Improved estimates of percolation and anisotropic permeability from 3-D X-ray microtomography using stochastic analyses and visualization

X-ray microtomography (micro-CT) with micron resolution enables new ways of characterizing microstructures and opens pathways for forward calculations of multiscale rock properties. A quantitative characterization of the microstructure is the first step in this challenge. We developed a new approach to extract scale-dependent characteristics of porosity, percolation, and anisotropic permeability from 3-D microstructural models of rocks. The Hoshen-Kopelman algorithm of percolation theory is employed for a standard percolation analysis. The anisotropy of permeability is calculated by means of the star volume distribution approach. The local porosity distribution and local percolation probability are obtained by using the local porosity theory. Additionally, the local anisotropy distribution is defined and analyzed through two empirical probability density functions, the isotropy index and the elongation index. For such a high-resolution data set, the typical data sizes of the CT images are on the order of gigabytes to tens of gigabytes; thus an extremely large number of calculations are required. To resolve this large memory problem parallelization in OpenMP was used to optimally harness the shared memory infrastructure on cache coherent Non-Uniform Memory Access architecture machines such as the iVEC SGI Altix 3700Bx2 Supercomputer. We see adequate visualization of the results as an important element in this first pioneering study.

Coordinated probabilistic optimal decision-making model for multi-area ATC with risk control

In the decision-making of multi-area ATC (Available Transfer Capacity) in electricity market environment, the existing resources of transmission network should be optimally dispatched and coordinately employed on the premise that the secure system operation is maintained and risk associated is controllable. The non-sequential Monte Carlo simulation is used to determine the ATC probability density distribution of specified areas under the influence of several uncertainty factors, based on which, a coordinated probabilistic optimal decision-making model with the maximal risk benefit as its objective is developed for multi-area ATC. The NSGA-II is applied to calculate the ATC of each area, which considers the risk cost caused by relevant uncertainty factors and the synchronous coordination among areas. The essential characteristics of the developed model and the employed algorithm are illustrated by the example of IEEE 118-bus test system. Simulative result shows that, the risk of multi-area ATC decision-making is influenced by the uncertainties in power system operation and the relative importance degrees of different areas.

How long does it take for aquifer recharge or aquifer discharge processes to reach steady state?

Groundwater flow models are usually characterized as being either transient flow models or steady state flow models. Given that steady state groundwater flow conditions arise as a long time asymptotic limit of a particular transient response, it is natural for us to seek a finite estimate of the amount of time required for a particular transient flow problem to effectively reach steady state. Here, we introduce the concept of mean action time (MAT) to address a fundamental question: How long does it take for a groundwater recharge process or discharge processes to effectively reach steady state? This concept relies on identifying a cumulative distribution function, $F(t;x)$, which varies from $F(0;x)=0$ to $F(t;x) \to \infty$ as $t\to \infty$, thereby providing us with a measurement of the progress of the system towards steady state. The MAT corresponds to the mean of the associated probability density function $f(t;x) = \dfrac{dF}{dt}$, and we demonstrate that this framework provides useful analytical insight by explicitly showing how the MAT depends on the parameters in the model and the geometry of the problem. Additional theoretical results relating to the variance of $f(t;x)$, known as the variance of action time (VAT), are also presented. To test our theoretical predictions we include measurements from a laboratory–scale experiment describing flow through a homogeneous porous medium. The laboratory data confirms that the theoretical MAT predictions are in good agreement with measurements from the physical model.

A multi-objective optimization approach for coordinating available transfer capability with risk control

In the electricity market environment, coordination of system reliability and economics of a power system is of great significance in determining the available transfer capability (ATC). In addition, the risks associated with uncertainties should be properly addressed in the ATC determination process for risk-benefit maximization. Against this background, it is necessary that the ATC be optimally allocated and utilized within relative security constraints. First of all, the non-sequential Monte Carlo stimulation is employed to derive the probability density distribution of ATC of designated areas incorporating uncertainty factors. Second, on the basis of that, a multi-objective optimization model is formulated to determine the multi-area ATC so as to maximize the risk-benefits. Then, the solution to the developed model is achieved by the fast non-dominated sorting (NSGA-II) algorithm, which could decrease the risk caused by uncertainties while coordinating the ATCs of different areas. Finally, the IEEE 118-bus test system is served for demonstrating the essential features of the developed model and employed algorithm.

A simplified approach for calculating the moments of action for linear reaction-diffusion equations

The mean action time is the mean of a probability density function that can be interpreted as a critical time, which is a finite estimate of the time taken for the transient solution of a reaction-diffusion equation to effectively reach steady state. For high-variance distributions, the mean action time under-approximates the critical time since it neglects to account for the spread about the mean. We can improve our estimate of the critical time by calculating the higher moments of the probability density function, called the moments of action, which provide additional information regarding the spread about the mean. Existing methods for calculating the nth moment of action require the solution of n nonhomogeneous boundary value problems which can be difficult and tedious to solve exactly. Here we present a simplified approach using Laplace transforms which allows us to calculate the nth moment of action without solving this family of boundary value problems and also without solving for the transient solution of the underlying reaction-diffusion problem. We demonstrate the generality of our method by calculating exact expressions for the moments of action for three problems from the biophysics literature. While the first problem we consider can be solved using existing methods, the second problem, which is readily solved using our approach, is intractable using previous techniques. The third problem illustrates how the Laplace transform approach can be used to study coupled linear reaction-diffusion equations.

