Permutation branes and linear matrix factorisations

All the known rational boundary states for Gepner models can be regarded as permutation branes. On general grounds, one expects that topological branes in Gepner models can be encoded as matrix factorisations of the corresponding Landau-Ginzburg potentials. In this paper we identify the matrix factorisations associated to arbitrary B-type permutation branes.Comment: 43 pages. v2: References adde

The Effect of Variability on the Estimation of Quasar Black Hole Masses

We investigate the time-dependent variations of ultraviolet (UV) black hole mass estimates of quasars in the Sloan Digital Sky Survey (SDSS). From SDSS spectra of 615 high-redshift (1.69 < z < 4.75) quasars with spectra from two epochs, we estimate black hole masses, using a single-epoch technique which employs an additional, automated night-sky-line removal, and relies on UV continuum luminosity and CIV (1549A) emission line dispersion. Mass estimates show variations between epochs at about the 30% level for the sample as a whole. We determine that, for our full sample, measurement error in the line dispersion likely plays a larger role than the inherent variability, in terms of contributing to variations in mass estimates between epochs. However, we use the variations in quasars with r-band spectral signal-to-noise ratio greater than 15 to estimate that the contribution to these variations from inherent variability is roughly 20%. We conclude that these differences in black hole mass estimates between epochs indicate variability is not a large contributer to the current factor of two scatter between mass estimates derived from low- and high-ionization emission lines.Comment: 76 pages, 15 figures, 2 (long) tables; Accepted for publication in ApJ (November 10, 2007

Defect Perturbations in Landau-Ginzburg Models

Perturbations of B-type defects in Landau-Ginzburg models are considered. In particular, the effect of perturbations of defects on their fusion is analyzed in the framework of matrix factorizations. As an application, it is discussed how fusion with perturbed defects induces perturbations on boundary conditions. It is shown that in some classes of models all boundary perturbations can be obtained in this way. Moreover, a universal class of perturbed defects is constructed, whose fusion under certain conditions obey braid relations. The functors obtained by fusing these defects with boundary conditions are twist functors as introduced in the work of Seidel and Thomas.Comment: 46 page

Non-24-Hour Sleep-Wake Disorder Revisited – A Case Study

The human sleep-wake cycle is governed by two major factors: a homeostatic hourglass process (process S), which rises linearly during the day, and a circadian process C, which determines the timing of sleep in a ~24-h rhythm in accordance to the external light–dark (LD) cycle. While both individual processes are fairly well characterized, the exact nature of their interaction remains unclear. The circadian rhythm is generated by the suprachiasmatic nucleus (“master clock”) of the anterior hypothalamus, through cell-autonomous feedback loops of DNA transcription and translation. While the phase length (tau) of the cycle is relatively stable and genetically determined, the phase of the clock is reset by external stimuli (“zeitgebers”), the most important being the LD cycle. Misalignments of the internal rhythm with the LD cycle can lead to various somatic complaints and to the development of circadian rhythm sleep disorders (CRSD). Non-24-hour sleep-wake disorders (N24HSWD) is a CRSD affecting up to 50% of totally blind patients and characterized by the inability to maintain a stable entrainment of the typically long circadian rhythm (tau > 24.5 h) to the LD cycle. The disease is rare in sighted individuals and the pathophysiology less well understood. Here, we present the case of a 40-year-old sighted male, who developed a misalignment of the internal clock with the external LD cycle following the treatment for Hodgkin’s lymphoma (ABVD regimen, four cycles and AVD regimen, four cycles). A thorough clinical assessment, including actigraphy, melatonin profiles and polysomnography led to the diagnosis of non-24-hour sleep-wake disorders (N24HSWD) with a free-running rhythm of tau = 25.27 h. A therapeutic intervention with bright light therapy (30 min, 10,000 lux) in the morning and melatonin administration (0.5–0.75 mg) in the evening failed to entrain the free-running rhythm, although a longer treatment duration and more intense therapy might have been successful. The sudden onset and close timely connection led us to hypothesize that the chemotherapy might have caused a mutation of the molecular clock components leading to the observed elongation of the circadian period

Atomic Resonance and Scattering

Contains reports on eleven research projects.U.S. Air Force - Office of Scientific Research (Grant AFOSR-81-0067

A Snapshot Survey for Gravitational Lenses Among z>=4.0 Quasars: I. The z>5.7 Sample

