Efficient simulation of a Tandem Jackson Network

The two-node tandem Jackson network serves as a convenient reference model for the analysis and testing of different methodologies and techniques in rare event simulation. In this paper we consider a new approach to efficiently estimate the probability that the content of the second buffer exceeds some high level L before it becomes empty, starting from a given state. The approach is based on a Markov additive process representation of the buffer processes, leading to an exponential change of measure to be used in an importance sampling procedure. Unlike changes of measures proposed and studied in recent literature, the one derived here is a function of the content of the first buffer. We prove that when the first buffer is finite, this method yields asymptotically efficient simulation for any set of arrival and service rates. In fact, the relative error is bounded independent of the level L; a new result which is not established for any other known method. When the first buffer is infinite, we propose a natural extension of the exponential change of measure for the finite buffer case. In this case, the relative error is shown to be bounded (independent of L) only when the second server is the bottleneck; a result which is known to hold for some other methods derived through large deviations analysis. When the first server is the bottleneck, experimental results using our method seem to suggest that the relative error is bounded linearly in L.

Marker concentration patterns of labelled leaf and stem particles in the rumen of cattle grazing bermuda grass (Cynodon dactylon) analysed by reference to a raft model

Large (>1600 mum), ingestively masticated particles of bermuda grass (Cynodon dactylon L. Pers.) leaf and stem labelled with Yb-169 and Ce-144 respectively were inserted into the rumen digesta raft of heifers grazing bermuda grass. The concentration of markers in digesta sampled from the raft and ventral rumen were monitored at regular intervals over approximately 144 h. The data from the two sampling sites were simultaneously fitted to two pool (raft and ventral rumen-reticulum) models with either reversible or sequential flow between the two pools. The sequential flow model fitted the data equally as well as the reversible flow model but the reversible flow model was used because of its greater application. The reversible flow model, hereafter called the raft model, had the following features: a relatively slow age-dependent transfer rate from the raft (means for a gamma 2 distributed rate parameter for leaf 0.0740 v. stem 0.0478 h(-1)), a very slow first order reversible flow from the ventral rumen to the raft (mean for leaf and stem 0.010 h(-1)) and a very rapid first order exit from the ventral rumen (mean of leaf and stem 0.44 h(-1)). The raft was calculated to occupy approximately 0.82 total rumen DM of the raft and ventral rumen pools. Fitting a sequential two pool model or a single exponential model individually to values from each of the two sampling sites yielded similar parameter values for both sites and faster rate parameters for leaf as compared with stem, in agreement with the raft model. These results were interpreted as indicating that the raft forms a large relatively inert pool within the rumen. Particles generated within the raft have difficulty escaping but once into the ventral rumen pool they escape quickly with a low probability of return to the raft. It was concluded that the raft model gave a good interpretation of the data and emphasized escape from and movement within the raft as important components of the residence time of leaf and stem particles within the rumen digesta of cattle.

On the validity of the dispersion model of hepatic drug elimination when intravascular transit time densities are long-tailed

The dispersion model with mixed boundary conditions uses a single parameter, the dispersion number, to describe the hepatic elimination of xenobiotics and endogenous substances. An implicit a priori assumption of the model is that the transit time density of intravascular indicators is approximated by an inverse Gaussian distribution. This approximation is limited in that the model poorly describes the tail part of the hepatic outflow curves of vascular indicators. A sum of two inverse Gaussian functions is proposed as ail alternative, more flexible empirical model for transit time densities of vascular references. This model suggests that a more accurate description of the tail portion of vascular reference curves yields an elimination rate constant (or intrinsic clearance) which is 40% less than predicted by the dispersion model with mixed boundary conditions. The results emphasize the need to accurately describe outflow curves in using them as a basis for determining pharmacokinetic parameters using hepatic elimination models. (C) 1997 Society for Mathematical Biology.

