A quantitative central limit theorem for linear statistics of random matrix eigenvalues

It is known that the fluctuations of suitable linear statistics of Haar distributed elements of the compact classical groups satisfy a central limit theorem. We show that if the corresponding test functions are sufficiently smooth, a rate of convergence of order almost $1/n$ can be obtained using a quantitative multivariate CLT for traces of powers that was recently proven using Stein's method of exchangeable pairs.Comment: Title modified; main result stated under slightly weaker conditions; accepted for publication in the Journal of Theoretical Probabilit

Evaluation of a chemoresponse assay as a predictive marker in the treatment of recurrent ovarian cancer: Further analysis of a prospective study

BACKGROUND: Recently, a prospective study reported improved clinical outcomes for recurrent ovarian cancer patients treated with chemotherapies indicated to be sensitive by a chemoresponse assay, compared with those patients treated with non-sensitive therapies, thereby demonstrating the assay's prognostic properties. Due to cross-drug response over different treatments and possible association of in vitro chemosensitivity of a tumour with its inherent biology, further analysis is required to ascertain whether the assay performs as a predictive marker as well. METHODS: Women with persistent or recurrent epithelial ovarian cancer (n=262) were empirically treated with one of 15 therapies, blinded to assay results. Each patient's tumour was assayed for responsiveness to the 15 therapies. The assay's ability to predict progression-free survival (PFS) was assessed by comparing the association when the assayed therapy matches the administered therapy (match) with the association when the assayed therapy is randomly selected, not necessarily matching the administered therapy (mismatch). RESULTS: Patients treated with assay-sensitive therapies had improved PFS vs patients treated with non-sensitive therapies, with the assay result for match significantly associated with PFS (hazard ratio (HR)=0.67, 95% confidence interval (CI)=0.50–0.91, P=0.009). On the basis of 3000 simulations, the mean HR for mismatch was 0.81 (95% range=0.66–0.99), with 3.4% of HRs less than 0.67, indicating that HR for match is lower than for mismatch. While 47% of tumours were non-sensitive to all assayed therapies and 9% were sensitive to all, 44% displayed heterogeneity in assay results. Improved outcome was associated with the administration of an assay-sensitive therapy, regardless of homogeneous or heterogeneous assay responses across all of the assayed therapies. CONCLUSIONS: These analyses provide supportive evidence that this chemoresponse assay is a predictive marker, demonstrating its ability to discern specific therapies that are likely to be more effective among multiple alternatives

Phase transitions in quantum chromodynamics

The current understanding of finite temperature phase transitions in QCD is reviewed. A critical discussion of refined phase transition criteria in numerical lattice simulations and of analytical tools going beyond the mean-field level in effective continuum models for QCD is presented. Theoretical predictions about the order of the transitions are compared with possible experimental manifestations in heavy-ion collisions. Various places in phenomenological descriptions are pointed out, where more reliable data for QCD's equation of state would help in selecting the most realistic scenario among those proposed. Unanswered questions are raised about the relevance of calculations which assume thermodynamic equilibrium. Promising new approaches to implement nonequilibrium aspects in the thermodynamics of heavy-ion collisions are described.Comment: 156 pages, RevTex. Tables II,VIII,IX and Fig.s 1-38 are not included as postscript files. I would like to ask the requestors to copy the missing tables and figures from the corresponding journal-referenc