An Experimental Investigation of the Scaling of Columnar Joints

Columnar jointing is a fracture pattern common in igneous rocks in which cracks self-organize into a roughly hexagonal arrangement, leaving behind an ordered colonnade. We report observations of columnar jointing in a laboratory analog system, desiccated corn starch slurries. Using measurements of moisture density, evaporation rates, and fracture advance rates as evidence, we suggest an advective-diffusive system is responsible for the rough scaling behavior of columnar joints. This theory explains the order of magnitude difference in scales between jointing in lavas and in starches. We investigated the scaling of average columnar cross-sectional areas due to the evaporation rate, the analog of the cooling rate of igneous columnar joints. We measured column areas in experiments where the evaporation rate depended on lamp height and time, in experiments where the evaporation rate was fixed using feedback methods, and in experiments where gelatin was added to vary the rheology of the starch. Our results suggest that the column area at a particular depth is related to both the current conditions, and hysteretically to the geometry of the pattern at previous depths. We argue that there exists a range of stable column scales allowed for any particular evaporation rate.Comment: 12 pages, 11 figures, for supporting online movies, go to http://www.physics.utoronto.ca/nonlinear/movies/starch_movies.htm

Final fate of spherically symmetric gravitational collapse of a dust cloud in Einstein-Gauss-Bonnet gravity

We give a model of the higher-dimensional spherically symmetric gravitational collapse of a dust cloud in Einstein-Gauss-Bonnet gravity. A simple formulation of the basic equations is given for the spacetime $M \approx M^2 \times K^{n-2}$ with a perfect fluid and a cosmological constant. This is a generalization of the Misner-Sharp formalism of the four-dimensional spherically symmetric spacetime with a perfect fluid in general relativity. The whole picture and the final fate of the gravitational collapse of a dust cloud differ greatly between the cases with $n=5$ and $n \ge 6$. There are two families of solutions, which we call plus-branch and the minus-branch solutions. Bounce inevitably occurs in the plus-branch solution for $n \ge 6$, and consequently singularities cannot be formed. Since there is no trapped surface in the plus-branch solution, the singularity formed in the case of $n=5$ must be naked. In the minus-branch solution, naked singularities are massless for $n \ge 6$, while massive naked singularities are possible for $n=5$. In the homogeneous collapse represented by the flat Friedmann-Robertson-Walker solution, the singularity formed is spacelike for $n \ge 6$, while it is ingoing-null for $n=5$. In the inhomogeneous collapse with smooth initial data, the strong cosmic censorship hypothesis holds for $n \ge 10$ and for $n=9$ depending on the parameters in the initial data, while a naked singularity is always formed for $5 \le n \le 8$. These naked singularities can be globally naked when the initial surface radius of the dust cloud is fine-tuned, and then the weak cosmic censorship hypothesis is violated.Comment: 23 pages, 1 figure, final version to appear in Physical Review

Study of oxidative stress and C-Reactive protein in type-2 diabetes mellitus

Background: Diabetes mellitus is a group of metabolic diseases characterized by hyperglycemia resulting from defects in insulin secretion and insulin action or both. T2DM is associated with chronic low grade inflammation, possibly through a pathway involving a cytokine-mediated acute-phase response to infection and other inflammatory processes. authors aim to study C-reactive protein (CRP) which is an acute-phase reactant produced primarily in the liver hepatocytes. Oxidative stress levels in newly diagnosed T2M patients were analysed with respect to malondialdehyde (MDA) and nitric oxide (NO).Methods: Case-control study comprising of aged-sex matched subjects: newly diagnosed T2DM cases (n=30) and controls (n=30). The serum samples of subjects were analysed for levels of MDA by Buege and Aust method, while NO levels by Cortas and Wakid’s kinetic cadmium reduction method using spectrophotometer. CRP levels were analysed by using turbidimetry. Statistical analysis was done using Mini-tab 17 software with 95% confidence interval.Results: Serum levels of MDA, NO and CRP in newly diagnosed T2DM patients were significantly increased as compared to healthy controls.Conclusions:  Authors concluded that the oxidative stress and inflammation plays a pivotal role in the aetiology of hyperglycemia in T2DM. Oxidative stress and inflammatory markers might help prognosis of T2DM in hyperglycemic individuals with the help of which precautionary measure can be taken to reduce the rate of disease progression. Treatment involving anti-oxidant and anti-inflammatory medications might help to rescue vital organs from damage

