Wavelet based approaches and high resolution methods for complex process models

Many industrial processes and systems can be modelled mathematically by a set of Partial Differential Equations (PDEs). Finding a solution to such a PDF model is essential for system design, simulation, and process control purpose. However, major difficulties appear when solving PDEs with singularity. Traditional numerical methods, such as finite difference, finite element, and polynomial based orthogonal collocation, not only have limitations to fully capture the process dynamics but also demand enormous computation power due to the large number of elements or mesh points for accommodation of sharp variations. To tackle this challenging problem, wavelet based approaches and high resolution methods have been recently developed with successful applications to a fixedbed adsorption column model. Our investigation has shown that recent advances in wavelet based approaches and high resolution methods have the potential to be adopted for solving more complicated dynamic system models. This chapter will highlight the successful applications of these new methods in solving complex models of simulated-moving-bed (SMB) chromatographic processes. A SMB process is a distributed parameter system and can be mathematically described by a set of partial/ordinary differential equations and algebraic equations. These equations are highly coupled; experience wave propagations with steep front, and require significant numerical effort to solve. To demonstrate the numerical computing power of the wavelet based approaches and high resolution methods, a single column chromatographic process modelled by a Transport-Dispersive-Equilibrium linear model is investigated first. Numerical solutions from the upwind-1 finite difference, wavelet-collocation, and high resolution methods are evaluated by quantitative comparisons with the analytical solution for a range of Peclet numbers. After that, the advantages of the wavelet based approaches and high resolution methods are further demonstrated through applications to a dynamic SMB model for an enantiomers separation process. This research has revealed that for a PDE system with a low Peclet number, all existing numerical methods work well, but the upwind finite difference method consumes the most time for the same degree of accuracy of the numerical solution. The high resolution method provides an accurate numerical solution for a PDE system with a medium Peclet number. The wavelet collocation method is capable of catching up steep changes in the solution, and thus can be used for solving PDE models with high singularity. For the complex SMB system models under consideration, both the wavelet based approaches and high resolution methods are good candidates in terms of computation demand and prediction accuracy on the steep front. The high resolution methods have shown better stability in achieving steady state in the specific case studied in this Chapter.

Improving the performance of model-order selection criteria by partial-model selection search

The traditional searching method for model-order selection in linear regression is a nested full-parameters-set searching procedure over the desired orders, which we call full-model order selection. On the other hand, a method for model-selection searches for the best sub-model within each order. In this paper, we propose using the model-selection searching method for model-order selection, which we call partial-model order selection. We show by simulations that the proposed searching method gives better accuracies than the traditional one, especially for low signal-to-noise ratios over a wide range of model-order selection criteria (both information theoretic based and bootstrap-based). Also, we show that for some models the performance of the bootstrap-based criterion improves significantly by using the proposed partial-model selection searching method. Index Terms— Model order estimation, model selection, information theoretic criteria, bootstrap 1. INTRODUCTION Several model-order selection criteria can be applied to find the optimal order. Some of the more commonly used information theoretic-based procedures include Akaike’s information criterion (AIC) [1], corrected Akaike (AICc) [2], minimum description length (MDL) [3], normalized maximum likelihood (NML) [4], Hannan-Quinn criterion (HQC) [5], conditional model-order estimation (CME) [6], and the efficient detection criterion (EDC) [7]. From a practical point of view, it is difficult to decide which model order selection criterion to use. Many of them perform reasonably well when the signal-to-noise ratio (SNR) is high. The discrepancies in their performance, however, become more evident when the SNR is low. In those situations, the performance of the given technique is not only determined by the model structure (say a polynomial trend versus a Fourier series) but, more importantly, by the relative values of the parameters within the model. This makes the comparison between the model-order selection algorithms difficult as within the same model with a given order one could find an example for which one of the methods performs favourably well or fails [6, 8]. Our aim is to improve the performance of the model order selection criteria in cases where the SNR is low by considering a model-selection searching procedure that takes into account not only the full-model order search but also a partial model order search within the given model order. Understandably, the improvement in the performance of the model order estimation is at the expense of additional computational complexity.

