Evolution of stress deficit and changing rates of seismicity in cellular automaton models of earthquake faults

We investigate the internal dynamics of two cellular automaton models with heterogeneous strength fields and differing nearest neighbour laws. One model is a crack-like automaton, transferring ail stress from a rupture zone to the surroundings. The other automaton is a partial stress drop automaton, transferring only a fraction of the stress within a rupture zone to the surroundings. To study evolution of stress, the mean spectral density. f(k(r)) of a stress deficit held is: examined prior to, and immediately following ruptures in both models. Both models display a power-law relationship between f(k(r)) and spatial wavenumber (k(r)) of the form f(k(r)) similar tok(r)(-beta). In the crack model, the evolution of stress deficit is consistent with cyclic approach to, and retreat from a critical state in which large events occur. The approach to criticality is driven by tectonic loading. Short-range stress transfer in the model does not affect the approach to criticality of broad regions in the model. The evolution of stress deficit in the partial stress drop model is consistent with small fluctuations about a mean state of high stress, behaviour indicative of a self-organised critical system. Despite statistics similar to natural earthquakes these simplified models lack a physical basis. physically motivated models of earthquakes also display dynamical complexity similar to that of a critical point system. Studies of dynamical complexity in physical models of earthquakes may lead to advancement towards a physical theory for earthquakes.

Modelling solute transport in structured soils: Performance evaluation of the ADR and TRM models

The movement of chemicals through the soil to the groundwater or discharged to surface waters represents a degradation of these resources. In many cases, serious human and stock health implications are associated with this form of pollution. The chemicals of interest include nutrients, pesticides, salts, and industrial wastes. Recent studies have shown that current models and methods do not adequately describe the leaching of nutrients through soil, often underestimating the risk of groundwater contamination by surface-applied chemicals, and overestimating the concentration of resident solutes. This inaccuracy results primarily from ignoring soil structure and nonequilibrium between soil constituents, water, and solutes. A multiple sample percolation system (MSPS), consisting of 25 individual collection wells, was constructed to study the effects of localized soil heterogeneities on the transport of nutrients (NO3-, Cl-, PO43-) in the vadose zone of an agricultural soil predominantly dominated by clay. Very significant variations in drainage patterns across a small spatial scale were observed tone-way ANOVA, p < 0.001) indicating considerable heterogeneity in water flow patterns and nutrient leaching. Using data collected from the multiple sample percolation experiments, this paper compares the performance of two mathematical models for predicting solute transport, the advective-dispersion model with a reaction term (ADR), and a two-region preferential flow model (TRM) suitable for modelling nonequilibrium transport. These results have implications for modelling solute transport and predicting nutrient loading on a larger scale. (C) 2001 Elsevier Science Ltd. All rights reserved.

Disaggregation of polygons of surficial geology and soil maps using spatial modelling and legacy data

Examples from the Murray-Darling basin in Australia are used to illustrate different methods of disaggregation of reconnaissance-scale maps. One approach for disaggregation revolves around the de-convolution of the soil-landscape paradigm elaborated during a soil survey. The descriptions of soil ma units and block diagrams in a soil survey report detail soil-landscape relationships or soil toposequences that can be used to disaggregate map units into component landscape elements. Toposequences can be visualised on a computer by combining soil maps with digital elevation data. Expert knowledge or statistics can be used to implement the disaggregation. Use of a restructuring element and k-means clustering are illustrated. Another approach to disaggregation uses training areas to develop rules to extrapolate detailed mapping into other, larger areas where detailed mapping is unavailable. A two-level decision tree example is presented. At one level, the decision tree method is used to capture mapping rules from the training area; at another level, it is used to define the domain over which those rules can be extrapolated. (C) 2001 Elsevier Science B.V. All rights reserved.

