Heteroscedastic probabilistic linear discriminant analysis for manifold learning in video-based face recognition

To recognize faces in video, face appearances have been widely modeled as piece-wise local linear models which linearly approximate the smooth yet non-linear low dimensional face appearance manifolds. The choice of representations of the local models is crucial. Most of the existing methods learn each local model individually meaning that they only anticipate variations within each class. In this work, we propose to represent local models as Gaussian distributions which are learned simultaneously using the heteroscedastic probabilistic linear discriminant analysis (PLDA). Each gallery video is therefore represented as a collection of such distributions. With the PLDA, not only the within-class variations are estimated during the training, the separability between classes is also maximized leading to an improved discrimination. The heteroscedastic PLDA itself is adapted from the standard PLDA to approximate face appearance manifolds more accurately. Instead of assuming a single global within-class covariance, the heteroscedastic PLDA learns different within-class covariances specific to each local model. In the recognition phase, a probe video is matched against gallery samples through the fusion of point-to-model distances. Experiments on the Honda and MoBo datasets have shown the merit of the proposed method which achieves better performance than the state-of-the-art technique.

Forecasting time-varying value-at-risk

In this thesis we are interested in financial risk and the instrument we want to use is Value-at-Risk (VaR). VaR is the maximum loss over a given period of time at a given confidence level. Many definitions of VaR exist and some will be introduced throughout this thesis. There two main ways to measure risk and VaR: through volatility and through percentiles. Large volatility in financial returns implies greater probability of large losses, but also larger probability of large profits. Percentiles describe tail behaviour. The estimation of VaR is a complex task. It is important to know the main characteristics of financial data to choose the best model. The existing literature is very wide, maybe controversial, but helpful in drawing a picture of the problem. It is commonly recognised that financial data are characterised by heavy tails, time-varying volatility, asymmetric response to bad and good news, and skewness. Ignoring any of these features can lead to underestimating VaR with a possible ultimate consequence being the default of the protagonist (firm, bank or investor). In recent years, skewness has attracted special attention. An open problem is the detection and modelling of time-varying skewness. Is skewness constant or there is some significant variability which in turn can affect the estimation of VaR? This thesis aims to answer this question and to open the way to a new approach to model simultaneously time-varying volatility (conditional variance) and skewness. The new tools are modifications of the Generalised Lambda Distributions (GLDs). They are four-parameter distributions, which allow the first four moments to be modelled nearly independently: in particular we are interested in what we will call para-moments, i.e., mean, variance, skewness and kurtosis. The GLDs will be used in two different ways. Firstly, semi-parametrically, we consider a moving window to estimate the parameters and calculate the percentiles of the GLDs. Secondly, parametrically, we attempt to extend the GLDs to include time-varying dependence in the parameters. We used the local linear regression to estimate semi-parametrically conditional mean and conditional variance. The method is not efficient enough to capture all the dependence structure in the three indices —ASX 200, S&P 500 and FT 30—, however it provides an idea of the DGP underlying the process and helps choosing a good technique to model the data. We find that GLDs suggest that moments up to the fourth order do not always exist, there existence appears to vary over time. This is a very important finding, considering that past papers (see for example Bali et al., 2008; Hashmi and Tay, 2007; Lanne and Pentti, 2007) modelled time-varying skewness, implicitly assuming the existence of the third moment. However, the GLDs suggest that mean, variance, skewness and in general the conditional distribution vary over time, as already suggested by the existing literature. The GLDs give good results in estimating VaR on three real indices, ASX 200, S&P 500 and FT 30, with results very similar to the results provided by historical simulation.

Improved image set classification via joint sparse approximated nearest subspaces

Existing multi-model approaches for image set classification extract local models by clustering each image set individually only once, with fixed clusters used for matching with other image sets. However, this may result in the two closest clusters to represent different characteristics of an object, due to different undesirable environmental conditions (such as variations in illumination and pose). To address this problem, we propose to constrain the clustering of each query image set by forcing the clusters to have resemblance to the clusters in the gallery image sets. We first define a Frobenius norm distance between subspaces over Grassmann manifolds based on reconstruction error. We then extract local linear subspaces from a gallery image set via sparse representation. For each local linear subspace, we adaptively construct the corresponding closest subspace from the samples of a probe image set by joint sparse representation. We show that by minimising the sparse representation reconstruction error, we approach the nearest point on a Grassmann manifold. Experiments on Honda, ETH-80 and Cambridge-Gesture datasets show that the proposed method consistently outperforms several other recent techniques, such as Affine Hull based Image Set Distance (AHISD), Sparse Approximated Nearest Points (SANP) and Manifold Discriminant Analysis (MDA).

