Information-theoretic analysis of brain white matter fiber orientation distribution functions

We propose a new information-theoretic metric, the symmetric Kullback-Leibler divergence (sKL-divergence), to measure the difference between two water diffusivity profiles in high angular resolution diffusion imaging (HARDI). Water diffusivity profiles are modeled as probability density functions on the unit sphere, and the sKL-divergence is computed from a spherical harmonic series, which greatly reduces computational complexity. Adjustment of the orientation of diffusivity functions is essential when the image is being warped, so we propose a fast algorithm to determine the principal direction of diffusivity functions using principal component analysis (PCA). We compare sKL-divergence with other inner-product based cost functions using synthetic samples and real HARDI data, and show that the sKL-divergence is highly sensitive in detecting small differences between two diffusivity profiles and therefore shows promise for applications in the nonlinear registration and multisubject statistical analysis of HARDI data.

Beyond Gauss: Image-set matching on the Riemannian manifold of PDFs

State-of-the-art image-set matching techniques typically implicitly model each image-set with a Gaussian distribution. Here, we propose to go beyond these representations and model image-sets as probability distribution functions (PDFs) using kernel density estimators. To compare and match image-sets, we exploit Csiszar´ f-divergences, which bear strong connections to the geodesic distance defined on the space of PDFs, i.e., the statistical manifold. Furthermore, we introduce valid positive definite kernels on the statistical manifold, which let us make use of more powerful classification schemes to match image-sets. Finally, we introduce a supervised dimensionality reduction technique that learns a latent space where f-divergences reflect the class labels of the data. Our experiments on diverse problems, such as video-based face recognition and dynamic texture classification, evidence the benefits of our approach over the state-of-the-art image-set matching methods.

Analyzing multi-fiber reconstruction in high angular resolution diffusion imaging using the tensor distribution function

High-angular resolution diffusion imaging (HARDI) can reconstruct fiber pathways in the brain with extraordinary detail, identifying anatomical features and connections not seen with conventional MRI. HARDI overcomes several limitations of standard diffusion tensor imaging, which fails to model diffusion correctly in regions where fibers cross or mix. As HARDI can accurately resolve sharp signal peaks in angular space where fibers cross, we studied how many gradients are required in practice to compute accurate orientation density functions, to better understand the tradeoff between longer scanning times and more angular precision. We computed orientation density functions analytically from tensor distribution functions (TDFs) which model the HARDI signal at each point as a unit-mass probability density on the 6D manifold of symmetric positive definite tensors. In simulated two-fiber systems with varying Rician noise, we assessed how many diffusionsensitized gradients were sufficient to (1) accurately resolve the diffusion profile, and (2) measure the exponential isotropy (EI), a TDF-derived measure of fiber integrity that exploits the full multidirectional HARDI signal. At lower SNR, the reconstruction accuracy, measured using the Kullback-Leibler divergence, rapidly increased with additional gradients, and EI estimation accuracy plateaued at around 70 gradients.

Theoretical investigation of mechanisms of formation and interaction of nanoparticles

