Social polarization: introducing distances between and within groups

The measurement of social polarization has received little attention from the literature. The only social polarization index that has been used to measure religious or ethnic polarization (the RQ index) has several shortcomings that are critically discussed in the paper. In particular, that index is not taking into account the existing distance between and within different groups. A couple of axiomatically characterized social polarization indices that overcome these limitations are presented. In the empirical section we show that the rankings of countries according to the levels of polarization change to a great extent when we replace the RQ index by the indices presented in this paper.

Ecologic correlations of selected food groups with disease incidence and mortality in Switzerland.

Background: There is little information regarding the impact of diet on disease incidence and mortality in Switzerland. We assessed ecologic correlations between food availability and disease.Methods: In this ecologic study for the period 1970-2009, food availability was measured using the food balance sheets of the Food and Agriculture Organization of the United Nations. Standardized mortality rates (SMRs) were obtained from the Swiss Federal Office of Statistics. Cancer incidence data were obtained from the World Health Organization Health For All database and the Vaud Cancer Registry. Associations between food availability and mortality/incidence were assessed at lags 0, 5, 10, and 15 years by multivariate regression adjusted for total caloric intake.Results: Alcoholic beverages and fruit availability were positively associated, and fish availability was inversely associated, with SMRs for cardiovascular diseases. Animal products, meat, and animal fats were positively associated with the SMR for ischemic heart disease only. For cancer, the results of analysis using SMRs and incidence rates were contradictory. Alcoholic beverages and fruits were positively associated with SMRs for all cancer but inversely associated with all-cancer incidence rates. Similar findings were obtained for all other foods except vegetables, which were weakly inversely associated with SMRs and incidence rates. Use of a 15-year lag reversed the associations with animal and vegetal products, weakened the association with alcohol and fruits, and strengthened the association with fish.Conclusions: Ecologic associations between food availability and disease vary considerably on the basis of whether mortality or incidence rates are used in the analysis. Great care is thus necessary when interpreting our results.

Musical actions of dihedral groups

The sequence of pitches which form a musical melody can be transposed or inverted. Since the 1970s, music theorists have modeled musical transposition and inversion in terms of an action of the dihedral group of order 24. More recently music theorists have found an intriguing second way that the dihedral group of order 24 acts on the set of major and minor triads. We illustrate both geometrically and algebraically how these two actions are dual. Both actions and their duality have been used to analyze works of music as diverse as Hindemith and the Beatles.

Conjugacy in Thompson's groups

We give a unified solution the conjugacy problem in Thompson’s groups F, V , and T using strand diagrams, and we analyze the complexity of the resulting algorithms.

Mather invariants in groups of piecewise-linear homeomorphisms

We describe the relation between two characterizations of conjugacy in groups of piecewise-linear homeomorphisms, discovered by Brin and Squier in [2] and Kassabov and Matucci in [5]. Thanks to the interplay between the techniques, we produce a simplified point of view of conjugacy that allows ua to easily recover centralizers and lends itself to generalization.

Identification of particular groups of microRNAs that positively or negatively impact on beta cell function in obese models of type 2 diabetes.

AIMS/HYPOTHESIS: MicroRNAs are key regulators of gene expression involved in health and disease. The goal of our study was to investigate the global changes in beta cell microRNA expression occurring in two models of obesity-associated type 2 diabetes and to assess their potential contribution to the development of the disease. METHODS: MicroRNA profiling of pancreatic islets isolated from prediabetic and diabetic db/db mice and from mice fed a high-fat diet was performed by microarray. The functional impact of the changes in microRNA expression was assessed by reproducing them in vitro in primary rat and human beta cells. RESULTS: MicroRNAs differentially expressed in both models of obesity-associated type 2 diabetes fall into two distinct categories. A group including miR-132, miR-184 and miR-338-3p displays expression changes occurring long before the onset of diabetes. Functional studies indicate that these expression changes have positive effects on beta cell activities and mass. In contrast, modifications in the levels of miR-34a, miR-146a, miR-199a-3p, miR-203, miR-210 and miR-383 primarily occur in diabetic mice and result in increased beta cell apoptosis. These results indicate that obesity and insulin resistance trigger adaptations in the levels of particular microRNAs to allow sustained beta cell function, and that additional microRNA deregulation negatively impacting on insulin-secreting cells may cause beta cell demise and diabetes manifestation. CONCLUSIONS/INTERPRETATION: We propose that maintenance of blood glucose homeostasis or progression toward glucose intolerance and type 2 diabetes may be determined by the balance between expression changes of particular microRNAs.

The simultaneous conjugacy problem in groups of piecewise linear functions

Guba and Sapir asked, in their joint paper [8], if the simultaneous conjugacy problem was solvable in Diagram Groups or, at least, for Thompson's group F. We give an elementary proof for the solution of the latter question. This relies purely on the description of F as the group of piecewise linear orientation-preserving homeomorphisms of the unit. The techniques we develop allow us also to solve the ordinary conjugacy problem as well, and we can compute roots and centralizers. Moreover, these techniques can be generalized to solve the same questions in larger groups of piecewise-linear homeomorphisms.

Income stratification and the measurement of interdistributional inequality between multiple groups

This paper proposes a new class of stratification indices that measure interdistributional inequality between multiple groups. The class is based on a conceptualisation of stratification as a process that results in a hierarchical ordering of groups and therefore seeks to capture not only the extent to which groups form well-defined strata in the income distribution but also the scale of the resultant differences in income standards between them, where these two factors play the same role as identification and alienation respectively in the measurement of polarisation. The properties of the class as a whole are investigated as well as those of selected members of it: zeroth and first power indices may be interpreted as measuring the overall incidence and depth of stratification respectively, while higher power indices members are directly sensitive to the severity of stratification between groups. An illustrative application provides an empirical analysis of global income stratification by regions in 1993.

On uniform conjugators in torsion-free hyperbolic groups

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Vitellogenesis in insects and other groups: a review

The eggs from oviparous organisms contain large amounts of vitellus, or yolk, wich are utilized by the growing embryo. Vitellogenesis is the process of vitellus accumulation and involves massive heterosynthetic synthesis of the protein vitellogenin (Vg) and its deposition in the oocyte. This work summarizes data on Vg structure, synthesis, uptake by oocytes and its fate during embryogenesis. The hormonal control of vitellogenesis and its tissue, sex and temporal regulation are also discussed. Where it is available, data on structure and expression of Vg-coding genes are reviewed. Insect vitellogenesis is priorized although other oviparous animal groups outside insects are also treated.

Structure theorems for subgroups of homeomorphism groups

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Bounding the residual finiteness of free groups

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Statistical properties of subgroups of free groups

The usual way to investigate the statistical properties of finitely generated subgroups of free groups, and of finite presentations of groups, is based on the so-called word-based distribution: subgroups are generated (finite presentations are determined) by randomly chosen k-tuples of reduced words, whose maximal length is allowed to tend to infinity. In this paper we adopt a different, though equally natural point of view: we investigate the statistical properties of the same objects, but with respect to the so-called graph-based distribution, recently introduced by Bassino, Nicaud and Weil. Here, subgroups (and finite presentations) are determined by randomly chosen Stallings graphs whose number of vertices tends to infinity. Our results show that these two distributions behave quite differently from each other, shedding a new light on which properties of finitely generated subgroups can be considered frequent or rare. For example, we show that malnormal subgroups of a free group are negligible in the raph-based distribution, while they are exponentially generic in the word-based distribution. Quite surprisingly, a random finite presentation generically presents the trivial group in this new distribution, while in the classical one it is known to generically present an infinite hyperbolic group.