A new control-volume finite-element scheme for heterogeneous porous media : application to the drying of softwood

An improved mesoscopic model is presented for simulating the drying of porous media. The aim of this model is to account for two scales simultaneously: the scale of the whole product and the scale of the heterogeneities of the porous medium. The innovation of this method is the utilization of a new mass-conservative scheme based on the Control-Volume Finite-Element (CV-FE) method that partitions the moisture content field over the individual sub-control volumes surrounding each node within the mesh. Although the new formulation has potential for application across a wide range of transport processes in heterogeneous porous media, the focus here is on applying the model to the drying of small sections of softwood consisting of several growth rings. The results conclude that, when compared to a previously published scheme, only the new mass-conservative formulation correctly captures the true moisture content evolution in the earlywood and latewood components of the growth rings during drying.

Improved image quality for x-ray CT imaging of gel dosimeters

Purpose: This study provides a simple method for improving precision of x-ray computed tomography (CT) scans of irradiated polymer gel dosimetry. The noise affecting CT scans of irradiated gels has been an impediment to the use of clinical CT scanners for gel dosimetry studies. Method: In this study, it is shown that multiple scans of a single PAGAT gel dosimeter can be used to extrapolate a ‘zero-scan’ image which displays a similar level of precision to an image obtained by averaging multiple CT images, without the compromised dose measurement resulting from the exposure of the gel to radiation from the CT scanner. Results: When extrapolating the zero-scan image, it is shown that exponential and simple linear fits to the relationship between Hounsfield unit and scan number, for each pixel in the image, provides an accurate indication of gel density. Conclusions: It is expected that this work will be utilised in the analysis of three-dimensional gel volumes irradiated using complex radiotherapy treatments.

Stochastic modelling of T cell homeostasis for two competing clonotypes via the master equation

Stochastic models for competing clonotypes of T cells by multivariate, continuous-time, discrete state, Markov processes have been proposed in the literature by Stirk, Molina-París and van den Berg (2008). A stochastic modelling framework is important because of rare events associated with small populations of some critical cell types. Usually, computational methods for these problems employ a trajectory-based approach, based on Monte Carlo simulation. This is partly because the complementary, probability density function (PDF) approaches can be expensive but here we describe some efficient PDF approaches by directly solving the governing equations, known as the Master Equation. These computations are made very efficient through an approximation of the state space by the Finite State Projection and through the use of Krylov subspace methods when evolving the matrix exponential. These computational methods allow us to explore the evolution of the PDFs associated with these stochastic models, and bimodal distributions arise in some parameter regimes. Time-dependent propensities naturally arise in immunological processes due to, for example, age-dependent effects. Incorporating time-dependent propensities into the framework of the Master Equation significantly complicates the corresponding computational methods but here we describe an efficient approach via Magnus formulas. Although this contribution focuses on the example of competing clonotypes, the general principles are relevant to multivariate Markov processes and provide fundamental techniques for computational immunology.

Linear models for endocytic transformations from live cell imaging

Endocytosis is the process by which cells internalise molecules including nutrient proteins from the extracellular media. In one form, macropinocytosis, the membrane at the cell surface ruffles and folds over to give rise to an internalised vesicle. Negatively charged phospholipids within the membrane called phosphoinositides then undergo a series of transformations that are critical for the correct trafficking of the vesicle within the cell, and which are often pirated by pathogens such as Salmonella. Advanced fluorescent video microscopy imaging now allows the detailed observation and quantification of these events in live cells over time. Here we use these observations as a basis for building differential equation models of the transformations. An initial investigation of these interactions was modelled with reaction rates proportional to the sum of the concentrations of the individual constituents. A first order linear system for the concentrations results. The structure of the system enables analytical expressions to be obtained and the problem becomes one of determining the reaction rates which generate the observed data plots. We present results with reaction rates which capture the general behaviour of the reactions so that we now have a complete mathematical model of phosphoinositide transformations that fits the experimental observations. Some excellent fits are obtained with modulated exponential functions; however, these are not solutions of the linear system. The question arises as to how the model may be modified to obtain a system whose solution provides a more accurate fit.