Over the last few years, the Sloan Digital Sky Survey (SDSS) has discovered several hundred quasars with redshift between 4.0 and 6.4. Including the effects of magnification bias, one expects a priori that an appreciable fraction of these objects are gravitationally lensed. We have used the Advanced Camera for Surveys on the Hubble Space Telescope to carry out a snapshot imaging survey of high-redshift SDSS quasars to search for gravitationally split lenses. This paper, the first in a series reporting the results of the survey, describes snapshot observations of four quasars at z = 5.74, 5.82, 5.99 and 6.30, respectively. We find that none of these objects has a lensed companion within 5 magnitudes with a separation larger than 0.3 arcseconds; within 2.5 magnitudes, we can rule out companions within 0.1 arcseconds. Based on the non-detection of strong lensing in these four systems, we constrain the z~6 luminosity function to a slope of beta>-4.63 (3 sigma), assuming a break in the quasar luminosity function at M_{1450}^*=-24.0. We discuss the implications of this constraint on the ionizing background due to quasars in the early universe. Given that these quasars are not highly magnified, estimates of the masses of their central engines by the Eddington argument must be taken seriously, possibly challenging models of black hole formation.Comment: 23 pages, 8 figures, 2 tables, submitted to A

An Empirical Calibration of the Completeness of the SDSS Quasar Survey

Spectra of nearly 20000 point-like objects to a Galactic reddening corrected magnitude of i=19.1 have been obtained to test the completeness of the SDSS quasar survey. The spatially-unresolved objects were selected from all regions of color space, sparsely sampled from within a 278 sq. deg. area of sky covered by this study. Only ten quasars were identified that were not targeted as candidates by the SDSS quasar survey (including both color and radio source selection). The inferred density of unresolved quasars on the sky that are missed by the SDSS algorithm is 0.44 per sq. deg, compared to 8.28 per sq. deg. for the selected quasar density, giving a completeness of 94.9(+2.6,-3.8) to the limiting magnitude. Omitting radio selection reduces the color-only selection completeness by about 1%. Of the ten newly identified quasars, three have detected broad absorption line systems, six are significantly redder than other quasars at the same redshift, and four have redshifts between 2.7 and 3.0 (the redshift range where the SDSS colors of quasars intersect the stellar locus). The fraction of quasars missed due to image defects and blends is approximately 4%, but this number varies by a few percent with magnitude. Quasars with extended images comprise about 6% of the SDSS sample, and the completeness of the selection algorithm for extended quasars is approximately 81%, based on the SDSS galaxy survey. The combined end-to-end completeness for the SDSS quasar survey is approximately 89%. The total corrected density of quasars on the sky to i=19.1 is estimated to be 10.2 per sq. deg.Comment: 37 pages, 10 figures, accepted for publication in A

First Measurement of the Clustering Evolution of Photometrically-Classified Quasars

We present new measurements of the quasar autocorrelation from a sample of \~80,000 photometrically-classified quasars taken from SDSS DR1. We find a best-fit model of $\omega(\theta) = (0.066\pm^{0.026}_{0.024})\theta^{-(0.98\pm0.15)}$ for the angular autocorrelation, consistent with estimates from spectroscopic quasar surveys. We show that only models with little or no evolution in the clustering of quasars in comoving coordinates since z~1.4 can recover a scale-length consistent with local galaxies and Active Galactic Nuclei (AGNs). A model with little evolution of quasar clustering in comoving coordinates is best explained in the current cosmological paradigm by rapid evolution in quasar bias. We show that quasar biasing must have changed from b_Q~3 at a (photometric) redshift of z=2.2 to b_Q~1.2-1.3 by z=0.75. Such a rapid increase with redshift in biasing implies that quasars at z~2 cannot be the progenitors of modern L* objects, rather they must now reside in dense environments, such as clusters. Similarly, the duration of the UVX quasar phase must be short enough to explain why local UVX quasars reside in essentially unbiased structures. Our estimates of b_Q are in good agreement with recent spectroscopic results, which demonstrate the implied evolution in b_Q is consistent with quasars inhabiting halos of similar mass at every redshift. Treating quasar clustering as a function of both redshift and luminosity, we find no evidence for luminosity dependence in quasar clustering, and that redshift evolution thus affects quasar clustering more than changes in quasars' luminosity. We provide a new method for quantifying stellar contamination in photometrically-classified quasar catalogs via the correlation function.Comment: 34 pages, 10 figures, 1 table, Accepted to ApJ after: (i) Minor textual changes; (ii) extra points added to Fig.

Exploratory Chandra Observations of the Three Highest Redshift Quasars Known

We report on exploratory Chandra observations of the three highest redshift quasars known (z = 5.82, 5.99, and 6.28), all found in the Sloan Digital Sky Survey. These data, combined with a previous XMM-Newton observation of a z = 5.74 quasar, form a complete set of color-selected, z > 5.7 quasars. X-ray emission is detected from all of the quasars at levels that indicate that the X-ray to optical flux ratios of z ~ 6 optically selected quasars are similar to those of lower redshift quasars. The observations demonstrate that it will be feasible to obtain quality X-ray spectra of z ~ 6 quasars with current and future X-ray missions.Comment: 15 pages, ApJL, in press; small revisions to address referee Comment