Gibbs entropy and irreversible thermodynamics

Recently a number of approaches has been developed to connect the microscopic dynamics of particle systems to the macroscopic properties of systems in nonequilibrium stationary states, via the theory of dynamical systems. This way a direct connection between dynamics and Irreversible Thermodynamics has been claimed to have been found. However, the main quantity used in these studies is a (coarse-grained) Gibbs entropy, which to us does not seem suitable, in its present form, to characterize nonequilibrium states. Various simplified models have also been devised to give explicit examples of how the coarse-grained approach may succeed in giving a full description of the Irreversible Thermodynamics. We analyze some of these models pointing out a number of difficulties which, in our opinion, need to be overcome in order to establish a physically relevant connection between these models and Irreversible Thermodynamics.Comment: 19 pages, 4 eps figures, LaTeX2

Monodromy-data parameterization of spaces of local solutions of integrable reductions of Einstein's field equations

For the fields depending on two of the four space-time coordinates only, the spaces of local solutions of various integrable reductions of Einstein's field equations are shown to be the subspaces of the spaces of local solutions of the ``null-curvature'' equations constricted by a requirement of a universal (i.e. solution independent) structures of the canonical Jordan forms of the unknown matrix variables. These spaces of solutions of the ``null-curvature'' equations can be parametrized by a finite sets of free functional parameters -- arbitrary holomorphic (in some local domains) functions of the spectral parameter which can be interpreted as the monodromy data on the spectral plane of the fundamental solutions of associated linear systems. Direct and inverse problems of such mapping (``monodromy transform''), i.e. the problem of finding of the monodromy data for any local solution of the ``null-curvature'' equations with given canonical forms, as well as the existence and uniqueness of such solution for arbitrarily chosen monodromy data are shown to be solvable unambiguously. The linear singular integral equations solving the inverse problems and the explicit forms of the monodromy data corresponding to the spaces of solutions of the symmetry reduced Einstein's field equations are derived.Comment: LaTeX, 33 pages, 1 figure. Typos, language and reference correction

Collective Oscillations of Vortex Lattices in Rotating Bose-Einstein Condensates

The complete low-energy collective-excitation spectrum of vortex lattices is discussed for rotating Bose-Einstein condensates (BEC) by solving the Bogoliubov-de Gennes (BdG) equation, yielding, e.g., the Tkachenko mode recently observed at JILA. The totally symmetric subset of these modes includes the transverse shear, common longitudinal, and differential longitudinal modes. We also solve the time-dependent Gross-Pitaevskii (TDGP) equation to simulate the actual JILA experiment, obtaining the Tkachenko mode and identifying a pair of breathing modes. Combining both the BdG and TDGP approaches allows one to unambiguously identify every observed mode.Comment: 5 pages, 4 figure

The Moses–Littenberg meta-analytical method generates systematic differences in test accuracy compared to hierarchical meta-analytical models

AbstractObjectiveTo compare meta-analyses of diagnostic test accuracy using the Moses–Littenberg summary receiver operating characteristic (SROC) approach with those of the hierarchical SROC (HSROC) model.Study Design and SettingTwenty-six data sets from existing test accuracy systematic reviews were reanalyzed with the Moses–Littenberg model, using equal weighting (“E-ML”) and weighting by the inverse variance of the log DOR (“W-ML”), and with the HSROC model. The diagnostic odds ratios (DORs) were estimated and covariates added to both models to estimate relative DORs (RDORs) between subgroups. Models were compared by calculating the ratio of DORs, the ratio of RDORs, and P-values for detecting asymmetry and effects of covariates on DOR.ResultsCompared to the HSROC model, the Moses–Littenberg model DOR estimates were a median of 22% (“E-ML”) and 47% (“W-ML”) lower at Q*, and 7% and 42% lower at the central point in the data. Instances of the ML models giving estimates higher than the HSROC model also occurred. Investigations of heterogeneity also differed; the Moses–Littenberg models on average estimating smaller differences in RDOR.ConclusionsMoses–Littenberg meta-analyses can generate lower estimates of test accuracy, and smaller differences in accuracy, compared to mathematically superior hierarchical models. This has implications for the usefulness of meta-analyses using this approach. We recommend meta-analysis of diagnostic test accuracy studies to be conducted using available hierarchical model–based approaches