Estimating the loading condition of a diesel engine using instantaneous angular speed analysis

Continuing monitoring of diesel engine performance is critical for early detection of fault developments in the engine before they materialize and become a functional failure. Instantaneous crank angular speed (IAS) analysis is one of a few non intrusive condition monitoring techniques that can be utilized for such tasks. In this experimental study, IAS analysis was employed to estimate the loading condition of a 4-stroke 4-cylinder diesel engine in a laboratory condition. It was shown that IAS analysis can provide useful information about engine speed variation caused by the changing piston momentum and crankshaft acceleration during the engine combustion process. It was also found that the major order component of the IAS spectrum directly associated with the engine firing frequency (at twice the mean shaft revolution speed) can be utilized to estimate the engine loading condition regardless of whether the engine is operating at normal running conditions or in a simulated faulty injector case. The amplitude of this order component follows a clear exponential curve as the loading condition changes. A mathematical relationship was established for the estimation of the engine power output based on the amplitude of the major order component of the measured IAS spectrum.

Estimating the loading condition of a diesel engine using instantaneous angular speed analysis

Continuing monitoring of diesel engine performance is critical for early detection of fault developments in the engine before they materialize and become a functional failure. Instantaneous crank angular speed (IAS) analysis is one of a few non intrusive condition monitoring techniques that can be utilized for such tasks. In this experimental study, IAS analysis was employed to estimate the loading condition of a 4-stroke 4-cylinder diesel engine in a laboratory condition. It was shown that IAS analysis can provide useful information about engine speed variation caused by the changing piston momentum and crankshaft acceleration during the engine combustion process. It was also found that the major order component of the IAS spectrum directly associated with the engine firing frequency (at twice the mean shaft revolution speed) can be utilized to estimate the engine loading condition regardless of whether the engine is operating at normal running conditions or in a simulated faulty injector case. The amplitude of this order component follows a clear exponential curve as the loading condition changes. A mathematical relationship was established for the estimation of the engine power output based on the amplitude of the major order component of the measured IAS spectrum.

Philosophy, behaviour disorders, and the school

The recent exponential rise in the number of behaviour disorders has been the focus of a wide range of commentaries, ranging from the pedagogic and the administrative, to the sociological, and even the legal. This book will be the first to apply, in a systematic and thorough manner, the ideas of the foundational discipline of philosophy. A number of philosophical tools are applied here, tools arising through the medium of the traditional philosophical debates, such as those concerning governance, truth, logic, ethics, free-will, law and language. Each forms a separate chapter, but together they constitute a comprehensive, rigorous and original insight into what is now an important set of concerns for all those interested in the governance of children. The intention is threefold: first, to demonstrate the utility, accessibility and effectiveness of philosophical ideas within this important academic area. Philosophy does not have to be regarded an arcane and esoteric discipline, with only limited contemporary application, far from it. Second, the book offers a new set of approaches and ideas for both researchers and practitioners within education, a field is in danger of continually using the same ideas, to endlessly repeat the same conclusions. Third, the book offers a viable alternative to the dominant psychological model which increasingly employs pathology as its central rationale for conduct. The book would not only be of interest to mainstream educators, and to those students and academics interested in philosophy, and more specifically, the application of philosophical ideas to educational issues, it would also be an appropriate text for courses on education and difference, and due to the breadth of the philosophical issues addressed, courses on applied philosophy.

Free surface flow past topography : a beyond-all-orders approach

The problem of steady subcritical free surface flow past a submerged inclined step is considered. The asymptotic limit of small Froude number is treated, with particular emphasis on the effect that changing the angle of the step face has on the surface waves. As demonstrated by Chapman & Vanden-Broeck (2006), the divergence of a power series expansion in powers of the square of the Froude number is caused by singularities in the analytic continuation of the free surface; for an inclined step, these singularities may correspond to either the corners or stagnation points of the step, or both, depending on the angle of incline. Stokes lines emanate from these singularities, and exponentially small waves are switched on at the point the Stokes lines intersect with the free surface. Our results suggest that for a certain range of step angles, two wavetrains are switched on, but the exponentially subdominant one is switched on first, leading to an intermediate wavetrain not previously noted. We extend these ideas to the problem of flow over a submerged bump or trench, again with inclined sides. This time there may be two, three or four active Stokes lines, depending on the inclination angles. We demonstrate how to construct a base topography such that wave contributions from separate Stokes lines are of equal magnitude but opposite phase, thus cancelling out. Our asymptotic results are complemented by numerical solutions to the fully nonlinear equations.

