Nonlinear estimation with sparse temporal measurements

Nonlinear estimators based on the Kalman filter, the extended Kalman filter (EKF) and unscented Kalman filter (UKF) are commonly used in practical application. The Kalman filter is an optimal estimator for linear systems; the EKF and UKF are sub-optimal approximations of the Kalman filter. The EKF uses a first-order Taylor series approximation to linearize nonlinear models; the UKF uses an approximation of the states' joint probability distribution. Long measurement intervals exacerbate approximation error in each approach, particularly in covariance estimation. EKF and UKF performance under varied measurement frequency is studied through two problems, a single dimension falling body and simple pendulum. The EKF is shown more sensitive to measurement frequency than the UKF in the falling body problem. However, both estimators display insensitivity to measurement frequency in the simple pendulum problem. The literature's lack of consensus as to whether the EKF or UKF is the superior nonlinear estimator may be explained through covariance approximation error. Tools are presented to analyze EKF and UKF measurement frequency sensitivity. Covariance is propagated forward using the approximations of the EKF and UKF. Each propagated covariance is compared for similarity with a Monte Carlo propagation. The similarity of the covariance matrices is shown to predict filter performance. Portions of the state trajectory susceptible to EKF divergence are found using the Frobenius norm of the Jacobian matrix, limiting the need to consider covariance propagation along the entire state trajectory. Long measurement intervals also reveal a commonly overlooked challenge in UKF application: sigma point selection methods may produce sigma point vec-tors that violate physical state constraints. Although the UKF can function under this condition over short measurement intervals, unexpected failure may occur without consideration of physical constraints. A novel constrained UKF, using the scaled unscented transform, is proposed to address this issue.http://archive.org/details/nonlinearestimat1094550547Commander, United States NavyApproved for public release; distribution is unlimited

Evaluation of two doses of etoricoxib, a COX-2 selective non-steroidal anti-inflammatory drug (NSAID), in the treatment of Rheumatoid Arthritis in a double-blind, randomized controlled trial

List of Ethics Committees. (DOCX 38 kb

The Fading Optical Counterpart of GRB~970228, Six Months and One Year Later

We report on observations of the fading optical counterpart of the gamma-ray burst GRB 970228, made with the Hubble Space Telescope STIS CCD approximately six months after outburst and with the HST/NICMOS and Keck/NIRC approximately one year after outburst. The unresolved counterpart is detected by STIS at V=28.0 +/- 0.25, consistent with a continued power-law decline with exponent -1.14 +/- 0.05. The counterpart is located within, but near the edge of, a faint extended source with diameter ~0."8 and integrated magnitude V=25.8 +/- 0.25. A reanalysis of HST and NTT observations performed shortly after the burst shows no evidence of proper motion of the point source or fading of the extended emission. Only the extended source is visible in the NICMOS images with a magnitude of H=23.3 +/- 0.1. The Keck observations find K = 22.8 +/- 0.3. Several distinct and independent means of deriving the foreground extinction in the direction of GRB 970228 all agree with A_V = 0.75 +/- 0.2. After adjusting for Galactic extinction, we find that the size of the observed extended emission is consistent with that of galaxies of comparable magnitude found in the Hubble Deep Field (HDF) and other deep HST images. Only 2% of the sky is covered by galaxies of similar or greater surface brightness; therefore the extended source is almost certainly the host galaxy. Additionally, we find that the extinction-corrected V - H and V - K colors of the host are as blue as any galaxy of comparable or brighter magnitude in the HDF. Taken in concert with recent observations of GRB 970508, GRB 971214, and GRB 980703 our work suggests that all four GRBs with spectroscopic identification or deep multicolor broad-band imaging of the host lie in rapidly star-forming galaxies.Comment: 24 pages, Latex, 4 PostScript figures, to appear in the May 10 issue of The Astrophysical Journal (Note: displayed abstract is abridged

The Faint Optical Afterglow and Host Galaxy of GRB 020124: Implications for the Nature of Dark Gamma-ray Bursts

We present ground-based optical observations of GRB 020124 starting 1.6 hr after the burst, as well as subsequent Very Large Array and Hubble Space Telescope (HST) observations. The optical afterglow of GRB 020124 is one of the faintest afterglows detected to date, and it exhibits a relatively rapid decay, Fv ∝ t-1.60±0.04, followed by further steepening. In addition, a weak radio source was found coincident with the optical afterglow. The HST observations reveal that a positionally coincident host galaxy must be the faintest host to date, R ≳ 29.5 mag. The afterglow observations can be explained by several models requiring little or no extinction within the host galaxy, AVhost ≈ 0-0.9 mag. These observations have significant implications for the interpretation of the so-called dark bursts (bursts for which no optical afterglow is detected), which are usually attributed to dust extinction within the host galaxy. The faintness and relatively rapid decay of the afterglow of GRB 020124, combined with the low inferred extinction, indicate that some dark bursts are intrinsically dim and not dust obscured. Thus, the diversity in the underlying properties of optical afterglows must be observationally determined before substantive inferences can be drawn from the statistics of dark bursts.F. A. H. acknowledges support from a Presidential Early Career award. S. R. K. and S. G. D. thank the NSF for support. R. S. is grateful for support from a NASA ATP grant. R. S. and T. J. G. acknowledge support from the Sherman Fairchild Foundation. J. C. W. acknowledges support from NASA grant NAG 59302. K. H. is grateful for Ulysses support under JPL contract 958056 and for IPN support under NASA grants FDNAG 5-11451 and NAG 5-17100. Support for Proposal HST-GO-09180.01-A was provided by NASA through a grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555