Adapting a generic BEAMnrc model of the BrainLAB m3 micro-multileaf collimator to simulate a local collimation device

This work is focussed on developing a commissioning procedure so that a Monte Carlo model, which uses BEAMnrc’s standard VARMLC component module, can be adapted to match a specific BrainLAB m3 micro-multileaf collimator (μMLC). A set of measurements are recommended, for use as a reference against which the model can be tested and optimised. These include radiochromic film measurements of dose from small and offset fields, as well as measurements of μMLC transmission and interleaf leakage. Simulations and measurements to obtain μMLC scatter factors are shown to be insensitive to relevant model parameters and are therefore not recommended, unless the output of the linear accelerator model is in doubt. Ultimately, this note provides detailed instructions for those intending to optimise a VARMLC model to match the dose delivered by their local BrainLAB m3 μMLC device.

Person-independent facial expression detection using constrained local models

In automatic facial expression detection, very accurate registration is desired which can be achieved via a deformable model approach where a dense mesh of 60-70 points on the face is used, such as an active appearance model (AAM). However, for applications where manually labeling frames is prohibitive, AAMs do not work well as they do not generalize well to unseen subjects. As such, a more coarse approach is taken for person-independent facial expression detection, where just a couple of key features (such as face and eyes) are tracked using a Viola-Jones type approach. The tracked image is normally post-processed to encode for shift and illumination invariance using a linear bank of filters. Recently, it was shown that this preprocessing step is of no benefit when close to ideal registration has been obtained. In this paper, we present a system based on the Constrained Local Model (CLM) which is a generic or person-independent face alignment algorithm which gains high accuracy. We show these results against the LBP feature extraction on the CK+ and GEMEP datasets.

An investigation on multi-vehicle motorcycle crashes using log-linear models

Motorcyclists are the most crash-prone road-user group in many Asian countries including Singapore; however, factors influencing motorcycle crashes are still not well understood. This study examines the effects of various roadway characteristics, traffic control measures and environmental factors on motorcycle crashes at different location types including expressways and intersections. Using techniques of categorical data analysis, this study has developed a set of log-linear models to investigate multi-vehicle motorcycle crashes in Singapore. Motorcycle crash risks in different circumstances have been calculated after controlling for the exposure estimated by the induced exposure technique. Results show that night-time influence increases crash risks of motorcycles particularly during merging and diverging manoeuvres on expressways, and turning manoeuvres at intersections. Riders appear to exercise more care while riding on wet road surfaces particularly during night. Many hazardous interactions at intersections tend to be related to the failure of drivers to notice a motorcycle as well as to judge correctly the speed/distance of an oncoming motorcycle. Road side conflicts due to stopping/waiting vehicles and interactions with opposing traffic on undivided roads have been found to be as detrimental factors on motorcycle safety along arterial, main and local roads away from intersections. Based on the findings of this study, several targeted countermeasures in the form of legislations, rider training, and safety awareness programmes have been recommended.

