A Risk Comparison of Ordinary Least Squares vs Ridge Regression

We compare the risk of ridge regression to a simple variant of ordinary least squares, in which one simply projects the data onto a finite dimensional subspace (as specified by a Principal Component Analysis) and then performs an ordinary (un-regularized) least squares regression in this subspace. This note shows that the risk of this ordinary least squares method is within a constant factor (namely 4) of the risk of ridge regression.Comment: Appearing in JMLR 14, June 201

Reliability of clinical methods in evaluating patellofemoral pain syndrome with malalignment

Background: Diagnosis of patellofemroal pain syndrome has been challenging due to lack of clinical test with better sensitivity and specificity, axial imaging has been considered as the standard modality for evaluation. Patients with anterior knee pain because of patellofemoral pain syndrome can be sub-grouped as those with or without radiological positive parameter for patellar maltracking.  The aim of the present study was to evaluate reliability of clinical tests in two subgroups of patients presenting with patellofemoral pain syndrome.Methods: 45 knees with anterior knee pain without any episode of patellar instability were evaluated clinically using four standard tests (patellar apprehension test (PAT), eccentric step test (EST), active instability test (AIT) and Waldron’s test. On the basis of CT scan finding (at least one positive radiological parameter of instability) 28 knees were categorized in Group A (potential patellar instability group) and 17 knees in Group B (PFPS).Results: All patients with 3 or more than three clinical test positive were cases with potential patellofemroal instability except two. Whereas other true patellofemroal pain patients all except 2 were have less than 3 positive clinical tests. Conclusions: Clinical test have more diagnostic accuracy in evaluating anterior knee pain due to potential patellofemroal instability in comparison to patellofemroal pain without radiological instability

High-speed, multi-colour optical photometry of the anomalous X-ray pulsar 4U 0142+61 with ULTRACAM

We present high-speed, multi-colour optical photometry of the anomalous X-ray pulsar 4U 0142+61, obtained with ULTRACAM on the 4.2-m William Herschel Telescope. We detect 4U 0142+61 at magnitudes of i'=23.7+-0.1, g'=27.2+-0.2 and u'>25.8, consistent with the magnitudes found by Hulleman et al.(2004) and hence confirming their discovery of both a spectral break in the optical and a lack of long-term optical variability. We also confirm the discovery of Kern & Martin (2002) that 4U 0142+61 shows optical pulsations with an identical period (~8.7 s) to the X-ray pulsations. The rms pulsed fraction in our data is 29+-8%, 5-7 times greater than the 0.2-8 keV X-ray rms pulsed fraction. The optical and X-ray pulse profiles show similar morphologies and appear to be approximately in phase with each other, the former lagging the latter by only 0.04+-0.02 cycles. In conjunction with the constraints imposed by X-ray observations, the results presented here favour a magnetar interpretation for the anomalous X-ray pulsars.Comment: 6 pages, 4 figures, accepted for publication in MNRA

Stellar Variability in the Globular Cluster Terzan 5

We present the results of a search for variability in and near the core of the metal-rich, obscured globular cluster Terzan 5, using NICMOS on HST. This extreme cluster has approximately solar metallicity and a central density that places it in the upper few percent of all clusters. It is estimated to have the highest interaction rate of any galactic globular cluster. The large extinction towards Terzan 5 and the severe stellar crowding near the cluster center present a substantial observational challenge. Using time series analysis we discovered two variable stars in this cluster. The first is a RRab Lyrae variable with a period of ~0.61 days, a longer period than that of field stars with similar high metallicities. This period is, however, shorter than the average periods of RR Lyraes found in the metal-rich globular clusters NGC 6441, NGC 6388 and 47 Tuc. The second variable is a blue star with a 7-hour period sinusoidal variation and a likely orbital period of 14 hours. This star is probably an eclipsing blue straggler, or (less likely) the infrared counterpart to the low mass X-ray binary known in Terzan 5. Due to the extreme crowding and overlapping Airy profile of the IR PSF, we fall short of our original goal of detecting CVs via Palpha emission and detecting variable infrared emission from the location of the binary MSP in Terzan 5.Comment: 17 pages including 12 figures. Accepted for publication in Ap