Singular values of the Dirac operator in dense QCD-like theories

We study the singular values of the Dirac operator in dense QCD-like theories at zero temperature. The Dirac singular values are real and nonnegative at any nonzero quark density. The scale of their spectrum is set by the diquark condensate, in contrast to the complex Dirac eigenvalues whose scale is set by the chiral condensate at low density and by the BCS gap at high density. We identify three different low-energy effective theories with diquark sources applicable at low, intermediate, and high density, together with their overlapping domains of validity. We derive a number of exact formulas for the Dirac singular values, including Banks-Casher-type relations for the diquark condensate, Smilga-Stern-type relations for the slope of the singular value density, and Leutwyler-Smilga-type sum rules for the inverse singular values. We construct random matrix theories and determine the form of the microscopic spectral correlation functions of the singular values for all nonzero quark densities. We also derive a rigorous index theorem for non-Hermitian Dirac operators. Our results can in principle be tested in lattice simulations.Comment: 3 references added, version published in JHE

Comparison of imputation methods for handling missing covariate data when fitting a Cox proportional hazards model: a resampling study

<p>Abstract</p> <p>Background</p> <p>The appropriate handling of missing covariate data in prognostic modelling studies is yet to be conclusively determined. A resampling study was performed to investigate the effects of different missing data methods on the performance of a prognostic model.</p> <p>Methods</p> <p>Observed data for 1000 cases were sampled with replacement from a large complete dataset of 7507 patients to obtain 500 replications. Five levels of missingness (ranging from 5% to 75%) were imposed on three covariates using a missing at random (MAR) mechanism. Five missing data methods were applied; a) complete case analysis (CC) b) single imputation using regression switching with predictive mean matching (SI), c) multiple imputation using regression switching imputation, d) multiple imputation using regression switching with predictive mean matching (MICE-PMM) and e) multiple imputation using flexible additive imputation models. A Cox proportional hazards model was fitted to each dataset and estimates for the regression coefficients and model performance measures obtained.</p> <p>Results</p> <p>CC produced biased regression coefficient estimates and inflated standard errors (SEs) with 25% or more missingness. The underestimated SE after SI resulted in poor coverage with 25% or more missingness. Of the MI approaches investigated, MI using MICE-PMM produced the least biased estimates and better model performance measures. However, this MI approach still produced biased regression coefficient estimates with 75% missingness.</p> <p>Conclusions</p> <p>Very few differences were seen between the results from all missing data approaches with 5% missingness. However, performing MI using MICE-PMM may be the preferred missing data approach for handling between 10% and 50% MAR missingness.</p

Shock waves in strongly coupled plasmas

Shock waves are supersonic disturbances propagating in a fluid and giving rise to dissipation and drag. Weak shocks, i.e., those of small amplitude, can be well described within the hydrodynamic approximation. On the other hand, strong shocks are discontinuous within hydrodynamics and therefore probe the microscopics of the theory. In this paper we consider the case of the strongly coupled N=4 plasma whose microscopic description, applicable for scales smaller than the inverse temperature, is given in terms of gravity in an asymptotically $AdS_5$ space. In the gravity approximation, weak and strong shocks should be described by smooth metrics with no discontinuities. For weak shocks we find the dual metric in a derivative expansion and for strong shocks we use linearized gravity to find the exponential tail that determines the width of the shock. In particular we find that, when the velocity of the fluid relative to the shock approaches the speed of light $v\to 1$ the penetration depth $\ell$ scales as $\ell\sim (1-v^2)^{1/4}$. We compare the results with second order hydrodynamics and the Israel-Stewart approximation. Although they all agree in the hydrodynamic regime of weak shocks, we show that there is not even qualitative agreement for strong shocks. For the gravity side, the existence of shock waves implies that there are disturbances of constant shape propagating on the horizon of the dual black holes.Comment: 47 pages, 8 figures; v2:typos corrected, references adde

Tigecycline use in serious nosocomial infections: a drug use evaluation

<p>Abstract</p> <p>Background</p> <p>Tigecycline is a novel antibiotic with activity against multidrug resistant bacteria. The aim of this study was to assess the efficacy of tigecycline use in serious hospital-acquired infections (HAI)</p> <p>Case presentation</p> <p>Prospective observational study of tigecycline use was conducted in a 1500 beds university hospital. From January 1, 2007 and January 31, 2010, 207 pts were treated with tigecycline for the following indications: intra-abdominal, pneumonia, bloodstream and complicated skin and soft tissue infections and febrile neutropenia. The therapy was targeted in 130/207 (63%) and empirical in 77/207 (37%) patients. All bacteria treated were susceptible to tigecycline. Median duration of tigecycline therapy was 13 days (range, 6-28). Clinical success was obtained in 151/207 (73%) cases, with the highest success rate recorded in intra-abdominal infections [81/99 (82%)]. Microbiological success was achieved in 100/129 (78%) treated patients. Adverse clinical events were seen in 16/207 patients (7.7%):</p> <p>Conclusions</p> <p>Considering the lack of data on tigecycline for critically ill patients, we think that the reported data of our clinical experience despite some limitations can be useful for clinicians.</p

Standardisation of rates using logistic regression: a comparison with the direct method