In this thesis an investigation into theoretical models for formation and interaction of nanoparticles is presented. The work presented includes a literature review of current models followed by a series of five chapters of original research. This thesis has been submitted in partial fulfilment of the requirements for the degree of doctor of philosophy by publication and therefore each of the five chapters consist of a peer-reviewed journal article. The thesis is then concluded with a discussion of what has been achieved during the PhD candidature, the potential applications for this research and ways in which the research could be extended in the future. In this thesis we explore stochastic models pertaining to the interaction and evolution mechanisms of nanoparticles. In particular, we explore in depth the stochastic evaporation of molecules due to thermal activation and its ultimate effect on nanoparticles sizes and concentrations. Secondly, we analyse the thermal vibrations of nanoparticles suspended in a fluid and subject to standing oscillating drag forces (as would occur in a standing sound wave) and finally on lattice surfaces in the presence of high heat gradients. We have described in this thesis a number of new models for the description of multicompartment networks joined by a multiple, stochastically evaporating, links. The primary motivation for this work is in the description of thermal fragmentation in which multiple molecules holding parts of a carbonaceous nanoparticle may evaporate. Ultimately, these models predict the rate at which the network or aggregate fragments into smaller networks/aggregates and with what aggregate size distribution. The models are highly analytic and describe the fragmentation of a link holding multiple bonds using Markov processes that best describe different physical situations and these processes have been analysed using a number of mathematical methods. The fragmentation of the network/aggregate is then predicted using combinatorial arguments. Whilst there is some scepticism in the scientific community pertaining to the proposed mechanism of thermal fragmentation,we have presented compelling evidence in this thesis supporting the currently proposed mechanism and shown that our models can accurately match experimental results. This was achieved using a realistic simulation of the fragmentation of the fractal carbonaceous aggregate structure using our models. Furthermore, in this thesis a method of manipulation using acoustic standing waves is investigated. In our investigation we analysed the effect of frequency and particle size on the ability for the particle to be manipulated by means of a standing acoustic wave. In our results, we report the existence of a critical frequency for a particular particle size. This frequency is inversely proportional to the Stokes time of the particle in the fluid. We also find that for large frequencies the subtle Brownian motion of even larger particles plays a significant role in the efficacy of the manipulation. This is due to the decreasing size of the boundary layer between acoustic nodes. Our model utilises a multiple time scale approach to calculating the long term effects of the standing acoustic field on the particles that are interacting with the sound. These effects are then combined with the effects of Brownian motion in order to obtain a complete mathematical description of the particle dynamics in such acoustic fields. Finally, in this thesis, we develop a numerical routine for the description of "thermal tweezers". Currently, the technique of thermal tweezers is predominantly theoretical however there has been a handful of successful experiments which demonstrate the effect it practise. Thermal tweezers is the name given to the way in which particles can be easily manipulated on a lattice surface by careful selection of a heat distribution over the surface. Typically, the theoretical simulations of the effect can be rather time consuming with supercomputer facilities processing data over days or even weeks. Our alternative numerical method for the simulation of particle distributions pertaining to the thermal tweezers effect use the Fokker-Planck equation to derive a quick numerical method for the calculation of the effective diffusion constant as a result of the lattice and the temperature. We then use this diffusion constant and solve the diffusion equation numerically using the finite volume method. This saves the algorithm from calculating many individual particle trajectories since it is describes the flow of the probability distribution of particles in a continuous manner. The alternative method that is outlined in this thesis can produce a larger quantity of accurate results on a household PC in a matter of hours which is much better than was previously achieveable.

Component reliability estimations without field data

Maintenance activities in a large-scale engineering system are usually scheduled according to the lifetimes of various components in order to ensure the overall reliability of the system. Lifetimes of components can be deduced by the corresponding probability distributions with parameters estimated from past failure data. While failure data of the components is not always readily available, the engineers have to be content with the primitive information from the manufacturers only, such as the mean and standard deviation of lifetime, to plan for the maintenance activities. In this paper, the moment-based piecewise polynomial model (MPPM) are proposed to estimate the parameters of the reliability probability distribution of the products when only the mean and standard deviation of the product lifetime are known. This method employs a group of polynomial functions to estimate the two parameters of the Weibull Distribution according to the mathematical relationship between the shape parameter of two-parameters Weibull Distribution and the ratio of mean and standard deviation. Tests are carried out to evaluate the validity and accuracy of the proposed methods with discussions on its suitability of applications. The proposed method is particularly useful for reliability-critical systems, such as railway and power systems, in which the maintenance activities are scheduled according to the expected lifetimes of the system components.

