The Precambrian Villa Mónica Formation clay was analyzed using petrographic and scanning electron microscopy, X-ray diffraction and chemical analysis, with the aim of characterizing the Ti-bearing phases present and determining their possible origin and/or source. Two Ti-bearing minerals were found to be present, rutile and anatase. The crystals are needles between 5 and 15 µm in size, with no evidence of abrasion or corrosion. They are commonly found in association with the (001) faces of illite flakes or in the pores between the flakes. Their disposition is similar in the three quarries studied. No zonation or differential settling due to differences in specific gravity was observed. In addition, chemical analyses indicated a positive correlation between TiO2 and K2O suggesting that both oxides behave similarly after the deposition of the sediment. The TiO2 content in the bulk fraction ranges from 0.8 to 1.98 wt.%, values that are similar to those exhibited in other clay deposits from different ages and geneses.

All observations are consistent with an in situ origin of these Ti-bearing phases during post-depositional processes that included recrystallization of existing minerals and crystallization of new phases. The original detrital minerals such as biotite, ilmenite as well as detrital illite, were the primary sources of the TiO2 and of the Fe oxides that coat the clay. Understanding the origin and the reaction mechanisms involved during the post-depositional alteration of the Villa Mónica Formation suggests that the Ti-bearing phases in different sediment types were formed by similar mechanisms involving redox processes at low to medium temperatures, even in Precambrian sediments where the presence of rutile could lead to an incorrect assumption of high temperatures involved.

We tackle the problem of simulating seat- and vote-shares for a party system of a given size. We show how these shares can be generated using unordered and ordered Dirichlet distributions. We show that a distribution with a mean vector given by the rule described in Taagepera and Allik (2006, Electoral Studies 25, 696–713) fits real-world data almost as well as a saturated model where there is a parameter for each rank/system size combination.

Variational Bayesian inference is an important machine learning tool that finds application from statistics to robotics. The goal is to find an approximate probability density function (PDF) from a chosen family that is in some sense “closest” to the full Bayesian posterior. Closeness is typically defined through the selection of an appropriate loss functional such as the Kullback-Leibler (KL) divergence. In this paper, we explore a new formulation of variational inference by exploiting the fact that (most) PDFs are members of a Bayesian Hilbert space under careful definitions of vector addition, scalar multiplication, and an inner product. We show that, under the right conditions, variational inference based on KL divergence can amount to iterative projection, in the Euclidean sense, of the Bayesian posterior onto a subspace corresponding to the selected approximation family. We work through the details of this general framework for the specific case of the Gaussian approximation family and show the equivalence to another Gaussian variational inference approach. We furthermore discuss the implications for systems that exhibit sparsity, which is handled naturally in Bayesian space, and give an example of a high-dimensional robotic state estimation problem that can be handled as a result. We provide some preliminary examples of how the approach could be applied to non-Gaussian inference and discuss the limitations of the approach in detail to encourage follow-on work along these lines.

Using data from 20 years of Salmonella foodborne outbreaks, this study investigates significant trends in the proportion of outbreaks associated with 12 broad commodity groups. Outbreak counts are demonstrated to have a stronger trend signal than outbreak illness counts. The number of outbreaks with an identified food vehicle increased significantly between 1998 and 2000. This was followed by a 10-year period when the number of outbreaks decreased. The number of outbreaks increased significantly between 2010 and 2014 and then remained unchanged for the remainder of the study period. During the period of 1998 through 2017, the proportion of outbreaks for three commodities groups, consisting of eggs, pork and seeded vegetables, changed significantly. No significant changes were observed in the remaining nine commodity groups. Simple approximations are derived to highlight the effect of dependencies between outbreak proportions and a consumption analysis for meat and poultry is used to enhance the limited interpretability of the changes in these proportions. Given commodity-specific approaches to verifying food safety and promoting pathogen reduction, regulatory agencies benefit from analyses that elucidate illness trends attributable to the products under their jurisdiction. Results from this trend analysis can be used to inform the development and assessment of new pathogen reduction programmes in the United States.

When evaluating the impact of macronutrient intakes on health outcomes, researchers in nutritional epidemiology are mostly interested in two types of information: the relative importance of the individual macronutrients and the absolute effect of total energy intake. However, the usual substitution models do not allow these separate effects to be disentangled. Dietary data are typical examples of compositional data, which convey relative information and are, therefore, meaningfully expressed in the form of ratios. Various formulations of log-ratios have been proposed as a means of analysing compositional data, and their interrelationships when they are used as predictors in regression models have been previously reported. This note describes the application of distinct log-ratio transformations to the composition of dietary macronutrients and discusses the interpretative implications of using them as explanatory variables in regression models together with a term for the total composition (total energy intake). It also provides examples that consider serum glucose levels as the health outcome and are based on data coming from an Italian population-based study. The log-ratio transformation of dietary data has both numerical and conceptual advantages, and overcomes the drawbacks of traditional substitution models.