Cosmic Censorship in Higher dimension II

Generalizing earlier results on dust collapse in higher dimensions, we show here that cosmic censorship can be restored in gravitational collapse with tangential pressure present if we take the spacetime dimension to be $N\ge6$. This is under conditions to be motivated physically, such as the smoothness of initial data from which the collapse develops. The models considered here incorporating a non-zero tangential pressure include the Einstein cluster spacetime.Comment: 7 pages,1 figure,revtex

Fitting in a complex chi^2 landscape using an optimized hypersurface sampling

Fitting a data set with a parametrized model can be seen geometrically as finding the global minimum of the chi^2 hypersurface, depending on a set of parameters {P_i}. This is usually done using the Levenberg-Marquardt algorithm. The main drawback of this algorithm is that despite of its fast convergence, it can get stuck if the parameters are not initialized close to the final solution. We propose a modification of the Metropolis algorithm introducing a parameter step tuning that optimizes the sampling of parameter space. The ability of the parameter tuning algorithm together with simulated annealing to find the global chi^2 hypersurface minimum, jumping across chi^2{P_i} barriers when necessary, is demonstrated with synthetic functions and with real data

An experimental study of the dual-fuel performance of a small compression ignition diesel engine operating with three gaseous fuels

A dual-fuel engine is a compression ignition (CI) engine where the primary gaseous fuel source is premixed with air as it enters the combustion chamber. This homogenous mixture is ignited by a small quantity of diesel, the ‘pilot’, that is injected towards the end of the compression stroke. In the present study, a direct-injection CI engine, was fuelled with three different gaseous fuels: methane, propane, and butane. The engine performance at various gaseous concentrations was recorded at 1500 r/min and quarter, half, and three-quarters relative to full a load of 18.7 kW. In order to investigate the combustion performance, a novel three-zone heat release rate analysis was applied to the data. The resulting heat release rate data are used to aid understanding of the performance characteristics of the engine in dual-fuel mode. Data are presented for the heat release rates, effects of engine load and speed, brake specific energy consumption of the engine, and combustion phasing of the three different primary gaseous fuels. Methane permitted the maximum energy substitution, relative to diesel, and yielded the most significant reductions in CO2. However, propane also had significant reductions in CO2 but had an increased diffusional combustion stage which may lend itself to the modern high-speed direct-injection engine

Alterations in endogenous progesterone metabolism associated with spontaneous very preterm delivery

