An implicit RBF meshless approach for time fractional diffusion equations

This paper aims to develop an implicit meshless approach based on the radial basis function (RBF) for numerical simulation of time fractional diffusion equations. The meshless RBF interpolation is firstly briefed. The discrete equations for two-dimensional time fractional diffusion equation (FDE) are obtained by using the meshless RBF shape functions and the strong-forms of the time FDE. The stability and convergence of this meshless approach are discussed and theoretically proven. Numerical examples with different problem domains and different nodal distributions are studied to validate and investigate accuracy and efficiency of the newly developed meshless approach. It has proven that the present meshless formulation is very effective for modeling and simulation of fractional differential equations.

An advanced meshless method for time fractional diffusion equation

Recently, because of the new developments in sustainable engineering and renewable energy, which are usually governed by a series of fractional partial differential equations (FPDEs), the numerical modelling and simulation for fractional calculus are attracting more and more attention from researchers. The current dominant numerical method for modeling FPDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings including difficulty in simulation of problems with the complex problem domain and in using irregularly distributed nodes. Because of its distinguished advantages, the meshless method has good potential in simulation of FPDEs. This paper aims to develop an implicit meshless collocation technique for FPDE. The discrete system of FPDEs is obtained by using the meshless shape functions and the meshless collocation formulation. The stability and convergence of this meshless approach are investigated theoretically and numerically. The numerical examples with regular and irregular nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of fractional partial differential equations.

Change Point Estimation in Monitoring Survival Time

Precise identification of the time when a change in a hospital outcome has occurred enables clinical experts to search for a potential special cause more effectively. In this paper, we develop change point estimation methods for survival time of a clinical procedure in the presence of patient mix in a Bayesian framework. We apply Bayesian hierarchical models to formulate the change point where there exists a step change in the mean survival time of patients who underwent cardiac surgery. The data are right censored since the monitoring is conducted over a limited follow-up period. We capture the effect of risk factors prior to the surgery using a Weibull accelerated failure time regression model. Markov Chain Monte Carlo is used to obtain posterior distributions of the change point parameters including location and magnitude of changes and also corresponding probabilistic intervals and inferences. The performance of the Bayesian estimator is investigated through simulations and the result shows that precise estimates can be obtained when they are used in conjunction with the risk-adjusted survival time CUSUM control charts for different magnitude scenarios. The proposed estimator shows a better performance where a longer follow-up period, censoring time, is applied. In comparison with the alternative built-in CUSUM estimator, more accurate and precise estimates are obtained by the Bayesian estimator. These superiorities are enhanced when probability quantification, flexibility and generalizability of the Bayesian change point detection model are also considered.

Accurate stratospheric particle size distributions from two separate flat-plate collection surfaces

Over the past two decades, flat-plate particle collections have revealed the presence of a remarkable variety of both terrestrial and extraterrestrial material in the stratosphere [1-6]. The ratio of terrestrial to extraterrestrial material and the nature of material collected may vary over observable time scales. Variations in particle number density can be important since the earth’s atmospheric radiation balance, and therefore the earth’s climate, can be influenced by articulate absorption and scattering of radiation from the sun and earth [7-9]. In order to assess the number density of solid particles in the stratosphere, we have examined a representative fraction of the so1id particles from two flat-plate collection surfaces, whose collection dates are separated in time by 5 years.

Accurate stratospheric particle-size distributions from a flat-plate collection surface

The first representative chemical, structural, and morphological analysis of the solid particles from a single collection surface has been performed. This collection surface sampled the stratosphere between 17 and 19km in altitude in the summer of 1981, and therefore before the 1982 eruptions of El Chichón. A particle collection surface was washed free of all particles with rinses of Freon and hexane, and the resulting wash was directed through a series of vertically stacked Nucleopore filters. The size cutoff for the solid particle collection process in the stratosphere is found to be considerably less than 1 μm. The total stratospheric number density of solid particles larger than 1μm in diameter at the collection time is calculated to be about 2.7×10−1 particles per cubic meter, of which approximately 95% are smaller than 5μm in diameter. Previous classification schemes are expanded to explicitly recognize low atomic number material. With the single exception of the calcium-aluminum-silicate (CAS) spheres all solid particle types show a logarithmic increase in number concentration with decreasing diameter. The aluminum-rich particles are unique in showing bimodal size distributions. In addition, spheres constitute only a minor fraction of the aluminum-rich material. About 2/3 of the particles examined were found to be shards of rhyolitic glass. This abundant volcanic material could not be correlated with any eruption plume known to have vented directly to the stratosphere. The micrometeorite number density calculated from this data set is 5×10−2 micrometeorites per cubic meter of air, an order of magnitude greater than the best previous estimate. At the collection altitude, the maximum collision frequency of solid particles >5μm in average diameter is calculated to be 6.91×10−16 collisions per second, which indicates negligible contamination of extraterrestrial particles in the stratosphere by solid anthropogenic particles.

