Averaging geometrical objects on a differentiable manifold

We construct a framework within which a mathematically precise, fully covariant, and exact averaging procedure for tensor fields on a manifold can be formulated. In particular, we introduce the Weitzenb\"ock connection for parallel transport and argue that, within the context of averaging, frames and connections are the natural geometrical objects on the manifold

The Expansion Center and Dynamical Age of the Galactic Supernova Remnant Cassiopeia A

We present proper motions for 21 bright main shell and 17 faint, higher-velocity, outer ejecta knots in the Cas A supernova remnant and use them to derive new estimates for the remnant's expansion center and age. Our study included 1951 - 1976 Palomar 5 m prime focus plates, 1988 - 1999 CCD images from the KPNO 4 m and MDM 2.4 m telescopes, and 1999 HST WFPC2 images. Measurable positions covered a 23 to 41 yr time span for most knots, with a few outer knots followed for almost 48 yr. We derive an expansion center of alpha = 23h 23m 27s.77 +- 0s.05, delta = 58d 48' 49".4 +- 0".4 (ICRS), with little difference between centers derived using outer or main shell knots. This position is 3.0 arcsec due north of that estimated by van den Bergh and Kamper (1983). It also lies 6.6 +- 1.5 arcsec almost due north (PA = 354 deg) of the remnant's recently-detected central X-ray point source, implying a transverse velocity for the X-ray point source of about 330 km/s at a distance of 3.4 kpc. Using the knots which lie out ahead of the remnant's forward blast wave, we estimate a knot convergent date of A.D. 1671.3 +- 0.9, assuming no deceleration. However, a deceleration of just approximately 1.6 km/(s yr) over a 300 yr time span would produce an explosion date A.D. 1680, consistent with the suspected sighting of the Cas A supernova by J. Flamsteed.Comment: Astron. Journal in press, sched. July 2001. AASTex5, 17 pages, 2 jpeg greyscale figures, 3 postscript figure

On Local Equivalence, Surface Code States and Matroids

Recently, Ji et al disproved the LU-LC conjecture and showed that the local unitary and local Clifford equivalence classes of the stabilizer states are not always the same. Despite the fact this settles the LU-LC conjecture, a sufficient condition for stabilizer states that violate the LU-LC conjecture is missing. In this paper, we investigate further the properties of stabilizer states with respect to local equivalence. Our first result shows that there exist infinitely many stabilizer states which violate the LU-LC conjecture. In particular, we show that for all numbers of qubits $n\geq 28$, there exist distance two stabilizer states which are counterexamples to the LU-LC conjecture. We prove that for all odd $n\geq 195$, there exist stabilizer states with distance greater than two which are LU equivalent but not LC equivalent. Two important classes of stabilizer states that are of great interest in quantum computation are the cluster states and stabilizer states of the surface codes. To date, the status of these states with respect to the LU-LC conjecture was not studied. We show that, under some minimal restrictions, both these classes of states preclude any counterexamples. In this context, we also show that the associated surface codes do not have any encoded non-Clifford transversal gates. We characterize the CSS surface code states in terms of a class of minor closed binary matroids. In addition to making connection with an important open problem in binary matroid theory, this characterization does in some cases provide an efficient test for CSS states that are not counterexamples.Comment: LaTeX, 13 pages; Revised introduction, minor changes and corrections mainly in section V

Competing interactions in semiconductor quantum dots

We introduce an integrability-based method enabling the study of semiconductor quantum dot models incorporating both the full hyperfine interaction as well as a mean-field treatment of dipole-dipole interactions in the nuclear spin bath. By performing free induction decay and spin echo simulations we characterize the combined effect of both types of interactions on the decoherence of the electron spin, for external fields ranging from low to high values. We show that for spin echo simulations the hyperfine interaction is the dominant source of decoherence at short times for low fields, and competes with the dipole-dipole interactions at longer times. On the contrary, at high fields the main source of decay is due to the dipole-dipole interactions. In the latter regime an asymmetry in the echo is observed. Furthermore, the non-decaying fraction previously observed for zero field free induction decay simulations in quantum dots with only hyperfine interactions, is destroyed for longer times by the mean-field treatment of the dipolar interactions.Comment: 10 pages, 5 figures [v2: subsection and references added

Combined Modality Therapies for High-Risk Prostate Cancer: Narrative Review of Current Understanding and New Directions.