Linear and nonlinear propagation of localised plasmon in metallic nanostructures

A major challenge in modern photonics and nano-optics is the diffraction limit of light which does not allow field localisation into regions with dimensions smaller than half the wavelength. Localisation of light into nanoscale regions (beyond its diffraction limit) has applications ranging from the design of optical sensors and measurement techniques with resolutions as high as a few nanometres, to the effective delivery of optical energy into targeted nanoscale regions such as quantum dots, nano-electronic and nano-optical devices. This field has become a major research direction over the last decade. The use of strongly localised surface plasmons in metallic nanostructures is one of the most promising approaches to overcome this problem. Therefore, the aim of this thesis is to investigate the linear and non-linear propagation of surface plasmons in metallic nanostructures. This thesis will focus on two main areas of plasmonic research –– plasmon nanofocusing and plasmon nanoguiding. Plasmon nanofocusing – The main aim of plasmon nanofocusing research is to focus plasmon energy into nanoscale regions using metallic nanostructures and at the same time achieve strong local field enhancement. Various structures for nanofocusing purposes have been proposed and analysed such as sharp metal wedges, tapered metal films on dielectric substrates, tapered metal rods, and dielectric V-grooves in metals. However, a number of important practical issues related to nanofocusing in these structures still remain unclear. Therefore, one of the main aims of this thesis is to address two of the most important of issues which are the coupling efficiency and heating effects of surface plasmons in metallic nanostructures. The method of analysis developed throughout this thesis is a general treatment that can be applied to a diversity of nanofocusing structures, with results shown here for the specific case of sharp metal wedges. Based on the geometrical optics approximation, it is demonstrated that the coupling efficiency from plasmons generated with a metal grating into the nanofocused symmetric or quasi-symmetric modes may vary between ~50% to ~100% depending on the structural parameters. Optimal conditions for nanofocusing with the view to minimise coupling and dissipative losses are also determined and discussed. It is shown that the temperature near the tip of a metal wedge heated by nanosecond plasmonic pulses can increase by several hundred degrees Celsius. This temperature increase is expected to lead to nonlinear effects, self-influence of the focused plasmon, and ultimately self-destruction of the metal tip. This thesis also investigates a different type of nanofocusing structure which consists of a tapered high-index dielectric layer resting on a metal surface. It is shown that the nanofocusing mechanism that occurs in this structure is somewhat different from other structures that have been considered thus far. For example, the surface plasmon experiences significant backreflection and mode transformation at a cut-off thickness. In addition, the reflected plasmon shows negative refraction properties that have not been observed in other nanofocusing structures considered to date. Plasmon nanoguiding – Guiding surface plasmons using metallic nanostructures is important for the development of highly integrated optical components and circuits which are expected to have a superior performance compared to their electronicbased counterparts. A number of different plasmonic waveguides have been considered over the last decade including the recently considered gap and trench plasmon waveguides. The gap and trench plasmon waveguides have proven to be difficult to fabricate. Therefore, this thesis will propose and analyse four different modified gap and trench plasmon waveguides that are expected to be easier to fabricate, and at the same time acquire improved propagation characteristics of the guided mode. In particular, it is demonstrated that the guided modes are significantly screened by the extended metal at the bottom of the structure. This is important for the design of highly integrated optics as it provides the opportunity to place two waveguides close together without significant cross-talk. This thesis also investigates the use of plasmonic nanowires to construct a Fabry-Pérot resonator/interferometer. It is shown that the resonance effect can be achieved with the appropriate resonator length and gap width. Typical quality factors of the Fabry- Pérot cavity are determined and explained in terms of radiative and dissipative losses. The possibility of using a nanowire resonator for the design of plasmonic filters with close to ~100% transmission is also demonstrated. It is expected that the results obtained in this thesis will play a vital role in the development of high resolution near field microscopy and spectroscopy, new measurement techniques and devices for single molecule detection, highly integrated optical devices, and nanobiotechnology devices for diagnostics of living cells.

Bayesian hierarchical models in statistical quality control methods to improve healthcare in hospitals

Quality oriented management systems and methods have become the dominant business and governance paradigm. From this perspective, satisfying customers’ expectations by supplying reliable, good quality products and services is the key factor for an organization and even government. During recent decades, Statistical Quality Control (SQC) methods have been developed as the technical core of quality management and continuous improvement philosophy and now are being applied widely to improve the quality of products and services in industrial and business sectors. Recently SQC tools, in particular quality control charts, have been used in healthcare surveillance. In some cases, these tools have been modified and developed to better suit the health sector characteristics and needs. It seems that some of the work in the healthcare area has evolved independently of the development of industrial statistical process control methods. Therefore analysing and comparing paradigms and the characteristics of quality control charts and techniques across the different sectors presents some opportunities for transferring knowledge and future development in each sectors. Meanwhile considering capabilities of Bayesian approach particularly Bayesian hierarchical models and computational techniques in which all uncertainty are expressed as a structure of probability, facilitates decision making and cost-effectiveness analyses. Therefore, this research investigates the use of quality improvement cycle in a health vii setting using clinical data from a hospital. The need of clinical data for monitoring purposes is investigated in two aspects. A framework and appropriate tools from the industrial context are proposed and applied to evaluate and improve data quality in available datasets and data flow; then a data capturing algorithm using Bayesian decision making methods is developed to determine economical sample size for statistical analyses within the quality improvement cycle. Following ensuring clinical data quality, some characteristics of control charts in the health context including the necessity of monitoring attribute data and correlated quality characteristics are considered. To this end, multivariate control charts from an industrial context are adapted to monitor radiation delivered to patients undergoing diagnostic coronary angiogram and various risk-adjusted control charts are constructed and investigated in monitoring binary outcomes of clinical interventions as well as postintervention survival time. Meanwhile, adoption of a Bayesian approach is proposed as a new framework in estimation of change point following control chart’s signal. This estimate aims to facilitate root causes efforts in quality improvement cycle since it cuts the search for the potential causes of detected changes to a tighter time-frame prior to the signal. This approach enables us to obtain highly informative estimates for change point parameters since probability distribution based results are obtained. Using Bayesian hierarchical models and Markov chain Monte Carlo computational methods, Bayesian estimators of the time and the magnitude of various change scenarios including step change, linear trend and multiple change in a Poisson process are developed and investigated. The benefits of change point investigation is revisited and promoted in monitoring hospital outcomes where the developed Bayesian estimator reports the true time of the shifts, compared to priori known causes, detected by control charts in monitoring rate of excess usage of blood products and major adverse events during and after cardiac surgery in a local hospital. The development of the Bayesian change point estimators are then followed in a healthcare surveillances for processes in which pre-intervention characteristics of patients are viii affecting the outcomes. In this setting, at first, the Bayesian estimator is extended to capture the patient mix, covariates, through risk models underlying risk-adjusted control charts. Variations of the estimator are developed to estimate the true time of step changes and linear trends in odds ratio of intensive care unit outcomes in a local hospital. Secondly, the Bayesian estimator is extended to identify the time of a shift in mean survival time after a clinical intervention which is being monitored by riskadjusted survival time control charts. In this context, the survival time after a clinical intervention is also affected by patient mix and the survival function is constructed using survival prediction model. The simulation study undertaken in each research component and obtained results highly recommend the developed Bayesian estimators as a strong alternative in change point estimation within quality improvement cycle in healthcare surveillances as well as industrial and business contexts. The superiority of the proposed Bayesian framework and estimators are enhanced when probability quantification, flexibility and generalizability of the developed model are also considered. The empirical results and simulations indicate that the Bayesian estimators are a strong alternative in change point estimation within quality improvement cycle in healthcare surveillances. The superiority of the proposed Bayesian framework and estimators are enhanced when probability quantification, flexibility and generalizability of the developed model are also considered. The advantages of the Bayesian approach seen in general context of quality control may also be extended in the industrial and business domains where quality monitoring was initially developed.