Three-dimensional orthotropic viscoelastic finite element model of a human ligament

Ligaments undergo finite strain displaying hyperelastic behaviour as the initially tangled fibrils present straighten out, combined with viscoelastic behaviour (strain rate sensitivity). In the present study the anterior cruciate ligament of the human knee joint is modelled in three dimensions to gain an understanding of the stress distribution over the ligament due to motion imposed on the ends, determined from experimental studies. A three dimensional, finite strain material model of ligaments has recently been proposed by Pioletti in Ref. [2]. It is attractive as it separates out elastic stress from that due to the present strain rate and that due to the past history of deformation. However, it treats the ligament as isotropic and incompressible. While the second assumption is reasonable, the first is clearly untrue. In the present study an alternative model of the elastic behaviour due to Bonet and Burton (Ref. [4]) is generalized. Bonet and Burton consider finite strain with constant modulii for the fibres and for the matrix of a transversely isotropic composite. In the present work, the fibre modulus is first made to increase exponentially from zero with an invariant that provides a measure of the stretch in the fibre direction. At 12% strain in the fibre direction, a new reference state is then adopted, after which the material modulus is made constant, as in Bonet and Burton's model. The strain rate dependence can be added, either using Pioletti's isotropic approximation, or by making the effect depend on the strain rate in the fibre direction only. A solid model of a ligament is constructed, based on experimentally measured sections, and the deformation predicted using explicit integration in time. This approach simplifies the coding of the material model, but has a limitation due to the detrimental effect on stability of integration of the substantial damping implied by the nonlinear dependence of stress on strain rate. At present, an artificially high density is being used to provide stability, while the dynamics are being removed from the solution using artificial viscosity. The result is a quasi-static solution incorporating the effect of strain rate. Alternate approaches to material modelling and integration are discussed, that may result in a better model.

Determination of reference values for glucose tolerance, insulin tolerance, and insulin sensitivity tests in clinically normal cats

Objective-To determine reference values and test variability for glucose tolerance tests (GTT), insulin tolerance tests (ITT), and insulin sensitivity tests (IST) in cats, Animals-32 clinically normal cats. Procedure-GTT, ITT, and IST were performed on consecutive days. Tolerance intervals tie, reference values) were calculated as means +/- 2.397 SD for plasma glucose and insulin concentrations, half-life of glucose (T-1/2glucose), rate constants for glucose disappearance (K-glucose and K-itt), and insulin sensitivity index (S-l). Tests were repeated after 6 weeks in 8 cats to determine test variability. Results-Reference values for T-1/2glucose, K-glucose, and fasting plasma glucose and insulin concentrations during GTT were 45 to 74 minutes, 0.93 to 1.54 %/min, 37 to 104 mg/dl, and 2.8 to 20.6 muU/ml, respectively. Mean values did not differ between the 2 tests. Coefficients of variation for T-1/2glucose, K-glucose, and fasting plasma glucose and insulin concentrations were 20, 20, 11, and 23%, respectively. Reference values for K-itt were 1.14 to 7.3%/min, and for S-l were 0.57 to 10.99 x 10(-4) min/muU/ml. Mean values did not differ between the 2 tests performed 6 weeks apart, Coefficients of variation for K-itt and S-l were 60 and 47%, respectively. Conclusions and Clinical Relevance-GTT, ITT, and IST can be performed in cats, using standard protocols. Knowledge of reference values and test variability will enable researchers to better interpret test results for assessment of glucose tolerance, pancreatic beta -cell function, and insulin sensitivity in cats.

Monitoring the composition and form of urban environments based on the vegetation-impervious surface-soil (VIS) model by sub-pixel analysis techniques