Despite the many prospective randomized trials that have been available in the past decade regarding the optimization of radiation, hormonal, and surgical therapies for high-risk prostate cancer (PCa), many questions remain. There is currently a lack of level I evidence regarding the relative efficacy of radical prostatectomy (RP) followed by adjuvant radiation compared to radiation therapy (RT) combined with androgen deprivation therapy (ADT) for high-risk PCa. Current retrospective series have also described an improvement in biochemical outcomes and PCa-specific mortality through the use of augmented radiation strategies incorporating brachytherapy. The relative efficacy of modern augmented RT compared to RP is still incompletely understood. We present a narrative review regarding recent advances in understanding regarding comparisons of overall and PCa-specific mortality measures among patients with high-risk PCa treated with either an RP/adjuvant RT or an RT/ADT approach. We give special consideration to recent trends toward the assembly of multi-institutional series targeted at providing high-quality data to minimize the effects of residual confounding. We also provide a narrative review of recent studies examining brachytherapy boost and systemic therapies, as well as an overview of currently planned and ongoing studies that will further elucidate strategies for treatment optimization over the next decade

Public Sector Employees: Risk Averse and Altruistic?

We assess whether public sector employees have a stronger inclination to serve others and are more risk averse than employees in the private sector. A unique feature of our study is that we use revealed rather than stated preferences data. Respondents of a large-scale survey were offered a substantial reward and could choose between a widely redeemable gift certificate, a lottery ticket, or making a donation to a charity. Our analysis shows that public sector employees are significantly less likely to choose the risky option (lottery) and, at the start of their career, significantly more likely to choose the pro-social option (charity). However, when tenure increases, this difference in pro-social inclinations disappears and, later on, even reverses. Our results further suggest that quite a few public sector employees do not contribute to charity because they feel that they already contribute enough to society at work for too little pay.public service motivation, risk aversion, revealed preferences data

Long Gamma-Ray Bursts and Type Ic Core Collapse Supernovae Have Similar Locations in Hosts

When the afterglow fades at the site of a long-duration gamma-ray burst (LGRB), Type Ic supernovae (SN Ic) are the only type of core collapse supernova observed. Recent work found that a sample of LGRB in high-redshift galaxies had different environments from a collection of core-collapse environments, which were identified from their colors and light curves. LGRB were in the brightest regions of their hosts, but the core-collapse sample followed the overall distribution of the galaxy light. Here we examine 504 supernovae with types assigned based on their spectra that are located in nearby (z < 0.06) galaxies for which we have constructed surface photometry from the Sloan Digital Sky Survey (SDSS). The distributions of the thermonuclear supernovae (SN Ia) and some varieties of core-collapse supernovae (SN II and SN Ib) follow the galaxy light, but the SN Ic (like LGRB) are much more likely to erupt in the brightest regions of their hosts. The high-redshift hosts of LGRB are overwhelmingly irregulars, without bulges, while many low redshift SN Ic hosts are spirals with small bulges. When we remove the bulge light from our low-redshift sample, the SN Ic and LGRB distributions agree extremely well. If both LGRB and SN Ic stem from very massive stars, then it seems plausible that the conditions necessary for forming SN Ic are also required for LGRB. Additional factors, including metallicity, may determine whether the stellar evolution of a massive star leads to a LGRB with an underlying broad-lined SN Ic, or simply a SN Ic without a gamma-ray burst.Comment: Accepted by the Astrophysical Journal, 12 pages, 3 tables, 4 figures, SN sample size increases from 263 to 504 in v2, varying host magnitude and distance shown not to introduce systematic error in measurement