Improved estimates of percolation and anisotropic permeability from 3-D X-ray microtomography using stochastic analyses and visualization

X-ray microtomography (micro-CT) with micron resolution enables new ways of characterizing microstructures and opens pathways for forward calculations of multiscale rock properties. A quantitative characterization of the microstructure is the first step in this challenge. We developed a new approach to extract scale-dependent characteristics of porosity, percolation, and anisotropic permeability from 3-D microstructural models of rocks. The Hoshen-Kopelman algorithm of percolation theory is employed for a standard percolation analysis. The anisotropy of permeability is calculated by means of the star volume distribution approach. The local porosity distribution and local percolation probability are obtained by using the local porosity theory. Additionally, the local anisotropy distribution is defined and analyzed through two empirical probability density functions, the isotropy index and the elongation index. For such a high-resolution data set, the typical data sizes of the CT images are on the order of gigabytes to tens of gigabytes; thus an extremely large number of calculations are required. To resolve this large memory problem parallelization in OpenMP was used to optimally harness the shared memory infrastructure on cache coherent Non-Uniform Memory Access architecture machines such as the iVEC SGI Altix 3700Bx2 Supercomputer. We see adequate visualization of the results as an important element in this first pioneering study.

Assessment on the effect of pollution abatement on environmental efficiency with Markov chain Monte Carlo simulation

Both environmental economists and policy makers have shown a great deal of interest in the effect of pollution abatement on environmental efficiency. In line with the modern resources available, however, no contribution is brought to the environmental economics field with the Markov chain Monte Carlo (MCMC) application, which enables simulation from a distribution of a Markov chain and simulating from the chain until it approaches equilibrium. The probability density functions gained prominence with the advantages over classical statistical methods in its simultaneous inference and incorporation of any prior information on all model parameters. This paper concentrated on this point with the application of MCMC to the database of China, the largest developing country with rapid economic growth and serious environmental pollution in recent years. The variables cover the economic output and pollution abatement cost from the year 1992 to 2003. We test the causal direction between pollution abatement cost and environmental efficiency with MCMC simulation. We found that the pollution abatement cost causes an increase in environmental efficiency through the algorithm application, which makes it conceivable that the environmental policy makers should make more substantial measures to reduce pollution in the near future.

Prediction of highway truck conveyance configuration under over-limit prohibition and conveyance equilibrium

Aiming at the shortage of prevailing prediction methods about highway truck conveyance configuration in over-limit freight research that transferring the goods attributed to over-limit portion to another fully loaded truck of the same configuration and developing the truck traffic volume synchronously, a new way to get accumulated probability function of truck power tonnage in basal year by highway truck classified by wheel and axle type load mass spectrum investigation was presented. Logit models were used to forecast overall highway freight diversion and single cargo tonnage diversion when the weight rules and strict of enforcement intensity of overload were changed in scheme year. Assumption that the probability distribution of single truck loadage should be consistent with the probability distribution of single goods freighted, the model describes the truck conveyance configuration in the future under strict over-limit prohibition. The model was used and tested in Highway Over-limit Research Project in Anhui by World Bank.

The statistics of refractive error maps : managing wavefront aberration analysis without Zernike polynomials

The refractive error of a human eye varies across the pupil and therefore may be treated as a random variable. The probability distribution of this random variable provides a means for assessing the main refractive properties of the eye without the necessity of traditional functional representation of wavefront aberrations. To demonstrate this approach, the statistical properties of refractive error maps are investigated. Closed-form expressions are derived for the probability density function (PDF) and its statistical moments for the general case of rotationally-symmetric aberrations. A closed-form expression for a PDF for a general non-rotationally symmetric wavefront aberration is difficult to derive. However, for specific cases, such as astigmatism, a closed-form expression of the PDF can be obtained. Further, interpretation of the distribution of the refractive error map as well as its moments is provided for a range of wavefront aberrations measured in real eyes. These are evaluated using a kernel density and sample moments estimators. It is concluded that the refractive error domain allows non-functional analysis of wavefront aberrations based on simple statistics in the form of its sample moments. Clinicians may find this approach to wavefront analysis easier to interpret due to the clinical familiarity and intuitive appeal of refractive error maps.

