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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On the intersection of free subgroups in free products of groups

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A classification, up to hyperbolicity, of groups given by 2 generators and one relator of length 8

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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.

Metabolic and respiratory effects of infused sodium acetate in healthy human subjects.

The metabolic and respiratory effects of intravenous 0.5 M sodium acetate (at a rate of 2.5 mmol/min during 120 min) were studied in nine normal human subjects. O2 consumption (VO2) and CO2 production (VCO2) were measured continuously by open-circuit indirect calorimetry. VO2 increased from 251 +/- 9 to 281 +/- 9 ml/min (P < 0.001), energy expenditure increased from 4.95 +/- 0.17 kJ/min baseline to 5.58 +/- 0.16 kJ/min (P < 0.001), and VCO2 decreased nonsignificantly (211 +/- 7 ml/min vs. 202 +/- 7 ml/min, NS). The extrapulmonary CO2 loss (i.e., bicarbonate generation and excretion) was estimated at 48 +/- 5 ml/min. This observation is consistent with 1 mol of bicarbonate generated from 1 mol of acetate metabolized. Alveolar ventilation decreased from 3.5 +/- 0.2 l/min basal to 3.1 +/- 0.2 l/min (P < 0.001). The minute ventilation (VE) to VO2 ratio decreased from 22.9 +/- 1.3 to 17.6 +/- 0.9 l/l (P < 0.005), arterial PO2 decreased from 93.2 +/- 1.9 to 78.7 +/- 1.6 mmHg (P < 0.0001), arterial PCO2 increased from 39.2 +/- 0.7 to 42.1 +/- 1.1 mmHg (P < 0.0001), pH from 7.40 +/- 0.005 to 7.50 +/- 0.007 (P < 0.005), and arterial bicarbonate concentration from 24.2 +/- 0.7 to 32.9 +/- 1.1 (P < 0.0001). These observations indicate that sodium acetate infusion results in substantial extrapulmonary CO2 loss, which leads to a relative decrease of total and alveolar ventilation.

Preferential assembly of epithelial sodium channel (ENaC) subunits in Xenopus oocytes: role of furin-mediated endogenous proteolysis.

The epithelial sodium channel (ENaC) is preferentially assembled into heteromeric alphabetagamma complexes. The alpha and gamma (not beta) subunits undergo proteolytic cleavage by endogenous furin-like activity correlating with increased ENaC function. We identified full-length subunits and their fragments at the cell surface, as well as in the intracellular pool, for all homo- and heteromeric combinations (alpha, beta, gamma, alphabeta, alphagamma, betagamma, and alphabetagamma). We assayed corresponding channel function as amiloride-sensitive sodium transport (I(Na)). We varied furin-mediated proteolysis by mutating the P1 site in alpha and/or gamma subunit furin consensus cleavage sites (alpha(mut) and gamma(mut)). Our findings were as follows. (i) The beta subunit alone is not transported to the cell surface nor cleaved upon assembly with the alpha and/or gamma subunits. (ii) The alpha subunit alone (or in combination with beta and/or gamma) is efficiently transported to the cell surface; a surface-expressed 65-kDa alpha ENaC fragment is undetected in alpha(mut)betagamma, and I(Na) is decreased by 60%. (iii) The gamma subunit alone does not appear at the cell surface; gamma co-expressed with alpha reaches the surface but is not detectably cleaved; and gamma in alphabetagamma complexes appears mainly as a 76-kDa species in the surface pool. Although basal I(Na) of alphabetagamma(mut) was similar to alphabetagamma, gamma(mut) was not detectably cleaved at the cell surface. Thus, furin-mediated cleavage is not essential for participation of alpha and gamma in alphabetagamma heteromers. Basal I(Na) is reduced by preventing furin-mediated cleavage of the alpha, but not gamma, subunits. Residual current in the absence of furin-mediated proteolysis may be due to non-furin endogenous proteases.

Effect of rufinamide on gating properties of voltage-gated sodium channel Na(v)1.7

Background: Voltage-gated sodium channels (Nav1.x) are important players in chronic pain. A particular interest has grown in Nav1.7, expressed in nociceptors, since mutations in its gene are associated to two inherited pain syndromes or insensitivity to pain. Rufinamide, a drug used to treat refractory epilepsy such as the Lennox-Gastaut syndrome, has been shown to reduce the number of action potentials in cortical neurons without completely blocking Na channels. Aim: The goal of this study was to investigate the effect of rufinamide on Nav1.7 current. Methods and results: Whole-cell patch clamp experiments were performed using HEK293 cells stably expressing Nav1.7. Rufinamide significantly decreased peak sodium current by 28.3, 21.2 and 12.5% at concentrations of 500, 100 and 50μM respectively (precise EC50 could not be calculated since higher rufinamide concentrations could not be achieved in physiological buffer solution). No significant difference on the V1/2 of voltage-dependence of activation was seen; however a shift in the steady-state inactivation curve was observed (-82.6 mV to -88.8 mV and -81.8 to -87.6 mV for 50 and 100 μM rufinamide respectively, p <0.005). Frequency-dependent inhibition of Nav1.7 was also influenced by the drug. One hundred μM rufinamide reduced the peak sodium current (in % of the peak current taken at the first sweep of a train of 50) from 90.8 to 80.8% (5Hz), 88.7 to 71.8% (10 Hz), 69.1 to 49.2% (25 Hz) and 22.3 to 9.8% (50 Hz) (all p <0.05). Onset of fast inactivation was not influenced by the drug since no difference in the time constant of current decay was observed. Conclusion: In the concentration range of plasma level in human treated for epilepsy, 15 μM, rufinamide only minimally blocks Nav1.7. However, it stabilizes the inactivated state and exerts frequencydependent inhibition of Nav1.7. These pharmacological properties may be of use in reducing ectopic discharges as a causal and symptom related contributor of neuropathic pain syndrome.

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.