L'objectif général du travail de cette thèse est de proposer des méthodes robustes pour permettre d’obtenir des critères sur l’évolution de la pathologie tumorale à partir d’études dynamiques. Actuellement, l’appréciation de l’efficacité d’un traitement antiangiogénique (destruction des vaisseaux alimentant la tumeur) repose principalement sur l’imagerie fonctionnelle dont l’objectif est de quantifier la microcirculation tumorale à partir d’acquisitions dynamiques de perfusion. Cependant, différentes limites concernant le suivi de la réponse précoce des lésions par imagerie existent (mauvaise maîtrise des mouvements respiratoires, pas de consensus sur les paramètres permettant de quantifier la microcirculation tumorale, estimation paramétrique faite à partir de données extrêmement bruitées et pour un grand nombre de zones - une estimation par voxel de la séquence dynamique d’images). Dans un contexte clinique extrêmement contraignant, nous avons mis en place un cadre rigoureux comprenant l’ensemble des étapes nécessaires pour une caractérisation plus fiable de la microcirculation tumorale à partir de séquences d’images acquises sous perfusion de produit de contraste : les contributions principales de cette thèse couvrent ainsi l’optimisation des paramètres de reconstruction, le développement d’une méthode de recalage adaptée à nos données, la sélection argumentée d’un modèle de perfusion et enfin le développement d’une méthode robuste d’estimation des paramètres. Ces travaux permettent d’envisager l’utilisation des modèles de perfusion pour la caractérisation et la prédiction de la réponse d’un patient à différents traitements antitumoraux. / The main objective is to propose robust methods to allow estimation of functional markers reflecting the tumor evolution from dynamic studies. Currently, in this domain, assessing of the efficiency evaluation of an anti-angiogenic therapy (destruction of vessels which feed the tumor) is mainly based on the functional imaging of the microcirculation, which the objective is to quantify the tumor microcirculation by dynamic acquisitions with injection of contrast product. However, several limitations are present (lack of control of the breathing movement, no consensus on the parameters permitting the quantification of tumor microcirculation, parameter estimation computed from noisy data and a large number of regions - one estimation by voxel or group of voxel of the dynamic image sequence). In a restrictive clinical context (noisy data, few number), we have developed a complete pipeline with a set of necessary steps to a reliable characterization of the tumor microcirculation from dynamic perfusion image sequence: the main contributions of this thesis cover the reconstruction parameters optimization, the development of a registration method, the argued selection of a perfusion model and the development of a robust method of parameter estimation. With these works, we can envision the utilization of these perfusion models to the characterization and the prediction of the therapy response of a patient