The majority of the world's population now resides in urban environments and information on the internal composition and dynamics of these environments is essential to enable preservation of certain standards of living. Remotely sensed data, especially the global coverage of moderate spatial resolution satellites such as Landsat, Indian Resource Satellite and Systeme Pour I'Observation de la Terre (SPOT), offer a highly useful data source for mapping the composition of these cities and examining their changes over time. The utility and range of applications for remotely sensed data in urban environments could be improved with a more appropriate conceptual model relating urban environments to the sampling resolutions of imaging sensors and processing routines. Hence, the aim of this work was to take the Vegetation-Impervious surface-Soil (VIS) model of urban composition and match it with the most appropriate image processing methodology to deliver information on VIS composition for urban environments. Several approaches were evaluated for mapping the urban composition of Brisbane city (south-cast Queensland, Australia) using Landsat 5 Thematic Mapper data and 1:5000 aerial photographs. The methods evaluated were: image classification; interpretation of aerial photographs; and constrained linear mixture analysis. Over 900 reference sample points on four transects were extracted from the aerial photographs and used as a basis to check output of the classification and mixture analysis. Distinctive zonations of VIS related to urban composition were found in the per-pixel classification and aggregated air-photo interpretation; however, significant spectral confusion also resulted between classes. In contrast, the VIS fraction images produced from the mixture analysis enabled distinctive densities of commercial, industrial and residential zones within the city to be clearly defined, based on their relative amount of vegetation cover. The soil fraction image served as an index for areas being (re)developed. The logical match of a low (L)-resolution, spectral mixture analysis approach with the moderate spatial resolution image data, ensured the processing model matched the spectrally heterogeneous nature of the urban environments at the scale of Landsat Thematic Mapper data.

A compartmental model of hepatic disposition kinetics: 1. Model development and application to linear kinetics

The conventional convection-dispersion model is widely used to interrelate hepatic availability (F) and clearance (Cl) with the morphology and physiology of the liver and to predict effects such as changes in liver blood flow on F and Cl. The extension of this model to include nonlinear kinetics and zonal heterogeneity of the liver is not straightforward and requires numerical solution of partial differential equation, which is not available in standard nonlinear regression analysis software. In this paper, we describe an alternative compartmental model representation of hepatic disposition (including elimination). The model allows the use of standard software for data analysis and accurately describes the outflow concentration-time profile for a vascular marker after bolus injection into the liver. In an evaluation of a number of different compartmental models, the most accurate model required eight vascular compartments, two of them with back mixing. In addition, the model includes two adjacent secondary vascular compartments to describe the tail section of the concentration-time profile for a reference marker. The model has the added flexibility of being easy to modify to model various enzyme distributions and nonlinear elimination. Model predictions of F, MTT, CV2, and concentration-time profile as well as parameter estimates for experimental data of an eliminated solute (palmitate) are comparable to those for the extended convection-dispersion model.

Adjustment of homeless adolescents to a crisis shelter: Application of a stress and coping model

The present study examined the utility of a stress and coping model of adaptation to a homeless shelter among homeless adolescents. Seventy-eight homeless adolescents were interviewed and completed self-administered scales at Time 1 (day of shelter entry) and Time 2 (day of discharge). The mean duration of stay at the shelter was 7.23 days (SD = 7.01). Predictors included appraisal (threat and self-efficacy), coping resources, and coping strategies (productive, nonproductive, and reference to others coping). Adjustment outcomes were Time I measures of global distress, physical health, clinician-and youthworker- rated social adjustment, and externalizing behavior and Time 2 youthworker-rated social adjustment and goal achievement. Results of hierarchical regression analyses indicated that after controlling for the effects of relevant background variables (number of other shelters visited, sexual, emotional, and physical abuse), measures of coping resources, appraisal, and coping strategies evidenced distinct relations with measures of adjustment in ways consistent with the model's predictions with few exceptions. In cross-sectional analyses better Time I adjustment was related to reports of higher levels of coping resources, self-efficacy beliefs, and productive coping strategies, and reports of lower levels of threat appraisal and nonproductive coping strategies. Prospective analyses showed a link between reports of higher levels of reference to others coping strategies and greater goal achievement and, unexpectedly, an association between lower self-efficacy beliefs and better Time 2 youthworker-rated social adjustment. Hence, whereas prospective analyses provide only limited support for the use of a stress and coping model in explaining the adjustment of homeless adolescents to a crisis shelter, cross-sectional findings provide stronger support.

