Minimal lenght elements of Thompson's groups F(p)

We describe a method for determining the minimal length of elements in the generalized Thompson's groups F(p). We compute the length of an element by constructing a tree pair diagram for the element, classifying the nodes of the tree and summing associated weights from the pairs of node classifications. We use this method to effectively find minimal length representatives of an element.

Parabolic and quasiparabolic subgroups of free partially commutative groups

Let Γ be a finite graph and G be the corresponding free partially commutative group. In this paper we study subgroups generated by vertices of the graph Γ, which we call canonical parabolic subgroups. A natural extension of the definition leads to canonical quasiparabolic subgroups. It is shown that the centralisers of subsets of G are the conjugates of canonical quasiparabolic centralisers satisfying certain graph theoretic conditions.

Elements of algebraic geometry and the positive theory of partially commutative groups

The first main result of the paper is a criterion for a partially commutative group G to be a domain. It allows us to reduce the study of algebraic sets over G to the study of irreducible algebraic sets, and reduce the elementary theory of G (of a coordinate group over G) to the elementary theories of the direct factors of G (to the elementary theory of coordinate groups of irreducible algebraic sets). Then we establish normal forms for quantifier-free formulas over a non-abelian directly indecomposable partially commutative group H. Analogously to the case of free groups, we introduce the notion of a generalised equation and prove that the positive theory of H has quantifier elimination and that arbitrary first-order formulas lift from H to H * F, where F is a free group of finite rank. As a consequence, the positive theory of an arbitrary partially commutative group is decidable.

Metric properties of the braided Thompson's groups

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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.

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.

Structure theorems for subgroups of homeomorphism groups

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Bounding the residual finiteness of free groups

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Clinical follow-up of women infected with human papillomavirus-16, either alone or with other human papillomavirus types: identification of different risk groups.

OBJECTIVES: Evaluation of the clinical impact of multiple infections of the cervix by human papillomavirus, including human papillomavirus-16, compared with single human papillomavirus-16 infection. STUDY DESIGN: One hundred sixty-nine women were classified in 3 categories depending on their human papillomavirus profile: human papillomavirus-16 only, human papillomavirus-16 and low-risk type(s), and human papillomavirus-16 and other high-risk type(s). Cervical brush samples were analyzed for human papillomavirus DNA by polymerase chain reaction and reverse line blot hybridization. All women were evaluated with colposcopy during 24 months or more. Management was according to the Bethesda recommendations. RESULTS: Women infected with human papillomavirus-16 and other high-risk human papillomavirus type(s) presented more progression or no change in the grade of dysplasia, compared with women of the other groups (relative risk [RR], 1.39; 95% confidence interval [CI], 1.07-1.82; P = .02 at 6 months; RR, 2.10; 95% CI, 1.46-3.02; P < .001 at 12 months; RR, 1.82; 95% CI, 1.21-2.72; P = .004 at 24 months). CONCLUSION: Coinfection of women with human papillomavirus-16 and other high-risk human papillomavirus type(s) increases the risk of unfavorable evolution.

The Influence of Self-fertilization performance and Copulation Behaviour in Reproduction by Cross-fertilization in Groups of Biomphalaria tenagophila (Mollusca, Planorbidae)

The following hypotheses were tested for groups of simultaneous hermaphrodites Biomphalaria tenagophila: (a) snails that have low reproductive success during the process of self-fertilization do not increase their reproductive success after the end of grouping; (b) the copulation behaviour and the presence of one snail whose eggs have a low viability rate influence the partner's reproductive success by cross-fertilization. Groups were constituted by a homozygous pigmented snail and two albinos: one with a viability rate higher than 70% ("good reproducers") and the other less than 10% ("bad reproducers"). All pigmented snails had viability rates higher than 70%. The "good" and "bad" reproducer albino snails had similar copulation behaviour. However, after the end of grouping, the "bad reproducers" continued to have viability rates less than 10% over 30 days. In 100% of the cases that pigmented snails copulated (performing either a male role or simultaneously male and female roles) exclusively with "good" reproducer albinos, they presented high reproductive success (producing, on average of 8.4 pigmented embryos/egg-mass). However, in 100% of the cases that pigmented snails copulated with both partners, the "good" reproducer albino snails produced none or very few embryos (the highest average was 2.2 pigmented embryos/egg-mass). Therefore, the production of viable embryos by cross-fertilization was more influenced by self-fertilization performance than by copulation behaviour. The presence of a snail whose eggs have a low viability rate could decrease their partners reproductive success