A Fast Algorithm for Robust Regression with Penalised Trimmed Squares

The presence of groups containing high leverage outliers makes linear regression a difficult problem due to the masking effect. The available high breakdown estimators based on Least Trimmed Squares often do not succeed in detecting masked high leverage outliers in finite samples. An alternative to the LTS estimator, called Penalised Trimmed Squares (PTS) estimator, was introduced by the authors in \cite{ZiouAv:05,ZiAvPi:07} and it appears to be less sensitive to the masking problem. This estimator is defined by a Quadratic Mixed Integer Programming (QMIP) problem, where in the objective function a penalty cost for each observation is included which serves as an upper bound on the residual error for any feasible regression line. Since the PTS does not require presetting the number of outliers to delete from the data set, it has better efficiency with respect to other estimators. However, due to the high computational complexity of the resulting QMIP problem, exact solutions for moderately large regression problems is infeasible. In this paper we further establish the theoretical properties of the PTS estimator, such as high breakdown and efficiency, and propose an approximate algorithm called Fast-PTS to compute the PTS estimator for large data sets efficiently. Extensive computational experiments on sets of benchmark instances with varying degrees of outlier contamination, indicate that the proposed algorithm performs well in identifying groups of high leverage outliers in reasonable computational time.Comment: 27 page

Spatial variation in the fine-structure constant -- new results from VLT/UVES

(abridged) We present a new analysis of a large sample of quasar absorption-line spectra obtained using UVES (the Ultraviolet and Visual Echelle Spectrograph) on the VLT (Very Large Telescope) in Chile. In the VLT sample (154 absorbers), we find evidence that alpha increases with increasing cosmological distance from Earth. However, as previously shown, the Keck sample (141 absorbers) provided evidence for a smaller alpha in the distant absorption clouds. Upon combining the samples an apparent variation of alpha across the sky emerges which is well represented by an angular dipole model pointing in the direction RA=(17.3 +/- 1.0) hr, dec. = (-61 +/- 10) deg, with amplitude (0.97 +0.22/-0.20) x 10^(-5). The dipole model is required at the 4.1 sigma statistical significance level over a simple monopole model where alpha is the same across the sky (but possibly different to the current laboratory value). The data sets reveal a number of remarkable consistencies: various data cuts are consistent and there is consistency in the overlap region of the Keck and VLT samples. Assuming a dipole-only (i.e. no-monopole) model whose amplitude grows proportionally with `lookback-time distance' (r=ct, where t is the lookback time), the amplitude is (1.1 +/- 0.2) x 10^(-6) GLyr^(-1) and the model is significant at the 4.2 sigma confidence level over the null model [Delta alpha]/alpha = 0). We apply robustness checks and demonstrate that the dipole effect does not originate from a small subset of the absorbers or spectra. We present an analysis of systematic effects, and are unable to identify any single systematic effect which can emulate the observed variation in alpha.Comment: 47 pages, 35 figures. Accepted for publication by Monthly Notices of the Royal Astronomical Society. Please see http://astronomy.swin.edu.au/~mmurphy/pub.html for an ASCII version of table A1 and the full set of Voigt profile fits for appendix

Effect of intravenous clarithromycin in patients with sepsis, respiratory and multiple organ dysfunction syndrome: a randomized clinical trial.

Clarithromycin may act as immune-regulating treatment in sepsis and acute respiratory dysfunction syndrome. However, clinical evidence remains inconclusive. We aimed to evaluate whether clarithromycin improves 28-day mortality among patients with sepsis, respiratory and multiple organ dysfunction syndrome. We conducted a multicenter, randomized, clinical trial in patients with sepsis. Participants with ratio of partial oxygen pressure to fraction of inspired oxygen less than 200 and more than 3 SOFA points from systems other than the respiratory function were enrolled between December 2017 and September 2019. Patients were randomized to receive 1 gr of clarithromycin or placebo intravenously once daily for 4 consecutive days. The primary endpoint was 28-day all-cause mortality. Secondary outcomes were 90-day mortality; sepsis response (defined as at least 25% decrease in SOFA score by day 7); sepsis recurrence; and differences in peripheral blood cell populations and leukocyte transcriptomics. Fifty-five patients were allocated to each arm. By day 28, 27 (49.1%) patients in the clarithromycin and 25 (45.5%) in the placebo group died (risk difference 3.6% [95% confidence interval (CI) - 15.7 to 22.7]; P = 0.703, adjusted OR 1.03 [95%CI 0.35-3.06]; P = 0.959). There were no statistical differences in 90-day mortality and sepsis response. Clarithromycin was associated with lower incidence of sepsis recurrence (OR 0.21 [95%CI 0.06-0.68]; P = 0.012); significant increase in monocyte HLA-DR expression; expansion of non-classical monocytes; and upregulation of genes involved in cholesterol homeostasis. Serious and non-serious adverse events were equally distributed. Clarithromycin did not reduce mortality among patients with sepsis with respiratory and multiple organ dysfunction. Clarithromycin was associated with lower sepsis recurrence, possibly through a mechanism of immune restoration. Clinical trial registration clinicaltrials.gov identifier NCT03345992 registered 17 November 2017; EudraCT 2017-001056-55

Arms Racing, Military Build-Ups and Dispute Intensity: Evidence from the Greek-Turkish Rivalry, 1985-2020

Arms races are linked in the public conscience to potential violence. Following gas discoveries in eastern Mediterranean, Greece and Turkey nearly came to blows in August 2020 and both states have enacted military expansion plans, further risking escalation. We present a novel approach to study the effect of military build-ups on dispute intensity, using monthly data on Turkish incursions into Greek-claimed airspace. Because airspace claims feature strongly in the dispute, these contestations represent an appropriate measure of the intensity with which Turkey pursues the conflict. Theoretically, we suggest that bilateral factors drive this intensity. We argue that increased Greek military capabilities deter incursions whereas increased Turkish military capabilities fuel them. Results from time-series models support the second expectation. Consequently, the study provides a novel methodological approach to studying interstate conflict intensity and shines new light on escalation dynamics in the Greek-Turkish dispute

Persistency and matroid intersection

Matroid intersection, Independence system, Persistency partition,