Investigating technical and scale efficiencies of Australian universities through data envelopment analysis

Performance indicators in the public sector have often been criticised for being inadequate and not conducive to analysing efficiency. The main objective of this study is to use data envelopment analysis (DEA) to examine the relative efficiency of Australian universities. Three performance models are developed, namely, overall performance, performance on delivery of educational services, and performance on fee-paying enrolments. The findings based on 1995 data show that the university sector was performing well on technical and scale efficiency but there was room for improving performance on fee-paying enrolments. There were also small slacks in input utilisation. More universities were operating at decreasing returns to scale, indicating a potential to downsize. DEA helps in identifying the reference sets for inefficient institutions and objectively determines productivity improvements. As such, it can be a valuable benchmarking tool for educational administrators and assist in more efficient allocation of scarce resources. In the absence of market mechanisms to price educational outputs, which renders traditional production or cost functions inappropriate, universities are particularly obliged to seek alternative efficiency analysis methods such as DEA.

Fluid-mobile trace element constraints on the role of slab melting and implications for Archaean crustal growth models

We use published and new trace element data to identify element ratios which discriminate between arc magmas from the supra-subduction zone mantle wedge and those formed by direct melting of subducted crust (i.e. adakites). The clearest distinction is obtained with those element ratios which are strongly fractionated during refertilisation of the depleted mantle wedge, ultimately reflecting slab dehydration. Hence, adakites have significantly lower Pb/Nd and B/Be but higher Nb/Ta than typical arc magmas and continental crust as a whole. Although Li and Be are also overenriched in continental crust, behaviour of Li/Yb and Be/Nd is more complex and these ratios do not provide unique signatures of slab melting. Archaean tonalite-trondhjemite-granodiorites (TTGs) strongly resemble ordinary mantle wedge-derived arc magmas in terms of fluid-mobile trace element content, implying that they-did not form by slab melting but that they originated from mantle which was hydrated and enriched in elements lost from slabs during prograde dehydration. We suggest that Archaean TTGs formed by extensive fractional crystallisation from a mafic precursor. It is widely claimed that the time between the creation and subduction of oceanic lithosphere was significantly shorter in the Archaean (i.e. 20 Ma) than it is today. This difference was seen as an attractive explanation for the presumed preponderance of adakitic magmas during the first half of Earth's history. However, when we consider the effects of a higher potential mantle temperature on the thickness of oceanic crust, it follows that the mean age of oceanic lithosphere has remained virtually constant. Formation of adakites has therefore always depended on local plate geometry and not on potential mantle temperature.

Validation and refinement of survival models for liver retransplantation

Orthotopic liver retransplantation (re-OLT) is highly controversial. The objectives of this study were to determine the validity of a recently developed United Network for Organ Sharing (UNOS) multivariate model using an independent cohort of patients undergoing re-OLT outside the United States, to determine whether incorporation of other variables that were incomplete in the UNOS registry would provide additional prognostic information, to develop new models combining data sets from both cohorts, and to evaluate the validity of the model for end-stage liver disease (MELD) in patients undergoing re-OLT. Two hundred eighty-one adult patients undergoing re-OLT (between 1986 and 1999) at 6 foreign transplant centers comprised the validation cohort. We found good agreement between actual survival and predicted survival in the validation cohort; 1-year patient survival rates in the low-, intermediate-, and high-risk groups (as assigned by the original UNOS model) were 72%, 68%, and 36%, respectively (P < .0001). In the patients for whom the international normalized ratio (INR) of prothrombin time was available, MELD correlated with outcome following re-OLT; the median MELD scores for patients surviving at least 90 days compared with those dying within 90 days were 20.75 versus 25.9, respectively (P = .004). Utilizing both patient cohorts (n = 979), a new model, based on recipient age, total serum bilirubin, creatinine, and interval to re-OLT, was constructed (whole model χ(2) = 105, P < .0001). Using the c-statistic with 30-day, 90-day, 1-year, and 3-year mortality as the end points, the area under the receiver operating characteristic (ROC) curves for 4 different models were compared. In conclusion, prospective validation and use of these models as adjuncts to clinical decision making in the management of patients being considered for re-OLT are warranted.