Multifractal characterisation and analysis of complex networks

Complex networks have been studied extensively due to their relevance to many real-world systems such as the world-wide web, the internet, biological and social systems. During the past two decades, studies of such networks in different fields have produced many significant results concerning their structures, topological properties, and dynamics. Three well-known properties of complex networks are scale-free degree distribution, small-world effect and self-similarity. The search for additional meaningful properties and the relationships among these properties is an active area of current research. This thesis investigates a newer aspect of complex networks, namely their multifractality, which is an extension of the concept of selfsimilarity. The first part of the thesis aims to confirm that the study of properties of complex networks can be expanded to a wider field including more complex weighted networks. Those real networks that have been shown to possess the self-similarity property in the existing literature are all unweighted networks. We use the proteinprotein interaction (PPI) networks as a key example to show that their weighted networks inherit the self-similarity from the original unweighted networks. Firstly, we confirm that the random sequential box-covering algorithm is an effective tool to compute the fractal dimension of complex networks. This is demonstrated on the Homo sapiens and E. coli PPI networks as well as their skeletons. Our results verify that the fractal dimension of the skeleton is smaller than that of the original network due to the shortest distance between nodes is larger in the skeleton, hence for a fixed box-size more boxes will be needed to cover the skeleton. Then we adopt the iterative scoring method to generate weighted PPI networks of five species, namely Homo sapiens, E. coli, yeast, C. elegans and Arabidopsis Thaliana. By using the random sequential box-covering algorithm, we calculate the fractal dimensions for both the original unweighted PPI networks and the generated weighted networks. The results show that self-similarity is still present in generated weighted PPI networks. This implication will be useful for our treatment of the networks in the third part of the thesis. The second part of the thesis aims to explore the multifractal behavior of different complex networks. Fractals such as the Cantor set, the Koch curve and the Sierspinski gasket are homogeneous since these fractals consist of a geometrical figure which repeats on an ever-reduced scale. Fractal analysis is a useful method for their study. However, real-world fractals are not homogeneous; there is rarely an identical motif repeated on all scales. Their singularity may vary on different subsets; implying that these objects are multifractal. Multifractal analysis is a useful way to systematically characterize the spatial heterogeneity of both theoretical and experimental fractal patterns. However, the tools for multifractal analysis of objects in Euclidean space are not suitable for complex networks. In this thesis, we propose a new box covering algorithm for multifractal analysis of complex networks. This algorithm is demonstrated in the computation of the generalized fractal dimensions of some theoretical networks, namely scale-free networks, small-world networks, random networks, and a kind of real networks, namely PPI networks of different species. Our main finding is the existence of multifractality in scale-free networks and PPI networks, while the multifractal behaviour is not confirmed for small-world networks and random networks. As another application, we generate gene interactions networks for patients and healthy people using the correlation coefficients between microarrays of different genes. Our results confirm the existence of multifractality in gene interactions networks. This multifractal analysis then provides a potentially useful tool for gene clustering and identification. The third part of the thesis aims to investigate the topological properties of networks constructed from time series. Characterizing complicated dynamics from time series is a fundamental problem of continuing interest in a wide variety of fields. Recent works indicate that complex network theory can be a powerful tool to analyse time series. Many existing methods for transforming time series into complex networks share a common feature: they define the connectivity of a complex network by the mutual proximity of different parts (e.g., individual states, state vectors, or cycles) of a single trajectory. In this thesis, we propose a new method to construct networks of time series: we define nodes by vectors of a certain length in the time series, and weight of edges between any two nodes by the Euclidean distance between the corresponding two vectors. We apply this method to build networks for fractional Brownian motions, whose long-range dependence is characterised by their Hurst exponent. We verify the validity of this method by showing that time series with stronger correlation, hence larger Hurst exponent, tend to have smaller fractal dimension, hence smoother sample paths. We then construct networks via the technique of horizontal visibility graph (HVG), which has been widely used recently. We confirm a known linear relationship between the Hurst exponent of fractional Brownian motion and the fractal dimension of the corresponding HVG network. In the first application, we apply our newly developed box-covering algorithm to calculate the generalized fractal dimensions of the HVG networks of fractional Brownian motions as well as those for binomial cascades and five bacterial genomes. The results confirm the monoscaling of fractional Brownian motion and the multifractality of the rest. As an additional application, we discuss the resilience of networks constructed from time series via two different approaches: visibility graph and horizontal visibility graph. Our finding is that the degree distribution of VG networks of fractional Brownian motions is scale-free (i.e., having a power law) meaning that one needs to destroy a large percentage of nodes before the network collapses into isolated parts; while for HVG networks of fractional Brownian motions, the degree distribution has exponential tails, implying that HVG networks would not survive the same kind of attack.