Empirical evaluation of public transport travel time variability

Although transit travel time variability is essential for understanding the deterioration of reliability, optimising transit schedule and route choice; it has not attracted enough attention from the literature. This paper proposes public transport-oriented definitions of travel time variability and explores the distributions of public transport travel time using the Transit Signal Priority data. First, definitions of public transport travel time variability are established by extending the common definitions of variability in the literature and by using route and services data of public transport vehicles. Second, the paper explores the distribution of public transport travel time. A new approach for analysing the distributions involving all transit vehicles as well as vehicles from a specific route is proposed. The Lognormal distribution is revealed as the descriptors for public transport travel time from the same route and service. The methods described in this study could be of interest for both traffic managers and transit operators for planning and managing the transit systems.

Traffic incident clearance time and arrival time prediction based on hazard models

Accurate prediction of incident duration is not only important information of Traffic Incident Management System, but also an ffective input for travel time prediction. In this paper, the hazard based prediction odels are developed for both incident clearance time and arrival time. The data are obtained from the Queensland Department of Transport and Main Roads’ STREAMS Incident Management System (SIMS) for one year ending in November 2010. The best fitting distributions are drawn for both clearance and arrival time for 3 types of incident: crash, stationary vehicle, and hazard. The results show that Gamma, Log-logistic, and Weibull are the best fit for crash, stationary vehicle, and hazard incident, respectively. The obvious impact factors are given for crash clearance time and arrival time. The quantitative influences for crash and hazard incident are presented for both clearance and arrival. The model accuracy is analyzed at the end.

Charge-carrier velocity distributions in high-mobility polymer dual-gate thin-film transistors

We report charge-carrier velocity distributions in high-mobility polymer thin-film transistors (PTFTs) employing a dual-gate configuration. Our time-domain measurements of dual-gate PTFTs indicate higher effective mobility as well as fewer low-velocity carriers than in single-gate operation. Such nonquasi-static (NQS) measurements support and clarify the previously reported results of improved device performance in dual-gate devices by various groups. We believe that this letter demonstrates the utility of NQS measurements in studying charge-carrier transport in dual-gate thin-film transistors.

Calibration of treatment time intensity modulated EPID images for anatomical imaging

Intensity Modulated Radiotherapy (IMRT) is a well established technique for delivering highly conformal radiation dose distributions. The complexity of the delivery techniques and high dose gradients around the target volume make verification of the patient treatment crucial to the success of the treatment. Conventional treatment protocols involve imaging the patient prior to treatment, comparing the patient set-up to the planned set-up and then making any necessary shifts in the patient position to ensure target volume coverage. This paper presents a method for calibrating electronic portal imaging device (EPID) images acquired during IMRT delivery so that they can be used for verifying the patient set-up.

Hydrological consequences of land-cover change: Quantifying the influence of plants on soil moisture with time-lapse electrical resistivity

Electrical resistivity of soils and sediments is strongly influenced by the presence of interstitial water. Taking advantage of this dependency, electrical-resistivity imaging (ERI) can be effectively utilized to estimate subsurface soil-moisture distributions. The ability to obtain spatially extensive data combined with time-lapse measurements provides further opportunities to understand links between land use and climate processes. In natural settings, spatial and temporal changes in temperature and porewater salinity influence the relationship between soil moisture and electrical resistivity. Apart from environmental factors, technical, theoretical, and methodological ambiguities may also interfere with accurate estimation of soil moisture from ERI data. We have examined several of these complicating factors using data from a two-year study at a forest-grassland ecotone, a boundary between neighboring but different plant communities.At this site, temperature variability accounts for approximately 20-45 of resistivity changes from cold winter to warm summer months. Temporal changes in groundwater conductivity (mean=650 S/cm =57.7) and a roughly 100-S/cm spatial difference between the forest and grassland had only a minor influence on the moisture estimates. Significant seasonal fluctuations in temperature and precipitation had negligible influence on the basic measurement errors in data sets. Extracting accurate temporal changes from ERI can be hindered by nonuniqueness of the inversion process and uncertainties related to time-lapse inversion schemes. The accuracy of soil moisture obtained from ERI depends on all of these factors, in addition to empirical parameters that define the petrophysical soil-moisture/resistivity relationship. Many of the complicating factors and modifying variables to accurately quantify soil moisture changes with ERI can be accounted for using field and theoretical principles.

