Bayesian analysis of the scatterometer wind retrieval inverse problem:Some new approaches

The retrieval of wind vectors from satellite scatterometer observations is a non-linear inverse problem. A common approach to solving inverse problems is to adopt a Bayesian framework and to infer the posterior distribution of the parameters of interest given the observations by using a likelihood model relating the observations to the parameters, and a prior distribution over the parameters. We show how Gaussian process priors can be used efficiently with a variety of likelihood models, using local forward (observation) models and direct inverse models for the scatterometer. We present an enhanced Markov chain Monte Carlo method to sample from the resulting multimodal posterior distribution. We go on to show how the computational complexity of the inference can be controlled by using a sparse, sequential Bayes algorithm for estimation with Gaussian processes. This helps to overcome the most serious barrier to the use of probabilistic, Gaussian process methods in remote sensing inverse problems, which is the prohibitively large size of the data sets. We contrast the sampling results with the approximations that are found by using the sparse, sequential Bayes algorithm.

Hidden state models for time series

Amongst all the objectives in the study of time series, uncovering the dynamic law of its generation is probably the most important. When the underlying dynamics are not available, time series modelling consists of developing a model which best explains a sequence of observations. In this thesis, we consider hidden space models for analysing and describing time series. We first provide an introduction to the principal concepts of hidden state models and draw an analogy between hidden Markov models and state space models. Central ideas such as hidden state inference or parameter estimation are reviewed in detail. A key part of multivariate time series analysis is identifying the delay between different variables. We present a novel approach for time delay estimating in a non-stationary environment. The technique makes use of hidden Markov models and we demonstrate its application for estimating a crucial parameter in the oil industry. We then focus on hybrid models that we call dynamical local models. These models combine and generalise hidden Markov models and state space models. Probabilistic inference is unfortunately computationally intractable and we show how to make use of variational techniques for approximating the posterior distribution over the hidden state variables. Experimental simulations on synthetic and real-world data demonstrate the application of dynamical local models for segmenting a time series into regimes and providing predictive distributions.

Financial liberalization and dynamics of firm-level financing and investment decisions in the Southeast Asian countries

This thesis examines the dynamics of firm-level financing and investment decisions for six Southeast Asian countries. The study provides empirical evidence on the impacts of changes in the firm-level financing decisions during the period of financial liberalization by considering the debt and equity financing decisions of a set of non-financial firms. The empirical results show that firms in Indonesia, Pakistan, and South Korea have relatively faster speed of adjustment than other Southeast Asian countries to attain optimal debt and equity ratios in response to banking sector and stock market liberalization. In addition, contrary to widely held belief that firms adjust their financial ratios to industry levels, the results indicate that industry factors do not significantly impact on the speed of capital structure adjustments. This study also shows that non-linear estimation methods are more appropriate than linear estimation methods for capturing changes in capital structure. The empirical results also show that international stock market integration of these countries has significantly reduced the equity risk premium as well as the firm-level cost of equity capital. Thus stock market liberalization is associated with a decrease in the cost of equity capital of the firms. Developments in the securities markets infrastructure have also reduced the cost of equity capital. However, with increased integration there is the possibility of capital outflows from the emerging markets, which might reverse the pattern of decrease in cost of capital in these markets.

An advanced real-time predictive maintenance framework for large scale machine systems

This thesis introduces and develops a novel real-time predictive maintenance system to estimate the machine system parameters using the motion current signature. Recently, motion current signature analysis has been addressed as an alternative to the use of sensors for monitoring internal faults of a motor. A maintenance system based upon the analysis of motion current signature avoids the need for the implementation and maintenance of expensive motion sensing technology. By developing nonlinear dynamical analysis for motion current signature, the research described in this thesis implements a novel real-time predictive maintenance system for current and future manufacturing machine systems. A crucial concept underpinning this project is that the motion current signature contains infor­mation relating to the machine system parameters and that this information can be extracted using nonlinear mapping techniques, such as neural networks. Towards this end, a proof of con­cept procedure is performed, which substantiates this concept. A simulation model, TuneLearn, is developed to simulate the large amount of training data required by the neural network ap­proach. Statistical validation and verification of the model is performed to ascertain confidence in the simulated motion current signature. Validation experiment concludes that, although, the simulation model generates a good macro-dynamical mapping of the motion current signature, it fails to accurately map the micro-dynamical structure due to the lack of knowledge regarding performance of higher order and nonlinear factors, such as backlash and compliance. Failure of the simulation model to determine the micro-dynamical structure suggests the pres­ence of nonlinearity in the motion current signature. This motivated us to perform surrogate data testing for nonlinearity in the motion current signature. Results confirm the presence of nonlinearity in the motion current signature, thereby, motivating the use of nonlinear tech­niques for further analysis. Outcomes of the experiment show that nonlinear noise reduction combined with the linear reverse algorithm offers precise machine system parameter estimation using the motion current signature for the implementation of the real-time predictive maintenance system. Finally, a linear reverse algorithm, BJEST, is developed and applied to the motion current signature to estimate the machine system parameters.