Analytical benchmark solutions for steel frame structures subject to local buckling effects

Application of "advanced analysis" methods suitable for non-linear analysis and design of steel frame structures permits direct and accurate determination of ultimate system strengths, without resort to simplified elastic methods of analysis and semi-empirical specification equations. However, the application of advanced analysis methods has previously been restricted to steel frames comprising only compact sections that are not influenced by the effects of local buckling. A research project has been conducted with the aim of developing concentrated plasticity methods suitable for practical advanced analysis of steel frame structures comprising non-compact sections. This paper contains a comprehensive set of analytical benchmark solutions for steel frames comprising non-compact sections, which can be used to verify the accuracy of simplified concentrated plasticity methods of advanced analysis. The analytical benchmark solutions were obtained using a distributed plasticity shell finite element model that explicitly accounts for the effects of gradual cross-sectional yielding, longitudinal spread of plasticity, initial geometric imperfections, residual stresses, and local buckling. A brief description and verification of the shell finite element model is provided in this paper.

On the advanced analysis of steel frames allowing for flexural, local and lateral-torsional buckling

Detailed procedure for second-order analysis has been coded in the newest Eurocode 3 and the Hong Kong steel code (2005). The effective length method has been noted to be inapplicable to analysis of shallow domes of imperfect members exhibiting snap-through buckling, to portals with leaning columns and others. On the other hand, the advanced analysis is not limited to buckling design of these structures. This paper demonstrates its application to the design of a simple plane sway portal and a three diminsional non-sway steel building. The results by the advanced analysis and the first-order linear analysis are compared and the technique for practical second-order analysis steel structures is described. It is observed that the use of a straight element by itself cannot model the buckling resistance of columns governed by different buckling curves for hot-rolled and cold-formed sections of various shapes like I, H, hollow etc. Also the curvature of the conventional cubic Hermite element is not varied by the external axial force and thus it cannot simulate the response of a buckling column. Thus its use for second-order analysis is basically unacceptable. A technique for additional checking of beams undergoing lateral-torsional buckling is also suggested making the advanced analysis a complete design tool for conventional steel frames.