Evaluation of 1-site and 5-site models of methane on its adsorption on graphite and in graphitic slit pores

In this paper, we evaluate the performance of the 1- and 5-site models of methane on the description of adsorption on graphite surfaces and in graphitic slit pores. These models have been known to perform well in the description of the fluid-phase behavior and vapor-liquid equilibria. Their performance in adsorption is evaluated in this work for nonporous graphitized thermal carbon black, and simulation results are compared with the experimental data of Avgul and Kiselev (Chemistry and Physics of Carbon; Dekker: New York, 1970; Vol. 6, p 1). On this nonporous surface, it is found that these models perform as well on isotherms at various temperatures as they do on the experimental isosteric heat for adsorption on a graphite surface. They are then tested for their performance in predicting the adsorption isotherms in graphitic slit pores, in which we would like to explore the effect of confinement on the molecule packing. Pore widths of 10 and 20 angstrom are chosen in this investigation, and we also study the effects of temperature by choosing 90.7, 113, and 273 K. The first two are for subcritical conditions, with 90.7 K being the triple point of methane and 113 K being its boiling point. The last temperature is chosen to represent the supercritical condition so that we can investigate the performance of these models at extremely high pressures. We have found that for the case of slit pores investigated in this paper, although the two models yield comparable pore densities (provided the accessible pore width is used in the calculation of pore density), the number of particles predicted by the I-site model is always greater than that predicted by the 5-site model, regardless of whether temperature is subcritical or supercritical. This is due to the packing effect in the confined space such that a methane molecule modeled as a spherical particle in the I-site model would pack better than the fused five-sphere model in the case of the 5-site model. Because the 5-site model better describes the liquid- and solid-phase behavior, we would argue that the packing density in small pores is better described with a more detailed 5-site model, and care should be exercised when using the 1-site model to study adsorption in small pores.

Repeated occurrence of basal cell carcinoma of the skin and multifailure survival analysis: Follow-up data from the nambour skin cancer prevention trial

The aim of this study was to apply multifailure survival methods to analyze time to multiple occurrences of basal cell carcinoma (BCC). Data from 4.5 years of follow-up in a randomized controlled trial, the Nambour Skin Cancer Prevention Trial (1992-1996), to evaluate skin cancer prevention were used to assess the influence of sunscreen application on the time to first BCC and the time to subsequent BCCs. Three different approaches of time to ordered multiple events were applied and compared: the Andersen-Gill, Wei-Lin-Weissfeld, and Prentice-Williams-Peterson models. Robust variance estimation approaches were used for all multifailure survival models. Sunscreen treatment was not associated with time to first occurrence of a BCC (hazard ratio = 1.04, 95% confidence interval: 0.79, 1.45). Time to subsequent BCC tumors using the Andersen-Gill model resulted in a lower estimated hazard among the daily sunscreen application group, although statistical significance was not reached (hazard ratio = 0.82, 95% confidence interval: 0.59, 1.15). Similarly, both the Wei-Lin-Weissfeld marginal-hazards and the Prentice-Williams-Peterson gap-time models revealed trends toward a lower risk of subsequent BCC tumors among the sunscreen intervention group. These results demonstrate the importance of conducting multiple-event analysis for recurring events, as risk factors for a single event may differ from those where repeated events are considered.

Forecasting Helicoverpa populations in Australia: A comparison of regression based models and a bio-climatic based modeling approach

Long-term forecasts of pest pressure are central to the effective management of many agricultural insect pests. In the eastern cropping regions of Australia, serious infestations of Helicoverpa punctigera (Wallengren) and H. armigera (Hübner)(Lepidoptera: Noctuidae) are experienced annually. Regression analyses of a long series of light-trap catches of adult moths were used to describe the seasonal dynamics of both species. The size of the spring generation in eastern cropping zones could be related to rainfall in putative source areas in inland Australia. Subsequent generations could be related to the abundance of various crops in agricultural areas, rainfall and the magnitude of the spring population peak. As rainfall figured prominently as a predictor variable, and can itself be predicted using the Southern Oscillation Index (SOI), trap catches were also related to this variable. The geographic distribution of each species was modelled in relation to climate and CLIMEX was used to predict temporal variation in abundance at given putative source sites in inland Australia using historical meteorological data. These predictions were then correlated with subsequent pest abundance data in a major cropping region. The regression-based and bioclimatic-based approaches to predicting pest abundance are compared and their utility in predicting and interpreting pest dynamics are discussed.