Formulation of topical non-steroidal anti-inflammatory agents

Reversed-pahse high-performance liquid chromatographic (HPLC) methods were developed for the assay of indomethacin, its decomposition products, ibuprofen and its (tetrahydro-2-furanyl)methyl-, (tetrahydro-2-(2H)pyranyl)methyl- and cyclohexylmethyl esters. The development and application of these HPLC systems were studied. A number of physico-chemical parameters that affect percutaneous absorption were investigated. The pKa values of indomethacin and ibuprofen were determined using the solubility method. Potentiometric titration and the Taft equation were also used for ibuprofen. The incorporation of ethanol or propylene glycol in the solvent resulted in an improvement in the aqueous solubility of these compounds. The partition coefficients were evaluated in order to establish the affinity of these drugs towards the stratum corneum. The stability of indomethacin and of ibuprofen esters were investigated and the effect of temperature and pH on the decomposition rates were studied. The effect of cetyltrimethylammonium bromide on the alkaline degradation of indomethacin was also followed. In the presence of alcohol, indomethacin alcoholysis was observed and the kinetics of decomposition were subjected to non-linear regression analysis and the rate constants for the various pathways were quantified. The non-isothermal, sufactant non-isoconcentration and non-isopH degradation of indomethacin were investigated. The analysis of the data was undertaken using NONISO, a BASIC computer program. The degradation profiles obtained from both non-iso and iso-kinetic studies show that there is close concordance in the results. The metabolic biotransformation of ibuprofen esters was followed using esterases from hog liver and rat skin homogenates. The results showed that the esters were very labile under these conditions. The presence of propylene glycol affected the rates of enzymic hydrolysis of the ester. The hydrolysis is modelled using an equation involving the dielectric constant of the medium. The percutaneous absorption of indomethacin and of ibuprofen and its esters was followed from solutions using an in vitro excised human skin model. The absorption profiles followed first order kinetics. The diffusion process was related to their solubility and to the human skin/solvent partition coefficient. The percutaneous absorption of two ibuprofen esters from suspensions in 20% propylene glycol-water were also followed through rat skin with only ibuprofen being detected in the receiver phase. The sensitivity of ibuprofen esters to enzymic hydrolysis compared to the chemical hydrolysis may prove valuable in the formulation of topical delivery systems.

Bayesian data assimilation

This thesis addresses data assimilation, which typically refers to the estimation of the state of a physical system given a model and observations, and its application to short-term precipitation forecasting. A general introduction to data assimilation is given, both from a deterministic and' stochastic point of view. Data assimilation algorithms are reviewed, in the static case (when no dynamics are involved), then in the dynamic case. A double experiment on two non-linear models, the Lorenz 63 and the Lorenz 96 models, is run and the comparative performance of the methods is discussed in terms of quality of the assimilation, robustness "in the non-linear regime and computational time. Following the general review and analysis, data assimilation is discussed in the particular context of very short-term rainfall forecasting (nowcasting) using radar images. An extended Bayesian precipitation nowcasting model is introduced. The model is stochastic in nature and relies on the spatial decomposition of the rainfall field into rain "cells". Radar observations are assimilated using a Variational Bayesian method in which the true posterior distribution of the parameters is approximated by a more tractable distribution. The motion of the cells is captured by a 20 Gaussian process. The model is tested on two precipitation events, the first dominated by convective showers, the second by precipitation fronts. Several deterministic and probabilistic validation methods are applied and the model is shown to retain reasonable prediction skill at up to 3 hours lead time. Extensions to the model are discussed.