A Bayesian analysis of an agricultural field trial with three spatial dimensions

Modern technology now has the ability to generate large datasets over space and time. Such data typically exhibit high autocorrelations over all dimensions. The field trial data motivating the methods of this paper were collected to examine the behaviour of traditional cropping and to determine a cropping system which could maximise water use for grain production while minimising leakage below the crop root zone. They consist of moisture measurements made at 15 depths across 3 rows and 18 columns, in the lattice framework of an agricultural field. Bayesian conditional autoregressive (CAR) models are used to account for local site correlations. Conditional autoregressive models have not been widely used in analyses of agricultural data. This paper serves to illustrate the usefulness of these models in this field, along with the ease of implementation in WinBUGS, a freely available software package. The innovation is the fitting of separate conditional autoregressive models for each depth layer, the ‘layered CAR model’, while simultaneously estimating depth profile functions for each site treatment. Modelling interest also lay in how best to model the treatment effect depth profiles, and in the choice of neighbourhood structure for the spatial autocorrelation model. The favoured model fitted the treatment effects as splines over depth, and treated depth, the basis for the regression model, as measured with error, while fitting CAR neighbourhood models by depth layer. It is hierarchical, with separate onditional autoregressive spatial variance components at each depth, and the fixed terms which involve an errors-in-measurement model treat depth errors as interval-censored measurement error. The Bayesian framework permits transparent specification and easy comparison of the various complex models compared.

A subject-specific model of human buttocks and thighs in a seated posture

Finite element analyses of the human body in seated postures requires digital models capable of providing accurate and precise prediction of the tissue-level response of the body in the seated posture. To achieve such models, the human anatomy must be represented with high fidelity. This information can readily be defined using medical imaging techniques such as Magnetic Resonance Imaging (MRI) or Computed Tomography (CT). Current practices for constructing digital human models, based on the magnetic resonance (MR) images, in a lying down (supine) posture have reduced the error in the geometric representation of human anatomy relative to reconstructions based on data from cadaveric studies. Nonetheless, the significant differences between seated and supine postures in segment orientation, soft-tissue deformation and soft tissue strain create a need for data obtained in postures more similar to the application posture. In this study, we present a novel method for creating digital human models based on seated MR data. An adult-male volunteer was scanned in a simulated driving posture using a FONAR 0.6T upright MRI scanner with a T1 scanning protocol. To compensate for unavoidable image distortion near the edges of the study, images of the same anatomical structures were obtained in transverse and sagittal planes. Combinations of transverse and sagittal images were used to reconstruct the major anatomical features from the buttocks through the knees, including bone, muscle and fat tissue perimeters, using Solidworks® software. For each MR image, B-splines were created as contours for the anatomical structures of interest, and LOFT commands were used to interpolate between the generated Bsplines. The reconstruction of the pelvis, from MR data, was enhanced by the use of a template model generated in previous work CT images. A non-rigid registration algorithm was used to fit the pelvis template into the MR data. Additionally, MR image processing was conducted to both the left and the right sides of the model due to the intended asymmetric posture of the volunteer during the MR measurements. The presented subject-specific, three-dimensional model of the buttocks and thighs will add value to optimisation cycles in automotive seat development when used in simulating human interaction with automotive seats.

Developing sustainable IT-related capabilities : instrument development and test

Research has established that firms' IT-related capabilities at a point in time explain IT-related performance differences across firms. IT resources, however, are dynamic, and evolve at an exponential rate. This means we need to understand how to sustain firms' existing capabilities to leverage opportunities offered by new IT resources. Wet suggests a higher-level resource that can sustain firms' existing IT-related capabilities. Second, we report on the development of a valid and reliable measurement instrument for measuring this higher-level resource in four stages, which includes expert feedback and a field test. The validated instrument would be useful in extending the IT business value studies to investigate how firms can sustain their IT-related capabilities. This effort will provide a deeper understanding of how firms can secure sustainable IT-related business value from their acquired IT resources.