An enriched radial point interpolation method (e-RPIM) for analysis of crack tip fields

In this paper, an enriched radial point interpolation method (e-RPIM) is developed the for the determination of crack tip fields. In e-RPIM, the conventional RBF interpolation is novelly augmented by the suitable trigonometric basis functions to reflect the properties of stresses for the crack tip fields. The performance of the enriched RBF meshfree shape functions is firstly investigated to fit different surfaces. The surface fitting results have proven that, comparing with the conventional RBF shape function, the enriched RBF shape function has: (1) a similar accuracy to fit a polynomial surface; (2) a much better accuracy to fit a trigonometric surface; and (3) a similar interpolation stability without increase of the condition number of the RBF interpolation matrix. Therefore, it has proven that the enriched RBF shape function will not only possess all advantages of the conventional RBF shape function, but also can accurately reflect the properties of stresses for the crack tip fields. The system of equations for the crack analysis is then derived based on the enriched RBF meshfree shape function and the meshfree weak-form. Several problems of linear fracture mechanics are simulated using this newlydeveloped e-RPIM method. It has demonstrated that the present e-RPIM is very accurate and stable, and it has a good potential to develop a practical simulation tool for fracture mechanics problems.

An enriched radial point interpolation method (e-RPIM) for analysis of crack tip fields

In this paper, an enriched radial point interpolation method (e-RPIM) is developed the for the determination of crack tip fields. In e-RPIM, the conventional RBF interpolation is novelly augmented by the suitable trigonometric basis functions to reflect the properties of stresses for the crack tip fields. The performance of the enriched RBF meshfree shape functions is firstly investigated to fit different surfaces. The surface fitting results have proven that, comparing with the conventional RBF shape function, the enriched RBF shape function has: (1) a similar accuracy to fit a polynomial surface; (2) a much better accuracy to fit a trigonometric surface; and (3) a similar interpolation stability without increase of the condition number of the RBF interpolation matrix. Therefore, it has proven that the enriched RBF shape function will not only possess all advantages of the conventional RBF shape function, but also can accurately reflect the properties of stresses for the crack tip fields. The system of equations for the crack analysis is then derived based on the enriched RBF meshfree shape function and the meshfree weak-form. Several problems of linear fracture mechanics are simulated using this newlydeveloped e-RPIM method. It has demonstrated that the present e-RPIM is very accurate and stable, and it has a good potential to develop a practical simulation tool for fracture mechanics problems.

