Convex Optimization Algorithms and Statistical Bounds for Learning Structured Models

Thesis (Ph.D.)--University of Washington, 2016-08

ArrayMining: a modular web-application for microarray analysis combining ensemble and consensus methods with cross-study normalization

Background: Statistical analysis of DNA microarray data provides a valuable diagnostic tool for the investigation of genetic components of diseases. To take advantage of the multitude of available data sets and analysis methods, it is desirable to combine both different algorithms and data from different studies. Applying ensemble learning, consensus clustering and cross-study normalization methods for this purpose in an almost fully automated process and linking different analysis modules together under a single interface would simplify many microarray analysis tasks. Results: We present ArrayMining.net, a web-application for microarray analysis that provides easy access to a wide choice of feature selection, clustering, prediction, gene set analysis and cross-study normalization methods. In contrast to other microarray-related web-tools, multiple algorithms and data sets for an analysis task can be combined using ensemble feature selection, ensemble prediction, consensus clustering and cross-platform data integration. By interlinking different analysis tools in a modular fashion, new exploratory routes become available, e.g. ensemble sample classification using features obtained from a gene set analysis and data from multiple studies. The analysis is further simplified by automatic parameter selection mechanisms and linkage to web tools and databases for functional annotation and literature mining. Conclusion: ArrayMining.net is a free web-application for microarray analysis combining a broad choice of algorithms based on ensemble and consensus methods, using automatic parameter selection and integration with annotation databases.

Quality evaluation of cortex berberidis from different geographical origins by simultaneous high performance liquid chromatography combined with statistical methods

Purpose: To develop an effective method for evaluating the quality of Cortex berberidis from different geographical origins. Methods: A simple, precise and accurate high performance liquid chromatography (HPLC) method was first developed for simultaneous quantification of four active alkaloids (magnoflorine, jatrorrhizine, palmatine, and berberine) in Cortex berberidis obtained from Qinghai, Tibet and Sichuan Provinces of China. Method validation was performed in terms of precision, repeatability, stability, accuracy, and linearity. Besides, partial least squares discriminant analysis (PLS-DA) and one-way analysis of variance (ANOVA) were applied to study the quality variations of Cortex berberidis from various geographical origins. Results: The proposed HPLC method showed good linearity, precision, repeatability, and accuracy. The four alkaloids were detected in all samples of Cortex berberidis. Among them, magnoflorine (36.46 - 87.30 mg/g) consistently showed the highest amounts in all the samples, followed by berberine (16.00 - 37.50 mg/g). The content varied in the range of 0.66 - 4.57 mg/g for palmatine and 1.53 - 16.26 mg/g for jatrorrhizine, respectively. The total content of the four alkaloids ranged from 67.62 to 114.79 mg/g. Moreover, the results obtained by the PLS-DA and ANOVA showed that magnoflorine level and the total content of these four alkaloids in Qinghai and Tibet samples were significantly higher (p < 0.01) than those in Sichuan samples. Conclusion: Quantification of multi-ingredients by HPLC combined with statistical methods provide an effective approach for achieving origin discrimination and quality evaluation of Cortex berberidis. The quality of Cortex berberidis closely correlates to the geographical origin of the samples, with Cortex berberidis samples from Qinghai and Tibet exhibiting superior qualities to those from Sichuan.

Review of vibration-based damage detection and condition assessment of bridge structures using structural health monitoring

As a part of vital infrastructure and transportation networks, bridge structures must function safely at all times. However, due to heavier and faster moving vehicular loads and function adjustment, such as Busway accommodation, many bridges are now operating at an overload beyond their design capacity. Additionally, the huge renovation and replacement costs always make the infrastructure owners difficult to undertake. Structural health monitoring (SHM) is set to assess condition and foresee probable failures of designated bridge(s), so as to monitor the structural health of the bridges. The SHM systems proposed recently are incorporated with Vibration-Based Damage Detection (VBDD) techniques, Statistical Methods and Signal processing techniques and have been regarded as efficient and economical ways to solve the problem. The recent development in damage detection and condition assessment techniques based on VBDD and statistical methods are reviewed. The VBDD methods based on changes in natural frequencies, curvature/strain modes, modal strain energy (MSE) dynamic flexibility, artificial neural networks (ANN) before and after damage and other signal processing methods like Wavelet techniques and empirical mode decomposition (EMD) / Hilbert spectrum methods are discussed here.

Study of wheel-rail impact at insulated rail joint through experimental and numerical methods

As part of an ongoing research on the development of a longer life insulated rail joint (IRJ), this paper reports a field experiment and a simplified 2D numerical modelling for the purpose of investigating the behaviour of rail web in the vicinity of endpost in an insulated rail joint (IRJ) due to wheel passages. A simplified 2D plane stress finite element model is used to simulate the wheel-rail rolling contact impact at IRJ. This model is validated using data from a strain gauged IRJ that was installed in a heavy haul network; data in terms of the vertical and shear strains at specific positions of the IRJ during train passing were captured and compared with the results of the FE model. The comparison indicates a satisfactory agreement between the FE model and the field testing. Furthermore, it demonstrates that the experimental and numerical analyses reported in this paper provide a valuable datum for developing further insight into the behaviour of IRJ under wheel impacts.

