Dilating covariant representations of the non-commutative disc algebras

Let $\phi$ be an isometric automorphism of the non-commutative disc algebra \fA_n for $n \geq 2$. We show that every contractive covariant representation of (\fA_n, \phi) dilates to a unitary covariant representation of (\O_n, \phi). Hence the C*-envelope of the semicrossed product \fA_n \times_{\phi} \bZ^+ is \O_n \times_{\phi} \bZ.Comment: 18 page

Progress in noncommutative function theory

In this expository paper we describe the study of certain non-self-adjoint operator algebras, the Hardy algebras, and their representation theory. We view these algebras as algebras of (operator valued) functions on their spaces of representations. We will show that these spaces of representations can be parameterized as unit balls of certain $W^{*}$-correspondences and the functions can be viewed as Schur class operator functions on these balls. We will provide evidence to show that the elements in these (non commutative) Hardy algebras behave very much like bounded analytic functions and the study of these algebras should be viewed as noncommutative function theory

An epidemiological model for prediction of endometrial cancer risk in Europe

Endometrial cancer (EC) is the fourth most frequent cancer in women in Europe, and as its incidence is increasing, prevention strategies gain further pertinence. Risk prediction models can be a useful tool for identifying women likely to benefit from targeted prevention measures. On the basis of data from 201,811 women (mostly aged 30–65 years) including 855 incident EC cases from eight countries in the European Prospective Investigation into Cancer and Nutrition cohort, a model to predict EC was developed. A step-wise model selection process was used to select confirmed predictive epidemiologic risk factors. Piece-wise constant hazard rates in 5-year age-intervals were estimated in a cause-specific competing risks model, five-fold-cross-validation was applied for internal validation. Risk factors included in the risk prediction model were body-mass index (BMI), menopausal status, age at menarche and at menopause, oral contraceptive use, overall and by different BMI categories and overall duration of use, parity, age at first full-term pregnancy, duration of menopausal hormone therapy and smoking status (specific for pre, peri- and post-menopausal women). These variables improved the discriminating capacity to predict risk over 5 years from 71 % for a model based on age alone to 77 % (overall C statistic), and the model was well-calibrated (ratio of expected to observed cases = 0.99). Our model could be used for the identification of women at increased risk of EC in Western Europe. To achieve an EC-risk model with general validity, a large-scale cohort-consortium approach would be needed to assess and adjust for population variation

Constraints on the χ_(c1) versus χ_(c2) polarizations in proton-proton collisions at √s = 8 TeV

The polarizations of promptly produced χ_(c1) and χ_(c2) mesons are studied using data collected by the CMS experiment at the LHC, in proton-proton collisions at √s=8  TeV. The χ_c states are reconstructed via their radiative decays χ_c → J/ψγ, with the photons being measured through conversions to e⁺e⁻, which allows the two states to be well resolved. The polarizations are measured in the helicity frame, through the analysis of the χ_(c2) to χ_(c1) yield ratio as a function of the polar or azimuthal angle of the positive muon emitted in the J/ψ → μ⁺μ⁻ decay, in three bins of J/ψ transverse momentum. While no differences are seen between the two states in terms of azimuthal decay angle distributions, they are observed to have significantly different polar anisotropies. The measurement favors a scenario where at least one of the two states is strongly polarized along the helicity quantization axis, in agreement with nonrelativistic quantum chromodynamics predictions. This is the first measurement of significantly polarized quarkonia produced at high transverse momentum