Abstract The multiple–input multiple–output (MIMO) technique, applying several transmit and receive antennas in wireless communications, has emerged as one of the most prominent technical breakthroughs of the last decade. Wideband MIMO parameter estimation and its applications to the MIMO orthogonal frequency division multiplexing (MIMO–OFDM) channel estimation and mobile positioning are studied in this thesis. Two practical MIMO channel models, i.e., correlated-receive independent-transmit channel and correlated-transmit-receive channel, and associated space-time parameter estimation algorithms are considered. Thanks to the specified structure of the proposed training signals for multiple transmit antennas, the iterative quadrature maximum likelihood (IQML) algorithm is applied to estimate the time delay and spatial signature for the correlated-receive independent-transmit MIMO channels. For the correlated-transmit-receive MIMO channels, the spatial signature matrix corresponding to a time delay can be further decomposed in such a way that the angle of arrival (AOA) and the angle of departure (AOD) can be estimated simultaneously by the 2-D unitary ESPRIT algorithm. Therefore, the combination of the IQML algorithm and the 2-D unitary ESPRIT algorithm provides a novel solution to jointly estimate the time delay, the AOA and the AOD for the correlated-transmit-receive MIMO channels. It is demonstrated from the numerical examples that the proposed algorithms can obtain good performance at a reasonable cost. Considering the correlated-receive independent-transmit MIMO channels, channel coefficient estimation for the MIMO–OFDM system is studied. Based on the parameters of the correlated-receive independent-transmit MIMO channels, the channel statistics in terms of the correlation matrix are developed. By virtue of the derived channel statistics, a joint spatial-temporal (JST) filtering based MMSE channel estimator is proposed which takes full advantage of the channel correlation properties. The mean square error (MSE) of the proposed channel estimator is analyzed, and its performance is also demonstrated by Monte Carlo computer simulations. It is shown that the proposed JST minimum mean square error (MMSE) channel estimator outperforms the more conventional temporal MMSE channel estimator in terms of the MSE when the signals in the receive antenna array elements are significantly correlated. The closed form bit error probability of the space-time block coded OFDM system with correlation at the receiver is also developed by taking the channel estimation errors and channel statistics, i.e., correlation at the receiver, into account. Mobile positioning in the non-line of sight (NLOS) scenarios is studied. With the knowledge of the time delay, the AOA and the AOD associated with each NLOS propagation path, a novel geometric approach is proposed to calculate the MS's position by only exploiting two NLOS paths. On top of this, the least squares and the maximum likelihood (ML) algorithms are developed to utilize multiple NLOS paths to improve the positioning accuracy. Moreover, the ML algorithm is able to estimate the scatterers' positions as well as those of the MSs. The Cramer-Rao lower bound related to the position estimation in the NLOS scenarios is derived. It is shown both analytically and through computer simulations that the proposed algorithms are able to estimate the mobile position only by employing the NLOS paths.

The dissertation forms part of an ongoing project for the modelling and eventual control of an electric arc furnace (EAF) process. The main motivation behind such a project is the potential benefits that can result from automation of a process that has largely been operator controlled, often with results that leave sufficient room for improvement. Previous work in the project has resulted in the development of a generic model of the process. A later study concentrated on the control of the EAF where economic factors were taken into account. Simulation results from both studies clearly demonstrate the benefits that can accrue from successful implementation of process control. A major drawback to the practical implementation of the results is the lack of a model that is proven to be an accurate depiction of the specific plant where control is to be applied. Furthermore, the accuracy of any process model can only be verified against actual process data. There lies the raison d'etre for this dissertation: to take the existing model from the simulation environment to the real process. The main objective is to obtain a model that is able to mimic a selected set of process outputs. This is commonly a problem of system identification (SID): to select an appropriate model then fit the model to plant input/output data until the model response is similar to the plant under the same inputs (and initial conditions). The model fitting is carried out on an existing EAF model primarily by estimation of the model parameters for the EAF refining stage. Therefore the contribution of this dissertation is a model that is able to depict the EAF refining stage with reasonable accuracy. An important aspect of model fitting is experiment design. This deals with the selection of inputs and outputs that must be measured in order to estimate the desired parameters. This constitutes the problem of identifiability: what possibilities exist for estimating parameters using available I/O data or, what additional data is necessary to estimate desired parameters. In the dissertation an analysis is carried out to determine which parameters are estimable from available data. For parameters that are not estimable recommendations are made about additional measurements required to remedy the situation. Additional modelling is carried out to adapt the model to the particular process. This includes modelling to incorporate the oxyfuel subsystem, the bath oxygen content, water cooling and the effect of foaming on the arc efficiency. / Dissertation (MEng (Electronic Engineering))--University of Pretoria, 2006. / Electrical, Electronic and Computer Engineering / unrestricted

