Solving the linear quadratic regulator (LQR) problem for partial differential equations (PDEs) leads to many computational challenges. The primary challenge comes from the fact that discretization methods for PDEs typically lead to very large systems of differential or differential algebraic equations. These systems are used to form algebraic Riccati equations involving high rank matrices. Although we restrict our attention to control problems with small numbers of control inputs, we allow for potentially high order control outputs. Problems with this structure appear in a number of practical applications yet no suitable algorithm exists. We propose and analyze solution strategies based on applying model order reduction methods to Chandrasekhar equations, Lyapunov/Sylvester equations, or combinations of these equations. Our numerical examples illustrate improvements in computational time up to several orders of magnitude over standard tools (when these tools can be used). We also present examples that cannot be solved using existing methods. These cases are motivated by flow control problems that are solved by computing feedback controllers for the linearized system. / Ph. D.

Analyses based upon rank correlation methods, such as Spearman's Rho and Kendall's Tau, can provide quick insights into large biological data sets. Comparing expression levels between different technologies and models is problematic due to the different units of measure. Here again, rank correlation provides an effective means of comparison between the two techniques. Massively Parallel Signature Sequencing (MPSS) transcript abundance levels to microarray signal intensities for Arabidopsis thaliana are compared. Rank correlations can be applied to subsets as well as the entire set. Results of subset comparisons can be used to improve the capabilities of predictive models, such as Predicted Highly Expressed (PHX). This is done for Escherichia coli. Methods are given to combine predictive models based upon feedback from experimental data. The problem of feature selection in supervised learning situations is also considered, where all features are drawn from a common domain and are best interpreted via ordinal comparisons with other features, rather than as numerical values. This is done for synthetic data as well as for microarray experiments examining the life cycle of Drosophila melanogaster and human leukemia cells. Two novel methods are presented based upon Rho and Tau, and their efficacy is tested with synthetic and real world data. The method based upon Spearman's Rho is shown to be more effective. / Ph. D.

The research in this dissertation addresses reduced rank adaptive signal processing, with specific emphasis on the multistage Wiener filter (MWF). The MWF is a generalization of the classical Wiener filter that performs a stage-by-stage decomposition based on orthogonal projections. Truncation of this decomposition produces a reduced rank filter with many benefits, for example, improved performance. This dissertation extends knowledge of the MWF in four areas. The first area is rank and sample support compression. This dissertation examines, under a wide variety of conditions, the size of the adaptive subspace required by the MWF (i.e., the rank) as well as the required number of training samples. Comparisons are made with other algorithms such as the eigenvector-based principal components algorithm. The second area investigated in this dissertation concerns "soft stops", i.e., the insertion of diagonal loading into the MWF. Several methods for inserting loading into the MWF are described, as well as methods for choosing the amount of loading. The next area investigated is MWF rank selection. The MWF will outperform the classical Wiener filter when the rank is properly chosen. This dissertation presents six approaches for selecting MWF rank. The algorithms are compared to one another and an overall design space taxonomy is presented. Finally, as digital modelling capabilities become more sophisticated there is emerging interest in augmenting adaptive processing algorithms to incorporate prior knowledge. This dissertation presents two methods for augmenting the MWF, one based on linear constraints and a second based on non-zero weight vector initialization. Both approaches are evaluated under ideal and perturbed conditions. Together the research described in this dissertation increases the utility and robustness of the multistage Wiener filter. The analysis is presented in the context of adaptive array processing, both spatial array processing and space-time adaptive processing for airborne radar. The results, however, are applicable across the entire spectrum of adaptive signal processing applications. / Ph. D.

