Generalized Weyl solutions

It was shown by Weyl that the general static axisymmetric solution of the vacuum Einstein equations in four dimensions is given in terms of a single axisymmetric solution of the Laplace equation in three-dimensional flat space. Weyls construction is generalized here to arbitrary dimension D>~4. The general solution of the D-dimensional vacuum Einstein equations that admits D-2 orthogonal commuting non-null Killing vector fields is given either in terms of D-3 independent axisymmetric solutions of Laplaces equation in three-dimensional flat space or by D-4 independent solutions of Laplaces equation in two-dimensional flat space. Explicit examples of new solutions are given. These include a five-dimensional asymptotically flat black ring with an event horizon of topology S1S2 held in equilibrium by a conical singularity in the form of a disk.

Generalized Onsager symmetry

Onsager's symmetry theorem for transport near equilibrium is extended in two directions. A corresponding symmetry is obtained for linear transport near nonequilibrium stationary states, and the class of transport laws is extended to include nonlocality in both space and time. The results are formally exact and independent of any specific model for the nonequilibrium state.

Generalized percolation in random directed networks

We develop a general theory for percolation in directed random networks with arbitrary two-point correlations and bidirectional edgesthat is, edges pointing in both directions simultaneously. These two ingredients alter the previously known scenario and open new views and perspectives on percolation phenomena. Equations for the percolation threshold and the sizes of the giant components are derived in the most general case. We also present simulation results for a particular example of uncorrelated network with bidirectional edges confirming the theoretical predictions.

Modelling the influence of change in fire regime on the local distribution of a Mediterranean pyrophytic plant species (Cistus salviifolius) at its northern range limit

Aims: To assess the potential distribution of an obligate seeder and active pyrophyte, Cistus salviifolius, a vulnerable species in the Swiss Red List; to derive scenarios by changing the fire return interval; and to discuss the results from a conservation perspective. A more general aim is to assess the impact of fire as a natural factor influencing the vegetation of the southern slopes of the Alps. Locations: Alps, southern Switzerland. Methods: Presence-absence data to fit the model were obtained from the most recent field mapping of C. salviifolius. The quantitative environmental predictors used in this study include topographic, climatic and disturbance (fire) predictors. Models were fitted by logistic regression and evaluated by jackknife and bootstrap approaches. Changes in fire regime were simulated by increasing the time-return interval of fire (simulating longer periods without fire). Two scenarios were considered: no fire in the past 15 years; or in the past 35 years. Results: Rock cover, slope, topographic position, potential evapotranspiration and time elapsed since the last fire were selected in the final model. The Nagelkerke R-2 of the model for C. salviifolius was 0.57 and the Jackknife area under the curve evaluation was 0.89. The bootstrap evaluation revealed model robustness. By increasing the return interval of fire by either up to 15 years, or 35 years, the modelled C. salviifolius population declined by 30-40%, respectively. Main conclusions: Although fire plays a significant role, topography and rock cover appear to be the most important predictors, suggesting that the distribution of C. salviifolius in the southern Swiss Alps is closely related to the availability of supposedly competition-free sites, such as emerging bedrock, ridge locations or steep slopes. Fire is more likely to play a secondary role in allowing C. salviifolius to extend its occurrence temporarily, by increasing germination rates and reducing the competition from surrounding vegetation. To maintain a viable dormant seed bank for C. salviifolius, conservation managers should consider carrying out vegetation clearing and managing wild fire propagation to reduce competition and ensure sufficient recruitment for this species.

Generalized Langevin equations: Anomalous diffusion and probability distributions

We study the motion of a particle governed by a generalized Langevin equation. We show that, when no fluctuation-dissipation relation holds, the long-time behavior of the particle may be from stationary to superdiffusive, along with subdiffusive and diffusive. When the random force is Gaussian, we derive the exact equations for the joint and marginal probability density functions for the position and velocity of the particle and find their solutions.

Generalized adiabatic invariance

In this paper we find the quantities that are adiabatic invariants of any desired order for a general slowly time-dependent Hamiltonian. In a preceding paper, we chose a quantity that was initially an adiabatic invariant to first order, and sought the conditions to be imposed upon the Hamiltonian so that the quantum mechanical adiabatic theorem would be valid to mth order. [We found that this occurs when the first (m - 1) time derivatives of the Hamiltonian at the initial and final time instants are equal to zero.] Here we look for a quantity that is an adiabatic invariant to mth order for any Hamiltonian that changes slowly in time, and that does not fulfill any special condition (its first time derivatives are not zero initially and finally).

