Conjugacy width in uniform higher rank arithmetic groups of orthogonal type

Let $n \geq 10$ and let $f_a$ be the quadratic form $f_a(x_1,\ldots,x_{2n})=\sum_{i=1}^{2n}x_i^2$. Assuming the Generalized Riemann Hypothesis, we prove that every conjugacy class of $\mathrm{Spin}_{f_a}\left( \mathbb{Z} \left[ \frac{1}{2} \right] \right)$ has finite width and describe some consequences. To the best of our knowledge, this is the first time that such a boundedness result is proved for an anisotropic higher rank arithmetic group. In addition, we show that every higher rank arithmetic group in which every conjugacy class has a finite width, with some natural upper bound on this width, has the Congruence Subgroup Property. While the group $\mathrm{Spin}_{f_a}(\mathbb{Z}[\frac{1}{2}])$ is known to have CSP, we hope that the approach to CSP via conjugacy width will be fruitful. In a forthcoming paper, we will extend this result to many other anisotropic spin groups.Comment: preliminary versio

Compact Nuclei in Galaxies at Moderate Redshift:II. Their Nature and Implications for the AGN Luminosity Function

This study explores the space density and properties of active galaxies to z=0.8. We have investigated the frequency and nature of unresolved nuclei in galaxies at moderate redshift as indicators of nuclear activity such as Active Galactic Nuclei (AGN) or starbursts. Candidates are selected by fitting imaged galaxies with multi-component models using maximum likelihood estimate techniques to determine the best model fit. We select those galaxies requiring an unresolved point-source component in the galaxy nucleus, in addition to a disk and/or bulge component, to adequately model the galaxy light. We have searched 70 WFPC2 images primarily from the Medium Deep Survey for galaxies containing compact nuclei. In our survey of 1033 galaxies, the fraction containing an unresolved nuclear component greater than 5% of the total galaxy light is 9+/-1% corrected for incompleteness. In this second of two papers in this series, we discuss the nature of the compact nuclei and their hosts. We present the upper limit luminosity function (LF) for low-luminosity AGN (LLAGN) in two redshift bins to z=0.8. Mild number density evolution is detected for nuclei at -18 -16 and this flatness, combined with the increase in number density, is inconsistent with pure luminosity evolution. Based on the amount of density evolution observed for these objects, we find that almost all present-day spiral galaxies could have hosted a LLAGN at some point in their lives. We also comment on the likely contribution of these compact nuclei to the soft X-ray background.Comment: 50 pages, 14 figures, to appear in ApJ, April 199

LNCS

In resource allocation games, selfish players share resources that are needed in order to fulfill their objectives. The cost of using a resource depends on the load on it. In the traditional setting, the players make their choices concurrently and in one-shot. That is, a strategy for a player is a subset of the resources. We introduce and study dynamic resource allocation games. In this setting, the game proceeds in phases. In each phase each player chooses one resource. A scheduler dictates the order in which the players proceed in a phase, possibly scheduling several players to proceed concurrently. The game ends when each player has collected a set of resources that fulfills his objective. The cost for each player then depends on this set as well as on the load on the resources in it – we consider both congestion and cost-sharing games. We argue that the dynamic setting is the suitable setting for many applications in practice. We study the stability of dynamic resource allocation games, where the appropriate notion of stability is that of subgame perfect equilibrium, study the inefficiency incurred due to selfish behavior, and also study problems that are particular to the dynamic setting, like constraints on the order in which resources can be chosen or the problem of finding a scheduler that achieves stability

Spectroscopy and Stellar Populations of Star-forming Galaxies at z~3 in the Hubble Deep Field - South

