Unbiased estimating equations from working correlation models for irregularly timed repeated measures

The method of generalized estimating equation-, (GEEs) has been criticized recently for a failure to protect against misspecification of working correlation models, which in some cases leads to loss of efficiency or infeasibility of solutions. However, the feasibility and efficiency of GEE methods can be enhanced considerably by using flexible families of working correlation models. We propose two ways of constructing unbiased estimating equations from general correlation models for irregularly timed repeated measures to supplement and enhance GEE. The supplementary estimating equations are obtained by differentiation of the Cholesky decomposition of the working correlation, or as score equations for decoupled Gaussian pseudolikelihood. The estimating equations are solved with computational effort equivalent to that required for a first-order GEE. Full details and analytic expressions are developed for a generalized Markovian model that was evaluated through simulation. Large-sample ".sandwich" standard errors for working correlation parameter estimates are derived and shown to have good performance. The proposed estimating functions are further illustrated in an analysis of repeated measures of pulmonary function in children.

Working correlation structure misspecification, estimation and covariate design: Implications for generalised estimating equations performance

The method of generalised estimating equations for regression modelling of clustered outcomes allows for specification of a working matrix that is intended to approximate the true correlation matrix of the observations. We investigate the asymptotic relative efficiency of the generalised estimating equation for the mean parameters when the correlation parameters are estimated by various methods. The asymptotic relative efficiency depends on three-features of the analysis, namely (i) the discrepancy between the working correlation structure and the unobservable true correlation structure, (ii) the method by which the correlation parameters are estimated and (iii) the 'design', by which we refer to both the structures of the predictor matrices within clusters and distribution of cluster sizes. Analytical and numerical studies of realistic data-analysis scenarios show that choice of working covariance model has a substantial impact on regression estimator efficiency. Protection against avoidable loss of efficiency associated with covariance misspecification is obtained when a 'Gaussian estimation' pseudolikelihood procedure is used with an AR(1) structure.

Structure-reactivity correlation in inclusion complexes: deoxycholic acid di-tert-butyl thioketone

Ultraviolet irradiation of crystalline molecular inclusion complexes of deoxycholic acid with di-tert-butyl thioketone results in no reaction. The structure of the above complex has been determined via X-ray diffraction. The absence of expected photoreactions. namely, photoreduction and photooxidation, is rationalized on the basis of the X-ray structure analysis of the complex.

Correlation of plasma IGF-I concentrations and growth rate in aquacultured finfish: a tool for assessing the potential of new diets

A recently developed radioimmunoassay (RIA) for measuring insulin-like growth factor (IGF-I) in a variety of fish species was used to investigate the correlation between growth rate and circulating IGF-I concentrations of barramundi (Lates calcarifer), Atlantic salmon (Salmo salar) and Southern Bluefin tuna (Thunnus maccoyii). Plasma IGF-I concentration significantly increased with increasing ration size in barramundi and IGF-I concentration was positively correlated to growth rates obtained in Atlantic salmon (r2=0.67) and barramundi (r2=0.65) when fed a variety of diet formulations. IGF-I was also positively correlated to protein concentration (r2=0.59). This evidence suggested that measuring IGF-I concentration may provide a useful tool for monitoring fish growth rate and also as a method to rapidly assess different aquaculture diets. However, no such correlation was demonstrated in the tuna study probably due to seasonal cooling of sea surface temperature shortly before blood was sampled. Thus, some recommendations for the design and sampling strategy of nutritional trials where IGF-I concentrations are measured are discussed