Analysis of nocturnal oxygen saturation recordings using kernel entropy to assist in sleep apnea-hypopnea diagnosis

In this study, a new entropy measure known as kernel entropy (KerEnt), which quantifies the irregularity in a series, was applied to nocturnal oxygen saturation (SaO 2) recordings. A total of 96 subjects suspected of suffering from sleep apnea-hypopnea syndrome (SAHS) took part in the study: 32 SAHS-negative and 64 SAHS-positive subjects. Their SaO 2 signals were separately processed by means of KerEnt. Our results show that a higher degree of irregularity is associated to SAHS-positive subjects. Statistical analysis revealed significant differences between the KerEnt values of SAHS-negative and SAHS-positive groups. The diagnostic utility of this parameter was studied by means of receiver operating characteristic (ROC) analysis. A classification accuracy of 81.25% (81.25% sensitivity and 81.25% specificity) was achieved. Repeated apneas during sleep increase irregularity in SaO 2 data. This effect can be measured by KerEnt in order to detect SAHS. This non-linear measure can provide useful information for the development of alternative diagnostic techniques in order to reduce the demand for conventional polysomnography (PSG). © 2011 IEEE.

Hydrodynamics and mass transfer studies in a scheibel extractor

A 10 cm diameter four-stage Scheibel column with dispersed phase wetted packing sections has been constructed to study the hydrodynamics and mass transfer using the system toluene-acetone-water. The literature pertaining to the above extractor has been examined and the important phenomena such as droplet break-up and coalescence, mass transfer and backmixing have been reviewed. A critical analysis of the backmixing or axial mixing models and the corresponding techniques for parameter estimation was applied and an optimization technique based on Marquardt's algorithm was implemented. A single phase sampling technique was developed to estimate the acetone concentration profile in both phases along the column. Column flooding characteristics were investigated under various operating conditions and it was found that, when the impellers were located at about DI/5cm from the upper surface of the pads, the limiting flow rates increased with impeller speed. This unusual behaviour was explained in terms of the pumping effect created by the turbine impellers. Correlations were developed to predict Sauter mean drop diameters. A five-cell with backflow model was used to estimate the column performance (stage efficiency) and phases non-ideality (backflow parameters). Overall mass transfer coefficients were computed using the above model and compared with those calculated using the correlations based on single drop mechanism.

Population pharmacokinetic and pharmacogenetic analysis of tacrolimus in paediatric liver transplant patients

Aims - To build a population pharmacokinetic model that describes the apparent clearance of tacrolimus and the potential demographic, clinical and genetically controlled factors that could lead to inter-patient pharmacokinetic variability within children following liver transplantation. Methods - The present study retrospectively examined tacrolimus whole blood pre-dose concentrations (n = 628) of 43 children during their first year post-liver transplantation. Population pharmacokinetic analysis was performed using the non-linear mixed effects modelling program (nonmem) to determine the population mean parameter estimate of clearance and influential covariates. Results - The final model identified time post-transplantation and CYP3A5*1 allele as influential covariates on tacrolimus apparent clearance according to the following equation: TVCL = 12.9 x (Weight/13.2)0.35 x EXP (-0.0058 x TPT) x EXP (0.428 x CYP3A5) where TVCL is the typical value for apparent clearance, TPT is time post-transplantation in days and the CYP3A5 is 1 where *1 allele is present and 0 otherwise. The population estimate and inter-individual variability (%CV) of tacrolimus apparent clearance were found to be 0.977 l h−1 kg−1 (95% CI 0.958, 0.996) and 40.0%, respectively, while the residual variability between the observed and predicted concentrations was 35.4%. Conclusion Tacrolimus apparent clearance was influenced by time post-transplantation and CYP3A5 genotypes. The results of this study, once confirmed by a large scale prospective study, can be used in conjunction with therapeutic drug monitoring to recommend tacrolimus dose adjustments that take into account not only body weight but also genetic and time-related changes in tacrolimus clearance.

Linear dispersive pre-defined peak amplitude modulation of spectrally modulated airy-based pulses

Spectrally modulated Airy-based pulses peak amplitude modulation (PAM) in linear dispersive media is investigated, designed, and numerically simulated. As it is shown here, it is possible to design the spectral modulation of the initial Airy-based pulses to obtain a pre-defined PAM profile as the pulse propagates. Although optical pulses self-amplitude modulation is a well-known effect under non-linear propagation, the designed Airy-based pulses exhibit PAM under linear dispersive propagation. This extraordinary linear propagation property can be applied in many kinds of dispersive media, enabling its use in a broad range of experiments and applications. © 2013 Optical Society of America.