Time series models are used to characterise uncertainty in many real-world dynamical phenomena. A time series model typically contains a static variable, called parameter, which parametrizes the joint law of the random variables involved in the definition of the model. When a time series model is to be fitted to some sequentially observed data, it is essential to decide on the value of the parameter that describes the data best, a procedure generally called parameter estimation. This thesis comprises novel contributions to the methodology on parameter estimation in time series models. Our primary interest is online estimation, although batch estimation is also considered. The developed methods are based on batch and online versions of expectation-maximisation (EM) and gradient ascent, two widely popular algorithms for maximum likelihood estimation (MLE). In the last two decades, the range of statistical models where parameter estimation can be performed has been significantly extended with the development of Monte Carlo methods. We provide contribution to the field in a similar manner, namely by combining EM and gradient ascent algorithms with sequential Monte Carlo (SMC) techniques. The time series models we investigate are widely used in statistical and engineering applications. The original work of this thesis is organised in Chapters 4 to 7. Chapter 4 contains an online EM algorithm using SMC for MLE in changepoint models, which are widely used to model heterogeneity in sequential data. In Chapter 5, we present batch and online EM algorithms using SMC for MLE in linear Gaussian multiple target tracking models. Chapter 6 contains a novel methodology for implementing MLE in a hidden Markov model having intractable probability densities for its observations. Finally, in Chapter 7 we formulate the nonnegative matrix factorisation problem as MLE in a specific hidden Markov model and propose online EM algorithms using SMC to perform MLE.

Algorithms will be domonstrated for how to embed complete bipartite graphs onto 2xn type grids, where the imimum grid cutwidth is attained.

The literature on compressive parameter estimation has been mostly focused on the use of sparsity dictionaries that encode a discretized sampling of the parameter space; these dictionaries, however, suffer from coherence issues that must be controlled for successful estimation. To bypass such issues with discretization, we propose the use of statistical parameter estimation methods within the Approximate Message Passing (AMP) algorithm for signal recovery. Our method leverages the recently proposed use of custom denoisers in place of the usual thresholding steps (which act as denoisers for sparse signals) in AMP. We introduce the design of analog denoisers that are based on statistical parameter estimation algorithms, and we focus on two commonly used examples: frequency estimation and bearing estimation, coupled with the Root MUSIC estimation algorithm. We first analyze the performance of the proposed analog denoiser for signal recovery, and then link the performance in signal estimation to that of parameter estimation. Numerical experiments show significant improvements in estimation performance versus previously proposed approaches for compressive parameter estimation.

Synthetic biology endeavors to forward engineer genetic circuits with novel function. A major inspiration for the field has been the enormous success in the engineering of digital electronic circuits over the past half century. This dissertation approaches synthetic biology from the perspective of the engineering design cycle, a concept ubiquitous across many engineering disciplines. First, an analysis of the state of the engineering design cycle in synthetic biology is presented, pointing out the most limiting challenges currently facing the field. Second, a principle commonly used in electronics to weigh the tradeoffs between hardware and software implementations of a function, called co-design, is applied to synthetic biology. Designs to implement a specific logical function in three distinct domains are proposed and their pros and cons weighed. Third, automatic transitioning between an abstract design, its physical implementation, and accurate models of the corresponding system are critical for success in synthetic biology. We present a framework for accomplishing this task and demonstrate how it can be used to explore a design space. A major limitation of the aforementioned approach is that adequate parameter values for the performance of genetic components do not yet exist. Thus far, it has not been possible to uniquely attribute the function of a device to the function of the individual components in a way that enables accurate prediction of the function of new devices assembled from the same components. This lack presents a major challenge to rapid progression through the design cycle. We address this challenge by first collecting high time-resolution fluorescence trajectories of individual cells expressing a fluorescent protein, as well as snapshots of the number of corresponding mRNA molecules per cell. We then leverage the information embedded in the cell-cell variability of the population to extract parameter values for a stochastic model of gene expression more complex than typically used. Such analysis opens the door for models of genetic components that can more reliably predict the function of new combinations of these basic components. / Ph. D.

