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

Application of Photogrammetry in Biomedical Science

Peer reviewedPostprin

The first transcriptome of Italian wall lizard, a new tool to infer about the Island Syndrome

Some insular lizards show a high degree of differentiation from their conspecific mainland populations, like Licosa island lizards, which are described as affected by Reversed Island Syndrome (RIS). In previous works, we demonstrated that some traits of RIS, as melanization, depend on a differential expression of gene encoding melanocortin receptors. To better understand the basis of syndrome, and providing raw data for future investigations, we generate the first de novo transcriptome of the Italian wall lizard. Comparing mainland and island transcriptomes, we link differences in life-traits to differential gene expression. Our results, taking together testis and brain sequences, generated 275,310 and 269,885 transcripts, 18,434 and 21,606 proteins in Gene Ontology annotation, for mainland and island respectively. Variant calling analysis identified about the same number of SNPs in island and mainland population. Instead, through a differential gene expression analysis we found some putative genes involved in syndrome more expressed in insular samples like Major Histocompatibility Complex class I, Immunoglobulins, Melanocortin 4 receptor, Neuropeptide Y and Proliferating Cell Nuclear Antigen

Biodiversity only makes sense in the light of evolution

The article discusses the significant role of biodiversity in the evolution. Topics discussed include importance of applying evolutionary principles in conservation and human well-being, fundamental relevance of evolution in the production, maintenance, and future of biodiversity and biodiversity arises from the approach that treats groups of taxa with similar traits as a significant functional unit

Phylogenetic approaches reveal biodiversity threats under climate change

Predicting the consequences of climate change for biodiversity is critical to conservation efforts(1-3). Extensive range losses have been predicted for thousands of individual species(4), but less is known about how climate change might impact whole clades(1) and landscape-scale patterns of biodiversity(5). Here, we show that climate change scenarios imply significant changes in phylogenetic diversity and phylogenetic endemism at a continental scale in Australia using the hyper-diverse clade of eucalypts. We predict that within the next 60 years the vast majority of species distributions (91%) across Australia will shrink in size (on average by 51%) and shift south on the basis of projected suitable climatic space. Geographic areas currently with high phylogenetic diversity and endemism are predicted to change substantially in future climate scenarios. Approximately 90% of the current areas with concentrations of palaeo-endemism(6) (that is, places with old evolutionary diversity) are predicted to disappear or shift their location. These findings show that climate change threatens whole clades of the phylogenetic tree, and that the outlined approach can be used to forecast areas of biodiversity losses and continental-scale impacts of climate change