Unbiased Linear Property Estimation For Spheres From Sections Exhibiting Overprojection And Truncation

In the biological sciences, stereological techniques are frequently used to infer changes in structural parameters (volume fraction, for example) between samples from different populations or subject to differing treatment regimes. Non-homogeneity of these parameters is virtually guaranteed, both between experimental animals and within the organ under consideration. A two-stage strategy is then desirable, the first stage involving unbiased estimation of the required parameter, separately for each experimental unit, the latter being defined as a subset of the organ for which homogeneity can reasonably be assumed. In the second stage, these point estimates are used as data inputs to a hierarchical analysis of variance, to distinguish treatment effects from variability between animals, for example. Techniques are therefore required for unbiased estimation of parameters from potentially small numbers of sample profiles. This paper derives unbiased estimates of linear properties in one special case—the sampling of spherical particles by transmission microscopy, when the section thickness is not negligible and the resulting circular profiles are subject to lower truncation. The derivation uses the general integral equation formulation of Nicholson (1970); the resulting formulae are simplified, algebraically, and their efficient computation discussed. Bias arising from variability in slice thickness is shown to be negligible in typical cases. The strategy is illustrated for data examining the effects, on the secondary lysosomes in the digestive cells, of exposure of the common mussel to hydrocarbons. Prolonged exposure, at 30 μg 1−1 total oil-derived hydrocarbons, is seen to increase the average volume of a lysosome, and the volume fraction that lysosomes occupy, but to reduce their number.

Thermal front variability along the North Atlantic Current observed using satellite microwave and infrared data

Thermal fronts detected using multiple satellite sensors have been integrated to provide new information on the spatial and seasonal distribution of oceanic fronts in the North Atlantic. The branching of the North Atlantic Current (NAC) as it encounters the Mid-Atlantic Ridge (MAR) is reflected in surface thermal fronts, which preferentially occur at the Charlie Gibbs Fracture Zone (CGFZ) and several smaller fracture zones. North of the CGFZ there are few thermal fronts, contrasting with the region to the south, where there are frequent surface thermal fronts that are persistent seasonally and interannually. The alignment of the fronts confirms that the shallower Reykjanes Ridge north of the CGFZ is more of a barrier to water movements than the ridge to the south. Comparison of front distributions with satellite altimetry data indicates that the MAR influence on deep ocean currents is also frequently exhibited in surface temperature. The improved spatial and temporal resolution of the front analysis has revealed consistent seasonality in the branching patterns. These results contribute to our understanding of the variability of the NAC, and the techniques for visualising oceanic fronts can be applied in other regions to reveal details of surface currents that cannot be resolved using satellite altimetry or in situ measurements.