Radon-222 activity flux measurement using activated charcoal canisters: Revisiting the methodology

The measurement of radon ((222)Rn) activity flux using activated charcoal canisters was examined to investigate the distribution of the adsorbed (222)Rn in the charcoal bed and the relationship between (222)Rn activity flux and exposure time. The activity flux of (222)Rn from five sources of varying strengths was measured for exposure times of one, two, three, five, seven, 10, and 14 days. The distribution of the adsorbed (222)Rn in the charcoal bed was obtained by dividing the bed into six layers and counting each layer separately after the exposure. (222)Rn activity decreased in the layers that were away from the exposed surface. Nevertheless, the results demonstrated that only a small correction might be required in the actual application of charcoal canisters for activity flux measurement, where calibration standards were often prepared by the uniform mixing of radium ((226)Ra) in the matrix. This was because the diffusion of (222)Rn in the charcoal bed and the detection efficiency as a function of the charcoal depth tended to counterbalance each other. The influence of exposure time on the measured (222)Rn activity flux was observed in two situations of the canister exposure layout: (a) canister sealed to an open bed of the material and (b) canister sealed over a jar containing the material. The measured (222)Rn activity flux decreased as the exposure time increased. The change in the former situation was significant with an exponential decrease as the exposure time increased. In the latter case, lesser reduction was noticed in the observed activity flux with respect to exposure time. This reduction might have been related to certain factors, such as absorption site saturation or the back diffusion of (222)Rn gas occurring at the canister-soil interface.

Fractal and complex network analyses of protein molecular dynamics

Based on protein molecular dynamics, we investigate the fractal properties of energy, pressure and volume time series using the multifractal detrended fluctuation analysis (MF-DFA) and the topological and fractal properties of their converted horizontal visibility graphs (HVGs). The energy parameters of protein dynamics we considered are bonded potential, angle potential, dihedral potential, improper potential, kinetic energy, Van der Waals potential, electrostatic potential, total energy and potential energy. The shape of the h(q)h(q) curves from MF-DFA indicates that these time series are multifractal. The numerical values of the exponent h(2)h(2) of MF-DFA show that the series of total energy and potential energy are non-stationary and anti-persistent; the other time series are stationary and persistent apart from series of pressure (with H≈0.5H≈0.5 indicating the absence of long-range correlation). The degree distributions of their converted HVGs show that these networks are exponential. The results of fractal analysis show that fractality exists in these converted HVGs. For each energy, pressure or volume parameter, it is found that the values of h(2)h(2) of MF-DFA on the time series, exponent λλ of the exponential degree distribution and fractal dimension dBdB of their converted HVGs do not change much for different proteins (indicating some universality). We also found that after taking average over all proteins, there is a linear relationship between 〈h(2)〉〈h(2)〉 (from MF-DFA on time series) and 〈dB〉〈dB〉 of the converted HVGs for different energy, pressure and volume.

Topological properties and fractal analysis of a recurrence network constructed from fractional Brownian motions

Many studies have shown that we can gain additional information on time series by investigating their accompanying complex networks. In this work, we investigate the fundamental topological and fractal properties of recurrence networks constructed from fractional Brownian motions (FBMs). First, our results indicate that the constructed recurrence networks have exponential degree distributions; the average degree exponent 〈λ〉 increases first and then decreases with the increase of Hurst index H of the associated FBMs; the relationship between H and 〈λ〉 can be represented by a cubic polynomial function. We next focus on the motif rank distribution of recurrence networks, so that we can better understand networks at the local structure level. We find the interesting superfamily phenomenon, i.e., the recurrence networks with the same motif rank pattern being grouped into two superfamilies. Last, we numerically analyze the fractal and multifractal properties of recurrence networks. We find that the average fractal dimension 〈dB〉 of recurrence networks decreases with the Hurst index H of the associated FBMs, and their dependence approximately satisfies the linear formula 〈dB〉≈2-H, which means that the fractal dimension of the associated recurrence network is close to that of the graph of the FBM. Moreover, our numerical results of multifractal analysis show that the multifractality exists in these recurrence networks, and the multifractality of these networks becomes stronger at first and then weaker when the Hurst index of the associated time series becomes larger from 0.4 to 0.95. In particular, the recurrence network with the Hurst index H=0.5 possesses the strongest multifractality. In addition, the dependence relationships of the average information dimension 〈D(1)〉 and the average correlation dimension 〈D(2)〉 on the Hurst index H can also be fitted well with linear functions. Our results strongly suggest that the recurrence network inherits the basic characteristic and the fractal nature of the associated FBM series.

