Multidimensional operator multipliers

We introduce multidimensional Schur multipliers and characterise them generalising well known results by Grothendieck and Peller. We define a multidimensional version of the two dimensional operator multipliers studied recently by Kissin and Shulman. The multidimensional operator multipliers are defined as elements of the minimal tensor product of several C*-algebras satisfying certain boundedness conditions. In the case of commutative C*-algebras, the multidimensional operator multipliers reduce to continuous multidimensional Schur multipliers. We show that the multipliers with respect to some given representations of the corresponding C*-algebras do not change if the representations are replaced by approximately equivalent ones. We establish a non-commutative and multidimensional version of the characterisations by Grothendieck and Peller which shows that universal operator multipliers can be obtained as certain weak limits of elements of the algebraic tensor product of the corresponding C*-algebras.Comment: A mistake in the previous versio

On stable finiteness of group rings

For an arbitrary field or division ring K and an arbitrary group G, stable finiteness of K[G] is equivalent to direct finiteness of K[G×H] for all finite groups H

Compactness properties of operator multipliers

We continue the study of multidimensional operator multipliers initiated in [arXiv:math/0701645]. We introduce the notion of the symbol of an operator multiplier. We characterise completely compact operator multipliers in terms of their symbol as well as in terms of approximation by finite rank multipliers. We give sufficient conditions for the sets of compact and completely compact multipliers to coincide and characterise the cases where an operator multiplier in the minimal tensor product of two C*-algebras is automatically compact. We give a description of multilinear modular completely compact completely bounded maps defined on the direct product of finitely many copies of the C*-algebra of compact operators in terms of tensor products, generalising results of Saar

Amenability of groups and GG-sets

This text surveys classical and recent results in the field of amenability of groups, from a combinatorial standpoint. It has served as the support of courses at the University of G\"ottingen and the \'Ecole Normale Sup\'erieure. The goals of the text are (1) to be as self-contained as possible, so as to serve as a good introduction for newcomers to the field; (2) to stress the use of combinatorial tools, in collaboration with functional analysis, probability etc., with discrete groups in focus; (3) to consider from the beginning the more general notion of amenable actions; (4) to describe recent classes of examples, and in particular groups acting on Cantor sets and topological full groups

Human Papillomavirus Testing with the Hybrid Capture 2 Assay and PCR as Screening Tools

The recognition of high-risk human papillomaviruses (HPVs) as etiological agents of cervical cancer has increased the demands to use testing for HPV for the detection of abnormal cervical smears and for cervical cancer screening. The present study compared the performance of the Hybrid Capture 2 (HC2) assay with that of PCR for the detection of significant cervical lesions in 1,511 women with different risks for HPV infections in three New Independent States of the former Soviet Union. The results showed that the level of agreement between the HC2 assay and PCR was substantial, with a kappa (Cohen) value of 0.669 (95% confidence interval [CI], 0.629 to 0.709). Of the 228 samples with discrepant results, 92 were positive by the HC2 assay but negative by PCR, whereas 136 samples were PCR positive but HC2 assay negative. The positive predictive values (PPVs) of the HC2 assay and PCR in detecting high-grade intraepithelial lesions (HSILs) were 4.5% (95% CI, 3.5 to 5.5%) and 3.6% (95% CI, 2.7 to 4.5%), respectively, and the negative predictive values (NPVs) were 99.6% (95% CI, 99.3 to 99.9%) and 99.3% (95% CI, 98.9 to 99.7%), respectively. The sensitivities of the HC2 assay and PCR for the detection of HSILs were 85.2 and 74.0%, respectively, and the specificities were 67.2 and 64.1%, respectively. In receiver operating characteristic (ROC) analysis, the performance of the HC2 assay for the detection of HSILs was excellent (P = 0.0001); the area under the ROC analysis curve was 0.858 (95% CI, 0.811 to 0.905), and the optimal balance between sensitivity (86.5%) and specificity (80%) was obtained with an HC2 assay cutoff level of 15.6 relative light units/positive control. Use of this cutoff would increase the specificity of the HC2 assay to 80.0% without compromising sensitivity. In conclusion, the results of PCR and the HC2 assay were concordant for 85% of samples, resulting in substantial reproducibility. Both tests had low PPVs, equal specificities, and equal (almost 100%) NPVs for the detection of HSILs; but the sensitivity of the HC2 assay was slightly better

Persistent high-risk human papillomavirus infections and other end-point markers of progressive cervical disease among women prospectively followed up in the New Independent States of the Former Soviet Union and the Latin American Screening study cohorts

New end points are needed in future human papillomavirus (HPV) vaccine efficacy studies that accurately predict disease progression. Background: New end points are needed in future human papillomavirus (HPV) vaccine efficacy studies that accurately predict disease progression. Objectives: Potential intermediate end points were analyzed in the combined New Independent States of the Former Soviet Union (NIS) and the Latin American Screening (LAMS) study cohorts. Study Design and Methods: Data files of 2 international screening trials, the NIS (n = 3187) and the LAMS (n = 12,114) study cohorts, were combined, and a subcohort of 1865 (n = 854 and n = 1011 for the NIS and the LAMS, respectively) women prospectively followed up for 19.7 (median, 22.2) months was analyzed for different intermediate end-point markers of disease progression to squamous intraepithelial lesion (SIL), cervical intraepithelial neoplasia grade 1 and higher (CIN1+), and CIN grade 2 and higher (CIN2+) as terminal events. Results: Altogether, 131 (7.0%), 90 (4.8%), and 39 (2.1%) cases progressed to SIL, CIN1+, and CIN2+, respectively, progression times being equal in the NIS (11.9, 16.8, and 19.6 months) and LAMS (13.6, 14.1, and 15.4 months) cohorts (P = 0.931, P = 0.335, and P = 0.535). The 2 most powerful end-point markers of disease progression to CIN2+ were high-grade squamous intraepithelial lesions based on Papanicolaou test results at 6-month (odds ratio [OR] = 47.1; 95% confidence interval [CI], 17.3-128.7) and 12-month (OR = 21.5; 95% CI, 5.1-90.8) follow-up visits, with longitudinal positive and negative predictive values of 42.1% and 98.0% (6 months) and 33.3% and 97.7% (12 months). Of the virological end points, more than 6 months of persistent high-risk HPV (HR-HPV) was the most powerful predictor of progression to CIN1+ (OR = 18.6; 95% CI, 2.5-136.5), with longitudinal positive and negative predictive values of 10.3% and 99.4%, respectively. No additional benefit was obtained using more than 12 months of persistent HR-HPV end point. Conclusions: High-grade squamous intraepithelial lesion based on a Papanicolaou test results at 6- or 12-month follow-up visits was the most powerful end point, either considering cytological end points alone or in comparison to any of the virological end points. Of the virological end points, more than 6-month HR-HPV persistence criteria give the most powerful estimate of a progressive disease