Comparison of beam theory and finite-element analysis with in vivo bone strain data from the alligator cranium

The mechanical behavior of the vertebrate skull is often modeled using free-body analysis of simple geometric structures and, more recently, finite-element (FE) analysis. In this study, we compare experimentally collected in vivo bone strain orientations and magnitudes from the cranium of the American alligator with those extrapolated from a beam model and extracted from an FE model. The strain magnitudes predicted from beam and FE skull models bear little similarity to relative and absolute strain magnitudes recorded during in vivo biting experiments. However, quantitative differences between principal strain orientations extracted from the FE skull model and recorded during the in vivo experiments were smaller, and both generally matched expectations from the beam model. The differences in strain magnitude between the data sets may be attributable to the level of resolution of the models, the material properties used in the FE model, and the loading conditions (i.e., external forces and constraints). This study indicates that FE models and modeling of skulls as simple engineering structures may give a preliminary idea of how these structures are loaded, but whenever possible, modeling results should be verified with either in vitro or preferably in vivo testing, especially if precise knowledge of strain magnitudes is desired. (c) 2005 Wiley-Liss, Inc.

Using epidemiological models to estimate the health effects of diet behaviour change: the example of tailored fruit and vegetable promotion

Objective: To explore the use of epidemiological modelling for the estimation of health effects of behaviour change interventions, using the example of computer-tailored nutrition education aimed at fruit and vegetable consumption in The Netherlands. Design: The effects of the intervention on changes in consumption were obtained from an earlier evaluation study. The effect on health outcomes was estimated using an epidemiological multi-state life table model. input data for the model consisted of relative risk estimates for cardiovascular disease and cancers, data on disease occurrence and mortality, and survey data on the consumption of fruits and vegetables. Results: if the computer-tailored nutrition education reached the entire adult population and the effects were sustained, it could result in a mortality decrease of 0.4 to 0.7% and save 72 to 115 life-years per 100000 persons aged 25 years or older. Healthy life expectancy is estimated to increase by 32.7 days for men and 25.3 days for women. The true effect is likely to lie between this theoretical maximum and zero effect, depending mostly on durability of behaviour change and reach of the intervention. Conclusion: Epidemiological models can be used to estimate the health impact of health promotion interventions.

Evaluation of different models to describe egg and pupal development of Xyleborus fornicatus Eichh. (Coleoptera: Scolytidae), the shot-hole borer of tea in Sri Lanka

Abstract Development data of eggs and pupae of Xyleborus fornicatus Eichh. (Coleoptera: Scolytidae), the shot-hole borer of tea in Sri Lanka, at constant temperatures were used to evaluate a linear and seven nonlinear models for insect development. Model evaluation was based on fit to data (residual sum of squares and coefficient of determination or coefficient of nonlinear regression), number of measurable parameters, the biological value of the fitted coefficients and accuracy in the estimation of thresholds. Of the nonlinear models, the Lactin model fitted experimental data well and along with the linear model, can be used to describe the temperature-dependent development of this species.

A D-optimal designed population pharmacokinetic study of itraconazole capsules and solution in adults with cystic fibrosis

