Bunches of cones in the divisor class group -- A new combinatorial language for toric varieties

As an alternative to the description of a toric variety by a fan in the lattice of one parameter subgroups, we present a new language in terms of what we call bunches -- these are certain collections of cones in the vector space of rational divisor classes. The correspondence between these bunches and fans is based on classical Gale duality. The new combinatorial language allows a much more natural description of geometric phenomena around divisors of toric varieties than the usual method by fans does. For example, the numerically effective cone and the ample cone of a toric variety can be read off immediately from its bunch. Moreover, the language of bunches appears to be useful for classification problems.Comment: Minor changes, to appear in Int. Math. Res. No

Demushkin's Theorem in Codimension One

Demushkin's Theorem says that any two toric structures on an affine variety X are conjugate in the automorphism group of X. We provide the following extension: Let an (n-1)-dimensional torus T act effectively on an n-dimensional affine toric variety X. Then T is conjugate in the automorphism group of X to a subtorus of the big torus of X.Comment: 6 pages, to appear in Math.

Homogeneous coordinates for algebraic varieties

We associate to every divisorial (e.g. smooth) variety $X$ with only constant invertible global functions and finitely generated Picard group a $Pic(X)$-graded homogeneous coordinate ring. This generalizes the usual homogeneous coordinate ring of the projective space and constructions of Cox and Kajiwara for smooth and divisorial toric varieties. We show that the homogeneous coordinate ring defines in fact a fully faithful functor. For normal complex varieties $X$ with only constant global functions, we even obtain an equivalence of categories. Finally, the homogeneous coordinate ring of a locally factorial complete irreducible variety with free finitely generated Picard group turns out to be a Krull ring admitting unique factorization.Comment: 30 page

Real-Time Analysis of Correlations Between On-Body Sensor Nodes

The topology of a body sensor network has, until recently, often been overlooked; either because the layout of the network is deemed to be sufficiently static (”we always know well enough where sensors are”), we always know exactly where the nodes are or because the location of the sensor is not inherently required (”as long as the node stays where it is, we do not need its location, just its data”). We argue in this paper that, especially as the sensor nodes become more numerous and densely interconnected, an analysis on the correlations between the data streams can be valuable for a variety of purposes. Two systems illustrate how a mapping of the network’s sensor data to a topology of the sensor nodes’ correlations can be applied to reveal more about the physical structure of body sensor networks

Foliations modeling nonrational simplicial toric varieties

We establish a correspondence between simplicial fans, not necessarily rational, and certain foliated compact complex manifolds called LVMB-manifolds. In the rational case, Meersseman and Verjovsky have shown that the leaf space is the usual toric variety. We compute the basic Betti numbers of the foliation for shellable fans. When the fan is in particular polytopal, we prove that the basic cohomology of the foliation is generated in degree two. We give evidence that the rich interplay between convex and algebraic geometries embodied by toric varieties carries over to our nonrational construction. In fact, our approach unifies rational and nonrational cases.Comment: 24 pages, 4 figures, expository changes, references updated. Link to the journal http://j.mp/BatZaf; Int. Math. Res. Not. 2015 (Published online February 24, 2015

Determinants for Bullying Victimization among 11–16-Year-Olds in 15 Low- and Middle-Income Countries:\ud A Multi-Level Study

Bullying is an issue of public health importance among adolescents worldwide. The present study aimed at explaining differences in bullying rates among adolescents in 15 low- and middle-income countries using globally comparable indicators of social and economic well-being. Using data derived from the Global School-based Health Survey, we performed bivariate analyses to examine differences in bullying rates by country and by bullying type. We then constructed a multi-level model using four fixed variables (age, gender, hunger and truancy) at the individual level, random effects at the classroom and\ud school levels and four fixed variables at the country level (Gini coefficient, per capita Gross Domestic Project, homicide rate and pupil to teacher ratio). Bullying rates differed significantly by classroom, school and by country, with Egypt (34.2%) and Macedonia (3.6%) having the highest and lowest rates, respectively. Eleven-year-olds were the most likely of the studied age groups to report being bullied, as was being a male. Hunger and truancy were found to significantly predict higher rates of bullying. None of the explanatory variables at the country level remained in the final model. While self-reported bullying varied significantly between countries, the variance between classrooms better explained these differences. Our findings suggest that classroom settings should be considered when designing approaches aimed at bullying prevention.\u

Le tour du monde de Saint-Preux : Désillusion du visionnaire et saccage du romanesque dans La nouvelle Héloïse

Cette étude rappelle la dimension artificielle bien établie des récits littéraires de « voyages maritimes » et de « tempêtes subies en mer », qui suscitent distance ironique ou défiance sarcastique chez les auteurs de romans. Dès lors, Jean-Jacques Rousseau, auteur du vaste roman continental La nouvelle Héloïse, prend position dans une dispute connue lorsqu’il inscrit une relation de navigation de quatre ans à l’axe de symétrie de son texte. La dénonciation anticolonialiste se veut aussi un réquisitoire antiromanesque qui dénonce l’effet d’accréditation produit par le témoignage subjectif du voyageur (« j’ai vu… »). Un dialogue est suggéré entre la lettre de Saint-Preux et La promenade Vernet de Diderot qui rend compte d’un point de vue sceptique à propos de l’observation objective et prolonge la mise en cause de l’« autorité oculaire » dans une voie à la fois plus ludique et plus onirique.This study recalls the well-established artificial dimension of the literary account of “sea voyages” and “sea storms” that most often provoke ironic distance or sarcastic defiance in the novelist. That being the case, Jean-Jacques Rousseau, author of the continental novel La nouvelle Héloïse, is in effect taking a stand in an ongoing controversy when he makes a four-year long navigational account the symmetrical axis of his text. His anti-colonialist denunciation is meant, in addition, to be an indictment of the novel in that it criticizes the legitimizing effect on the reader of the traveller’s subjective witness (“I saw…”). The article presents a dialogue between Saint-Preux’s letter and Diderot’s La promenade Vernet. The latter adopts a sceptical point of view concerning objective observation and thus continues the calling into question of “ocular authority” in a style that is at once more playful and dreamlike