On the Sample Information About Parameter and Prediction

The Bayesian measure of sample information about the parameter, known as Lindley's measure, is widely used in various problems such as developing prior distributions, models for the likelihood functions and optimal designs. The predictive information is defined similarly and used for model selection and optimal designs, though to a lesser extent. The parameter and predictive information measures are proper utility functions and have been also used in combination. Yet the relationship between the two measures and the effects of conditional dependence between the observable quantities on the Bayesian information measures remain unexplored. We address both issues. The relationship between the two information measures is explored through the information provided by the sample about the parameter and prediction jointly. The role of dependence is explored along with the interplay between the information measures, prior and sampling design. For the conditionally independent sequence of observable quantities, decompositions of the joint information characterize Lindley's measure as the sample information about the parameter and prediction jointly and the predictive information as part of it. For the conditionally dependent case, the joint information about parameter and prediction exceeds Lindley's measure by an amount due to the dependence. More specific results are shown for the normal linear models and a broad subfamily of the exponential family. Conditionally independent samples provide relatively little information for prediction, and the gap between the parameter and predictive information measures grows rapidly with the sample size.Comment: Published in at http://dx.doi.org/10.1214/10-STS329 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

A finite-difference solution of solute transport through a membrane bioreactor

The current paper presents a theoretical analysis of the transport of solutes through a fixed-film membrane bioreactor (MBR), immobilised with an active biocatalyst. The dimensionless convection-diffusion equation with variable coefficients was solved analytically and numerically for concentration profiles of the solutes through the MBR. The analytical solution makes use of regular perturbation and accounts for radial convective flow as well as axial diffusion of the substrate species. The Michaelis-Menten (or Monod) rate equation was assumed for the sink term, and the perturbation was extended up to second-order. In the analytical solution only the first-order limit of the Michaelis-Menten equation was considered; hence the linearized equation was solved. In the numerical solution, however, this restriction was lifted. The solution of the nonlinear, elliptic, partial differential equation was based on an implicit finite-difference method (FDM). An upwind scheme was employed for numerical stability. The resulting algebraic equations were solved simultaneously using the multivariate Newton-Raphson iteration method. The solution allows for the evaluation of the effect on the concentration profiles of (i) the radial and axial convective velocity, (ii) the convective mass transfer rates, (iii) the reaction rates, (iv) the fraction retentate, and (v) the aspect ratio

Conformal symmetry and light flavor baryon spectra

The degeneracy among parity pairs systematically observed in the N and Delta spectra is interpreted to hint on a possible conformal symmetry realization in the light flavor baryon sector in line with AdS_5/CFT_4. The case is made by showing that all the observed N and Delta resonances with masses below 2500 MeV distribute fairly well each over the first levels of a unitary representation of the conformal group, a representation that covers the spectrum of a quark-diquark system, placed directly on the AdS_5 cone, conformally compactified to R^1*S^3. The free geodesic motion on the S^3 manifold is described by means of the scalar conformal equation there, which is of the Klein-Gordon type. The equation is then gauged by the "curved" Coulomb potential that has the form of a cotangent function. Conformal symmetry is not exact, this because the gauge potential slightly modifies the conformal centrifugal barrier of the free geodesic motion. Thanks to this, the degeneracy between P11-S11 pairs from same level is relaxed, while the remaining states belonging to same level remain practically degenerate. The model describes the correct mass ordering in the P11-S11 pairs through the nucleon spectrum as a combined effect of the above conformal symmetry breaking, on the one side, and a parity change of the diquark from a scalar at low masses, to a pseudoscalar at higher masses, on the other. The quality of the wave functions is illustrated by calculations of realistic mean-square charge radii and electric charge form-factors on the examples of the proton, and the protonic P11(1440), and S11(1535) resonances. The scheme also allows for a prediction of the dressing function of an effective instantaneous gluon propagator from the Fourier transform of the gauge potential. We find a dressing function that is finite in the infrared and tends to zero at infinity.Comment: Latex, 5 figures, 2 tables; Paper upgraded in accord with the published version. Discussion on the meson sector include