Because the American states operate under balanced budget requirements, increases in spending in one area typically entail equal and opposite budget cuts in other programs. The literature analysing the correlates of government spending by policy area has mostly ignored these trade-offs inherent to policymaking, failing to address one of the most politically interesting and important dimensions of fiscal policy. Borrowing from the statistical literature on compositional data, we present more appropriate and efficient methods that explicitly incorporate the budget constraint into models of spending by budget category. We apply these methods to eight categories of spending from the American states over the years 1984–2009 to reveal winners and losers in the scramble for government spending. Our findings show that partisan governments finance their distinct priorities by raiding spending items that the opposition prefers, while different political institutions, economic conditions and state demographics impose different trade-offs across the budget.

The [MnO|SiO2,Al2O3,FeO,MgO] balanced ratio (i.e. the isometric log-ratio of the MnO concentration relative to the concentration of SiO2, Al2O3, FeO and MgO) of chlorite and of whole-rock composition is an effective discriminant between Mesozoic stratigraphic formations in the Magallanes Basin (Chile). The MnO content in chlorite is only controlled by the host rock chemistry and is dependent on the geological environment. The MnO content in chlorite remains unchanged at low-grade metamorphic conditions. Single-grain chlorite analysis (n = 1042, electron microprobe) and whole-rock analysis (n = 40, X-ray fluorescence) were used to discriminate stratigraphic formations and to decipher differences in the depositional environment in the Magallanes Basin. The samples are from one Upper Jurassic and three Cretaceous sedimentary units that were affected either by low-grade regional metamorphism or by Miocene contact metamorphism. The highest [MnO|SiO2,Al2O3,FeO,MgO] values are recorded in the upper Zapata Formation. The Punta Barrosa, Cerro Toro and Tobífera Formations show slightly lower [MnO|SiO2,Al2O3,FeO,MgO] values. Elevated [MnO|SiO2,Al2O3,FeO,MgO] values at the transition between Zapata and Punta Barrosa Formations record an oxygenated shallow marine environment that can be linked to the closure of the Rocas Verdes Basin and the onset of fold-and-thrust belt formation. Decreasing [MnO|SiO2,Al2O3,FeO,MgO] values from the Punta Barrosa towards the Cerro Toro Formation indicate gradually increasing water depths during the Upper Cretaceous that correlate well with the global sea level.

Intermediate levels of the Larga-Fatţa Báii field, Metaliferi Mts., Romania, are host to epithermal vein mineralization, small skarn-like bodies and ‘geode’-like replacement ores, that together form a complex hydrothermal system rooted in the subjacent andesite stock. Silver-Pb-Bi sulphosalts, some with Sb and/or Se, are intimately associated with hessite and a range of Bi-tellurides with Bi/(Te+S+Se) ≤1 (tetradymite, tellurobismuthite, tsumoite, Pb-free rucklidgeite) within all these ore types. Lillianite homologues, both ordered 4L and 7L derivatives (lillianite, gustavite), and disordered varieties are the most abundant sulphosalts, with subordinate bismuthinite derivatives (aikinite, krupkaite, bismuthinite). An exceptionally Ag-rich lillianite homologue, intimately intergrown with tetradymite and hessite, is identified as treasureite on the basis of chemical composition. Porphyry-style mineralization from 600 m beneath the studied level contains rucklidgeite as the single stable Bi-telluride. The trace mineralogy of the system is suggestive of a hydrothermal system strongly zoned with respect to fTe2 and, to a lesser extent, also fS2. Mineralogical and textural evidence suggests that initial crystallization took place at temperatures in excess of 400°C. The association of gold with Bi-minerals is linked to the role of Bimelt as a scavenger for gold, and deposition within ‘droplets’ simultaneous with the formation of arsenopyrite from löllingite + pyrrhotite. Both Bi-tellurosulphides and sulphosalts are commonly non-stoichiometric, a fact that can be correlated with order-disorder in both series. When widely distributed, as in the Larga system, trace amounts of Bi-minerals (sulphosalts, tellurides/tellurosulphides) have considerable, untapped potential as tracers of the physical-chemical character of an evolving hydrothermal system.

In a real n-1 dimensional affine space E, consider a tetrahedron T0, i.e. the convex hull of n points α1, α2, …, αn of E. Choose n independent points β1, β2, …, βn randomly and uniformly in T0, thus obtaining a new tetrahedron T1 contained in T0. Repeat the operation with T1 instead of T0, obtaining T2, and so on. The sequence of the Tk shrinks to a point Y of T0 and this note computes the distribution of the barycentric coordinates of Y with respect to (α1, α2, …, αn) (Corollary 2.3). We also obtain the explicit distribution of Y in more general cases. The technique used is to reduce the problem to the study of a random walk on the semigroup of stochastic (n,n) matrices, and this note is a geometrical application of a former result of Chamayou and Letac (1994).