Two-scale computational modelling of water flow in unsaturated soils containing irregular-shaped inclusions

The focus of this paper is two-dimensional computational modelling of water flow in unsaturated soils consisting of weakly conductive disconnected inclusions embedded in a highly conductive connected matrix. When the inclusions are small, a two-scale Richards’ equation-based model has been proposed in the literature taking the form of an equation with effective parameters governing the macroscopic flow coupled with a microscopic equation, defined at each point in the macroscopic domain, governing the flow in the inclusions. This paper is devoted to a number of advances in the numerical implementation of this model. Namely, by treating the micro-scale as a two-dimensional problem, our solution approach based on a control volume finite element method can be applied to irregular inclusion geometries, and, if necessary, modified to account for additional phenomena (e.g. imposing the macroscopic gradient on the micro-scale via a linear approximation of the macroscopic variable along the microscopic boundary). This is achieved with the help of an exponential integrator for advancing the solution in time. This time integration method completely avoids generation of the Jacobian matrix of the system and hence eases the computation when solving the two-scale model in a completely coupled manner. Numerical simulations are presented for a two-dimensional infiltration problem.

Temporal dependence of in vivo USPIO-enhanced MRI signal changes in human carotid atheromatous plaques

Introduction: Ultrasmall superparamagnetic iron oxide (USPIO)-enhanced MRI has been shown to be a useful modality to image activated macrophages in vivo, which are principally responsible for plaque inflammation. This study determined the optimum imaging time-window to detect maximal signal change post-USPIO infusion using T1-weighted (T1w), T2*- weighted (T2*w) and quantitative T2*(qT 2*) imaging. Methods: Six patients with an asymptomatic carotid stenosis underwent high resolution T1w, T2*w and qT2*MR imaging of their carotid arteries at 1.5 T. Imaging was performed before and at 24, 36, 48, 72 and 96 h after USPIO (Sinerem™, Guerbet, France) infusion. Each slice showing atherosclerotic plaque was manually segmented into quadrants and signal changes in each quadrant were fitted to an exponential power function to model the optimum time for post-infusion imaging. Results: The power function determining the mean time to convergence for all patients was 46, 41 and 39 h for the T1w, T 2*w and qT2*sequences, respectively. When modelling each patient individually, 90% of the maximum signal intensity change was observed at 36 h for three, four and six patients on T1w, T 2*w and qT2*, respectively. The rates of signal change decrease after this period but signal change was still evident up to 96 h. Conclusion: This study showed that a suitable imaging window for T 1w, T2*w and qT2*signal changes post-USPIO infusion was between 36 and 48 h. Logistically, this would be convenient in bringing patients back for one post-contrast MRI, but validation is required in a larger cohort of patients.

Model selection with misspecified spatial covariance structure

Spatial data analysis has become more and more important in the studies of ecology and economics during the last decade. One focus of spatial data analysis is how to select predictors, variance functions and correlation functions. However, in general, the true covariance function is unknown and the working covariance structure is often misspecified. In this paper, our target is to find a good strategy to identify the best model from the candidate set using model selection criteria. This paper is to evaluate the ability of some information criteria (corrected Akaike information criterion, Bayesian information criterion (BIC) and residual information criterion (RIC)) for choosing the optimal model when the working correlation function, the working variance function and the working mean function are correct or misspecified. Simulations are carried out for small to moderate sample sizes. Four candidate covariance functions (exponential, Gaussian, Matern and rational quadratic) are used in simulation studies. With the summary in simulation results, we find that the misspecified working correlation structure can still capture some spatial correlation information in model fitting. When the sample size is large enough, BIC and RIC perform well even if the the working covariance is misspecified. Moreover, the performance of these information criteria is related to the average level of model fitting which can be indicated by the average adjusted R square ( [GRAPHICS] ), and overall RIC performs well.

Smoothed rank-based procedure for censored data

A smoothed rank-based procedure is developed for the accelerated failure time model to overcome computational issues. The proposed estimator is based on an EM-type procedure coupled with the induced smoothing. "The proposed iterative approach converges provided the initial value is based on a consistent estimator, and the limiting covariance matrix can be obtained from a sandwich-type formula. The consistency and asymptotic normality of the proposed estimator are also established. Extensive simulations show that the new estimator is not only computationally less demanding but also more reliable than the other existing estimators.