Synthesis of complementary RNA by RNA-dependent RNA polymerases in plant extracts is independent of an RNA primer

RNA-dependent RNA polymerase (RDR) activities were readily detected in extracts from cauliflower and broccoli florets, Arabidopsis thaliana (L.) Heynh callus tissue and broccoli nuclei. The synthesis of complementary RNA (cRNA) was independent of a RNA primer, whether or not the primer contained a 3′ terminal 2′-O-methyl group or was phosphorylated at the 5′ terminus. cRNA synthesis in plant extracts was not affected by loss-of-function mutations in the DICER-LIKE (DCL) proteins DCL2, DCL3, and DCL4, indicating that RDRs function independently of these DCL proteins. A loss-of-function mutation in RDR1, RDR2 or RDR6 did not significantly reduce the amount of cRNA synthesis. This indicates that these RDRs did not account for the bulk RDR activities in plant extracts, and suggest that either the individual RDRs each contribute a fraction of polymerase activity or another RDR(s) is predominant in the plant extract. © CSIRO 2008.

Establishing definitions and modeling public transport travel time variability

Public transport travel time variability (PTTV) is essential for understanding deteriorations in the reliability of travel time, optimizing transit schedules and route choices. This paper establishes key definitions of PTTV in which firstly include all buses, and secondly include only a single service from a bus route. The paper then analyses the day-to-day distribution of public transport travel time by using Transit Signal Priority data. A comprehensive approach using both parametric bootstrapping Kolmogorov-Smirnov test and Bayesian Information Creation technique is developed, recommends Lognormal distribution as the best descriptor of bus travel time on urban corridors. The probability density function of Lognormal distribution is finally used for calculating probability indicators of PTTV. The findings of this study are useful for both traffic managers and statisticians for planning and researching the transit systems.

Novelty-based visual obstacle detection in agriculture

This paper describes a novel obstacle detection system for autonomous robots in agricultural field environments that uses a novelty detector to inform stereo matching. Stereo vision alone erroneously detects obstacles in environments with ambiguous appearance and ground plane such as in broad-acre crop fields with harvested crop residue. The novelty detector estimates the probability density in image descriptor space and incorporates image-space positional understanding to identify potential regions for obstacle detection using dense stereo matching. The results demonstrate that the system is able to detect obstacles typical to a farm at day and night. This system was successfully used as the sole means of obstacle detection for an autonomous robot performing a long term two hour coverage task travelling 8.5 km.

Public transport travel time variability definitions and monitoring

Public Transport Travel Time Variability (PTTV) is essential for understanding the deteriorations in the reliability of travel time, optimizing transit schedules and route choices. This paper establishes the key definitions of PTTV in which firstly include all buses, and secondly include only a single service from a bus route. The paper then analyzes the day-to-day distribution of public transport travel time by using Transit Signal Priority data. A comprehensive approach, using both parametric bootstrapping Kolmogorov-Smirnov test and Bayesian Information Creation technique is developed, recommends Lognormal distribution as the best descriptor of bus travel time on urban corridors. The probability density function of Lognormal distribution is finally used for calculating probability indicators of PTTV. The findings of this study are useful for both traffic managers and statisticians for planning and analyzing the transit systems.

Assessment on the effect of pollution abatement on environmental efficiency with Markov chain Monte Carlo simulation

Both environmental economists and policy makers have shown a great deal of interest in the effect of pollution abatement on environmental efficiency. In line with the modern resources available, however, no contribution is brought to the environmental economics field with the Markov chain Monte Carlo (MCMC) application, which enables simulation from a distribution of a Markov chain and simulating from the chain until it approaches equilibrium. The probability density functions gained prominence with the advantages over classical statistical methods in its simultaneous inference and incorporation of any prior information on all model parameters. This paper concentrated on this point with the application of MCMC to the database of China, the largest developing country with rapid economic growth and serious environmental pollution in recent years. The variables cover the economic output and pollution abatement cost from the year 1992 to 2003. We test the causal direction between pollution abatement cost and environmental efficiency with MCMC simulation. We found that the pollution abatement cost causes an increase in environmental efficiency through the algorithm application, which makes it conceivable that the environmental policy makers should make more substantial measures to reduce pollution in the near future.