Anatomy of a hemiramphid pharyngeal mill with reference to arrhamphus sclerolepis krefftii (steindachner) (teleostei: hemiramphidae)

The structure and function of the pharyngeal jaw apparatus (PJA) and postpharyngeal alimentary tract of Arrhamphus sclerolepis krefftii, an herbivorous hemiramphid, were investigated by dissection, light and scanning electron microscopy, and X-ray analysis of live specimens. A simple model of PJA operation is proposed, consisting of an adductive power stroke of the third pharyngobranchial that draws it posteriorly while the fifth ceratobranchial is adducted, and a return stroke in which the third pharyngobranchial bone is drawn anteriorly during abduction of the fifth ceratobranchial. Teeth in the posteromedial region of the PJA are eroded into an occlusion zone where the teeth of the third pharyngobranchial are spatulate incisiform and face posteriorly in opposition to the rostrally oriented spatulate incisiform teeth in the wear zone of the fifth ceratobranchial. The shape of the teeth and their pedestals (bone of attachment) is consistent with the model and with the forces likely to operate on the elements of the PJA during mastication. The role of pharyngeal tooth replacement in maintaining the occlusal surfaces in the PJA during growth is described. The postpharyngeal alimentary tract of A. sclerolepis krefftii comprises a stomachless cylinder that attenuates gradually as it passes straight to the anus, interrupted only by a rectal valve. The ratio of gut length to standard length is about 0.5. Despite superficial similarities to the cichlid PJA (Stiassny and Jensen [1987] Bull Mus Comp Zool 151: 269-319), the hemiramphid PJA differs in the fusion of the third pharyngobranchial bones, teeth in the second pharyngobranchials and the fifth ceratobranchial face anteriorly, the presence of a slide-like diarthroses between the heads of the fourth epibranchials and the third pharyngobranchial, the occlusion zone of constantly wearing teeth, and the unusual form of the muscularis craniopharyngobranchialis. The functional relationship between these structures is explained and the consequence for the fish of a complex PJA and a simple gut is discussed. (C) 2002 Wiley-Liss, Inc.

Investigation of factors related to employment outcome following traumatic brain injury: a critical review and conceptual model

Purpose : The purpose of this article is to critically review the literature to examine factors that are most consistently related to employment outcome following traumatic brain injury (TBI), with a particular focus on metacognitive skills. It also aims to develop a conceptual model of factors related to employment outcome. Method : The first stage of the review considered 85 studies published between 1980 and December 2003 which investigated factors associated with employment outcome following TBI. English-language studies were identified through searches of Medline and PsycINFO, as well as manual searches of journals and reference lists. The studies were evaluated and rated by two independent raters (Kappa = 0.835) according to the quality of their methodology based upon nine criteria. Fifty studies met the criteria for inclusion in the second stage of the review, which examined the relationship between a broad range of variables and employment outcome. Results : The factors most consistently associated with employment outcome included pre-injury occupational status, functional status at discharge, global cognitive functioning, perceptual ability, executive functioning, involvement in vocational rehabilitation services and emotional status. Conclusions : A conceptual model is presented which emphasises the importance of metacognitive, emotional and social environment factors for improving employment outcome.

A simulation model of cereal-legume intercropping systems for semi-arid regions II. Model application

Smallholder farmers in Africa practice traditional cropping techniques such as intercropping. Intercropping is thought to offer higher productivity and resource milisation than sole cropping. In this study, risk associated with maize-bean intercropping was evaluated by quantifying long-term yield in both intercropping and sole cropping in a semi-arid region of South Africa (Bloemfontein, Free State) with reference to rainfall variability. The crop simulation model was run with different cultural practices (planting date and plant density) for 52 summer crop growing seasons (1950/1951-2001/2002). Eighty-one scenarios, consisted of three levels of initial soil water, planting date, maize population, and bean population, were simulated. From the simulation outputs, the total land equivalent ratio (LER) was greater than one. The intercrop (equivalent to sole maize) had greater energy value (EV) than sole beans, and the intercrop (equivalent to sole beans) had greater monetary value (MV) than sole maize. From these results, it can be concluded that maize-bean intercropping is advantageous for this semi-arid region. Soil water at planting was the most important factor of all scenario factors, followed by planting date. Irrigation application at planting, November/December planting and high plant density of maize for EV and beans for MV can be one of the most effective cultural practices in the study region. With regard to rainfall variability, seasonal (October-April) rainfall positively affected EV and MV, but not LER. There was more intercrop production in La Nina years than in El Nino years. Thus, better cultural practices may be selected to maximize maize-bean intercrop yields for specific seasons in the semi-arid region based on the global seasonal outlook. (c) 2004 Elsevier B.V. All rights reserved.