Non-invasive assessment of tear film surface quality

The tear film plays an important role preserving the health of the ocular surface and maintaining the optimal refractive power of the cornea. Moreover dry eye syndrome is one of the most commonly reported eye health problems. This syndrome is caused by abnormalities in the properties of the tear film. Current clinical tools to assess the tear film properties have shown certain limitations. The traditional invasive methods for the assessment of tear film quality, which are used by most clinicians, have been criticized for the lack of reliability and/or repeatability. A range of non-invasive methods of tear assessment have been investigated, but also present limitations. Hence no “gold standard” test is currently available to assess the tear film integrity. Therefore, improving techniques for the assessment of the tear film quality is of clinical significance and the main motivation for the work described in this thesis. In this study the tear film surface quality (TFSQ) changes were investigated by means of high-speed videokeratoscopy (HSV). In this technique, a set of concentric rings formed in an illuminated cone or a bowl is projected on the anterior cornea and their reflection from the ocular surface imaged on a charge-coupled device (CCD). The reflection of the light is produced in the outer most layer of the cornea, the tear film. Hence, when the tear film is smooth the reflected image presents a well structure pattern. In contrast, when the tear film surface presents irregularities, the pattern also becomes irregular due to the light scatter and deviation of the reflected light. The videokeratoscope provides an estimate of the corneal topography associated with each Placido disk image. Topographical estimates, which have been used in the past to quantify tear film changes, may not always be suitable for the evaluation of all the dynamic phases of the tear film. However the Placido disk image itself, which contains the reflected pattern, may be more appropriate to assess the tear film dynamics. A set of novel routines have been purposely developed to quantify the changes of the reflected pattern and to extract a time series estimate of the TFSQ from the video recording. The routine extracts from each frame of the video recording a maximized area of analysis. In this area a metric of the TFSQ is calculated. Initially two metrics based on the Gabor filter and Gaussian gradient-based techniques, were used to quantify the consistency of the pattern’s local orientation as a metric of TFSQ. These metrics have helped to demonstrate the applicability of HSV to assess the tear film, and the influence of contact lens wear on TFSQ. The results suggest that the dynamic-area analysis method of HSV was able to distinguish and quantify the subtle, but systematic degradation of tear film surface quality in the inter-blink interval in contact lens wear. It was also able to clearly show a difference between bare eye and contact lens wearing conditions. Thus, the HSV method appears to be a useful technique for quantitatively investigating the effects of contact lens wear on the TFSQ. Subsequently a larger clinical study was conducted to perform a comparison between HSV and two other non-invasive techniques, lateral shearing interferometry (LSI) and dynamic wavefront sensing (DWS). Of these non-invasive techniques, the HSV appeared to be the most precise method for measuring TFSQ, by virtue of its lower coefficient of variation. While the LSI appears to be the most sensitive method for analyzing the tear build-up time (TBUT). The capability of each of the non-invasive methods to discriminate dry eye from normal subjects was also investigated. The receiver operating characteristic (ROC) curves were calculated to assess the ability of each method to predict dry eye syndrome. The LSI technique gave the best results under both natural blinking conditions and in suppressed blinking conditions, which was closely followed by HSV. The DWS did not perform as well as LSI or HSV. The main limitation of the HSV technique, which was identified during the former clinical study, was the lack of the sensitivity to quantify the build-up/formation phase of the tear film cycle. For that reason an extra metric based on image transformation and block processing was proposed. In this metric, the area of analysis was transformed from Cartesian to Polar coordinates, converting the concentric circles pattern into a quasi-straight lines image in which a block statistics value was extracted. This metric has shown better sensitivity under low pattern disturbance as well as has improved the performance of the ROC curves. Additionally a theoretical study, based on ray-tracing techniques and topographical models of the tear film, was proposed to fully comprehend the HSV measurement and the instrument’s potential limitations. Of special interested was the assessment of the instrument’s sensitivity under subtle topographic changes. The theoretical simulations have helped to provide some understanding on the tear film dynamics, for instance the model extracted for the build-up phase has helped to provide some insight into the dynamics during this initial phase. Finally some aspects of the mathematical modeling of TFSQ time series have been reported in this thesis. Over the years, different functions have been used to model the time series as well as to extract the key clinical parameters (i.e., timing). Unfortunately those techniques to model the tear film time series do not simultaneously consider the underlying physiological mechanism and the parameter extraction methods. A set of guidelines are proposed to meet both criteria. Special attention was given to a commonly used fit, the polynomial function, and considerations to select the appropriate model order to ensure the true derivative of the signal is accurately represented. The work described in this thesis has shown the potential of using high-speed videokeratoscopy to assess tear film surface quality. A set of novel image and signal processing techniques have been proposed to quantify different aspects of the tear film assessment, analysis and modeling. The dynamic-area HSV has shown good performance in a broad range of conditions (i.e., contact lens, normal and dry eye subjects). As a result, this technique could be a useful clinical tool to assess tear film surface quality in the future.

Assessing the relationship between global warming and mortality : lag effects of temperature fluctuations by age and mortality categories

Although interests in assessing the relationship between temperature and mortality have arisen due to climate change, relatively few data are available on lag structure of temperature-mortality relationship, particularly in the Southern Hemisphere. This study identified the lag effects of mean temperature on mortality among age groups and death categories using polynomial distributed lag models in Brisbane, Australia, a subtropical city, 1996-2004. For a 1 °C increase above the threshold, the highest percent increase in mortality on the current day occurred among people over 85 years (7.2% (95% CI: 4.3%, 10.2%)). The effect estimates among cardiovascular deaths were higher than those among all-cause mortality. For a 1 °C decrease below the threshold, the percent increases in mortality at 21 lag days were 3.9% (95% CI: 1.9%, 6.0%) and 3.4% (95% CI: 0.9%, 6.0%) for people aged over 85 years and with cardiovascular diseases, respectively. These findings may have implications for developing intervention strategies to reduce and prevent temperature-related mortality.