Study question: Do maternal serum levels of progesterone metabolites early in pregnancy correspond to an increased risk for very preterm delivery prior to 32 weeks? Summary answer: Maternal serum levels of 11-deoxycorticosterone (DOC) measured during the late first trimester or early second trimester correlate with an increased risk for preterm delivery prior to 32 weeks, and the correlation becomes stronger when the ratio of DOC to 16-alpha-hydroxyprogesterone was measured. What is known already: Progesterone is a pro-gestational steroid hormone that has been shown to decrease the risk of preterm birth in some pregnant women. Progesterone is metabolized by the body into various metabolites including members of the mineralocorticoid and glucocorticoid families. Our group has previously demonstrated that some progesterone metabolites enhance myometrial contractility in an ex vivo system, while others result in myometrial relaxation. The current exploratory study was designed to determine if pre-specified metabolites of progesterone measured early in pregnancy were associated with a woman's risk for delivery prior to 32 weeks, which is referred to as a very preterm delivery. Study design size duration: The Building Blocks of Pregnancy Biobank (BBPB) is a biorepository at Indiana University (IU) that follows women prospectively through their pregnancy. A variety of biospecimens are collected at various time points during a woman's pregnancy. Women participating in the IU BBPB who were enrolled after 8 weeks' gestation with pregnancy outcome data were eligible for participation. Participants/materials setting methods: Women delivering prior to 37 weeks (preterm) and at or after 37 weeks (term) who had blood samples collected during the late first trimester/early second trimester and/or during the early third trimester were identified. These samples were then processed for mass spectroscopy, and the amount of progesterone and progesterone metabolites in the samples were measured. Mean values of each measured steroid metabolite were calculated and compared among women delivering at less than 32 weeks, less than 37 weeks and greater than or equal to 37 weeks. Receiver operating characteristic (ROC) curves were constructed and threshold levels determined for each compound to identify a level above or below which best predicted a woman's risk for delivery prior to 32 and prior to 37 weeks. Mann-Whitney U nonparametric testing with Holm-Bonferroni correction for multiple comparisons was utilized to identify steroid ratios that could differentiate women delivering spontaneously at less than 32 weeks from all other pregnancies. Main results and the role of chance: Steroid hormone levels and pregnancy outcome data were available for 93 women; 28 delivering prior to 32 weeks, 40 delivering between 32 0/7 and 36 6/7 weeks and 25 delivering at or greater than 37 weeks: the mean gestational age at delivery within the three groups was 27.0, 34.4 and 38.8 weeks, respectively. Among women delivering spontaneously at less than 37 weeks, maternal 11-deoxycorticosterone (DOC) levels drawn in the late first trimester/early second trimester were significantly associated with spontaneous preterm delivery prior to 32 weeks; a threshold level of 47.5 pg/ml had 78% sensitivity, 73% specificity and an AUC of 0.77 (P = 0.044). When DOC levels were analyzed as a ratio with other measured steroid hormones, the ratio of DOC to 16-alpha-hydroxyprogesterone among women delivering spontaneously prior to 37 weeks was able to significantly discriminate women delivering prior to 32 weeks from those delivering at or greater than 32 weeks, with a threshold value of 0.2 with 89% sensitivity, 91% specificity and an AUC of 0.92 (P = 0.002). When the entire study cohort population was considered, including women delivering at term and women having an iatrogenic preterm delivery, the ratio of DOC to 16-alpha-hydroxyprogesterone was able to discriminate women delivering spontaneously prior to 32 weeks from the rest of the population at a threshold of 0.18 and 89% sensitivity, 59% specificity and an AUC of 0.81 (P = 0.003). Limitations reasons for caution: This is a discovery study, and the findings have not been validated on an independent cohort. To mitigate issues with multiple comparisons, we limited our study to pre-specified metabolites that are most representative of the major metabolic pathways for progesterone, and adjustments for multiple comparisons were made. Wider implications of the findings: Spontaneous preterm birth is increasingly being recognized to represent a common end pathway for a number of different disease phenotypes that include infection, inflammation, premature rupture of the membranes, uterine over distension, cervical insufficiency, placental dysfunction and genetic predisposition. In addition to these phenotypes, longitudinal changes in the maternal-fetal hypothalamic-pituitary-adrenal (HPA) axis also likely contribute to a significant proportion of the disease burden of spontaneous preterm birth. Here, we demonstrate that differential production of steroid metabolites is associated with very early preterm birth. The identified biomarkers may hint at a pathophysiologic mechanism and changes in the maternal-fetal dyad that result in preterm delivery. The early identification of abnormal changes in HPA axis metabolites may allow for targeted interventions that reverse the aberrant steroid metabolic profile to a more favorable one, thereby decreasing the risk for early delivery. Further research is therefore required to validate and extend the results presented here. Study funding/competing interests: Funding for this study was provided from the Office of the Vice Chancellor for Research at IUPUI, 'Funding Opportunities for Research Commercialization and Economic Success (FORCES) grant'.Both A.S.P. and C.A.G. are affiliated with Nixxi, a biotech startup. The remaining authors report no conflict of interest

Bandwidth selection for kernel density estimation with length-biased data

Length-biased data are a particular case of weighted data, which arise in many situations: biomedicine, quality control or epidemiology among others. In this paper we study the theoretical properties of kernel density estimation in the context of length-biased data, proposing two consistent bootstrap methods that we use for bandwidth selection. Apart from the bootstrap bandwidth selectors we suggest a rule-of-thumb. These bandwidth selection proposals are compared with a least-squares cross-validation method. A simulation study is accomplished to understand the behaviour of the procedures in finite samples