Compositional data-driven alternatives to single geochemical component maps

Conventional practice in Regional Geochemistry includes as a final step of any geochemical campaign the generation of a series of maps, to show the spatial distribution of each of the components considered. Such maps, though necessary, do not comply with the compositional, relative nature of the data, which unfortunately make any conclusion based on them sensitive
to spurious correlation problems. This is one of the reasons why these maps are never interpreted isolated. This contribution aims at gathering a series of statistical methods to produce individual maps of multiplicative combinations of components (logcontrasts), much in the flavor of equilibrium constants, which are designed on purpose to capture certain aspects of the data.
We distinguish between supervised and unsupervised methods, where the first require an external, non-compositional variable (besides the compositional geochemical information) available in an analogous training set. This external variable can be a quantity (soil density, collocated magnetics, collocated ratio of Th/U spectral gamma counts, proportion of clay particle fraction, etc) or a category (rock type, land use type, etc). In the supervised methods, a regression-like model between the external variable and the geochemical composition is derived in the training set, and then this model is mapped on the whole region. This case is illustrated with the Tellus dataset, covering Northern Ireland at a density of 1 soil sample per 2 square km, where we map the presence of blanket peat and the underlying geology. The unsupervised methods considered include principal components and principal balances
(Pawlowsky-Glahn et al., CoDaWork2013), i.e. logcontrasts of the data that are devised to capture very large variability or else be quasi-constant. Using the Tellus dataset again, it is found that geological features are highlighted by the quasi-constant ratios Hf/Nb and their ratio against SiO2; Rb/K2O and Zr/Na2O and the balance between these two groups of two variables; the balance of Al2O3 and TiO2 vs. MgO; or the balance of Cr, Ni and Co vs. V and Fe2O3. The largest variability appears to be related to the presence/absence of peat.

Schizophrenia risk from complex variation of complement component 4

Schizophrenia is a heritable brain illness with unknown pathogenic mechanisms. Schizophrenia's strongest genetic association at a population level involves variation in the major histocompatibility complex (MHC) locus, but the genes and molecular mechanisms accounting for this have been challenging to identify. Here we show that this association arises in part from many structurally diverse alleles of the complement component 4 (C4) genes. We found that these alleles generated widely varying levels of C4A and C4B expression in the brain, with each common C4 allele associating with schizophrenia in proportion to its tendency to generate greater expression of C4A. Human C4 protein localized to neuronal synapses, dendrites, axons, and cell bodies. In mice, C4 mediated synapse elimination during postnatal development. These results implicate excessive complement activity in the development of schizophrenia and may help explain the reduced numbers of synapses in the brains of individuals with schizophrenia.