Optimal Estimation of Several Linear Parameters in the Presence of Lorentzian Thermal Noise

In a previous article we developed an approach to the optimal (minimum variance, unbiased) statistical estimation technique for the equilibrium displacement of a damped, harmonic oscillator in the presence of thermal noise. Here, we expand that work to include the optimal estimation of several linear parameters from a continuous time series. We show that working in the basis of the thermal driving force both simplifies the calculations and provides additional insight to why various approximate (not optimal) estimation techniques perform as they do. To illustrate this point, we compare the variance in the optimal estimator that we derive for thermal noise with those of two approximate methods which, like the optimal estimator, suppress the contribution to the variance that would come from the irrelevant, resonant motion of the oscillator. We discuss how these methods fare when the dominant noise process is either white displacement noise or noise with power spectral density that is inversely proportional to the frequency ($1/f$ noise). We also construct, in the basis of the driving force, an estimator that performs well for a mixture of white noise and thermal noise. To find the optimal multi-parameter estimators for thermal noise, we derive and illustrate a generalization of traditional matrix methods for parameter estimation that can accommodate continuous data. We discuss how this approach may help refine the design of experiments as they allow an exact, quantitative comparison of the precision of estimated parameters under various data acquisition and data analysis strategies.Comment: 16 pages, 10 figures. Accepted for publication in Classical and Quantum Gravit

Laboratory Tests of Gravitational Physics Using a Cryogenic Torsion Pendulum

Progress and plans are reported for a program of gravitational physics experiments using cryogenic torsion pendula undergoing large amplitude torsional oscillation. The program includes a UC Irvine project to measure the gravitational constant G and joint UC Irvine - U. Washington projects to test the gravitational inverse square law at a range of about 10 cm and to test the weak equivalence principle.Comment: 17 pages, 11 figures, contribution to the 10th Marcel Grossman Conference Proceedings (Rio de Janeiro, July 20 - 26, 2003) - changed wording in first paragraph of section

An exceptionally bright flare from SGR1806-20 and the origins of short-duration gamma-ray bursts

Soft-gamma-ray repeaters (SGRs) are galactic X-ray stars that emit numerous short-duration (about 0.1 s) bursts of hard X-rays during sporadic active periods. They are thought to be magnetars: strongly magnetized neutron stars with emissions powered by the dissipation of magnetic energy. Here we report the detection of a long (380 s) giant flare from SGR 1806-20, which was much more luminous than any previous transient event observed in our Galaxy. (In the first 0.2 s, the flare released as much energy as the Sun radiates in a quarter of a million years.) Its power can be explained by a catastrophic instability involving global crust failure and magnetic reconnection on a magnetar, with possible large-scale untwisting of magnetic field lines outside the star. From a great distance this event would appear to be a short-duration, hard-spectrum cosmic gamma-ray burst. At least a significant fraction of the mysterious short-duration gamma-ray bursts therefore may come from extragalactic magnetars.Comment: 21 pages, 5 figures. Published in Natur

