Network Geometry and Complexity

(28 pages, 11 figures)Higher order networks are able to characterize data as different as functional brain networks, protein interaction networks and social networks beyond the framework of pairwise interactions. Most notably higher order networks include simplicial complexes formed not only by nodes and links but also by triangles, tetrahedra, etc. More in general, higher-order networks can be cell-complexes formed by gluing convex polytopes along their faces. Interestingly, higher order networks have a natural geometric interpretation and therefore constitute a natural way to explore the discrete network geometry of complex networks. Here we investigate the rich interplay between emergent network geometry of higher order networks and their complexity in the framework of a non-equilibrium model called Network Geometry with Flavor. This model, originally proposed for capturing the evolution of simplicial complexes, is here extended to cell-complexes formed by subsequently gluing different copies of an arbitrary regular polytope. We reveal the interplay between complexity and geometry of the higher order networks generated by the model by studying the emergent community structure and the degree distribution as a function of the regular polytope forming its building blocks. Additionally, we discuss the underlying hyperbolic nature of the emergent geometry and we relate the spectral dimension of the higher-order network to the dimension and nature of its building blocks

Association study in three different populations between the GPR88 gene and major psychoses

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Association study in three different populations between the GPR88 gene and major psychoses

GPR88, coding for a G protein-coupled orphan receptor that is highly represented in the striatum, is a strong functional candidate gene for neuropsychiatric disorders and is located at 1p22-p21, a chromosomal region that we have previously linked to bipolar disorder (BD) in the Sardinian population. In order to ascertain the relevance of GPR88 as a risk factor for psychiatric diseases, we performed a genetic association analysis between GPR88 and BD in a sample of triads (patient and both parents) recruited in the Sardinian and the Palestinian population as well as between GPR88 and schizophrenia (SZ) in triads from the Xhosa population in South Africa. We found a positive association between GPR88 and BD in the Sardinian and Palestinian triads. Moreover, we found a positive association between GPR88 and SZ in triads from the Xhosa population in South Africa. When these results were corrected for multiple testing, the association between GPR88 and BD was maintained in the Palestinian population. Thus, these results suggest that GPR88 deserves consideration as a candidate gene for psychiatric diseases and requires to be further investigated in other populations