Time course of temperature effects on cardiovascular mortality in Brisbane, Australia

Objective To quantify the lagged effects of mean temperature on deaths from cardiovascular diseases in Brisbane, Australia. Design Polynomial distributed lag models were used to assess the percentage increase in mortality up to 30 days associated with an increase (or decrease) of 1°C above (or below) the threshold temperature. Setting Brisbane, Australia. Patients 22 805 cardiovascular deaths registered between 1996 and 2004. Main outcome measures Deaths from cardiovascular diseases. Results The results show a longer lagged effect in cold days and a shorter lagged effect in hot days. For the hot effect, a statistically significant association was observed only for lag 0–1 days. The percentage increase in mortality was found to be 3.7% (95% CI 0.4% to 7.1%) for people aged ≥65 years and 3.5% (95% CI 0.4% to 6.7%) for all ages associated with an increase of 1°C above the threshold temperature of 24°C. For the cold effect, a significant effect of temperature was found for 10–15 lag days. The percentage estimates for older people and all ages were 3.1% (95% CI 0.7% to 5.7%) and 2.8% (95% CI 0.5% to 5.1%), respectively, with a decrease of 1°C below the threshold temperature of 24°C. Conclusions The lagged effects lasted longer for cold temperatures but were apparently shorter for hot temperatures. There was no substantial difference in the lag effect of temperature on mortality between all ages and those aged ≥65 years in Brisbane, Australia.

Prediction of cis/trans isomerization in proteins using PSI-BLAST profiles and secondary structure information

Background The majority of peptide bonds in proteins are found to occur in the trans conformation. However, for proline residues, a considerable fraction of Prolyl peptide bonds adopt the cis form. Proline cis/trans isomerization is known to play a critical role in protein folding, splicing, cell signaling and transmembrane active transport. Accurate prediction of proline cis/trans isomerization in proteins would have many important applications towards the understanding of protein structure and function. Results In this paper, we propose a new approach to predict the proline cis/trans isomerization in proteins using support vector machine (SVM). The preliminary results indicated that using Radial Basis Function (RBF) kernels could lead to better prediction performance than that of polynomial and linear kernel functions. We used single sequence information of different local window sizes, amino acid compositions of different local sequences, multiple sequence alignment obtained from PSI-BLAST and the secondary structure information predicted by PSIPRED. We explored these different sequence encoding schemes in order to investigate their effects on the prediction performance. The training and testing of this approach was performed on a newly enlarged dataset of 2424 non-homologous proteins determined by X-Ray diffraction method using 5-fold cross-validation. Selecting the window size 11 provided the best performance for determining the proline cis/trans isomerization based on the single amino acid sequence. It was found that using multiple sequence alignments in the form of PSI-BLAST profiles could significantly improve the prediction performance, the prediction accuracy increased from 62.8% with single sequence to 69.8% and Matthews Correlation Coefficient (MCC) improved from 0.26 with single local sequence to 0.40. Furthermore, if coupled with the predicted secondary structure information by PSIPRED, our method yielded a prediction accuracy of 71.5% and MCC of 0.43, 9% and 0.17 higher than the accuracy achieved based on the singe sequence information, respectively. Conclusion A new method has been developed to predict the proline cis/trans isomerization in proteins based on support vector machine, which used the single amino acid sequence with different local window sizes, the amino acid compositions of local sequence flanking centered proline residues, the position-specific scoring matrices (PSSMs) extracted by PSI-BLAST and the predicted secondary structures generated by PSIPRED. The successful application of SVM approach in this study reinforced that SVM is a powerful tool in predicting proline cis/trans isomerization in proteins and biological sequence analysis.

Computing with motile bio-agents

We describe a model of computation of the parallel type, which we call 'computing with bio-agents', based on the concept that motions of biological objects such as bacteria or protein molecular motors in confined spaces can be regarded as computations. We begin with the observation that the geometric nature of the physical structures in which model biological objects move modulates the motions of the latter. Consequently, by changing the geometry, one can control the characteristic trajectories of the objects; on the basis of this, we argue that such systems are computing devices. We investigate the computing power of mobile bio-agent systems and show that they are computationally universal in the sense that they are capable of computing any Boolean function in parallel. We argue also that using appropriate conditions, bio-agent systems can solve NP-complete problems in probabilistic polynomial time.

The undirected feedback vertex set problem has a Poly(k) Kernel

Resolving a noted open problem, we show that the Undirected Feedback Vertex Set problem, parameterized by the size of the solution set of vertices, is in the parameterized complexity class Poly(k), that is, polynomial-time pre-processing is sufficient to reduce an initial problem instance (G, k) to a decision-equivalent simplified instance (G', k') where k' � k, and the number of vertices of G' is bounded by a polynomial function of k. Our main result shows an O(k11) kernelization bound.

The effect of various temperature indicators on different mortality categories in a subtropical city of Brisbane, Australia.

