Mineral Prospectivity Prediction from High-Dimensional Geoscientific Data Using a Similarity-Based Density Estimation Model

Assuming a study region in which each cell has associated with it an N-dimensional vector of values corresponding to N predictor variables, one means of predicting the potential of some cell to host mineralization is to estimate, on the basis of historical data, a probability density function that describes the distribution of vectors for cells known to contain deposits. This density estimate can then be employed to predict the mineralization likelihood of other cells in the study region. However, owing to the curse of dimensionality, estimating densities in high-dimensional input spaces is exceedingly difficult, and conventional statistical approaches often break down. This article describes an alternative approach to estimating densities. Inspired by recent work in the area of similarity-based learning, in which input takes the form of a matrix of pairwise similarities between training points, we show how the density of a set of mineralized training examples can be estimated from a graphical representation of those examples using the notion of eigenvector graph centrality. We also show how the likelihood for a test example can be estimated from these data without having to construct a new graph. Application of the technique to the prediction of gold deposits based on 16 predictor variables shows that its predictive performance far exceeds that of conventional density estimation methods, and is slightly better than the performance of a discriminative approach based on multilayer perceptron neural networks.     

Time-varying transformations for Hill–Clohessy–Wiltshire solutions in elliptic orbits

The relative motion of chief and deputy satellites in close proximity with orbits of arbitrary eccentricity can be approximated by linearized time-periodic equations of motion. The linear time-invariant Hill–Clohessy–Wiltshire equations are typically derived from these equations by assuming the chief satellite is in a circular orbit. Two Lyapunov–Floquet transformations and an integral-preserving transformation are here presented which relate the linearized time-varying equations of relative motion to the Hill–Clohessy–Wiltshire equations in a one-to-one manner through time-varying coordinate transformations. These transformations allow the Hill–Clohessy–Wiltshire equations to describe the linearized relative motion for elliptic chief satellites.     

Atom‐probe analyses of nanodiamonds from Allende

Atom‐probe tomography (APT) is currently the only analytical technique that, due to its spatial resolution and detection efficiency, has the potential to measure the carbon isotope ratios of individual nanodiamonds. We describe three different sample preparation protocols that we developed for the APT analysis of meteoritic nanodiamonds at sub‐nm resolution and present carbon isotope peak ratios of meteoritic and synthetic nanodiamonds. The results demonstrate an instrumental bias associated with APT that needs to be quantified and corrected to obtain accurate isotope ratios. After this correction is applied, this technique should allow determination of the distribution of ¹²C/¹³C ratios in individual diamond grains, solving the decades‐old question of the origin of meteoritic nanodiamonds: what fraction, if any, formed in the solar system and in presolar environments? Furthermore, APT could help us identify the stellar sources of any presolar nanodiamonds that are detected.     

Restriction of parent body heating by metal‐troilite melting: Thermal models for the ordinary chondrites

Ordinary chondrite meteorites contain silicates, Fe,Ni‐metal grains, and troilite (FeS). Conjoined metal‐troilite grains would be the first phase to melt during radiogenic heating in the parent body, if temperatures reached over approximately 910–960 °C (the Fe,Ni‐FeS eutectic). On the basis of two‐pyroxene thermometry of 13 ordinary chondrites, we argue that peak temperatures in some type 6 chondrites exceeded the Fe,Ni‐FeS eutectic and thus conjoined metal‐troilite grains would have begun to melt. Melting reactions consume energy, so thermal models were constructed to investigate the effect of melting on the thermal history of the H, L, and LL parent asteroids. We constrained the models by finding the proportions of conjoined metal‐troilite grains in ordinary chondrites using high‐resolution X‐ray computed tomography. The models show that metal‐troilite melting causes thermal buffering and inhibits the onset of silicate melting. Compared with models that ignore the effect of melting, our models predict longer cooling histories for the asteroids and accretion times that are earlier by 61, 124, or 113 kyr for the H, L, and LL asteroids, respectively. Because the Ni/Fe ratio of the metal and the bulk troilite/metal ratio is higher in L and LL chondrites than H chondrites, thermal buffering has the greatest effect in models for the L and LL chondrite parent bodies, and least effect for the H chondrite parent. Metal‐troilite melting is also relevant to models of primitive achondrite parent bodies, particularly those that underwent only low degrees of silicate partial melting. Thermal models can predict proportions of petrologic types formed within an asteroid, but are systematically different from the statistics of meteorite collections. A sampling bias is interpreted to explain these differences.     

REGIONAL TRENDS IN ELECTORAL SUPPORT IN BRITAIN, 1950–1983*

Analyses of the geography of British elections have typically stressed the continuity in patterns of party support. This paper challenges that conclusion. Employing an alternative method of analysis, it identifies significant regional trends in the Conservative and Labour vote between 1950 and 1983. Pro-Labour trends in Scotland and Northwest England are contrasted with secular changes favoring the Conservatives in non-metropolitan Southern England. These long-term trends have not been associated with growing regional polarization in party support. While the findings are specific to Britain, the method of assessing electoral change might be usefully applied to patterns in other countries.