We present results of VLT/FORS2 spectroscopy of galaxies at z~3 in the Hubble Deep Field-South (HDF-S). A sample of galaxies was drawn from the photo-z catalogue based on the HST/WFPC2 optical images and the deep near-infrared images obtained with VLT/ISAAC as a part of the FIRES project. We selected galaxies with photometric redshift between 2.5 and 4. Most of the selected galaxies are bright in rest-frame UV wavelengths and satisfy color selection criteria of Lyman break galaxies (LBGs) at z~3. The number of target galaxies with I(AB)<25.0 was 15. We identified new 5 firm and 2 probable redshifts in addition to confirmations of previously known 6 galaxies at z~3. We found 6 among these 13 galaxies lie at a quite narrow redshift range at z = 2.80+-0.01. We examined stellar populations of the galaxies with spectroscopic redshifts through comparisons of their optical and near-IR photometry data with template spectra generated by a population synthesis code. The ages from the onset of star formation for these star-forming galaxies with I<=25.0 are typically 50-200 Myr, and their stellar masses are between (0.5-5) x 10^10 M_sun, consistent with previous studies. We also compared these SED fitting results with those for distant red galaxies (DRGs) at z>2 discovered by FIRES. DRGs have larger stellar masses, larger dust attenuation than our UV-luminous LBG sample, and their star formation rates are often comparable to LBGs. These trends suggest that majority of DRGs are indeed the most massive systems at the redshift and are still in the active star-forming phase. Unless the number density of DRGs is much smaller than LBGs, estimates based on UV selected sample could miss substantial part of stellar mass density at z~3.Comment: 13 pages, 10 Postscript figures, accepted for publication in A&

A0620-00 revisited: a black-hole transient case-study

For the first time we have performed a detailed study of the X-ray, optical and infra-red light curves of the 1975/1976 outburst of the famous black-hole transient A0620-00 (Nova Mon 1975, V616 Mon). During the various stages of its outburst the X-rays lag the optical by ~5-20 days. Moreover, the activity associated with the secondary maximum started even earlier in the infra-red. This suggests that most of the outburst processes occur in the outer parts of the disk. We also find various drops in the X-ray intensity (lasting ~1 day or more). Near one of these a local maximum in the optical light curve occurs. This maximum appears ~30 days after the secondary maximum, i.e. close to the viscous time scale of an irradiated disk. We suggest this feature to be an `echo' of the secondary maximum. At the end of the outburst a similar local optical maximum occurs, which might be an `echo' of the tertiary maximum. We find that the drops in the optical and X-rays near the tertiary maximum are also present in other SXTs. They always occur ~150 days after the start of the outburst. We find for the first time that the X-ray spectrum of A0620-00 starts to harden ~100-150 days after the start of its outburst, similar to GS2000+25 and GS1124-68. This suggests we witness the transition from the so-called high to low state at that time. We show that the optical outburst light curve of A0620-00 closely resembles that of the cataclysmic variable AL Com. This strengthens the similarity in the properties of the SXTs and TOADs (or WZ Sge stars), and shows that the optical outburst light curves of both groups are governed by the disk properties and not by the compact object. Since irradiation provides a natural mechanism to prolong the outburst of SXTs, we suggest this could be of influence as well during TOAD outbursts.Comment: 38 pages, 10 figures, accepted for New Astronomy Review

Determinants of a transcriptionally competent environment at the GM-CSF promoter

Granulocyte macrophage-colony stimulating factor (GM-CSF) is produced by T cells, but not B cells, in response to immune signals. GM-CSF gene activation in response to T-cell stimulation requires remodelling of chromatin associated with the gene promoter, and these changes do not occur in B cells. While the CpG methylation status of the murine GM-CSF promoter shows no correlation with the ability of the gene to respond to activation, we find that the basal chromatin environment of the gene promoter influences its ability to respond to immune signals. In unstimulated T cells but not B cells, the GM-CSF promoter is selectively marked by enrichment of histone acetylation, and association of the chromatin-remodelling protein BRG1. BRG1 is removed from the promoter upon activation concomitant with histone depletion and BRG1 is required for efficient chromatin remodelling and transcription. Increasing histone acetylation at the promoter in T cells is paralleled by increased BRG1 recruitment, resulting in more rapid chromatin remodelling, and an associated increase in GM-CSF mRNA levels. Furthermore, increasing histone acetylation in B cells removes the block in chromatin remodelling and transcriptional activation of the GM-CSF gene. These data are consistent with a model in which histone hyperacetylation and BRG1 enrichment at the GM-CSF promoter, generate a chromatin environment competent to respond to immune signals resulting in gene activation