Inverse Correlation between Vitamin D and C-Reactive Protein in Newborns

Some studies suggested that adequate vitamin D might reduce inflammation in adults. However, little is known about this association in early life. We aimed to determine the relationship between cord blood 25-hydroxyvitamin D (25(OH)D) and C-reactive protein (CRP) in neonates. Cord blood levels of 25(OH)D and CRP were measured in 1491 neonates in Hefei, China. Potential confounders including maternal sociodemographic characteristics, perinatal health status, lifestyle, and birth outcomes were prospectively collected. The average values of cord blood 25(OH)D and CRP were 39.43 nmol/L (SD = 20.35) and 6.71 mg/L (SD = 3.07), respectively. Stratified by 25(OH)D levels, per 10 nmol/L increase in 25(OH)D, CRP decreased by 1.42 mg/L (95% CI: 0.90, 1.95) among neonates with 25(OH)D <25.0 nmol/L, and decreased by 0.49 mg/L (95% CI: 0.17, 0.80) among neonates with 25(OH)D between 25.0 nmol/L and 49.9 nmol/L, after adjusting for potential confounders. However, no significant association between 25(OH)D and CRP was observed among neonates with 25(OH)D ≥50 nmol/L. Cord blood 25(OH)D and CRP levels showed a significant seasonal trend with lower 25(OH)D and higher CRP during winter-spring than summer-autumn. Stratified by season, a significant linear association of 25(OH)D with CRP was observed in neonates born in winter-spring (adjusted β = −0.11, 95% CI: −0.13, −0.10), but not summer-autumn. Among neonates born in winter-spring, neonates with 25(OH)D <25 nmol/L had higher risk of CRP ≥10 mg/L (adjusted OR = 3.06, 95% CI: 2.00, 4.69), compared to neonates with 25(OH)D ≥25 nmol/L. Neonates with vitamin D deficiency had higher risk of exposure to elevated inflammation at birth.

A Nonlinear System Under Combined Periodic and Random Excitation

The anharmonic oscillator under combined sinusoidal and white noise excitation is studied using the Gaussian closure approximation. The mean response and the steady-state variance of the system is obtained by the WKBJ approximation and also by the Fokker Planck equation. The multiple steadystate solutions are obtained and their stability analysis is presented. Numerical results are obtained for a particular set of system parameters. The theoretical results are compared with a digital simulation study to bring out the usefulness of the present approximate theory.

Strong-coupling expansion for the momentum distribution of the Bose-Hubbard model with benchmarking against exact numerical results

A strong-coupling expansion for the Green's functions, self-energies, and correlation functions of the Bose-Hubbard model is developed. We illustrate the general formalism, which includes all possible (normal-phase) inhomogeneous effects in the formalism, such as disorder or a trap potential, as well as effects of thermal excitations. The expansion is then employed to calculate the momentum distribution of the bosons in the Mott phase for an infinite homogeneous periodic system at zero temperature through third order in the hopping. By using scaling theory for the critical behavior at zero momentum and at the critical value of the hopping for the Mott insulator–to–superfluid transition along with a generalization of the random-phase-approximation-like form for the momentum distribution, we are able to extrapolate the series to infinite order and produce very accurate quantitative results for the momentum distribution in a simple functional form for one, two, and three dimensions. The accuracy is better in higher dimensions and is on the order of a few percent relative error everywhere except close to the critical value of the hopping divided by the on-site repulsion. In addition, we find simple phenomenological expressions for the Mott-phase lobes in two and three dimensions which are much more accurate than the truncated strong-coupling expansions and any other analytic approximation we are aware of. The strong-coupling expansions and scaling-theory results are benchmarked against numerically exact quantum Monte Carlo simulations in two and three dimensions and against density-matrix renormalization-group calculations in one dimension. These analytic expressions will be useful for quick comparison of experimental results to theory and in many cases can bypass the need for expensive numerical simulations.

Characterization of disease resistance gene candidates of the nucleotide binding site (NBS) type from banana and correlation of a transcriptional polymorphism with resistance to Fusarium oxysporum f.sp. cubense race 4

Most plant disease resistance (R) genes encode proteins with a nucleotide binding site and leucine-rich repeat structure (NBS-LRR). In this study, degenerate primers were used to amplify genomic NBS-type sequences from wild banana (Musa acuminata ssp. malaccensis) plants resistant to the fungal pathogen Fusarium oxysporum formae specialis (f. sp.) cubense (FOC) race 4. Five different classes of NBS-type sequences were identified and designated as resistance gene candidates (RGCs). The deduced amino acid sequences of the RGCs revealed the presence of motifs characteristic of the majority of known plant NBS-LRR resistance genes. Structural and phylogenetic analyses grouped the banana RGCs within the non-TIR (homology to Toll/interleukin-1 receptors) subclass of NBS sequences. Southern hybridization showed that each banana RGC is present in low copy number. The expression of the RGCs was assessed by RT-PCR in leaf and root tissues of plants resistant or susceptible to FOC race 4. RGC1, 3 and 5 showed a constitutive expression profile in both resistant and susceptible plants whereas no expression was detected for RGC4. Interestingly, RGC2 expression was found to be associated only to FOC race 4 resistant lines. This finding could assist in the identification of a FOC race 4 resistance gene.