BACKGROUND: The relationship between temperature and mortality has been explored for decades and many temperature indicators have been applied separately. However, few data are available to show how the effects of different temperature indicators on different mortality categories, particularly in a typical subtropical climate. OBJECTIVE: To assess the associations between various temperature indicators and different mortality categories in Brisbane, Australia during 1996-2004. METHODS: We applied two methods to assess the threshold and temperature indicator for each age and death groups: mean temperature and the threshold assessed from all cause mortality was used for all mortality categories; the specific temperature indicator and the threshold for each mortality category were identified separately according to the minimisation of AIC. We conducted polynomial distributed lag non-linear model to identify effect estimates in mortality with one degree of temperature increase (or decrease) above (or below) the threshold on current days and lagged effects using both methods. RESULTS: Akaike's Information Criterion was minimized when mean temperature was used for all non-external deaths and deaths from 75 to 84 years; when minimum temperature was used for deaths from 0 to 64 years, 65-74 years, ≥ 85 years, and from the respiratory diseases; when maximum temperature was used for deaths from cardiovascular diseases. The effect estimates using certain temperature indicators were similar as mean temperature both for current day and lag effects. CONCLUSION: Different age groups and death categories were sensitive to different temperature indicators. However, the effect estimates from certain temperature indicators did not significantly differ from those of mean temperature.

Mediators of the relationship between person-organisation fit and individual outcomes

To date, research on P-O fit has focused heavily on the effect of P-O fit on individual and organisational outcomes. Few studies have attempted to explain how or why P-O fit leads to these outcomes. Meglino, Ravlin, and Adkins (1989) and Schein (1985) identified several intervening mechanisms for explaining fit-outcome relationships but only few of these explanations have been tested empirically (Cable & Edwards, 2004; Edwards & Cable, 2009; Kalliath, Bluedorn, & Strube, 1999). This thesis investigates role conflict, cognitive style and organisational justice as three potential mediating mechanisms in the relationship between P-O fit (defined as fit between personal and organisational values – value congruence or value fit) and outcomes including job satisfaction, job performance, service performance, affective commitment and continuance commitment. The study operationalised P-O fit using three measures: subjective fit, perceived fit and objective fit. The mediation model of subjective fit was tested using a Mplus analytical technique, while the mediation models of both perceived and objective fit were tested by modeling the difference between two scores (that is, between personal values and organisational values) using a polynomial regression and response surface analysis (Edwards, 1993). A survey of 558 mid-level managers from seven Brunei public sector organisations provided the data. Our results showed that the relationship between P-O fit and outcomes was partially mediated by organisational justice and cognitive style - for all the three measures of fit, while role conflict had no mediating effects. The findings from this research therefore have both theoretical and practical implications. This research contributes to the literature by combining these theoretical explanations for value congruence effects into one integrated model, and by providing evidence on the partial mediating effects of organisational justice and cognitive style. Future research needs to address and investigate other potential mechanisms by which value congruence affects individual and organisational outcomes. In addition, the study is considered to be the first to test these mediating roles for a value fit-outcomes relationship using three different measures of fit in a non-Western context.

A comparative study of algorithms for the flowshop scheduling problem

In this paper, we propose three meta-heuristic algorithms for the permutation flowshop (PFS) and the general flowshop (GFS) problems. Two different neighborhood structures are used for these two types of flowshop problem. For the PFS problem, an insertion neighborhood structure is used, while for the GFS problem, a critical-path neighborhood structure is adopted. To evaluate the performance of the proposed algorithms, two sets of problem instances are tested against the algorithms for both types of flowshop problems. The computational results show that the proposed meta-heuristic algorithms with insertion neighborhood for the PFS problem perform slightly better than the corresponding algorithms with critical-path neighborhood for the GFS problem. But in terms of computation time, the GFS algorithms are faster than the corresponding PFS algorithms.

Group law computations on Jacobians of hyperelliptic Curves

We derive an explicit method of computing the composition step in Cantor’s algorithm for group operations on Jacobians of hyperelliptic curves. Our technique is inspired by the geometric description of the group law and applies to hyperelliptic curves of arbitrary genus. While Cantor’s general composition involves arithmetic in the polynomial ring F_q[x], the algorithm we propose solves a linear system over the base field which can be written down directly from the Mumford coordinates of the group elements. We apply this method to give more efficient formulas for group operations in both affine and projective coordinates for cryptographic systems based on Jacobians of genus 2 hyperelliptic curves in general form.