myr star clusters, and one X-ray binary in an ancient (t ~ 10 Gyr) globular cluster. Our results suggest that detailed information on star clusters can significantly improve constraints on X-ray binary populations in star-forming galaxies

Star Cluster Candidates in M81

We present a catalog of extended objects in the vicinity of M81 based a set of 24 Hubble Space Telescope Advanced Camera for Surveys (ACS) Wide Field Camera (WFC) F814W (I-band) images. We have found 233 good globular cluster candidates; 92 candidate HII regions, OB associations, or diffuse open clusters; 489 probable background galaxies; and 1719 unclassified objects. We have color data from ground-based g- and r-band MMT Megacam images for 79 galaxies, 125 globular cluster candidates, 7 HII regions, and 184 unclassified objects. The color-color diagram of globular cluster candidates shows that most fall into the range 0.25 < g-r < 1.25 and 0.5 < r-I < 1.25, similar to the color range of Milky Way globular clusters. Unclassified objects are often blue, suggesting that many of them are likely to be HII regions and open clusters, although a few galaxies and globular clusters may be among them.Comment: 35 pages, 11 figures, submitted to A

Communication under Strong Asynchronism

We consider asynchronous communication over point-to-point discrete memoryless channels. The transmitter starts sending one block codeword at an instant that is uniformly distributed within a certain time period, which represents the level of asynchronism. The receiver, by means of a sequential decoder, must isolate the message without knowing when the codeword transmission starts but being cognizant of the asynchronism level A. We are interested in how quickly can the receiver isolate the sent message, particularly in the regime where A is exponentially larger than the codeword length N, which we refer to as `strong asynchronism.' This model of sparse communication may represent the situation of a sensor that remains idle most of the time and, only occasionally, transmits information to a remote base station which needs to quickly take action. The first result shows that vanishing error probability can be guaranteed as N tends to infinity while A grows as Exp(N*k) if and only if k does not exceed the `synchronization threshold,' a constant that admits a simple closed form expression, and is at least as large as the capacity of the synchronized channel. The second result is the characterization of a set of achievable strictly positive rates in the regime where A is exponential in N, and where the rate is defined with respect to the expected delay between the time information starts being emitted until the time the receiver makes a decision. As an application of the first result we consider antipodal signaling over a Gaussian channel and derive a simple necessary condition between A, N, and SNR for achieving reliable communication.Comment: 26 page

Similarities in Populations of Star Clusters

We compare the observed mass functions and age distributions of star clusters in six well-studied galaxies: the Milky Way, Magellanic Clouds, M83, M51, and Antennae. In combination, these distributions span wide ranges of mass and age: 10^2\lea M/M_{\odot}\lea10^6 and 10^6\lea\tau/yr \lea10^9. We confirm that the distributions are well represented by power laws: $dN/dM\propto M^{\beta}$ with $\beta \approx-1.9$ and $dN/d\tau\propto\tau^{\gamma}$ with $\gamma\approx -0.8$. The mass and age distributions are approximately independent of each other, ruling out simple models of mass-dependent disruption. As expected, there are minor differences among the exponents, at a level close to the true uncertainties, $\epsilon_{\beta}\sim\epsilon_{\gamma}\sim$~0.1--0.2. However, the overwhelming impression is the similarity of the mass functions and age distributions of clusters in these different galaxies, including giant and dwarf, quiescent and interacting galaxies. This is an important empirical result, justifying terms such as "universal" or "quasi-universal." We provide a partial theoretical explanation for these observations in terms of physical processes operating during the formation and disruption of the clusters, including star formation and feedback, subsequent stellar mass loss, and tidal interactions with passing molecular clouds. A full explanation will require additional information about the molecular clumps and star clusters in galaxies beyond the Milky Way.Comment: 20 pages, 4 figures, 2 tables; published in the Astrophysical Journal, 752:96 (2012 June 20

Optimal Sequential Frame Synchronization

We consider the `one-shot frame synchronization problem' where a decoder wants to locate a sync pattern at the output of a channel on the basis of sequential observations. We assume that the sync pattern of length N starts being emitted at a random time within some interval of size A, that characterizes the asynchronism level between the transmitter and the receiver. We show that a sequential decoder can optimally locate the sync pattern, i.e., exactly, without delay, and with probability approaching one as N tends to infinity, if and only if the asynchronism level grows as O(exp(N*k)), with k below the `synchronization threshold,' a constant that admits a simple expression depending on the channel. This constant is the same as the one that characterizes the limit for reliable asynchronous communication, as was recently reported by the authors. If k exceeds the synchronization threshold, any decoder, sequential or non-sequential, locates the sync pattern with an error that tends to one as N tends to infinity. Hence, a sequential decoder can locate a sync pattern as well as the (non-sequential) maximum likelihood decoder that operates on the basis of output sequences of maximum length A+N-1, but with much fewer observations.Comment: 6 page