Mathematics and Morphogenesis of the City: A Geometrical Approach

Cities are living organisms. They are out of equilibrium, open systems that never stop developing and sometimes die. The local geography can be compared to a shell constraining its development. In brief, a city's current layout is a step in a running morphogenesis process. Thus cities display a huge diversity of shapes and none of traditional models from random graphs, complex networks theory or stochastic geometry takes into account geometrical, functional and dynamical aspects of a city in the same framework. We present here a global mathematical model dedicated to cities that permits describing, manipulating and explaining cities' overall shape and layout of their street systems. This street-based framework conciliates the topological and geometrical sides of the problem. From the static analysis of several French towns (topology of first and second order, anisotropy, streets scaling) we make the hypothesis that the development of a city follows a logic of division / extension of space. We propose a dynamical model that mimics this logic and which from simple general rules and a few parameters succeeds in generating a large diversity of cities and in reproducing the general features the static analysis has pointed out.Comment: 13 pages, 13 figure

Superposition of Planar Voronoi Tessellations

We study the tessellation defined as the intersection of two independent planar Poisson-Voronoi tessellations and derive the means of its main geometrical characteristics. For this intersection tessellation, we distinguis- h between six types of cells depending on whether they contain the nuclei of the two initial tessellations or not. The intensity and the mean area of each type of cell are computed either in closed form or via asymptotic expansions. The model can be used to represent the local zones of two competing telecommunication operators. Then the interconnection of two subscribers induces a specific cost within each type of cell of the intersecti- on tessellation associated with the two systems of local zones

Relations between Au / Sn-W mineralizations and late hercynian granite: Preliminary results from the Schistose Domain of Galicia-Trás-os-Montes Zone, Spain

International audienceAu and W-Sn mineralization of the Schistose Domain of Galicia-Trás-os-Montes are spatially related to late hercynian granites. The Bruès (Au) and the Mina Soriana W-(Sn) deposits are studied. Both show some similarities and are assumed to form in the same tectonic and metamorphic context, on top of the granites. The role of the granite as a source for mineralizing fluids and rheological control for vein emplacement is re-adressed and discussed

Meta-analyses of genome-wide association studies for postpartum depression

Objective: Postpartum depression (PPD) is a common subtype of major depressive disorder (MDD) that is more heritable, yet is understudied in psychiatric genetics. The authors conducted meta-analyses of genome-wide association studies (GWASs) to investigate the genetic architecture of PPD. Method: Meta-analyses were conducted on 18 cohorts of European ancestry (17,339 PPD cases and 53,426 controls), one cohort of East Asian ancestry (975 cases and 3,780 controls), and one cohort of African ancestry (456 cases and 1,255 controls), totaling 18,770 PPD cases and 58,461 controls. Post-GWAS analyses included 1) single-nucleotide polymorphism (SNP)–based heritability (), 2) genetic correlations between PPD and other phenotypes, and 3) enrichment of the PPD GWAS findings in 27 human tissues and 265 cell types from the mouse central and peripheral nervous system. Results: No SNP achieved genome-wide significance in the European or the trans-ancestry meta-analyses. The of PPD was 0.14 (SE=0.02). Significant genetic correlations were estimated for PPD with MDD, bipolar disorder, anxiety disorders, posttraumatic stress disorder, insomnia, age at menarche, and polycystic ovary syndrome. Cell-type enrichment analyses implicate inhibitory neurons in the thalamus and cholinergic neurons within septal nuclei of the hypothalamus, a pattern that differs from MDD. Conclusions: While more samples are needed to reach genome-wide levels of significance, the results presented confirm PPD as a polygenic and heritable phenotype. There is also evidence that despite a high correlation with MDD, PPD may have unique genetic components. Cell enrichment results suggest GABAergic neurons, which converge on a common mechanism with the only medication approved by the U.S. Food and Drug Administration for PPD (brexanolone)

Distribution of In and other rare metals in cassiterite and associated minerals in Sn ± W ore deposits of the western Variscan Belt

International audienceWe present data available on rare metal and indium distributions in cassiterite and associated minerals from thirteen Sn ± W granite-related ore deposits in the western Variscan Belt (Massif Central and Armorican Massif, France; Galicia, Spain; and SW England). Cassiterite and associated minerals including sulfides and titanium oxides were analysed using an electron probe micro-analyzer (EPMA). Significant indium contents were only measured in cassiterite from hydrothermal vein-type mineralizations associated with peraluminous granites of Montbelleux, Abbaretz (French Armorican Massif) and Marcofán (Galicia); they correlate with the highest Nb, Ta and Fe substitutions. Two coupled substitutions are proposed: (1) 2 (Sn4+, Ti4+)↔(Fe3+, In3+) + (Nb5+, Ta5+) and (2) Fe2+ + (Nb, Ta)5+↔In3++(Ti, Sn)4+ depending on Fe valence state. Sulfides (stannite, chalcopyrite, pyrite, arsenopyrite and sphalerite) and rutile associated with cassiterite contain significant amounts of indium, even when cassiterite is indium-free, suggesting preferential partitioning into the sulfides