The metamorphosis of SN1998bw

We present and discuss the photometric and spectroscopic evolution of the peculiar SN1998bw, associated with GRB980425, through an analysis of optical and near IR data collected at ESO-La Silla. The spectroscopic data, spanning the period from day -9 to day +376 (relative to B maximum), have shown that this SN was unprecedented, although somewhat similar to SN1997ef. Maximum expansion velocities as high as 3x10^4 km/s to some extent mask its resemblance to other Type Ic SNe. At intermediate phases, between photospheric and fully nebular, the expansion velocities (~10^4 km/s) remained exceptionally high compared to those of other recorded core-collapse SNe at a similar phase. The mild linear polarization detected at early epochs suggests the presence of asymmetry in the emitting material. The degree of asymmetry, however, cannot be decoded from these measurements alone. The HeI 1.083 mu and 2.058 mu lines are identified and He is suggested to lie in an outer region of the envelope. The temporal behavior of the fluxes and profiles of emission lines of MgI]4571A, [OI]6300,6364A and a feature ascribed to Fe are traced to stimulate future modeling work.Comment: 32 pages, 19 figures; ps file including figures at http://www.eso.org/~fpatat/sn98b

The general fault in our fault lines

Pervading global narratives suggest that political polarization is increasing, yet the accuracy of such group meta-perceptions has been drawn into question. A recent US study suggests that these beliefs are inaccurate and drive polarized beliefs about out-groups. However, it also found that informing people of inaccuracies reduces those negative beliefs. In this work, we explore whether these results generalize to other countries. To achieve this, we replicate two of the original experiments with 10,207 participants across 26 countries. We focus on local group divisions, which we refer to as fault lines. We find broad generalizability for both inaccurate meta-perceptions and reduced negative motive attribution through a simple disclosure intervention. We conclude that inaccurate and negative group meta-perceptions are exhibited in myriad contexts and that informing individuals of their misperceptions can yield positive benefits for intergroup relations. Such generalizability highlights a robust phenomenon with implications for political discourse worldwide

Association between convalescent plasma treatment and mortality in COVID-19: a collaborative systematic review and meta-analysis of randomized clinical trials.

Funder: laura and john arnold foundationBACKGROUND: Convalescent plasma has been widely used to treat COVID-19 and is under investigation in numerous randomized clinical trials, but results are publicly available only for a small number of trials. The objective of this study was to assess the benefits of convalescent plasma treatment compared to placebo or no treatment and all-cause mortality in patients with COVID-19, using data from all available randomized clinical trials, including unpublished and ongoing trials (Open Science Framework, https://doi.org/10.17605/OSF.IO/GEHFX ). METHODS: In this collaborative systematic review and meta-analysis, clinical trial registries (ClinicalTrials.gov, WHO International Clinical Trials Registry Platform), the Cochrane COVID-19 register, the LOVE database, and PubMed were searched until April 8, 2021. Investigators of trials registered by March 1, 2021, without published results were contacted via email. Eligible were ongoing, discontinued and completed randomized clinical trials that compared convalescent plasma with placebo or no treatment in COVID-19 patients, regardless of setting or treatment schedule. Aggregated mortality data were extracted from publications or provided by investigators of unpublished trials and combined using the Hartung-Knapp-Sidik-Jonkman random effects model. We investigated the contribution of unpublished trials to the overall evidence. RESULTS: A total of 16,477 patients were included in 33 trials (20 unpublished with 3190 patients, 13 published with 13,287 patients). 32 trials enrolled only hospitalized patients (including 3 with only intensive care unit patients). Risk of bias was low for 29/33 trials. Of 8495 patients who received convalescent plasma, 1997 died (23%), and of 7982 control patients, 1952 died (24%). The combined risk ratio for all-cause mortality was 0.97 (95% confidence interval: 0.92; 1.02) with between-study heterogeneity not beyond chance (I2 = 0%). The RECOVERY trial had 69.8% and the unpublished evidence 25.3% of the weight in the meta-analysis. CONCLUSIONS: Convalescent plasma treatment of patients with COVID-19 did not reduce all-cause mortality. These results provide strong evidence that convalescent plasma treatment for patients with COVID-19 should not be used outside of randomized trials. Evidence synthesis from collaborations among trial investigators can inform both evidence generation and evidence application in patient care