GIS-based mapping and statistical analysis of air pollution and mortality in Brisbane, Australia

In this thesis, the relationship between air pollution and human health has been investigated utilising Geographic Information System (GIS) as an analysis tool. The research focused on how vehicular air pollution affects human health. The main objective of this study was to analyse the spatial variability of pollutants, taking Brisbane City in Australia as a case study, by the identification of the areas of high concentration of air pollutants and their relationship with the numbers of death caused by air pollutants. A correlation test was performed to establish the relationship between air pollution, number of deaths from respiratory disease, and total distance travelled by road vehicles in Brisbane. GIS was utilized to investigate the spatial distribution of the air pollutants. The main finding of this research is the comparison between spatial and non-spatial analysis approaches, which indicated that correlation analysis and simple buffer analysis of GIS using the average levels of air pollutants from a single monitoring station or by group of few monitoring stations is a relatively simple method for assessing the health effects of air pollution. There was a significant positive correlation between variable under consideration, and the research shows a decreasing trend of concentration of nitrogen dioxide at the Eagle Farm and Springwood sites and an increasing trend at CBD site. Statistical analysis shows that there exists a positive relationship between the level of emission and number of deaths, though the impact is not uniform as certain sections of the population are more vulnerable to exposure. Further statistical tests found that the elderly people of over 75 years age and children between 0-15 years of age are the more vulnerable people exposed to air pollution. A non-spatial approach alone may be insufficient for an appropriate evaluation of the impact of air pollutant variables and their inter-relationships. It is important to evaluate the spatial features of air pollutants before modeling the air pollution-health relationships.

Novel analytical and numerical methods for solving fractional dynamical systems

During the past three decades, the subject of fractional calculus (that is, calculus of integrals and derivatives of arbitrary order) has gained considerable popularity and importance, mainly due to its demonstrated applications in numerous diverse and widespread fields in science and engineering. For example, fractional calculus has been successfully applied to problems in system biology, physics, chemistry and biochemistry, hydrology, medicine, and finance. In many cases these new fractional-order models are more adequate than the previously used integer-order models, because fractional derivatives and integrals enable the description of the memory and hereditary properties inherent in various materials and processes that are governed by anomalous diffusion. Hence, there is a growing need to find the solution behaviour of these fractional differential equations. However, the analytic solutions of most fractional differential equations generally cannot be obtained. As a consequence, approximate and numerical techniques are playing an important role in identifying the solution behaviour of such fractional equations and exploring their applications. The main objective of this thesis is to develop new effective numerical methods and supporting analysis, based on the finite difference and finite element methods, for solving time, space and time-space fractional dynamical systems involving fractional derivatives in one and two spatial dimensions. A series of five published papers and one manuscript in preparation will be presented on the solution of the space fractional diffusion equation, space fractional advectiondispersion equation, time and space fractional diffusion equation, time and space fractional Fokker-Planck equation with a linear or non-linear source term, and fractional cable equation involving two time fractional derivatives, respectively. One important contribution of this thesis is the demonstration of how to choose different approximation techniques for different fractional derivatives. Special attention has been paid to the Riesz space fractional derivative, due to its important application in the field of groundwater flow, system biology and finance. We present three numerical methods to approximate the Riesz space fractional derivative, namely the L1/ L2-approximation method, the standard/shifted Gr¨unwald method, and the matrix transform method (MTM). The first two methods are based on the finite difference method, while the MTM allows discretisation in space using either the finite difference or finite element methods. Furthermore, we prove the equivalence of the Riesz fractional derivative and the fractional Laplacian operator under homogeneous Dirichlet boundary conditions – a result that had not previously been established. This result justifies the aforementioned use of the MTM to approximate the Riesz fractional derivative. After spatial discretisation, the time-space fractional partial differential equation is transformed into a system of fractional-in-time differential equations. We then investigate numerical methods to handle time fractional derivatives, be they Caputo type or Riemann-Liouville type. This leads to new methods utilising either finite difference strategies or the Laplace transform method for advancing the solution in time. The stability and convergence of our proposed numerical methods are also investigated. Numerical experiments are carried out in support of our theoretical analysis. We also emphasise that the numerical methods we develop are applicable for many other types of fractional partial differential equations.

Structural health monitoring : vibration-based damage detection and condition assessment of bridges

Structural health is a vital aspect of infrastructure sustainability. As a part of a vital infrastructure and transportation network, bridge structures must function safely at all times. However, due to heavier and faster moving vehicular loads and function adjustment, such as Busway accommodation, many bridges are now operating at an overload beyond their design capacity. Additionally, the huge renovation and replacement costs are a difficult burden for infrastructure owners. The structural health monitoring (SHM) systems proposed recently are incorporated with vibration-based damage detection techniques, statistical methods and signal processing techniques and have been regarded as efficient and economical ways to assess bridge condition and foresee probable costly failures. In this chapter, the recent developments in damage detection and condition assessment techniques based on vibration-based damage detection and statistical methods are reviewed. The vibration-based damage detection methods based on changes in natural frequencies, curvature or strain modes, modal strain energy, dynamic flexibility, artificial neural networks, before and after damage, and other signal processing methods such as Wavelet techniques, empirical mode decomposition and Hilbert spectrum methods are discussed in this chapter.

Critical gap estimation by numerical and statistical highest likelihood search

Many traffic situations require drivers to cross or merge into a stream having higher priority. Gap acceptance theory enables us to model such processes to analyse traffic operation. This discussion demonstrated that numerical search fine tuned by statistical analysis can be used to determine the most likely critical gap for a sample of drivers, based on their largest rejected gap and accepted gap. This method shares some common features with the Maximum Likelihood Estimation technique (Troutbeck 1992) but lends itself well to contemporary analysis tools such as spreadsheet and is particularly analytically transparent. This method is considered not to bias estimation of critical gap due to very small rejected gaps or very large rejected gaps. However, it requires a sufficiently large sample that there is reasonable representation of largest rejected gap/accepted gap pairs within a fairly narrow highest likelihood search band.