Quantile regression for longitudinal data with a working correlation model

This paper proposes a linear quantile regression analysis method for longitudinal data that combines the between- and within-subject estimating functions, which incorporates the correlations between repeated measurements. Therefore, the proposed method results in more efficient parameter estimation relative to the estimating functions based on an independence working model. To reduce computational burdens, the induced smoothing method is introduced to obtain parameter estimates and their variances. Under some regularity conditions, the estimators derived by the induced smoothing method are consistent and have asymptotically normal distributions. A number of simulation studies are carried out to evaluate the performance of the proposed method. The results indicate that the efficiency gain for the proposed method is substantial especially when strong within correlations exist. Finally, a dataset from the audiology growth research is used to illustrate the proposed methodology.

Rank regression for accelerated failure time model with clustered and censored data

For clustered survival data, the traditional Gehan-type estimator is asymptotically equivalent to using only the between-cluster ranks, and the within-cluster ranks are ignored. The contribution of this paper is two fold: - (i) incorporating within-cluster ranks in censored data analysis, and; - (ii) applying the induced smoothing of Brown and Wang (2005, Biometrika) for computational convenience. Asymptotic properties of the resulting estimating functions are given. We also carry out numerical studies to assess the performance of the proposed approach and conclude that the proposed approach can lead to much improved estimators when strong clustering effects exist. A dataset from a litter-matched tumorigenesis experiment is used for illustration.

Rank regression analysis of correlated water quality data from South East Queensland

With growing population and fast urbanization in Australia, it is a challenging task to maintain our water quality. It is essential to develop an appropriate statistical methodology in analyzing water quality data in order to draw valid conclusions and hence provide useful advices in water management. This paper is to develop robust rank-based procedures for analyzing nonnormally distributed data collected over time at different sites. To take account of temporal correlations of the observations within sites, we consider the optimally combined estimating functions proposed by Wang and Zhu (Biometrika, 93:459-464, 2006) which leads to more efficient parameter estimation. Furthermore, we apply the induced smoothing method to reduce the computational burden. Smoothing leads to easy calculation of the parameter estimates and their variance-covariance matrix. Analysis of water quality data from Total Iron and Total Cyanophytes shows the differences between the traditional generalized linear mixed models and rank regression models. Our analysis also demonstrates the advantages of the rank regression models for analyzing nonnormal data.

Nonparametric rank regression for analyzing water quality concentration data with multiple detection limits

Environmental data usually include measurements, such as water quality data, which fall below detection limits, because of limitations of the instruments or of certain analytical methods used. The fact that some responses are not detected needs to be properly taken into account in statistical analysis of such data. However, it is well-known that it is challenging to analyze a data set with detection limits, and we often have to rely on the traditional parametric methods or simple imputation methods. Distributional assumptions can lead to biased inference and justification of distributions is often not possible when the data are correlated and there is a large proportion of data below detection limits. The extent of bias is usually unknown. To draw valid conclusions and hence provide useful advice for environmental management authorities, it is essential to develop and apply an appropriate statistical methodology. This paper proposes rank-based procedures for analyzing non-normally distributed data collected at different sites over a period of time in the presence of multiple detection limits. To take account of temporal correlations within each site, we propose an optimal linear combination of estimating functions and apply the induced smoothing method to reduce the computational burden. Finally, we apply the proposed method to the water quality data collected at Susquehanna River Basin in United States of America, which dearly demonstrates the advantages of the rank regression models.

A note on Gittins indexes for pharmaceutical research

The Bernoulli/exponential target process is considered. Such processes have been found useful in modelling the search for active compounds in pharmaceutical research. An inequality is presented which improves a result of Gittins (1989), thus providing a better approximation to the Gittins indices which define the optimal search policy.

Iterative estimating equations: Linear convergence and asymptotic properties

We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size increases to infinity. Furthermore, we show that the limiting estimator is consistent and asymptotically efficient, as expected. The method applies to semiparametric regression models with unspecified covariances among the observations. In the special case of linear models, the procedure reduces to iterative reweighted least squares. Finite sample performance of the procedure is studied by simulations, and compared with other methods. A numerical example from a medical study is considered to illustrate the application of the method.

Standard errors and covariance matrices for smoothed rank estimators

A 'pseudo-Bayesian' interpretation of standard errors yields a natural induced smoothing of statistical estimating functions. When applied to rank estimation, the lack of smoothness which prevents standard error estimation is remedied. Efficiency and robustness are preserved, while the smoothed estimation has excellent computational properties. In particular, convergence of the iterative equation for standard error is fast, and standard error calculation becomes asymptotically a one-step procedure. This property also extends to covariance matrix calculation for rank estimates in multi-parameter problems. Examples, and some simple explanations, are given.

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.