The L_X--M relation of Clusters of Galaxies

We present a new measurement of the scaling relation between X-ray luminosity and total mass for 17,000 galaxy clusters in the maxBCG cluster sample. Stacking sub-samples within fixed ranges of optical richness, N_200, we measure the mean 0.1-2.4 keV X-ray luminosity, , from the ROSAT All-Sky Survey. The mean mass, , is measured from weak gravitational lensing of SDSS background galaxies (Johnston et al. 2007). For 9 <= N_200 < 200, the data are well fit by a power-law, /10^42 h^-2 erg/s = (12.6+1.4-1.3 (stat) +/- 1.6 (sys)) (/10^14 h^-1 M_sun)^1.65+/-0.13. The slope agrees to within 10% with previous estimates based on X-ray selected catalogs, implying that the covariance in L_X and N_200 at fixed halo mass is not large. The luminosity intercent is 30%, or 2\sigma, lower than determined from the X-ray flux-limited sample of Reiprich & Bohringer (2002), assuming hydrostatic equilibrium. This difference could arise from a combination of Malmquist bias and/or systematic error in hydrostatic mass estimates, both of which are expected. The intercept agrees with that derived by Stanek et al. (2006) using a model for the statistical correspondence between clusters and halos in a WMAP3 cosmology with power spectrum normalization sigma_8 = 0.85. Similar exercises applied to future data sets will allow constraints on the covariance among optical and hot gas properties of clusters at fixed mass.Comment: 5 pages, 1 figure, MNRAS accepte

Recurrent geomagnetic storms and relativistic electron enhancements in the outer magnetosphere: ISTP coordinated measurements

New, coordinated measurements from the International Solar-Terrestrial Physics (ISTP) constellation of spacecraft are presented to show the causes and effects of recurrent geomagnetic activity during recent solar minimum conditions. It is found using WIND and POLAR data that even for modest geomagnetic storms, relativistic electron fluxes are strongly and rapidly enhanced within the outer radiation zone of the Earth\u27s magnetosphere. Solar wind data are utilized to identify the drivers of magnetospheric acceleration processes. Yohkoh solar soft X-ray data are also used to identify the solar coronal holes that produce the high-speed solar wind streams which, in turn, cause the recurrent geomagnetic activity. It is concluded that even during extremely quiet solar conditions (sunspot minimum) there are discernible coronal holes and resultant solar wind streams which can produce intense magnetospheric particle acceleration. As a practical consequence of this Sun-Earth connection, it is noted that a long-lasting E\u3e1MeV electron event in late March 1996 appears to have contributed significantly to a major spacecraft (Anik E1) operational failure

Penrose Diagram for a Transient Black Hole

A Penrose diagram is constructed for a spatially coherent black hole that smoothly begins an accretion, then excretes symmetrically as measured by a distant observer, with the initial and final states described by a metric of Minkowski form. Coordinate curves on the diagram are computationally derived. Causal relationships between space-time regions are briefly discussed. The life cycle of the black hole demonstrably leaves asymptotic observers in an unaltered Minkowski space-time of uniform conformal scale.Comment: 14 pages, 9 figures, spelling correction

Research in the Restricted Problems of Three and Four Bodies Final Scientific Report

Seven studies have been conducted on research in the existence and nature of solutions of the restricted problems of three and four bodies. The details and results of five of these research investigations have already been published, and the latest two studies will be published shortly. A complete bibliography of publications is included in this report. This research has been primarily qualitative and has yielded new information on the behavior of trajectories near the libration points in the Earth-Moon-Sun and Sun-Jupiter-Saturn systems, and on the existence of periodic trajectories about the libration points of the circular and elliptical restricted four-body models. We have also implemented Birkhoff's normalization process for conservative and nonconservative Hamiltonian systems with equilibrium points. This makes available a technique for analyzing stability properties of certain nonlinear dynamical systems, and we have applied this technique to the circular and elliptical restricted three-body models. A related study was also conducted to determine the feasibility of using cislunar periodic trajectories for various space missions. Preliminary results suggest that this concept is attractive for space flight safety operations in cislunar space. Results of this research will be of interest to mathematicians, particularly those working in ordinary differential equations, dynamical systems and celestial mechanics; to astronomers; and to space guidance and mission analysts

Nutrition impacts the prevalence of peripheral arterial disease in the United States