Identification of Mechanical Parameters in Mathematical Model of Human Abdominal Fascia

Миглена Г. Кирилова-Донева - Едномерен експеримент на релаксация беше извършен с 14 образци от човешка пъпна фасция. Механичното поведение на фасцията по време на релаксация беше моделирано прилагайки нелинейната теория на Максвел-Гуревич-Рабинович. Параметрите на модела за изследваните образци бяха определени и стойностите им бяха сравнени в зависимост от посоката на натоварване на образците по време на експеримента. Установено бе, че стойностите на началния вискозитет ∗η0 и на параметъра ∗m, който се влияе от скоростта на деформация на материала се изменят в много широки граници не само за образци от различни донори, но и за образци от един донор. В резултат от прилагането на модела бе изчислено изменението на вискозитета и вискозната деформация на материала по време на релаксацията. Бе показано, че изменението на вискозитета и вискозната деформация зависи от посоката на натоварване на образците.

Nonlinear Normalization in Limit Theorems for Extremes

2000 Mathematics Subject Classification: 60G70, 60F05.

Robust Estimation in Multitype Branching Processes Based on their Asymptotic Properties

2000 Mathematics Subject Classification: 60J80.

Parameterized Link Functions in Generalized Linear Random Effect Models: a Case Study on Breast Cancer Treatment

In non-linear random effects some attention has been very recently devoted to the analysis ofsuitable transformation of the response variables separately (Taylor 1996) or not (Oberg and Davidian 2000) from the transformations of the covariates and, as far as we know, no investigation has been carried out on the choice of link function in such models. In our study we consider the use of a random effect model when a parameterized family of links (Aranda-Ordaz 1981, Prentice 1996, Pregibon 1980, Stukel 1988 and Czado 1997) is introduced. We point out the advantages and the drawbacks associated with the choice of this data-driven kind of modeling. Difficulties in the interpretation of regression parameters, and therefore in understanding the influence of covariates, as well as problems related to loss of efficiency of estimates and overfitting, are discussed. A case study on radiotherapy usage in breast cancer treatment is discussed.

Hybrid multi-objective optimization and hybridized self-organizing response surface method

Numerical optimization is a technique where a computer is used to explore design parameter combinations to find extremes in performance factors. In multi-objective optimization several performance factors can be optimized simultaneously. The solution to multi-objective optimization problems is not a single design, but a family of optimized designs referred to as the Pareto frontier. The Pareto frontier is a trade-off curve in the objective function space composed of solutions where performance in one objective function is traded for performance in others. A Multi-Objective Hybridized Optimizer (MOHO) was created for the purpose of solving multi-objective optimization problems by utilizing a set of constituent optimization algorithms. MOHO tracks the progress of the Pareto frontier approximation development and automatically switches amongst those constituent evolutionary optimization algorithms to speed the formation of an accurate Pareto frontier approximation. Aerodynamic shape optimization is one of the oldest applications of numerical optimization. MOHO was used to perform shape optimization on a 0.5-inch ballistic penetrator traveling at Mach number 2.5. Two objectives were simultaneously optimized: minimize aerodynamic drag and maximize penetrator volume. This problem was solved twice. The first time the problem was solved by using Modified Newton Impact Theory (MNIT) to determine the pressure drag on the penetrator. In the second solution, a Parabolized Navier-Stokes (PNS) solver that includes viscosity was used to evaluate the drag on the penetrator. The studies show the difference in the optimized penetrator shapes when viscosity is absent and present in the optimization. In modern optimization problems, objective function evaluations may require many hours on a computer cluster to perform these types of analysis. One solution is to create a response surface that models the behavior of the objective function. Once enough data about the behavior of the objective function has been collected, a response surface can be used to represent the actual objective function in the optimization process. The Hybrid Self-Organizing Response Surface Method (HYBSORSM) algorithm was developed and used to make response surfaces of objective functions. HYBSORSM was evaluated using a suite of 295 non-linear functions. These functions involve from 2 to 100 variables demonstrating robustness and accuracy of HYBSORSM.