Pore size distribution analysis of activated carbons: Application of density functional theory using nongraphitized carbon black as a reference system

The application of nonlocal density functional theory (NLDFT) to determine pore size distribution (PSD) of activated carbons using a nongraphitized carbon black, instead of graphitized thermal carbon black, as a reference system is explored. We show that in this case nitrogen and argon adsorption isotherms in activated carbons are precisely correlated by the theory, and such an excellent correlation would never be possible if the pore wall surface was assumed to be identical to that of graphitized carbon black. It suggests that pore wall surfaces of activated carbon are closer to that of amorphous solids because of defects of crystalline lattice, finite pore length, and the presence of active centers.. etc. Application of the NLDFT adapted to amorphous solids resulted in quantitative description of N-2 and Ar adsorption isotherms on nongraphitized carbon black BP280 at their respective boiling points. In the present paper we determined solid-fluid potentials from experimental adsorption isotherms on nongraphitized carbon black and subsequently used those potentials to model adsorption in slit pores and generate a corresponding set of local isotherms, which we used to determine the PSD functions of different activated carbons. (c) 2005 Elsevier Ltd. All rights reserved.

Customised birthweight: Coefficients for an Australian population and validation of the model

Background: Published birthweight references in Australia do not fully take into account constitutional factors that influence birthweight and therefore may not provide an accurate reference to identify the infant with abnormal growth. Furthermore, studies in other regions that have derived adjusted (customised) birthweight references have applied untested assumptions in the statistical modelling. Aims: To validate the customised birthweight model and to produce a reference set of coefficients for estimating a customised birthweight that may be useful for maternity care in Australia and for future research. Methods: De-identified data were extracted from the clinical database for all births at the Mater Mother's Hospital, Brisbane, Australia, between January 1997 and June 2005. Births with missing data for the variables under study were excluded. In addition the following were excluded: multiple pregnancies, births less than 37 completed week's gestation, stillbirths, and major congenital abnormalities. Multivariate analysis was undertaken. A double cross-validation procedure was used to validate the model. Results: The study of 42 206 births demonstrated that, for statistical purposes, birthweight is normally distributed. Coefficients for the derivation of customised birthweight in an Australian population were developed and the statistical model is demonstrably robust. Conclusions: This study provides empirical data as to the robustness of the model to determine customised birthweight. Further research is required to define where normal physiology ends and pathology begins, and which segments of the population should be included in the construction of a customised birthweight standard.

Toy model for a relational formulation of quantum theory

In the absence of an external frame of reference-i.e., in background independent theories such as general relativity-physical degrees of freedom must describe relations between systems. Using a simple model, we investigate how such a relational quantum theory naturally arises by promoting reference systems to the status of dynamical entities. Our goal is twofold. First, we demonstrate using elementary quantum theory how any quantum mechanical experiment admits a purely relational description at a fundamental. Second, we describe how the original non-relational theory approximately emerges from the fully relational theory when reference systems become semi-classical. Our technique is motivated by a Bayesian approach to quantum mechanics, and relies on the noiseless subsystem method of quantum information science used to protect quantum states against undesired noise. The relational theory naturally predicts a fundamental decoherence mechanism, so an arrow of time emerges from a time-symmetric theory. Moreover, our model circumvents the problem of the collapse of the wave packet as the probability interpretation is only ever applied to diagonal density operators. Finally, the physical states of the relational theory can be described in terms of spin networks introduced by Penrose as a combinatorial description of geometry, and widely studied in the loop formulation of quantum gravity. Thus, our simple bottom-up approach (starting from the semiclassical limit to derive the fully relational quantum theory) may offer interesting insights on the low energy limit of quantum gravity.