Background: Oral itraconazole (ITRA) is used for the treatment of allergic bronchopulmonary aspergillosis in patients with cystic fibrosis (CF) because of its antifungal activity against Aspergillus species. ITRA has an active hydroxy-metabolite (OH-ITRA) which has similar antifungal activity. ITRA is a highly lipophilic drug which is available in two different oral formulations, a capsule and an oral solution. It is reported that the oral solution has a 60% higher relative bioavailability. The influence of altered gastric physiology associated with CF on the pharmacokinetics (PK) of ITRA and its metabolite has not been previously evaluated. Objectives: 1) To estimate the population (pop) PK parameters for ITRA and its active metabolite OH-ITRA including relative bioavailability of the parent after administration of the parent by both capsule and solution and 2) to assess the performance of the optimal design. Methods: The study was a cross-over design in which 30 patients received the capsule on the first occasion and 3 days later the solution formulation. The design was constrained to have a maximum of 4 blood samples per occasion for estimation of the popPK of both ITRA and OH-ITRA. The sampling times for the population model were optimized previously using POPT v.2.0.[1] POPT is a series of applications that run under MATLAB and provide an evaluation of the information matrix for a nonlinear mixed effects model given a particular design. In addition it can be used to optimize the design based on evaluation of the determinant of the information matrix. The model details for the design were based on prior information obtained from the literature, which suggested that ITRA may have either linear or non-linear elimination. The optimal sampling times were evaluated to provide information for both competing models for the parent and metabolite and for both capsule and solution simultaneously. Blood samples were assayed by validated HPLC.[2] PopPK modelling was performed using FOCE with interaction under NONMEM, version 5 (level 1.1; GloboMax LLC, Hanover, MD, USA). The PK of ITRA and OH‑ITRA was modelled simultaneously using ADVAN 5. Subsequently three methods were assessed for modelling concentrations less than the LOD (limit of detection). These methods (corresponding to methods 5, 6 & 4 from Beal[3], respectively) were (a) where all values less than LOD were assigned to half of LOD, (b) where the closest missing value that is less than LOD was assigned to half the LOD and all previous (if during absorption) or subsequent (if during elimination) missing samples were deleted, and (c) where the contribution of the expectation of each missing concentration to the likelihood is estimated. The LOD was 0.04 mg/L. The final model evaluation was performed via bootstrap with re-sampling and a visual predictive check. The optimal design and the sampling windows of the study were evaluated for execution errors and for agreement between the observed and predicted standard errors. Dosing regimens were simulated for the capsules and the oral solution to assess their ability to achieve ITRA target trough concentration (Cmin,ss of 0.5-2 mg/L) or a combined Cmin,ss for ITRA and OH-ITRA above 1.5mg/L. Results and Discussion: A total of 241 blood samples were collected and analysed, 94% of them were taken within the defined optimal sampling windows, of which 31% where taken within 5 min of the exact optimal times. Forty six per cent of the ITRA values and 28% of the OH-ITRA values were below LOD. The entire profile after administration of the capsule for five patients was below LOD and therefore the data from this occasion was omitted from estimation. A 2-compartment model with 1st order absorption and elimination best described ITRA PK, with 1st order metabolism of the parent to OH-ITRA. For ITRA the clearance (ClItra/F) was 31.5 L/h; apparent volumes of central and peripheral compartments were 56.7 L and 2090 L, respectively. Absorption rate constants for capsule (kacap) and solution (kasol) were 0.0315 h-1 and 0.125 h-1, respectively. Comparative bioavailability of the capsule was 0.82. There was no evidence of nonlinearity in the popPK of ITRA. No screened covariate significantly improved the fit to the data. The results of the parameter estimates from the final model were comparable between the different methods for accounting for missing data, (M4,5,6)[3] and provided similar parameter estimates. The prospective application of an optimal design was found to be successful. Due to the sampling windows, most of the samples could be collected within the daily hospital routine, but still at times that were near optimal for estimating the popPK parameters. The final model was one of the potential competing models considered in the original design. The asymptotic standard errors provided by NONMEM for the final model and empirical values from bootstrap were similar in magnitude to those predicted from the Fisher Information matrix associated with the D-optimal design. Simulations from the final model showed that the current dosing regimen of 200 mg twice daily (bd) would provide a target Cmin,ss (0.5-2 mg/L) for only 35% of patients when administered as the solution and 31% when administered as capsules. The optimal dosing schedule was 500mg bd for both formulations. The target success for this dosing regimen was 87% for the solution with an NNT=4 compared to capsules. This means, for every 4 patients treated with the solution one additional patient will achieve a target success compared to capsule but at an additional cost of AUD $220 per day. The therapeutic target however is still doubtful and potential risks of these dosing schedules need to be assessed on an individual basis. Conclusion: A model was developed which described the popPK of ITRA and its main active metabolite OH-ITRA in adult CF after administration of both capsule and solution. The relative bioavailability of ITRA from the capsule was 82% that of the solution, but considerably more variable. To incorporate missing data, using the simple Beal method 5 (using half LOD for all samples below LOD) provided comparable results to the more complex but theoretically better Beal method 4 (integration method). The optimal sparse design performed well for estimation of model parameters and provided a good fit to the data.