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

Correlation between X-ray flux and rotational acceleration in Vela X-1

The results of a search for correlations between X-ray flux and angular acceleration for the accreting binary pulsar Vela X-1 are presented. Results are based on data obtained with the Hakucho satellite during the interval 1982 to 1984. In undertaking this correlation analysis, it was necessary to modify the usual statistical method to deal with conditions imposed by generally unavoidable satellite observing constraints, most notably a mismatch in sampling between the two variables. The results are suggestive of a correlation between flux and the absolute value of the angular acceleration, at a significance level of 96 percent. The implications of the methods and results for future observations and analysis are discussed

Forest Saccharomyces paradoxus are robust to seasonal biotic and abiotic changes

Microorganisms are famous for adapting quickly to new environments. However, most evidence for rapid microbial adaptation comes from laboratory experiments or domesticated environments, and it is unclear how rates of adaptation scale from human-influenced environments to the great diversity of wild microorganisms. We examined potential monthly-scale selective pressures in the model forest yeast Saccharomyces paradoxus. Contrary to expectations of seasonal adaptation, the S. paradoxus population was stable over four seasons in the face of abiotic and biotic environmental changes. While the S. paradoxus population was diverse, including 41 unique genotypes among 192 sampled isolates, there was no correlation between S. paradoxus genotypes and seasonal environments. Consistent with observations from other S. paradoxus populations, the forest population was highly clonal and inbred. This lack of recombination, paired with population stability, implies that S. paradoxus evolved the phenotypic plasticity needed to resist seasonal environmental fluctuations long ago, and that individual S. paradoxus are generalists with regard to seasonal environments. Similarly, while the forest population included diversity among phenotypes related to intraspecific interference competition, there was no evidence for active coevolution among these phenotypes. At least ten percent of the forest S. paradoxus individuals produced “}killer toxins{”, which kill sensitive Saccharomyces cells, but the presence of a toxin-producing isolate did not predict resistance to the toxin among nearby isolates. How forest yeasts acclimate to changing environments remains an open question, and future studies should investigate the physiological responses that allow microbial cells to cope with environmental fluctuations in their native habitats.Competing Interest StatementThe authors have declared no competing interest

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

Evidence for Calcium Carbonate at the Phoenix Landing Site

The Phoenix mission has recently finished its study of the north polar environment of Mars with the aim to help understand both the current climate and to put constraints on past climate. An important part of understanding the past climate is the study of secondary minerals, those formed by reaction with volatile compounds such as H2O and CO2. This work describes observations made by the Thermal and Evolved-Gas Analyzer (TEGA) on the Phoenix Lander related to carbonate minerals. Carbonates are generally considered to be products of aqueous processes. A wet and warmer climate during the early history of Mars coupled with a much denser CO2 atmosphere are ideal conditions for the aqueous alteration of basaltic materials and the subsequent formation of carbonates. Carbonates (Mg- and Ca-rich) are predicted to be thermodynamically stable minerals in the present martian environment, however, there have been only a few indications of carbonates on the surface by a host of orbiting and landed missions to Mars. Carbonates (Mg-rich) have been suggested to be a component (2-5 wt %) of the martian global dust based upon orbital thermal emission spectroscopy. The identifications, based on the presence of a 1480 cm-1 absorption feature, are consistent with Mgcarbonates. A similar feature is observed in brighter, undisturbed soils by Mini-TES on the Gusev plains. Recently, Mg-rich carbonates have been identified in the Nili Fossae region by the CRISM instrument onboard the Mars Reconnaissance Orbiter. Carbonates have also been confirmed as aqueous alteration phases in martian meteorites so it is puzzling why there have not been more discoveries of carbonates by landers, rovers, and orbiters. Carbonates may hold important clues about the history of liquid water and aqueous processes on the surface of Mars

Estimation of Orbital Neutron Detector Spatial Resolution by Systematic Shifting of Differential Topographic Masks

We present a method and preliminary results related to determining the spatial resolution of orbital neutron detectors using epithermal maps and differential topographic masks. Our technique is similar to coded aperture imaging methods for optimizing photonic signals in telescopes [I]. In that approach photon masks with known spatial patterns in a telescope aperature are used to systematically restrict incoming photons which minimizes interference and enhances photon signal to noise. Three orbital neutron detector systems with different stated spatial resolutions are evaluated. The differing spatial resolutions arise due different orbital altitudes and the use of neutron collimation techniques. 1) The uncollimated Lunar Prospector Neutron Spectrometer (LPNS) system has spatial resolution of 45km FWHM from approx. 30km altitude mission phase [2]. The Lunar Rennaissance Orbiter (LRO) Lunar Exploration Neutron Detector (LEND) with two detectors at 50km altitude evaluated here: 2) the collimated 10km FWHM spatial resolution detector CSETN and 3) LEND's collimated Sensor for Epithermal Neutrons (SETN). Thus providing two orbital altitudes to study factors of: uncollimated vs collimated and two average altitudes for their effect on fields-of-view