Accuracy of rate estimation using relaxed-clock models with a critical focus on the early metazoan radiation

In recent years, a number of phylogenetic methods have been developed for estimating molecular rates and divergence dates under models that relax the molecular clock constraint by allowing rate change throughout the tree. These methods are being used with increasing frequency, but there have been few studies into their accuracy. We tested the accuracy of several relaxed-clock methods (penalized likelihood and Bayesian inference using various models of rate change) using nucleotide sequences simulated on a nine-taxon tree. When the sequences evolved with a constant rate, the methods were able to infer rates accurately, but estimates were more precise when a molecular clock was assumed. When the sequences evolved under a model of autocorrelated rate change, rates were accurately estimated using penalized likelihood and by Bayesian inference using lognormal and exponential models of rate change, while other models did not perform as well. When the sequences evolved under a model of uncorrelated rate change, only Bayesian inference using an exponential rate model performed well. Collectively, the results provide a strong recommendation for using the exponential model of rate change if a conservative approach to divergence time estimation is required. A case study is presented in which we use a simulation-based approach to examine the hypothesis of elevated rates in the Cambrian period, and it is found that these high rate estimates might be an artifact of the rate estimation method. If this bias is present, then the ages of metazoan divergences would be systematically underestimated. The results of this study have implications for studies of molecular rates and divergence dates.

Time dependency of molecular rate estimates and systematic overestimation of recent divergence times

Studies of molecular evolutionary rates have yielded a wide range of rate estimates for various genes and taxa. Recent studies based on population-level and pedigree data have produced remarkably high estimates of mutation rate, which strongly contrast with substitution rates inferred in phylogenetic (species-level) studies. Using Bayesian analysis with a relaxed-clock model, we estimated rates for three groups of mitochondrial data: avian protein-coding genes, primate protein-coding genes, and primate d-loop sequences. In all three cases, we found a measurable transition between the high, short-term (<1–2 Myr) mutation rate and the low, long-term substitution rate. The relationship between the age of the calibration and the rate of change can be described by a vertically translated exponential decay curve, which may be used for correcting molecular date estimates. The phylogenetic substitution rates in mitochondria are approximately 0.5% per million years for avian protein-coding sequences and 1.5% per million years for primate protein-coding and d-loop sequences. Further analyses showed that purifying selection offers the most convincing explanation for the observed relationship between the estimated rate and the depth of the calibration. We rule out the possibility that it is a spurious result arising from sequence errors, and find it unlikely that the apparent decline in rates over time is caused by mutational saturation. Using a rate curve estimated from the d-loop data, several dates for last common ancestors were calculated: modern humans and Neandertals (354 ka; 222–705 ka), Neandertals (108 ka; 70–156 ka), and modern humans (76 ka; 47–110 ka). If the rate curve for a particular taxonomic group can be accurately estimated, it can be a useful tool for correcting divergence date estimates by taking the rate decay into account. Our results show that it is invalid to extrapolate molecular rates of change across different evolutionary timescales, which has important consequences for studies of populations, domestication, conservation genetics, and human evolution.

Use of Bayesian MUNE to show differing rate of loss of motor units in subgroups of ALS

Objectives To evaluate differences among patients with different clinical features of ALS, we used our Bayesian method of motor unit number estimation (MUNE). Methods We performed serial MUNE studies on 42 subjects who fulfilled the diagnostic criteria for ALS during the course of their illness. Subjects were classified into three subgroups according to whether they had typical ALS (with upper and lower motor neurone signs) or had predominantly upper motor neurone weakness with only minor LMN signs, or predominantly lower motor neurone weakness with only minor UMN signs. In all subjects we calculated the half life of MUs, defined as the expected time for the number of MUs to halve, in one or more of the abductor digiti minimi (ADM), abductor pollicis brevis (APB) and extensor digitorum brevis (EDB) muscles. Results The mean half life of MUs was less in subjects who had typical ALS with both upper and lower motor neurone signs than in those with predominantly upper motor neurone weakness or predominantly lower motor neurone weakness. In 18 subjects we analysed the estimated size of the MUs and demonstrated the appearance of large MUs in subjects with upper or lower motor neurone predominant weakness. We found that the appearance of large MUs was correlated with the half life of MUs. Conclusions Patients with different clinical features of ALS have different rates of loss and different sizes of MUs. Significance: These findings could indicate differences in disease pathogenesis.