Estimation of the time of a linear trend in monitoring survival time

Change point estimation is recognized as an essential tool of root cause analyses within quality control programs as it enables clinical experts to search for potential causes of change in hospital outcomes more effectively. In this paper, we consider estimation of the time when a linear trend disturbance has occurred in survival time following an in-control clinical intervention in the presence of variable patient mix. To model the process and change point, a linear trend in the survival time of patients who underwent cardiac surgery is formulated using hierarchical models in a Bayesian framework. The data are right censored since the monitoring is conducted over a limited follow-up period. We capture the effect of risk factors prior to the surgery using a Weibull accelerated failure time regression model. We use Markov Chain Monte Carlo to obtain posterior distributions of the change point parameters including the location and the slope size of the trend and also corresponding probabilistic intervals and inferences. The performance of the Bayesian estimator is investigated through simulations and the result shows that precise estimates can be obtained when they are used in conjunction with the risk-adjusted survival time cumulative sum control chart (CUSUM) control charts for different trend scenarios. In comparison with the alternatives, step change point model and built-in CUSUM estimator, more accurate and precise estimates are obtained by the proposed Bayesian estimator over linear trends. These superiorities are enhanced when probability quantification, flexibility and generalizability of the Bayesian change point detection model are also considered.

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.

Distributions of lesser mealworm (Coleoptera: Tenebrionidae) in litter of a compacted earth floor broiler house in subtropical Queensland, Australia

Distributions of lesser mealworm, Alphitobius diaperinus (Panzer) (Coleoptera: Tenebrionidae), in litter of a compacted earth floor broiler house in southeastern Queensland, Australia, were studied over two flocks. Larvae were the predominant stage recorded. Significantly low densities occurred in open locations and under drinker cups where chickens had complete access, whereas high densities were found under feed pans and along house edges where chicken access was restricted. For each flock, lesser mealworm numbers increased at all locations over the first 14 d, especially under feed pans and along house edges, peaking at 26 d and then declining over the final 28 d. A life stage profile per flock was devised that consisted of the following: beetles emerge from the earth floor at the beginning of each flock, and females lay eggs, producing larvae that peak in numbers at 3 wk; after a further 3 to 4 wk, larvae leave litter to pupate in the earth floor, and beetles then emerge by the end of the flock time. Removing old litter from the brooder section at the end of a flock did not greatly reduce mealworm numbers over the subsequent flock, but it seemed to prevent numbers increasing, while an increase in numbers in the grow-out section was recorded after reusing litter. Areas under feed pans and along house edges accounted for 5% of the total house area, but approximately half the estimated total number of lesser mealworms in the broiler house occurred in these locations. The results of this study will be used to determine optimal deployment of site-specific treatments for lesser mealworm control.

Bayesian mixture model estimation of aerosol particle size distributions

In this paper, we examine approaches to estimate a Bayesian mixture model at both single and multiple time points for a sample of actual and simulated aerosol particle size distribution (PSD) data. For estimation of a mixture model at a single time point, we use Reversible Jump Markov Chain Monte Carlo (RJMCMC) to estimate mixture model parameters including the number of components which is assumed to be unknown. We compare the results of this approach to a commonly used estimation method in the aerosol physics literature. As PSD data is often measured over time, often at small time intervals, we also examine the use of an informative prior for estimation of the mixture parameters which takes into account the correlated nature of the parameters. The Bayesian mixture model offers a promising approach, providing advantages both in estimation and inference.

Convergence analysis of the Newton algorithm and a pseudo-time marching scheme for diffuse correlation tomography

We propose a self-regularized pseudo-time marching scheme to solve the ill-posed, nonlinear inverse problem associated with diffuse propagation of coherent light in a tissuelike object. In particular, in the context of diffuse correlation tomography (DCT), we consider the recovery of mechanical property distributions from partial and noisy boundary measurements of light intensity autocorrelation. We prove the existence of a minimizer for the Newton algorithm after establishing the existence of weak solutions for the forward equation of light amplitude autocorrelation and its Frechet derivative and adjoint. The asymptotic stability of the solution of the ordinary differential equation obtained through the introduction of the pseudo-time is also analyzed. We show that the asymptotic solution obtained through the pseudo-time marching converges to that optimal solution provided the Hessian of the forward equation is positive definite in the neighborhood of optimal solution. The superior noise tolerance and regularization-insensitive nature of pseudo-dynamic strategy are proved through numerical simulations in the context of both DCT and diffuse optical tomography. (C) 2010 Optical Society of America.