Adaptive dual control of topic-based information retrieval

Information Retrieval is an important albeit imperfect component of information technologies. A problem of insufficient diversity of retrieved documents is one of the primary issues studied in this research. This study shows that this problem leads to a decrease of precision and recall, traditional measures of information retrieval effectiveness. This thesis presents an adaptive IR system based on the theory of adaptive dual control. The aim of the approach is the optimization of retrieval precision after all feedback has been issued. This is done by increasing the diversity of retrieved documents. This study shows that the value of recall reflects this diversity. The Probability Ranking Principle is viewed in the literature as the “bedrock” of current probabilistic Information Retrieval theory. Neither the proposed approach nor other methods of diversification of retrieved documents from the literature conform to this principle. This study shows by counterexample that the Probability Ranking Principle does not in general lead to optimal precision in a search session with feedback (for which it may not have been designed but is actively used). Retrieval precision of the search session should be optimized with a multistage stochastic programming model to accomplish the aim. However, such models are computationally intractable. Therefore, approximate linear multistage stochastic programming models are derived in this study, where the multistage improvement of the probability distribution is modelled using the proposed feedback correctness method. The proposed optimization models are based on several assumptions, starting with the assumption that Information Retrieval is conducted in units of topics. The use of clusters is the primary reasons why a new method of probability estimation is proposed. The adaptive dual control of topic-based IR system was evaluated in a series of experiments conducted on the Reuters, Wikipedia and TREC collections of documents. The Wikipedia experiment revealed that the dual control feedback mechanism improves precision and S-recall when all the underlying assumptions are satisfied. In the TREC experiment, this feedback mechanism was compared to a state-of-the-art adaptive IR system based on BM-25 term weighting and the Rocchio relevance feedback algorithm. The baseline system exhibited better effectiveness than the cluster-based optimization model of ADTIR. The main reason for this was insufficient quality of the generated clusters in the TREC collection that violated the underlying assumption.

Improving automatic speaker verification using SVM techniques

Automatic recognition of people is an active field of research with important forensic and security applications. In these applications, it is not always possible for the subject to be in close proximity to the system. Voice represents a human behavioural trait which can be used to recognise people in such situations. Automatic Speaker Verification (ASV) is the process of verifying a persons identity through the analysis of their speech and enables recognition of a subject at a distance over a telephone channel { wired or wireless. A significant amount of research has focussed on the application of Gaussian mixture model (GMM) techniques to speaker verification systems providing state-of-the-art performance. GMM's are a type of generative classifier trained to model the probability distribution of the features used to represent a speaker. Recently introduced to the field of ASV research is the support vector machine (SVM). An SVM is a discriminative classifier requiring examples from both positive and negative classes to train a speaker model. The SVM is based on margin maximisation whereby a hyperplane attempts to separate classes in a high dimensional space. SVMs applied to the task of speaker verification have shown high potential, particularly when used to complement current GMM-based techniques in hybrid systems. This work aims to improve the performance of ASV systems using novel and innovative SVM-based techniques. Research was divided into three main themes: session variability compensation for SVMs; unsupervised model adaptation; and impostor dataset selection. The first theme investigated the differences between the GMM and SVM domains for the modelling of session variability | an aspect crucial for robust speaker verification. Techniques developed to improve the robustness of GMMbased classification were shown to bring about similar benefits to discriminative SVM classification through their integration in the hybrid GMM mean supervector SVM classifier. Further, the domains for the modelling of session variation were contrasted to find a number of common factors, however, the SVM-domain consistently provided marginally better session variation compensation. Minimal complementary information was found between the techniques due to the similarities in how they achieved their objectives. The second theme saw the proposal of a novel model for the purpose of session variation compensation in ASV systems. Continuous progressive model adaptation attempts to improve speaker models by retraining them after exploiting all encountered test utterances during normal use of the system. The introduction of the weight-based factor analysis model provided significant performance improvements of over 60% in an unsupervised scenario. SVM-based classification was then integrated into the progressive system providing further benefits in performance over the GMM counterpart. Analysis demonstrated that SVMs also hold several beneficial characteristics to the task of unsupervised model adaptation prompting further research in the area. In pursuing the final theme, an innovative background dataset selection technique was developed. This technique selects the most appropriate subset of examples from a large and diverse set of candidate impostor observations for use as the SVM background by exploiting the SVM training process. This selection was performed on a per-observation basis so as to overcome the shortcoming of the traditional heuristic-based approach to dataset selection. Results demonstrate the approach to provide performance improvements over both the use of the complete candidate dataset and the best heuristically-selected dataset whilst being only a fraction of the size. The refined dataset was also shown to generalise well to unseen corpora and be highly applicable to the selection of impostor cohorts required in alternate techniques for speaker verification.