Petrou type-D perfect-fluid solutions in generalized Kerr-Schild form.

Generalized KerrSchild space-times for a perfect-fluid source are investigated. New Petrov type D perfect fluid solutions are obtained starting from conformally flat perfect-fluid metrics.

Petrou types D and II perfect-fluid solutions in generalized Kerr-Schild form.

Petrov types D and II perfect-fluid solutions are obtained starting from conformally flat perfect-fluid metrics and by using a generalized KerrSchild ansatz. Most of the Petrov type D metrics obtained have the property that the velocity of the fluid does not lie in the two-space defined by the principal null directions of the Weyl tensor. The properties of the perfect-fluid sources are studied. Finally, a detailed analysis of a new class of spherically symmetric static perfect-fluid metrics is given.

Rgtsp: a generalized top scoring pairs package for class prediction.

SUMMARY: A top scoring pair (TSP) classifier consists of a pair of variables whose relative ordering can be used for accurately predicting the class label of a sample. This classification rule has the advantage of being easily interpretable and more robust against technical variations in data, as those due to different microarray platforms. Here we describe a parallel implementation of this classifier which significantly reduces the training time, and a number of extensions, including a multi-class approach, which has the potential of improving the classification performance. AVAILABILITY AND IMPLEMENTATION: Full C++ source code and R package Rgtsp are freely available from http://lausanne.isb-sib.ch/~vpopovic/research/. The implementation relies on existing OpenMP libraries.

Divergent fifteen-year trends in traditional and cardiometabolic risk factors of cardiovascular diseases in the Seychelles.

OBJECTIVE: Few studies have assessed secular changes in the levels of cardiovascular risk factors (CV-RF) in populations of low or middle income countries. The systematic collection of a broad set of both traditional and metabolic CV-RF in 1989 and 2004 in the population of the Seychelles islands provides a unique opportunity to examine trends at a fairly early stage of the "diabesity" era in a country in the African region. METHODS: Two examination surveys were conducted in independent random samples of the population aged 25-64 years in 1989 and 2004, attended by respectively 1081 and 1255 participants (participation rates >80%). All results are age-standardized to the WHO standard population. RESULTS: In 2004 vs. 1989, the levels of the main traditional CV-RF have either decreased, e.g. smoking (17% vs. 30%, p < 0.001), mean blood pressure (127.8/84.8 vs. 130.0/83.4 mmHg, p < 0.05), or only moderately increased, e.g. median LDL-cholesterol (3.58 vs. 3.36 mmol/l, p < 0. 01). In contrast, marked detrimental trends were found for obesity (37% vs. 21%, p < 0.001) and several cardiometabolic CVD-RF, e.g. mean HDL-cholesterol (1.36 vs. 1.40 mmol/l, p < 0.05), median triglycerides (0.80 vs. 0.78 mmol/l, p < 0.01), mean blood glucose (5.89 vs. 5.22 mmol/l, p < 0.001), median insulin (11.6 vs. 8.3 micromol/l, p < 0.001), median HOMA-IR (2.9 vs. 1.8, p < 0.001) and diabetes (9.4% vs. 6.2%, p < 0.001). At age 40-64, the prevalence of elevated total cardiovascular risk tended to decrease (e.g. WHO-ISH risk score > or =10; 11% vs. 13%, ns), whereas the prevalence of the metabolic syndrome (which integrates several cardiometabolic CVD-RF) nearly doubled (36% vs. 20%, p < 0.001). Data on physical activity and on intake of alcohol, fruit and vegetables are also provided. Awareness and treatment rates improved substantially for hypertension and diabetes, but control rates improved for the former only. Median levels of the cardiometabolic CVD-RF increased between 1989 and 2004 within all BMI strata, suggesting that the worsening levels of cardiometabolic CVD-RF in the population were not only related to increasing BMI levels in the interval. CONCLUSION: The levels of several traditional CVD-RF improved over time, while marked detrimental trends were observed for obesity, diabetes and several cardiometabolic factors. Thus, in this population, the rapid health transition was characterized by substantial changes in the patterns of CVD-RF. More generally, this analysis suggests the importance of surveillance systems to identify risk factor trends and the need for preventive strategies to promote healthy lifestyles and nutrition.