Pulsed laser surface treatment of magnesium alloy: Correlation between thermal model and experimental observations

The effect of deposition of Al +Al2O3 on MRI 153 M Mg alloy processed using a pulsed Nd:YAG laser is presented in this study. A composite coating with metallurgical joint to the substrate was formed. The microstructure and phase constituents were characterized and correlated with the thermal predictions. The laser scan speed had an effect on the average melt depth and the amount of retained and/or reconstituted alumina in the final coating. The coating consisted of alumina particles and highly refined dendrites formed due to the extremely high cooling rates (of the order of 10(8) K/s). The microhardness of the coating was higher and several fold improvement of wear resistance compared to the substrate was observed for the coatings. These microstructural features and physical properties were correlated with the effects predicted by a thermal model.

Spectral analysis of pair-correlation bandwidth: Application to cell biology images

Images from cell biology experiments often indicate the presence of cell clustering, which can provide insight into the mechanisms driving the collective cell behaviour. Pair-correlation functions provide quantitative information about the presence, or absence, of clustering in a spatial distribution of cells. This is because the pair-correlation function describes the ratio of the abundance of pairs of cells, separated by a particular distance, relative to a randomly distributed reference population. Pair-correlation functions are often presented as a kernel density estimate where the frequency of pairs of objects are grouped using a particular bandwidth (or bin width), Δ>0. The choice of bandwidth has a dramatic impact: choosing Δ too large produces a pair-correlation function that contains insufficient information, whereas choosing Δ too small produces a pair-correlation signal dominated by fluctuations. Presently, there is little guidance available regarding how to make an objective choice of Δ. We present a new technique to choose Δ by analysing the power spectrum of the discrete Fourier transform of the pair-correlation function. Using synthetic simulation data, we confirm that our approach allows us to objectively choose Δ such that the appropriately binned pair-correlation function captures known features in uniform and clustered synthetic images. We also apply our technique to images from two different cell biology assays. The first assay corresponds to an approximately uniform distribution of cells, while the second assay involves a time series of images of a cell population which forms aggregates over time. The appropriately binned pair-correlation function allows us to make quantitative inferences about the average aggregate size, as well as quantifying how the average aggregate size changes with time.

Correlation Between The Stability Of Carbonates In Ternary Ln2o3-H2o-Co2 Hydrothermal Systems And Lanthanide Systematics

Phase diagrams for ternary Ln2O3-H2O-CO2 systems for the entire lanthanide series (except promethium) were studied at temperatures in the range 100–950 °C and pressures up to 3000 bar. The phase diagrams obtained for the heavier lanthanides are far more complex, with the appearance of a number of stable carbonate phases. New carbonates isolated from lanthanide systems (Ln ≡ Tm, Yb, Lu) include Ln6(OH)4(CO3)7, Ln4(OH)6-(CO3)3, Ln2O(OH)2CO3, Ln6O2(OH)8(CO3)3 and Ln12O7(OH)10(CO3)6. Stable carbonate phases common to all the lighter lanthanides are hexagonal LnOHCO3 and hexagonal Ln2O2CO3. Ln2(CO3)3• 3H2O is stable from samarium onwards and orthorhombic LnOHCO3 is stable from gadolinium onwards. On the basis of the appearance of stable carbonates, four different groups of lanthanides were established: lanthanum to neodymium, promethium to europium, terbium to erbium and thulium to lutetium. Gadolinium is the connecting element between groups II and III. This is in accordance with the tetrad classification for f transition elements.

A novel approach to structure—flammability correlation in polyphosphate esters

The relationship between the structure and flammability of a number of polyphosphate esters has been examined. The conventional correlation of char residue with limiting oxygen index was found to be unproductive in these polymers, giving insight into the importance of gas-phase reactions in addition to condensed-phase reactions in determining their flammability. A novel approach was sought in understanding the structure-flammability relationships of these polymers relating thermal stability, phosphorus content and limiting oxygen index. An empirical relationship has been derived amongst these three parameters.