Reliability analysis with suspended items

Reliability analysis has several important engineering applications. Designers and operators of equipment are often interested in the probability of the equipment operating successfully to a given age - this probability is known as the equipment's reliability at that age. Reliability information is also important to those charged with maintaining an item of equipment, as it enables them to model and evaluate alternative maintenance policies for the equipment. In each case, information on failures and survivals of a typical sample of items is used to estimate the required probabilities as a function of the item's age, this process being one of many applications of the statistical techniques known as distribution fitting. In most engineering applications, the estimation procedure must deal with samples containing survivors (suspensions or censorings); this thesis focuses on several graphical estimation methods that are widely used for analysing such samples. Although these methods have been current for many years, they share a common shortcoming: none of them is continuously sensitive to changes in the ages of the suspensions, and we show that the resulting reliability estimates are therefore more pessimistic than necessary. We use a simple example to show that the existing graphical methods take no account of any service recorded by suspensions beyond their respective previous failures, and that this behaviour is inconsistent with one's intuitive expectations. In the course of this thesis, we demonstrate that the existing methods are only justified under restricted conditions. We present several improved methods and demonstrate that each of them overcomes the problem described above, while reducing to one of the existing methods where this is justified. Each of the improved methods thus provides a realistic set of reliability estimates for general (unrestricted) censored samples. Several related variations on these improved methods are also presented and justified. - i

The role of non-factorizability in determining "pseudo-classical" non-separability

This article introduces a “pseudo classical” notion of modelling non-separability. This form of non-separability can be viewed as lying between separability and quantum-like non-separability. Non-separability is formalized in terms of the non-factorizabilty of the underlying joint probability distribution. A decision criterium for determining the non-factorizability of the joint distribution is related to determining the rank of a matrix as well as another approach based on the chi-square-goodness-of-fit test. This pseudo-classical notion of non-separability is discussed in terms of quantum games and concept combinations in human cognition.

A statistical framework for natural feature representation

This paper presents a robust stochastic framework for the incorporation of visual observations into conventional estimation, data fusion, navigation and control algorithms. The representation combines Isomap, a non-linear dimensionality reduction algorithm, with expectation maximization, a statistical learning scheme. The joint probability distribution of this representation is computed offline based on existing training data. The training phase of the algorithm results in a nonlinear and non-Gaussian likelihood model of natural features conditioned on the underlying visual states. This generative model can be used online to instantiate likelihoods corresponding to observed visual features in real-time. The instantiated likelihoods are expressed as a Gaussian mixture model and are conveniently integrated within existing non-linear filtering algorithms. Example applications based on real visual data from heterogenous, unstructured environments demonstrate the versatility of the generative models.

Continuous appearance-based trajectory SLAM

This paper describes a novel probabilistic approach to incorporating odometric information into appearance-based SLAM systems, without performing metric map construction or calculating relative feature geometry. The proposed system, dubbed Continuous Appearance-based Trajectory SLAM (CAT-SLAM), represents location as a probability distribution along a trajectory, and represents appearance continuously over the trajectory rather than at discrete locations. The distribution is evaluated using a Rao-Blackwellised particle filter, which weights particles based on local appearance and odometric similarity and explicitly models both the likelihood of revisiting previous locations and visiting new locations. A modified resampling scheme counters particle deprivation and allows loop closure updates to be performed in constant time regardless of map size. We compare the performance of CAT-SLAM to FAB-MAP (an appearance-only SLAM algorithm) in an outdoor environment, demonstrating a threefold increase in the number of correct loop closures detected by CAT-SLAM.