abstract: Cancer is a disease involving abnormal growth of cells. Its growth dynamics is perplexing. Mathematical modeling is a way to shed light on this progress and its medical treatments. This dissertation is to study cancer invasion in time and space using a mathematical approach. Chapter 1 presents a detailed review of literature on cancer modeling. Chapter 2 focuses sorely on time where the escape of a generic cancer out of immune control is described by stochastic delayed differential equations (SDDEs). Without time delay and noise, this system demonstrates bistability. The effects of response time of the immune system and stochasticity in the tumor proliferation rate are studied by including delay and noise in the model. Stability, persistence and extinction of the tumor are analyzed. The result shows that both time delay and noise can induce the transition from low tumor burden equilibrium to high tumor equilibrium. The aforementioned work has been published (Han et al., 2019b). In Chapter 3, Glioblastoma multiforme (GBM) is studied using a partial differential equation (PDE) model. GBM is an aggressive brain cancer with a grim prognosis. A mathematical model of GBM growth with explicit motility, birth, and death processes is proposed. A novel method is developed to approximate key characteristics of the wave profile, which can be compared with MRI data. Several test cases of MRI data of GBM patients are used to yield personalized parameterizations of the model. The aforementioned work has been published (Han et al., 2019a). Chapter 4 presents an innovative way of forecasting spatial cancer invasion. Most mathematical models, including the ones described in previous chapters, are formulated based on strong assumptions, which are hard, if not impossible, to verify due to complexity of biological processes and lack of quality data. Instead, a nonparametric forecasting method using Gaussian processes is proposed. By exploiting the local nature of the spatio-temporal process, sparse (in terms of time) data is sufficient for forecasting. Desirable properties of Gaussian processes facilitate selection of the size of the local neighborhood and computationally efficient propagation of uncertainty. The method is tested on synthetic data and demonstrates promising results. / Dissertation/Thesis / Doctoral Dissertation Applied Mathematics 2020

Generic simulations of tremor propagation through the upper limb have been achieved using a previously developed postural tremor model, but this model had not yet been compared with experimental data or utilized for subject-specific studies. This work addressed these two issues, which are important for optimizing peripheral tremor suppression techniques. For tractability, we focused on a subsystem of the upper limb: the isolated wrist, including the four prime wrist muscles (extensor carpi ulnaris, flexor carpi ulnaris, extensor carpi radialis, and flexor carpi radialis) and the two degrees of freedom of the wrist (flexion-extension and radial-ulnar deviation). Muscle excitation and joint displacement signals were collected while subjects with Essential Tremor resisted gravity. System identification was implemented for three subjects who experienced significant tremor using two approaches: 1. Generic linear time-invariant (LTI) models, including autoregressive-exogenous (ARX) and state-space forms, were identified from the experimental data, and characteristics including model order and modal parameters were compared with the previously developed postural tremor model; 2. Subject-specific parameters for the previously developed postural tremor model were directly estimated from experimental data using nonlinear least-squares optimization combined with regularization. The identified LTI models fit the experimental data well, with coefficients of determination of 0.74 ± 0.18 and 0.83 ± 0.13 for ARX and state-space forms, respectively. The optimal model orders identified from the experimental data (4.8 ± 1.9 and 6.4 ± 1.9) were slightly lower than the orders of the ARX and state-space forms of the previously developed model (6 and 8). For each subject, at least one pair of identified complex poles aligned with the complex poles of the previously developed model, whereas the identified real poles were assumed to represent drift in the data rather than characteristics of the system. Subject-specific parameter estimates reduced the sum of squared-error (SSE) between the measured and predicted joint displacement signals to be between 10% and 50% of the SSE using generic literature parameters. The predicted joint displacements maintained high coherence at the tremor frequency for flexion-extension (0.90 ± 0.10), which experienced the most tremor. We successfully applied multiple system identification techniques to identify tremor propagation models using only tremorogenic muscle activity as the input. These techniques identified model order, poles, and subject-specific model parameters, and indicate that tremor propagation at the wrist is well approximated by an LTI model.

The focus of this thesis is on developing theories and techniques to extract lossy microwave filter parameters from data. In the literature, the Cauchy methods have been used to extract filters’ characteristic polynomials from measured scattering parameters. These methods are described and some examples are constructed to test their performance. The results suggest that the Cauchy method does not work well when the Q factors representing the loss of filters are not even. Based on some prototype filters and the relationship between Q factors and the loss, we conduct preliminary studies on alternative representations of the characteristic polynomials. The parameters in these new models are extracted using the Levenberg–Marquardt algorithm to accurately estimate characteristic polynomials and the loss information.