Cohomological Finiteness Conditions in Bredon Cohomology

We show that any soluble group $G$ of type Bredon-\FP_{\infty} with respect to the family of all virtually cyclic subgroups such that centralizers of infinite order elements are of type \FP_{\infty} must be virtually cyclic. To prove this, we first reduce the problem to the case of polycyclic groups and then we show that a polycyclic-by-finite group with finitely many conjugacy classes of maximal virtually cyclic subgroups is virtually cyclic. Finally we discuss refinements of this result: we only impose the property Bredon-\FP_n for some $n \leq 3$ and restrict to abelian-by-nilpotent, abelian-by-polycyclic or (nilpotent of class 2)-by-abelian groups.Comment: Corrected a mistake in Lemma 2.4 of the previous version, which had an effect on the results in Section 5 (the condition that all centralisers of infinite order elements are of type $FP_\infty$ was added

Quantum state tomography by continuous measurement and compressed sensing

The need to perform quantum state tomography on ever larger systems has spurred a search for methods that yield good estimates from incomplete data. We study the performance of compressed sensing (CS) and least squares (LS) estimators in a fast protocol based on continuous measurement on an ensemble of cesium atomic spins. Both efficiently reconstruct nearly pure states in the 16-dimensional ground manifold, reaching average fidelities FCS = 0.92 and FLS = 0.88 using similar amounts of incomplete data. Surprisingly, the main advantage of CS in our protocol is an increased robustness to experimental imperfections

A Search for Planetary Nebulae With the SDSS: the outer regions of M31

We have developed a method to identify planetary nebula (PN) candidates in imaging data of the Sloan Digital Sky Survey (SDSS). This method exploits the SDSS' five-band sampling of emission lines in PN spectra, which results in a color signature distinct from that of other sources. Selection criteria based on this signature can be applied to nearby galaxies in which PNe appear as point sources. We applied these criteria to the whole area of M31 as scanned by the SDSS, selecting 167 PN candidates that are located in the outer regions of M31. The spectra of 80 selected candidates were then observed with the 2.2m telescope at Calar Alto Observatory. These observations and cross-checks with literature data show that our method has a selection rate efficiency of about 90%, but the efficiency is different for the different groups of PNe candidates. In the outer regions of M31, PNe trace different well-known morphological features like the Northern Spur, the NGC205 Loop, the G1 Clump, etc. In general, the distribution of PNe in the outer region 8<R<20 kpc along the minor axis shows the "extended disk" - a rotationally supported low surface brightness structure with an exponential scale length of 3.21+/-0.14 kpc and a total mass of ~10^10 M_{\sun}, which is equivalent to the mass of M33. We report the discovery of three PN candidates with projected locations in the center of Andromeda NE, a very low surface brightness giant stellar structure in the outer halo of M31. Two of the PNe were spectroscopically confirmed as genuine PNe. These two PNe are located at projected distances along the major axis of ~48 Kpc and ~41 Kpc from the center of M31 and are the most distant PNe in M31 found up to now.Comment: 58 pages, 17 figures, 2 tables, Accepted to Astronomical Journa

Effects of Inelastic Neutrino-Nucleus Scattering on Supernova Dynamics and Radiated Neutrino Spectra

Based on the shell model for Gamow-Teller and the Random Phase Approximation for forbidden transitions, we have calculated reaction rates for inelastic neutrino-nucleus scattering (INNS) under supernova (SN) conditions, assuming a matter composition given by Nuclear Statistical Equilibrium. The rates have been incorporated into state-of-the-art stellar core-collapse simulations with detailed energy-dependent neutrino transport. While no significant effect on the SN dynamics is observed, INNS increases the neutrino opacities noticeably and strongly reduces the high-energy tail of the neutrino spectrum emitted in the neutrino burst at shock breakout. Relatedly the expected event rates for the observation of such neutrinos by earthbound detectors are reduced by up to about 60%.Comment: 4 pages, 2 figures, 1 tabl