<p>Abstract</p> <p>Background</p> <p>Standardisation of rates in health services research is generally undertaken using the direct and indirect arithmetic methods. These methods can produce unreliable estimates when the calculations are based on small numbers. Regression based methods are available but are rarely applied in practice. This study demonstrates the advantages of using logistic regression to obtain smoothed standardised estimates of the prevalence of rare disease in the presence of covariates.</p> <p>Methods</p> <p>Step by step worked examples of the logistic and direct methods are presented utilising data from BETS, an observational study designed to estimate the prevalence of subclinical thyroid disease in the elderly. Rates calculated by the direct method were standardised by sex and age categories, whereas rates by the logistic method were standardised by sex and age as a continuous variable.</p> <p>Results</p> <p>The two methods produce estimates of similar magnitude when standardising by age and sex. The standard errors produced by the logistic method were lower than the conventional direct method.</p> <p>Conclusion</p> <p>Regression based standardisation is a practical alternative to the direct method. It produces more reliable estimates than the direct or indirect method when the calculations are based on small numbers. It has greater flexibility in factor selection and allows standardisation by both continuous and categorical variables. It therefore allows standardisation to be performed in situations where the direct method would give unreliable results.</p

Imputation strategies for missing binary outcomes in cluster randomized trials

<p>Abstract</p> <p>Background</p> <p>Attrition, which leads to missing data, is a common problem in cluster randomized trials (CRTs), where groups of patients rather than individuals are randomized. Standard multiple imputation (MI) strategies may not be appropriate to impute missing data from CRTs since they assume independent data. In this paper, under the assumption of missing completely at random and covariate dependent missing, we compared six MI strategies which account for the intra-cluster correlation for missing binary outcomes in CRTs with the standard imputation strategies and complete case analysis approach using a simulation study.</p> <p>Method</p> <p>We considered three within-cluster and three across-cluster MI strategies for missing binary outcomes in CRTs. The three within-cluster MI strategies are logistic regression method, propensity score method, and Markov chain Monte Carlo (MCMC) method, which apply standard MI strategies within each cluster. The three across-cluster MI strategies are propensity score method, random-effects (RE) logistic regression approach, and logistic regression with cluster as a fixed effect. Based on the community hypertension assessment trial (CHAT) which has complete data, we designed a simulation study to investigate the performance of above MI strategies.</p> <p>Results</p> <p>The estimated treatment effect and its 95% confidence interval (CI) from generalized estimating equations (GEE) model based on the CHAT complete dataset are 1.14 (0.76 1.70). When 30% of binary outcome are missing completely at random, a simulation study shows that the estimated treatment effects and the corresponding 95% CIs from GEE model are 1.15 (0.76 1.75) if complete case analysis is used, 1.12 (0.72 1.73) if within-cluster MCMC method is used, 1.21 (0.80 1.81) if across-cluster RE logistic regression is used, and 1.16 (0.82 1.64) if standard logistic regression which does not account for clustering is used.</p> <p>Conclusion</p> <p>When the percentage of missing data is low or intra-cluster correlation coefficient is small, different approaches for handling missing binary outcome data generate quite similar results. When the percentage of missing data is large, standard MI strategies, which do not take into account the intra-cluster correlation, underestimate the variance of the treatment effect. Within-cluster and across-cluster MI strategies (except for random-effects logistic regression MI strategy), which take the intra-cluster correlation into account, seem to be more appropriate to handle the missing outcome from CRTs. Under the same imputation strategy and percentage of missingness, the estimates of the treatment effect from GEE and RE logistic regression models are similar.</p

Gene set analysis exploiting the topology of a pathway

<p>Abstract</p> <p>Background</p> <p>Recently, a great effort in microarray data analysis is directed towards the study of the so-called gene sets. A gene set is defined by genes that are, somehow, functionally related. For example, genes appearing in a known biological pathway naturally define a gene set. The gene sets are usually identified from a priori biological knowledge. Nowadays, many bioinformatics resources store such kind of knowledge (see, for example, the Kyoto Encyclopedia of Genes and Genomes, among others). Although pathways maps carry important information about the structure of correlation among genes that should not be neglected, the currently available multivariate methods for gene set analysis do not fully exploit it.</p> <p>Results</p> <p>We propose a novel gene set analysis specifically designed for gene sets defined by pathways. Such analysis, based on graphical models, explicitly incorporates the dependence structure among genes highlighted by the topology of pathways. The analysis is designed to be used for overall surveillance of changes in a pathway in different experimental conditions. In fact, under different circumstances, not only the expression of the genes in a pathway, but also the strength of their relations may change. The methods resulting from the proposal allow both to test for variations in the strength of the links, and to properly account for heteroschedasticity in the usual tests for differential expression.</p> <p>Conclusions</p> <p>The use of graphical models allows a deeper look at the components of the pathway that can be tested separately and compared marginally. In this way it is possible to test single components of the pathway and highlight only those involved in its deregulation.</p

QGP Theory: Status and Perspectives

The current status of Quark-Gluon-Plasma Theory is reviewed. Special emphasis is placed on QGP signatures, the interpretation of current data and what to expect from RHIC in the near future.Comment: 20 pages, invited overview talk at the 4th International Conference on the Physcis and Astrophysics of the Quark-Gluon-Plasma, November 2001, Jaipur, India, to appear in Praman