Predicting the Starquakes in PSR J0537-6910

We report on more than 7 years of monitoring of PSR J0537-6910, the 16 ms pulsar in the Large Magellanic Cloud, using data acquired with the RXTE. During this campaign the pulsar experienced 23 sudden increases in frequency (``glitches'') amounting to a total gain of over six ppm of rotation frequency superposed on its gradual spindown of d(nu)/d(t) = -2e-10 Hz/s. The time interval from one glitch to the next obeys a strong linear correlation to the amplitude of the first glitch, with a mean slope of about 400 days ppm (6.5 days per uHz), such that these intervals can be predicted to within a few days, an accuracy which has never before been seen in any other pulsar. There appears to be an upper limit of ~40 uHz for the size of glitches in_all_ pulsars, with the 1999 April glitch of J0537 as the largest so far. The change in the spindown of J0537 across the glitches, Delta(d(nu)/d(t)), appears to have the same hard lower limit of -1.5e-13 Hz/s, as, again, that observed in all other pulsars. The spindown continues to increase in the long term, d(d(nu)/d(t))/d(t) = -1e-21 Hz/s/s, and thus the timing age of J0537 (-0.5 nu d(nu)/d(t)) continues to decrease at a rate of nearly one year every year, consistent with movement of its magnetic moment away from its rotational axis by one radian every 10,000 years, or about one meter per year. J0537 was likely to have been born as a nearly-aligned rotator spinning at 75-80 Hz, with a |d(nu)/d(t)| considerably smaller than its current value of 2e-10 Hz/s. The pulse profile of J0537 consists of a single pulse which is found to be flat at its peak for at least 0.02 cycles.Comment: 54 pages, 12 figures. Accepted for publication in The Astrophysical Journal. Cleaner figure 2. V4 -- in line with version accepted by Ap

Concurrent Acquisition of a Single Nucleotide Polymorphism in Diverse Influenza H5N1 Clade 2.2 Sub-clades

Highly pathogenic Influenza A H5N1 was first identified in Guangdong Province in 1996, followed by human cases in Hong Kong in 1997. The number of confirmed human cases now exceeds 300, and the associated Case Fatality Rate exceeds 60%. The genetic diversity of the serotype continues to increase. Four distinct clades or sub-clades have been linked to human cases. The gradual genetic changes identified in the sub-clades have been attributed to copy errors by viral encoded polymerases that lack an editing function, thereby resulting in antigenic drift. We report here the concurrent acquisition of the same polymorphism by multiple, genetically distinct, clade 2.2 sub-clades in Egypt, Russia, and Ghana. These changes are not easily explained by the current theory of “random mutation” through copy error, and are more easily explained by recombination with a common source. This conclusion is supported by additional polymorphisms shared by clade 2.2 isolates in Egypt and Germany

Integrating the Fermi Gamma-Ray Burst Monitor into the 3rd Interplanetary Network

We are integrating the Fermi Gamma-Ray Burst Monitor (GBM) into the Interplanetary Network (IPN) of Gamma-Ray Burst (GRB) detectors. With the GBM, the IPN will comprise 9 experiments. This will 1) assist the Fermi team in understanding and reducing their systematic localization uncertainties, 2) reduce the sizes of the GBM and Large Area Telescope (LAT) error circles by 1 to 4 orders of magnitude, 3) facilitate the identification of GRB sources with objects found by ground- and space-based observatories at other wavelengths, from the radio to very high energy gamma-rays, 4) reduce the uncertainties in associating some LAT detections of high energy photons with GBM bursts, and 5) facilitate searches for non-electromagnetic GRB counterparts, particularly neutrinos and gravitational radiation. We present examples and demonstrate the synergy between Fermi and the IPN. This is a Fermi Cycle 2 Guest Investigator project.Comment: 5 pages, 11 figures. 2009 Fermi Symposium. eConf Proceedings C09112

Aggregation of Single Nucleotide Polymorphisms in a Human H5N1 Clade 2.2 Hemagglutinin

The evolution of H5N1 has attracted significant interest 1-4 due to linkages with avian 5,6 and human infections 7,8. The basic tenets of influenza genetics 9 attribute genetic drift to replication errors caused by a polymerase complex that lacks a proof reading function. However, recent analysis 10 of swine influenza genes identifies regions copied with absolute fidelity for more than 25 years. In addition, polymorphism tracing of clade 2.2 H5N1 single nucleotide polymorphisms identify concurrent acquisition 11 of the same polymorphism onto multiple genetic backgrounds in widely dispersed geographical locations. Here we show the aggregation of regional clade 2.2 polymorphisms from Germany, Egypt, and sub-Sahara Africa onto a human Nigerian H5N1 hemagglutinin (HA), implicating recombination in the dispersal and aggregation of single nucleotide polymorphisms from closely related genomes