Segmented back-up bar Patent

Segmented back-up bar for butt welding large tubular structures such as rocket booster bodies or tank

Visible-IR Colors and Lightcurve Analysis of Two Bright TNOs: 1999 TC36 and 1998 SN165

We report on observations of two bright Trans-Neptunian Objects (TNOs) - 1999 TC36 and 1998 SN165}- during two observational campaigns, as part of the Meudon Multicolor Survey of Outer Solar System Objects. V-J color was measured for 1999 TC36 (V-J=2.34+/-0.18), which combined with previous measured colors in the visible, indicate a red reflectivity spectrum at all wavelengths. Photometric V-band lightcurves were taken for both objects over a time span of around 8 hours. We have determined a possible rotational period of P=10.1+/-0.8 h for 1998 SN165, making it the seventh TNO with an estimated period. From its lightcurve variation of Dm=0.151(+0.022/-0.030), we have inferred an asymmetry ratio of a/b >=1.148(+0.024/-0.031). For 1999 TC36, we did not detect any rotational period or periodic signal variation within the uncertainties, but the analysis of its lightcurve hints to a slight systematic magnitude decrease.Comment: Accepted for publication in New Astronomy (13 pages, inc. 4 figures

The first-passage area for drifted Brownian motion and the moments of the Airy distribution

An exact expression for the distribution of the area swept out by a drifted Brownian motion till its first-passage time is derived. A study of the asymptotic behaviour confirms earlier conjectures and clarifies their range of validity. The analysis also leads to a simple closed-form solution for the moments of the Airy distribution.Comment: 13 page

Fast global convergence of gradient methods for high-dimensional statistical recovery

Many statistical $M$-estimators are based on convex optimization problems formed by the combination of a data-dependent loss function with a norm-based regularizer. We analyze the convergence rates of projected gradient and composite gradient methods for solving such problems, working within a high-dimensional framework that allows the data dimension \pdim to grow with (and possibly exceed) the sample size \numobs. This high-dimensional structure precludes the usual global assumptions---namely, strong convexity and smoothness conditions---that underlie much of classical optimization analysis. We define appropriately restricted versions of these conditions, and show that they are satisfied with high probability for various statistical models. Under these conditions, our theory guarantees that projected gradient descent has a globally geometric rate of convergence up to the \emph{statistical precision} of the model, meaning the typical distance between the true unknown parameter $\theta^*$ and an optimal solution $\hat{\theta}$. This result is substantially sharper than previous convergence results, which yielded sublinear convergence, or linear convergence only up to the noise level. Our analysis applies to a wide range of $M$-estimators and statistical models, including sparse linear regression using Lasso ($\ell_1$-regularized regression); group Lasso for block sparsity; log-linear models with regularization; low-rank matrix recovery using nuclear norm regularization; and matrix decomposition. Overall, our analysis reveals interesting connections between statistical precision and computational efficiency in high-dimensional estimation

Relativistically Covariant Symmetry in QED

We construct a relativistically covariant symmetry of QED. Previous local and nonlocal symmetries are special cases. This generalized symmetry need not be nilpotent, but nilpotency can be arranged with an auxiliary field and a certain condition. The Noether charge generating the symmetry transformation is obtained, and it imposes a constraint on the physical states.Comment: Latex file, 9 page

Comparing supernova remnants around strongly magnetized and canonical pulsars

The origin of the strong magnetic fields measured in magnetars is one of the main uncertainties in the neutron star field. On the other hand, the recent discovery of a large number of such strongly magnetized neutron stars, is calling for more investigation on their formation. The first proposed model for the formation of such strong magnetic fields in magnetars was through alpha-dynamo effects on the rapidly rotating core of a massive star. Other scenarios involve highly magnetic massive progenitors that conserve their strong magnetic moment into the core after the explosion, or a common envelope phase of a massive binary system. In this work, we do a complete re-analysis of the archival X-ray emission of the Supernova Remnants (SNR) surrounding magnetars, and compare our results with all other bright X-ray emitting SNRs, which are associated with Compact Central Objects (CCOs; which are proposed to have magnetar-like B-fields buried in the crust by strong accretion soon after their formation), high-B pulsars and normal pulsars. We find that emission lines in SNRs hosting highly magnetic neutron stars do not differ significantly in elements or ionization state from those observed in other SNRs, neither averaging on the whole remnants, nor studying different parts of their total spatial extent. Furthermore, we find no significant evidence that the total X-ray luminosities of SNRs hosting magnetars, are on average larger than that of typical young X-ray SNRs. Although biased by a small number of objects, we found that for a similar age, there is the same percentage of magnetars showing a detectable SNR than for the normal pulsar population.Comment: 16 pages, 5 figures, Accepted for publication in MNRA