Second trimester serum tests for Down's Syndrome screening

Background Down's syndrome occurs when a person has three copies of chromosome 21 - or the specific area of chromosome 21 implicated in causing Down's syndrome - rather than two. It is the commonest congenital cause of mental retardation. Noninvasive screening based on biochemical analysis of maternal serum or urine, or fetal ultrasound measurements, allows estimates of the risk of a pregnancy being affected and provides information to guide decisions about definitive testing. Objectives To estimate and compare the accuracy of second trimester serum markers for the detection of Down’s syndrome. Search methods We carried out a sensitive and comprehensive literature search of MEDLINE (1980 to May 2007), EMBASE (1980 to 18 May 2007), BIOSIS via EDINA (1985 to 18 May 2007), CINAHL via OVID (1982 to 18 May 2007), The Database of Abstracts of Reviews of Effectiveness (The Cochrane Library 2007, Issue 1), MEDION (May 2007), The Database of Systematic Reviews and Meta-Analyses in Laboratory Medicine (May 2007), The National Research Register (May 2007), Health Services Research Projects in Progress database (May 2007). We studied reference lists and published review articles. Selection criteria Studies evaluating tests of maternal serum in women at 14-24 weeks of gestation for Down's syndrome, compared with a reference standard, either chromosomal verification or macroscopic postnatal inspection. Data collection and analysis Data were extracted as test positive/test negative results for Down's and non-Down's pregnancies allowing estimation of detection rates (sensitivity) and false positive rates (1-specificity). We performed quality assessment according to QUADAS criteria. We used hierarchical summary ROC meta-analytical methods to analyse test performance and compare test accuracy. Analysis of studies allowing direct comparison between tests was undertaken. We investigated the impact of maternal age on test performance in subgroup analyses. Main results Fifty-nine studies involving 341,261 pregnancies (including 1,994 with Down's syndrome) were included. Studies were generally high quality, although differential verification was common with invasive testing of only high-risk pregnancies. Seventeen studies made direct comparisons between tests. Fifty-four test combinations were evaluated formed from combinations of 12 different tests and maternal age; alpha-fetoprotein (AFP), unconjugated oestriol (uE3), total human chorionic gonadotrophin (hCG), free beta human chorionic gonadotrophin (βhCG), free alpha human chorionic gonadotrophin (αhCG), Inhibin A, SP2, CA125, troponin, pregnancy-associated plasma protein A (PAPP-A), placental growth factor (PGF) and proform of eosinophil major basic protein (ProMBP). Meta-analysis of 12 best performing or frequently evaluated test combinations showed double and triple tests (involving AFP, uE3, total hCG, free βhCG) significantly outperform individual markers, detecting six to seven out of every 10 Down's syndrome pregnancies at a 5% false positive rate. Tests additionally involving inhibin performed best (eight out of every 10 Down's syndrome pregnancies) but were not shown to be significantly better than standard triple tests in direct comparisons. Significantly lower sensitivity occurred in women over the age of 35 years. Women who miscarried in the over 35 group were more likely to have been offered an invasive test to verify a negative screening results, whereas those under 35 were usually not offered invasive testing for a negative screening result. Pregnancy loss in women under 35 therefore leads to under ascertainment of screening results, potentially missing a proportion of affected pregnancies and affecting the accuracy of the sensitivity. Authors' conclusions Tests involving two or more markers in combination with maternal age are significantly more sensitive than those involving one marker. The value of combining four or more tests or including inhibin have not been proven to show statistically significant improvement. Further study is required to investigate reduced test performance in women aged over 35 and the impact of differential pregnancy loss on study findings