Orbit decidability and the conjugacy problem for some extensions of groups

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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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Morbidity and aging in HIV-infected persons: the Swiss HIV cohort study.

BACKGROUND: Patterns of morbidity and mortality among human immunodeficiency virus (HIV)-infected individuals taking antiretroviral therapy are changing as a result of immune reconstitution and improved survival. We studied the influence of aging on the epidemiology of non-AIDS diseases in the Swiss HIV Cohort Study. METHODS: The Swiss HIV Cohort Study is a prospective observational cohort established in 1988 with continuous enrollment. We determined the incidence of clinical events (per 1000 person-years) from January 2008 (when a new questionnaire on non-AIDS-related morbidity was introduced) through December 2010. Differences across age groups were analyzed using Cox regression, adjusted for CD4 cell count, viral load, sex, injection drug use, smoking, and years of HIV infection. RESULTS: Overall, 8444 (96%) of 8848 participants contributed data from 40,720 semiannual visits; 2233 individuals (26.4%) were aged 50-64 years, and 450 (5.3%) were aged ≥65 years. The median duration of HIV infection was 15.4 years (95% confidence interval [CI], 9.59-22.0 years); 23.2% had prior clinical AIDS. We observed 994 incident non-AIDS events in the reference period: 201 cases of bacterial pneumonia, 55 myocardial infarctions, 39 strokes, 70 cases of diabetes mellitus, 123 trauma-associated fractures, 37 fractures without adequate trauma, and 115 non-AIDS malignancies. Multivariable hazard ratios for stroke (17.7; CI, 7.06-44.5), myocardial infarction (5.89; 95% CI, 2.17-16.0), diabetes mellitus (3.75; 95% CI, 1.80-7.85), bone fractures without adequate trauma (10.5; 95% CI, 3.58-30.5), osteoporosis (9.13; 95% CI, 4.10-20.3), and non-AIDS-defining malignancies (6.88; 95% CI, 3.89-12.2) were elevated for persons aged ≥65 years. CONCLUSIONS: Comorbidity and multimorbidity because of non-AIDS diseases, particularly diabetes mellitus, cardiovascular disease, non-AIDS-defining malignancies, and osteoporosis, become more important in care of HIV-infected persons and increase with older age.

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.

Differential effect of long versus short wavelength light exposure on pupillary re-dilation in patients with outer retinal disease.

BACKGROUND: In patients with outer retinal degeneration, a differential pupil response to long wavelength (red) versus short wavelength (blue) light stimulation has been previously observed. The goal of this study was to quantify differences in the pupillary re-dilation following exposure to red versus blue light in patients with outer retinal disease and compare them with patients with optic neuropathy and with healthy subjects. DESIGN: Prospective comparative cohort study. PARTICIPANTS: Twenty-three patients with outer retinal disease, 13 patients with optic neuropathy and 14 normal subjects. METHODS: Subjects were tested using continuous red and blue light stimulation at three intensities (1, 10 and 100 cd/m2) for 13 s per intensity. Pupillary re-dilation dynamics following the brightest intensity was analysed and compared between the three groups. MAIN OUTCOME MEASURES: The parameters of pupil re-dilation used in this study were: time to recover 90% of baseline size; mean pupil size at early and late phases of re-dilation; and differential re-dilation time for blue versus red light. RESULTS: Patients with outer retinal disease showed a pupil that tended to stay smaller after light termination and thus had a longer time to recovery. The differential re-dilation time was significantly greater in patients with outer retinal disease (median = 28.0 s, P < 0.0001) compared with controls and patients with optic neuropathy. CONCLUSIONS: A differential response of pupil re-dilation following red versus blue light stimulation is present in patients with outer retinal disease but is not found in normal eyes or among patients with visual loss from optic neuropathy.

The effect of the N-methyl-D-aspartate receptor antagonist dextromethorphan on perioperative brain injury in children undergoing cardiac surgery with cardiopulmonary bypass: results of a pilot study.

Experimental evidence indicates a role of the N-methyl-D-aspartate receptor in the pathogenesis of brain injury occurring during cardiac surgery with cardiopulmonary bypass (CPB). Dextromethorphan is a noncompetitive antagonist of this receptor with a favorable safety profile. Thirteen children age 3-36 months undergoing cardiac surgery with expected CPB of 60 minutes or more were randomly assigned to treatment with dextromethorphan (36-38 mg/kg/day) or placebo administered by naso-gastric tube. Dextromethorphan was absorbed well and reached putative therapeutic levels in blood and cerebrospinal fluid. Adverse effects were not observed. Mild hemiparesis developed after operation in one child of each group, and severe encephalopathy in one of the placebo group. Sharp waves were recorded in postoperative continuous electroencephalography in all placebo (n = 7) but only in 2/6 dextromethorphan treated children (p = 0.02). Pre- and postoperative cranial magnetic resonance imaging (MRI) revealed less pronounced ventricular enlargement in the dextromethorphan group (not significant). An increase of periventricular white matter lesions was visible in two placebo-treated children only. No elevations of cerebrospinal fluid enzymes were observed in either group. Although children with dextromethorphan showed less abnormalities in electroencephalography and MRI, dissimilarities of the treatment groups by chance diminished conclusions to possible protective effects of dextromethorphan at this time.

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.

Adaptive Continuous time Markov Chain Approximation Model to General Jump-Diusions

We propose a non-equidistant Q rate matrix formula and an adaptive numerical algorithm for a continuous time Markov chain to approximate jump-diffusions with affine or non-affine functional specifications. Our approach also accommodates state-dependent jump intensity and jump distribution, a flexibility that is very hard to achieve with other numerical methods. The Kolmogorov-Smirnov test shows that the proposed Markov chain transition density converges to the one given by the likelihood expansion formula as in Ait-Sahalia (2008). We provide numerical examples for European stock option pricing in Black and Scholes (1973), Merton (1976) and Kou (2002).

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.