Quantized reduction as a tensor product

Symplectic reduction is reinterpreted as the composition of arrows in the category of integrable Poisson manifolds, whose arrows are isomorphism classes of dual pairs, with symplectic groupoids as units. Morita equivalence of Poisson manifolds amounts to isomorphism of objects in this category. This description paves the way for the quantization of the classical reduction procedure, which is based on the formal analogy between dual pairs of Poisson manifolds and Hilbert bimodules over C*-algebras, as well as with correspondences between von Neumann algebras. Further analogies are drawn with categories of groupoids (of algebraic, measured, Lie, and symplectic type). In all cases, the arrows are isomorphism classes of appropriate bimodules, and their composition may be seen as a tensor product. Hence in suitable categories reduction is simply composition of arrows, and Morita equivalence is isomorphism of objects.Comment: 44 pages, categorical interpretation adde

A high resolution atlas of gene expression in the domestic sheep (Ovis aries)

Sheep are a key source of meat, milk and fibre for the global livestock sector, and an important biomedical model. Global analysis of gene expression across multiple tissues has aided genome annotation and supported functional annotation of mammalian genes. We present a large-scale RNA-Seq dataset representing all the major organ systems from adult sheep and from several juvenile, neonatal and prenatal developmental time points. The Ovis aries reference genome (Oar v3.1) includes 27,504 genes (20,921 protein coding), of which 25,350 (19,921 protein coding) had detectable expression in at least one tissue in the sheep gene expression atlas dataset. Network-based cluster analysis of this dataset grouped genes according to their expression pattern. The principle of 'guilt by association' was used to infer the function of uncharacterised genes from their co-expression with genes of known function. We describe the overall transcriptional signatures present in the sheep gene expression atlas and assign those signatures, where possible, to specific cell populations or pathways. The findings are related to innate immunity by focusing on clusters with an immune signature, and to the advantages of cross-breeding by examining the patterns of genes exhibiting the greatest expression differences between purebred and crossbred animals. This high-resolution gene expression atlas for sheep is, to our knowledge, the largest transcriptomic dataset from any livestock species to date. It provides a resource to improve the annotation of the current reference genome for sheep, presenting a model transcriptome for ruminants and insight into gene, cell and tissue function at multiple developmental stages

Studying dynamic neural interactions with MEG

Interactions between functionally specialized brain regions are crucial for normal brain function. Magnetoencephalography (MEG) is suited to capture these interactions because it provides whole head measurements of brain activity with temporal resolution in the millisecond range. Many different measures of connectivity exist and in order to take the connectivity analysis results at face value one should be aware of the strengths and weaknesses of these measures. Next to this, an important challenge in MEG connectivity analysis lies in the fact that more than one sensor picks up the activity of any underlying source. This field spread severely limits the utility of connectivity measures computed directly between sensor recordings. As a consequence, neuronal interactions should be ideally studied on the level of the reconstructed sources. MEG is well suited for this purpose, since its signal properties and high spatial sampling allows for relatively accurate unmixing of the sensor recordings. This chapter provides some necessary background on connectivity analysis in general, and proceeds by describing the challenges that are associated with the analysis of MEG-based connectivity at the sensor level. Source level approaches are described and some recent advances with respect to MEG-based connectivity during the resting state and graph theoretic approaches are described