A new approach to spatial data interpolation using higher-order statistics

Interpolation techniques for spatial data have been applied frequently in various fields of geosciences. Although most conventional interpolation methods assume that it is sufficient to use first- and second-order statistics to characterize random fields, researchers have now realized that these methods cannot always provide reliable interpolation results, since geological and environmental phenomena tend to be very complex, presenting non-Gaussian distribution and/or non-linear inter-variable relationship. This paper proposes a new approach to the interpolation of spatial data, which can be applied with great flexibility. Suitable cross-variable higher-order spatial statistics are developed to measure the spatial relationship between the random variable at an unsampled location and those in its neighbourhood. Given the computed cross-variable higher-order spatial statistics, the conditional probability density function (CPDF) is approximated via polynomial expansions, which is then utilized to determine the interpolated value at the unsampled location as an expectation. In addition, the uncertainty associated with the interpolation is quantified by constructing prediction intervals of interpolated values. The proposed method is applied to a mineral deposit dataset, and the results demonstrate that it outperforms kriging methods in uncertainty quantification. The introduction of the cross-variable higher-order spatial statistics noticeably improves the quality of the interpolation since it enriches the information that can be extracted from the observed data, and this benefit is substantial when working with data that are sparse or have non-trivial dependence structures.

Feature selection using expected attainable discrimination

We propose expected attainable discrimination (EAD) as a measure to select discrete valued features for reliable discrimination between two classes of data. EAD is an average of the area under the ROC curves obtained when a simple histogram probability density model is trained and tested on many random partitions of a data set. EAD can be incorporated into various stepwise search methods to determine promising subsets of features, particularly when misclassification costs are difficult or impossible to specify. Experimental application to the problem of risk prediction in pregnancy is described.

A new approach to estimating trends in chlamydia incidence

Objectives Directly measuring disease incidence in a population is difficult and not feasible to do routinely. We describe the development and application of a new method of estimating at a population level the number of incident genital chlamydia infections, and the corresponding incidence rates, by age and sex using routine surveillance data. Methods A Bayesian statistical approach was developed to calibrate the parameters of a decision-pathway tree against national data on numbers of notifications and tests conducted (2001-2013). Independent beta probability density functions were adopted for priors on the time-independent parameters; the shape parameters of these beta distributions were chosen to match prior estimates sourced from peer-reviewed literature or expert opinion. To best facilitate the calibration, multivariate Gaussian priors on (the logistic transforms of) the time-dependent parameters were adopted, using the Matérn covariance function to favour changes over consecutive years and across adjacent age cohorts. The model outcomes were validated by comparing them with other independent empirical epidemiological measures i.e. prevalence and incidence as reported by other studies. Results Model-based estimates suggest that the total number of people acquiring chlamydia per year in Australia has increased by ~120% over 12 years. Nationally, an estimated 356,000 people acquired chlamydia in 2013, which is 4.3 times the number of reported diagnoses. This corresponded to a chlamydia annual incidence estimate of 1.54% in 2013, increased from 0.81% in 2001 (~90% increase). Conclusions We developed a statistical method which uses routine surveillance (notifications and testing) data to produce estimates of the extent and trends in chlamydia incidence.

Information-theoretic analysis of brain white matter fiber orientation distribution functions

We propose a new information-theoretic metric, the symmetric Kullback-Leibler divergence (sKL-divergence), to measure the difference between two water diffusivity profiles in high angular resolution diffusion imaging (HARDI). Water diffusivity profiles are modeled as probability density functions on the unit sphere, and the sKL-divergence is computed from a spherical harmonic series, which greatly reduces computational complexity. Adjustment of the orientation of diffusivity functions is essential when the image is being warped, so we propose a fast algorithm to determine the principal direction of diffusivity functions using principal component analysis (PCA). We compare sKL-divergence with other inner-product based cost functions using synthetic samples and real HARDI data, and show that the sKL-divergence is highly sensitive in detecting small differences between two diffusivity profiles and therefore shows promise for applications in the nonlinear registration and multisubject statistical analysis of HARDI data.

Fluid registration of diffusion tensor images using information theory

We apply an information-theoretic cost metric, the symmetrized Kullback-Leibler (sKL) divergence, or $J$-divergence, to fluid registration of diffusion tensor images. The difference between diffusion tensors is quantified based on the sKL-divergence of their associated probability density functions (PDFs). Three-dimensional DTI data from 34 subjects were fluidly registered to an optimized target image. To allow large image deformations but preserve image topology, we regularized the flow with a large-deformation diffeomorphic mapping based on the kinematics of a Navier-Stokes fluid. A driving force was developed to minimize the $J$-divergence between the deforming source and target diffusion functions, while reorienting the flowing tensors to preserve fiber topography. In initial experiments, we showed that the sKL-divergence based on full diffusion PDFs is adaptable to higher-order diffusion models, such as high angular resolution diffusion imaging (HARDI). The sKL-divergence was sensitive to subtle differences between two diffusivity profiles, showing promise for nonlinear registration applications and multisubject statistical analysis of HARDI data.