Effect of broadcast baiting on abundance patterns of red imported fire ants (Hymenoptera: Formicidae) and key local ant genera at long-term monitoring sites in Brisbane, Australia

In 2001, the red imported fire ant (Solenopsis invicta Buren) was identified in Brisbane, Australia. An eradication program involving broadcast bait treatment with two insect growth regulators and a metabolic inhibitor began in September of that year and is currently ongoing. To gauge the impacts of these treatments on local ant populations, we examined long-term monitoring data and quantified abundance patterns of S. invicta and common local ant genera using a linear mixed-effects model. For S. invicta, presence in pitfalls reduced over time to zero on every site. Significantly higher numbers of S. invicta workers were collected on high-density polygyne sites, which took longer to disinfest compared with monogyne and low-density polygyne sites. For local ants, nine genus groups of the 10 most common genera analyzed either increased in abundance or showed no significant trend. Five of these genus groups were significantly less abundant at the start of monitoring on high-density polygyne sites compared with monogyne and low-density polygyne sites. The genus Pheidole significantly reduced in abundance over time, suggesting that it was affected by treatment efforts. These results demonstrate that the treatment regime used at the time successfully removed S. invicta from these sites in Brisbane, and that most local ant genera were not seriously impacted by the treatment. These results have important implications for current and future prophylactic treatment efforts, and suggest that native ants remain in treated areas to provide some biological resistance to S. invicta.

Adaptive finite element analysis of elliptic problems based on bubble-type local mesh generation

A new mesh adaptivity algorithm that combines a posteriori error estimation with bubble-type local mesh generation (BLMG) strategy for elliptic differential equations is proposed. The size function used in the BLMG is defined on each vertex during the adaptive process based on the obtained error estimator. In order to avoid the excessive coarsening and refining in each iterative step, two factor thresholds are introduced in the size function. The advantages of the BLMG-based adaptive finite element method, compared with other known methods, are given as follows: the refining and coarsening are obtained fluently in the same framework; the local a posteriori error estimation is easy to implement through the adjacency list of the BLMG method; at all levels of refinement, the updated triangles remain very well shaped, even if the mesh size at any particular refinement level varies by several orders of magnitude. Several numerical examples with singularities for the elliptic problems, where the explicit error estimators are used, verify the efficiency of the algorithm. The analysis for the parameters introduced in the size function shows that the algorithm has good flexibility.

Quantification of stability in an agility drill using linear and nonlinear measures of variability

This study implemented linear and nonlinear methods of measuring variability to determine differences in stability of two groups of skilled (n = 10) and unskilled (n = 10) participants performing 3m forward/backward shuttle agility drill. We also determined whether stability measures differed between the forward and backward segments of the drill. Finally, we sought to investigate whether local dynamic stability, measured using largest finite-time Lyapunov exponents, changed from distal to proximal lower extremity segments. Three-dimensional coordinates of five lower extremity markers data were recorded. Results revealed that the Lyapunov exponents were lower (P < 0.05) for skilled participants at all joint markers indicative of higher levels of local dynamic stability. Additionally, stability of motion did not differ between forward and backward segments of the drill (P > 0.05), signifying that almost the same control strategy was used in forward and backward directions by all participants, regardless of skill level. Furthermore, local dynamic stability increased from distal to proximal joints (P < 0.05) indicating that stability of proximal segments are prioritized by the neuromuscular control system. Finally, skilled participants displayed greater foot placement standard deviation values (P < 0.05), indicative of adaptation to task constraints. The results of this study provide new methods for sport scientists, coaches to characterize stability in agility drill performance.

Estimation of the time of a linear trend in monitoring survival time

Change point estimation is recognized as an essential tool of root cause analyses within quality control programs as it enables clinical experts to search for potential causes of change in hospital outcomes more effectively. In this paper, we consider estimation of the time when a linear trend disturbance has occurred in survival time following an in-control clinical intervention in the presence of variable patient mix. To model the process and change point, a linear trend in the survival time of patients who underwent cardiac surgery is formulated using hierarchical models in a Bayesian framework. The data are right censored since the monitoring is conducted over a limited follow-up period. We capture the effect of risk factors prior to the surgery using a Weibull accelerated failure time regression model. We use Markov Chain Monte Carlo to obtain posterior distributions of the change point parameters including the location and the slope size of the trend and also corresponding probabilistic intervals and inferences. The performance of the Bayesian estimator is investigated through simulations and the result shows that precise estimates can be obtained when they are used in conjunction with the risk-adjusted survival time cumulative sum control chart (CUSUM) control charts for different trend scenarios. In comparison with the alternatives, step change point model and built-in CUSUM estimator, more accurate and precise estimates are obtained by the proposed Bayesian estimator over linear trends. These superiorities are enhanced when probability quantification, flexibility and generalizability of the Bayesian change point detection model are also considered.

Iterative estimating equations: Linear convergence and asymptotic properties

We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size increases to infinity. Furthermore, we show that the limiting estimator is consistent and asymptotically efficient, as expected. The method applies to semiparametric regression models with unspecified covariances among the observations. In the special case of linear models, the procedure reduces to iterative reweighted least squares. Finite sample performance of the procedure is studied by simulations, and compared with other methods. A numerical example from a medical study is considered to illustrate the application of the method.