Periodic Rayleigh waves of finite amplitude on an isotropic solid

Existence of a periodic progressive wave solution to the nonlinear boundary value problem for Rayleigh surface waves of finite amplitude is demonstrated using an extension of the method of strained coordinates. The solution, obtained as a second-order perturbation of the linearized monochromatic Rayleigh wave solution, contains harmonics of all orders of the fundamental frequency. It is shown that the higher harmonic content of the wave increases with amplitude, but the slope of the waveform remains finite so long as the amplitude is less than a critical value.

Adult-type hypolactasia: Genotype-phenotype correlation

Adult-type hypolactasia (primary lactose malabsorption, lactase non-persistence) is the most common enzyme deficiency worldwide, and manifests with symptoms of lactose intolerance such as abdominal pain, gas formation and diarrhea. In humans with adult-type hypolactasia, lactase activity is high at birth, but declines during childhood to about one-tenth of the activity at birth. In 2002, a one base polymorphism C/T-13910, located 14 kilobases from the starting codon of the lactase-phlorizin hydrolase (LPH) gene was observed to be associated with the persistence of lactase activity. The T-13910 allele (C/T-13910 and T/T-13910 genotypes) associates with persistence of lactase activity throughout life, whereas the C/C-13910 genotype associates with adult-type hypolactasia. In this thesis work, the timing and mechanism of decline of lactase enzyme activity during development was studied using the C/T-13910 polymorphism as a molecular marker. We observed an excellent correlation between low lactase activity and the C/C-13910 genotype in all subjects > 12 years of age, irrespective their ethnicity. In children of African origin, the lactase activity declined somewhat earlier than among Finnish children. Furthermore, we observed an increasing imbalance in the relative lactase mRNA expression from the C-13910 and T-13910 alleles in Finnish children beginning from five years of age. The genetic test for adult-type hypolactasia showed a sensitivity of 93% and a specificity of 100% in the Finnish children and adolescents > 12 years of age. The relation of milk consumption and the milk-related abdominal complaints to the C/T-13910 genotypes associated with lactase persistence/non-persistence was studied by a questionnaire-based approach in > 2100 Finns. Both Finnish children and adults with the C/C-13910 genotype consumed significantly less dairy products compared to those with the C/T-13910 and T/T-13910 genotypes. Flatulence was the only of the abdominal symptoms of lactose intolerance that subjects with the C/C-13910 genotype reported significantly more often than those with the C/T-13910 and T/T-13910 genotypes. A minor proportion (<10%) of subjects with the C/C-13910 genotype, nevertheless, reported drinking milk without any symptoms afterwards. There was no association between cow's milk allergy starting as a newborn and adult-type hypolactasia. In an association study an increased risk of colorectal cancer was observed among those with molecular diagnosis of adult-type hypolactasia. It warrants further studies to clarify whether the increased risk observed in the Finnish population is associated with lactose or decreased intake of dairy products in these subjects.

A new method for generation of quasi-periodic structures withn fold axes: Application to five and seven folds

A new geometrical method for generating aperiodic lattices forn-fold non-crystallographic axes is described. The method is based on the self-similarity principle. It makes use of the principles of gnomons to divide the basic triangle of a regular polygon of 2n sides to appropriate isosceles triangles and to generate a minimum set of rhombi required to fill that polygon. The method is applicable to anyn-fold noncrystallographic axis. It is first shown how these regular polygons can be obtained and how these can be used to generate aperiodic structures. In particular, the application of this method to the cases of five-fold and seven-fold axes is discussed. The present method indicates that the recursion rule used by others earlier is a restricted one and that several aperiodic lattices with five fold symmetry could be generated. It is also shown how a limited array of approximately square cells with large dimensions could be detected in a quasi lattice and these are compared with the unit cell dimensions of MnAl6 suggested by Pauling. In addition, the recursion rule for sub-dividing the three basic rhombi of seven-fold structure was obtained and the aperiodic lattice thus generated is also shown.