ObjectiveTraditional recommendations for peripheral arterial disease (PAD) risk factor reduction include smoking cessation, low-fat/low-salt diet, exercise, and optimal medical management of chronic disease. Little attention has been paid to the role of dietary supplementation of specific nutrients in the prevention of PAD.MethodsThis cross-sectional study used the National Health and Nutrition Examination Survey (NHANES) to determine specific nutrients that are associated with prevalent PAD in the United States (US) population. NHANES data include nationwide sampling of the US population, using physical examination, questionnaire, and laboratory testing. PAD status was defined by an ankle-brachial index (ABI) of <0.9. Nutritional information was collected by 24-hour dietary recall using the US Department of Agriculture dietary collection instrument. Data were linked to a database of foods and their nutrient composition. Univariate and multivariate logistic regression analyses were performed to evaluate associations between specific nutrient intake and the presence of PAD. Multivariate models adjusted for the effects of age, gender, hypertension, coronary vascular disease, diabetes, and smoking.ResultsNHANES data for 1999 to 2004 included 7203 lower extremity examinations, of which 422 individuals had prevalent PAD (5.9%). Examinees with PAD had significantly higher rates of hypertension, coronary artery disease, diabetes, and smoking than those without PAD. Univariate analysis revealed that consumption of all nutrients considered were associated with lower odds of PAD, including antioxidants (vitamins A, C, and E), folate, other B vitamins (B6, B12), fiber, and polyunsaturated and saturated fatty acids. After adjustment for traditional risk factors, nutrients associated with reduced prevalence of PAD were vitamin A (odds ratio [OR], 0.79; P = .036), vitamin C (OR, 0.84; P < .001), vitamin E (OR, 0.78; P = .011), vitamin B6 (OR, 0.71; P = .023), fiber (OR, 0.65; P < .001), folate (OR, 0.67; P = .006), and ω-3 (α-linolenic) fatty acid (OR, 0.79; P = .028).ConclusionsImproved nutrition is associated with a reduced prevalence of PAD in the US population. Higher consumption of specific nutrients, including antioxidants (vitamin A, C, and E), vitamin B6, fiber, folate, and ω-3 fatty acids have a significant protective effect, irrespective of traditional cardiovascular risk factors. These findings suggest specific dietary supplementation may afford additional protection, above traditional risk factor modification, for the prevention of PAD

Resonant Transfer and Excitation in Li-Like F Colliding with H₂

We have measured coincidences between x rays and projectiles that have captured one electron in F6+ + H2 collisions at projectile energies between 15 and 33 MeV. The cross sections for capture and simultaneous x-ray emission as a function of projectile energy show clear structures. Indications of an unexpectedly high population of high-n states predominantly formed by resonant transfer and excitation (RTE) were found. Above the Kln (n\u3e1) RTE resonance energies another maximum was observed

Cyanobacterial life at low O 2 : community genomics and function reveal metabolic versatility and extremely low diversity in a Great Lakes sinkhole mat

Cyanobacteria are renowned as the mediators of Earth’s oxygenation. However, little is known about the cyanobacterial communities that flourished under the low‐O 2 conditions that characterized most of their evolutionary history. Microbial mats in the submerged Middle Island Sinkhole of Lake Huron provide opportunities to investigate cyanobacteria under such persistent low‐O 2 conditions. Here, venting groundwater rich in sulfate and low in O 2 supports a unique benthic ecosystem of purple‐colored cyanobacterial mats. Beneath the mat is a layer of carbonate that is enriched in calcite and to a lesser extent dolomite. In situ benthic metabolism chambers revealed that the mats are net sinks for O 2 , suggesting primary production mechanisms other than oxygenic photosynthesis. Indeed, 14 C‐bicarbonate uptake studies of autotrophic production show variable contributions from oxygenic and anoxygenic photosynthesis and chemosynthesis, presumably because of supply of sulfide. These results suggest the presence of either facultatively anoxygenic cyanobacteria or a mix of oxygenic/anoxygenic types of cyanobacteria. Shotgun metagenomic sequencing revealed a remarkably low‐diversity mat community dominated by just one genotype most closely related to the cyanobacterium Phormidium autumnale , for which an essentially complete genome was reconstructed. Also recovered were partial genomes from a second genotype of Phormidium and several Oscillatoria . Despite the taxonomic simplicity, diverse cyanobacterial genes putatively involved in sulfur oxidation were identified, suggesting a diversity of sulfide physiologies. The dominant Phormidium genome reflects versatile metabolism and physiology that is specialized for a communal lifestyle under fluctuating redox conditions and light availability. Overall, this study provides genomic and physiologic insights into low‐O 2 cyanobacterial mat ecosystems that played crucial geobiological roles over long stretches of Earth history.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90535/1/j.1472-4669.2012.00322.x.pd