U.S.-Norway Comparison of Interval Breast Cancers

Background: Publications from the International Breast Screening Network (IBSN) have shown that varying definitions create hurdles for comparison of screening performance. Interval breast cancer rates are particularly affected. Objective: to test whether variations in definition of interval cancer rates (ICR) affect comparisons of international ICR, specific to a comparison of ICR in Norway and North Carolina (NC). Methods: An interval cancer (IC) was defined as a cancer diagnosed following a negative screening mammogram in a defined follow-up period. ICR was calculated for women ages 50-69, at subsequent screening in Norway and NC, during the time period 1996 - 2002. ICR was defined using three different denominators (negative screens, negative final assessments and all screens) and three different numerators (DCIS, invasive cancer and all cancers). ICR was then calculated with two methods: 1) number of ICs divided by the number of screens, and ICs divided by the number of women-years at risk for IC. Results: There were no differences in ICR depending on the definition used. In the 1-12 month follow up period ICR (based on number of screens) were: 0.53, 0.54, and 0.54 for Norway; and 1.20, 1.25 and 1.17 for NC, for negative screens, negative final assessment and all screens, respectively: The same trend was seen for 13-24 and 1-24 months follow-up. Using women-years for the analysis did not change the trend. ICR was higher in NC compared to Norway under all definitions and in all follow-up time periods, regardless of calculation method. Conclusion: The ICR within or between Norway and NC did not differ by definition used. ICR were higher in NC than Norway. There are many potential explanations for the difference.

The set of undominated imputations and the core: an axiomatic approach

This paper provides an axiomatic framework to compare the D-core (the set of undominatedimputations) and the core of a cooperative game with transferable utility. Theorem1 states that the D-core is the only solution satisfying projection consistency, reasonableness (from above), (*)-antimonotonicity, and modularity. Theorem 2 characterizes the core replacing (*)-antimonotonicity by antimonotonicity. Moreover, these axioms alsocharacterize the core on the domain of convex games, totally balanced games, balancedgames, and superadditive games

Low E2F1 transcript levels are a strong determinant of favorable breast cancer outcome.

INTRODUCTION: We investigated whether mRNA levels of E2F1, a key transcription factor involved in proliferation, differentiation and apoptosis, could be used as a surrogate marker for the determination of breast cancer outcome. METHODS: E2F1 and other proliferation markers were measured by quantitative RT-PCR in 317 primary breast cancer patients from the Stiftung Tumorbank Basel. Correlations to one another as well as to the estrogen receptor and ERBB2 status and clinical outcome were investigated. Results were validated and further compared with expression-based prognostic profiles using The Netherlands Cancer Institute microarray data set reported by Fan and colleagues. RESULTS: E2F1 mRNA expression levels correlated strongly with the expression of other proliferation markers, and low values were mainly found in estrogen receptor-positive and ERBB2-negative phenotypes. Patients with low E2F1-expressing tumors were associated with favorable outcome (hazard ratio = 4.3 (95% confidence interval = 1.8-9.9), P = 0.001). These results were consistent in univariate and multivariate Cox analyses, and were successfully validated in The Netherlands Cancer Institute data set. Furthermore, E2F1 expression levels correlated well with the 70-gene signature displaying the ability of selecting a common subset of patients at good prognosis. Breast cancer patients' outcome was comparably predictable by E2F1 levels, by the 70-gene signature, by the intrinsic subtype gene classification, by the wound response signature and by the recurrence score. CONCLUSION: Assessment of E2F1 at the mRNA level in primary breast cancer is a strong determinant of breast cancer patient outcome. E2F1 expression identified patients at low risk of metastasis irrespective of the estrogen receptor and ERBB2 status, and demonstrated similar prognostic performance to different gene expression-based predictors.

Time of ruin in a risk model with generalized Erlang (n) interclaim times and a constant dividend barrier

In this paper we analyze the time of ruin in a risk process with the interclaim times being Erlang(n) distributed and a constant dividend barrier. We obtain an integro-differential equation for the Laplace Transform of the time of ruin. Explicit solutions for the moments of the time of ruin are presented when the individual claim amounts have a distribution with rational Laplace transform. Finally, some numerical results and a compare son with the classical risk model, with interclaim times following an exponential distribution, are given.