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

Cetacean Habitat Selection in the Alaskan Arctic during Summer and Autumn

Ten years (1982-91) of sighting data from aerial surveys offshore of northern Alaska were analyzed to investigate seasonal variability in cetacean habitat selection. Distinct habitats were described for bowhead whales (Balaena mysticetus), white whales (Delphinapterus leucas), and gray whales (Eschrichtius robustus) on the basis of habitat selection ratios calculated for bathymetric and ice cover regimes. In summer, bowheads selected continental slope waters and moderate ice conditions; white whales selected slope and basin waters and moderate to heavy ice conditions; and gray whales selected coastal/shoal waters and open water. In autumn, bowheads selected inner shelf waters and light ice conditions; white whales selected outer shelf and slope waters and moderate to heavy ice; and gray whales selected coastal and shoal/trough habitats in light ice and open water. Habitat differences among species were significant in both seasons (ANOVA F > 28, p < 0.00001). Interseasonal depth and ice cover habitats were significantly different for bowhead whales (p < 0.00002), but not for gray whales (p > 0.35). White whale depth habitat was significantly different between seasons (p < 0.00002), but ice cover habitat was not (p < 0.08). Des données d'observation réalisées sur dix années (1982-1991) grâce à des relevés aériens au large de l'Alaska septentrional ont été analysées dans le cadre de recherches sur la variabilité saisonnière dans la sélection de l'habitat des cétacés. On a décrit des habitats distincts pour la baleine boréale (Balaena mysticetus), la baleine blanche (Delphinapterus leucas) et la baleine grise de Californie (Eschrichtius robustus) en se fondant sur les taux de sélection de l'habitat calculés pour le régime bathymétrique et celui de la couverture de glace. En été, la baleine boréale choisissait les eaux de la pente continentale et des conditions de glace modérée; la baleine blanche choisissait les eaux de la pente continentale et du bassin océanique, et des conditions de glace allant de modérée à épaisse; et la baleine grise choisissait des eaux côtières et de hauts-fonds ainsi que l'eau libre. En automne, la baleine boréale choisissait les eaux intérieures du plateau continental, où se trouvait une faible concentration de glace; la baleine blanche choisissait les eaux à l'extérieur du plateau et sur la pente, ainsi qu'une glace allant de modérée à épaisse; et la baleine grise choisissait des habitats côtiers et de hauts-fonds ou des fossés à faible concentration de glace et à eau libre. Les différences d'habitat entre les espèces étaient importantes durant les deux saisons (ANOVA F > 28, p < 0,00001). D'une saison à une autre, les habitats différaient sensiblement quant à la profondeur et à la couverture de glace pour la baleine boréale (p < 0,00002), mais pas pour la baleine grise (p > 0,35). La profondeur de l'habitat pour la baleine blanche variait sensiblement d'une saison à une autre (p <0,00002), mais pas la couverture de glace (p < 0,08).

Dynamic Mechanical Properties of Epoxy-Poplar Composite Materials

The effects of impregnation on the dynamic mechanical properties of yellow-poplar (Liriodendron tulipifera L.) sapwood have been investigated for stoichiometric and nonstoichiometric mixtures of a diglycidyl ether of bisphenol-A based epoxy resin and meta-phenylenediamine. For the temperature range from 0 to 100 C, the measured values for the dynamic modulus of these wood-polymer composites exceeded the predicted values based upon the rule of mixtures. In contrast, the actual results for the internal friction values were significantly lower than those predicted by the rule of mixtures. Modification of this equation for strain energy sharing effects resulted in much improved estimates for the internal friction values, however

Impregnation of Wood With a High Viscosity Epoxy Resin

A method is described for impregnating small wood specimens with a high viscosity epoxy resin, without the use of a diluent to reduce viscosity. The method relies upon the strong temperature-dependence of viscosity, in conjunction with a curing agent that does not polymerize rapidly at high temperatures. Some preliminary results for a variety of Northeastern species are presented

Effect of Epoxy Impregnation on the Moe and Mor of Intact and Failed Yellow-Poplar (Liriodendron Tulipifera L.) Sapwood Beams

The effects of epoxy impregnation on the MOR and MOE of intact and failed yellow-poplar (Liriodendron tulipifera L.) clear sapwood beams were investigated. Both impregnated and unimpregnated specimens were partially failed in bending, impregnated to stabilize the cracks, and retested. The presence of induced cracks had a significant effect on the MOR of the material after impregnation or reimpregnation, but not on the MOE. Both the MOR and MOE of the failed, then impregnated material exceeded the values for unimpregnated yellow-poplar

Multivariate models from RNA-Seq SNVs yield candidate molecular targets for biomarker discovery: SNV-DA

Breast: up and downstream SNVs model. (CSV 22.1 kb