There is a growing interest in robust and nonparametric methods with engineering applications, due to the nature of the data. Here, we study two power systems engineering applications that employ or recommend robust and nonparametric methods; topology error identification and voltage calibration. Topology errors are a well-known, well-documented problem for utility companies. A topology error occurs when a line's status in a power network, whether active or deactive, is misclassified. This will lead to an incorrect Jacobian matrix used to estimate the unknown parameters of a network in a nonlinear regression model. We propose a solution using nonlinear regression techniques to identify the correct status of every line in the network by deriving a statistical model of the power flows and injections while employing Kirchhoff's Current Law. Simulation results on the IEEE-118 bus system showed that the methodology was able to detect where topology errors occurred as well as identify gross measurement errors. The Friedman Two-Way Analysis of Variance by Ranks test is advocated to calibrate voltage measurements at a bus in a power network. However, it was found that the Friedman test was only slightly more robust or resistant in the presence of discordant measurements than the classical F-test. The resistance of a statistical test is defined as the fraction of bad data necessary to switch a statistical conclusion. We mathematically derive the maximum resistance to rejection and to acceptance of the Friedman test, as well as the Brown-Mood test, and show that the Brown-Mood test has a higher maximum resistance to rejection and to acceptance than the Friedman test. In addition, we simulate the expected resistance to rejection and to acceptance of both tests and show that on average the Brown-Mood test is slightly more robust to rejection while on average the Friedman test is more robust to acceptance. / Ph. D.

Information retrieval is widely used for retrieving relevant information among a variety of data, such as text documents, images, audio and videos. Since the first medical batch retrieval system was developed in mid 1960s, significant research efforts have focused on applying information retrieval to medical data. However, despite the vast developments in medical information retrieval and accompanying technologies, the actual promise of this area remains unfulfilled due to properties of medical data and the huge volume of medical literature. Specifically, the recall and precision of the selected dataset from the TREC clinical decision support track are low. The overriding objective of this thesis is to improve the performance of information retrieval techniques applied to biomedical text documents. We have focused on improving recall and precision among the top retrieved results. To that end, we have removed redundant words, and then expanded queries by adding MeSH terms in TREC CDS topics. We have also used other external data sources and domain knowledge to implement the expansion. In addition, we have also considered using the doc2vec model to optimize retrieval. Finally, we have applied learning to rank which sorts documents based on relevance and put relevant documents in front of irrelevant documents, so as to return the relevant retrieved data on the top. We have discovered that queries, expanded with external data sources and domain knowledge, perform better than applying the TREC topic information directly. / Master of Science / Information retrieval is widely used for retrieving relevant information among a variety of data. Since the first medical batch retrieval system was developed in mid 1960s, significant research efforts have focused on applying information retrieval to medical data. However the actual promise of this area remains unfulfilled due to certain properties of medical data and the sheer volume of medical literature. The overriding objective of this thesis is to improve the performance of information retrieval techniques applied to biomedical text documents. This thesis presents several ways to implement query expansion in order to make more efficient retrieval. Then this thesis discusses some approaches to put documents relevant to the queries at the top.

Accelerated life tests (ALT) are appealing to practitioners seeking to maximize information gleaned from reliability studies, while navigating resource constraints due to time and specimen costs. A popular approach to accelerated life testing is to design test regimes such that experimental specimens are exposed to variable stress levels across time. Such ALT experiments allow the practitioner to observe lifetime behavior across various stress levels and infer product life at use conditions using a greater number of failures than would otherwise be observed with a constant stress experiment. The downside to accelerated life tests, however, particularly for those that utilize non-constant stress levels across time on test, is that the corresponding lifetime models are largely dependent upon assumptions pertaining to variant stress. Although these assumptions drive inference at product use conditions, little to no statistical methods exist for assessing their validity. One popular assumption that is prevalent in both literature and practice is the cumulative exposure model which assumes that, at a given time on test, specimen life is solely driven by the integrated stress history and that current lifetime behavior is path independent of the stress trajectory. This dissertation challenges such black box ALT modeling procedures and focuses on the cumulative exposure model in particular. For a simple strep-stress accelerated life test, using two constant stress levels across time on test, we propose a four-parameter Weibull lifetime model that utilizes a threshold parameter to account for the stress transition. To circumvent regularity conditions imposed by maximum likelihood procedures, we use median rank regression to fit and assess our lifetime model. We improve the model fit using a novel incorporation of desirability functions and ultimately evaluate our proposed methods using an extensive simulation study. Finally, we provide an illustrative example to highlight the implementation of our method, comparing it to a corresponding Bayesian analysis. / Ph. D. / Have you ever wondered how manufacturers determine the guaranteed lifetime warranty for the products they produce? From automotive showrooms to store shelves, consumer goods often have a unique story to tell, one involving meticulous research, engineered design, and statistically driven testing. This is the realm of accelerated life testing (ALT) where reliability engineers, in their e↵orts to estimate overall product life, subject test specimens to harsher conditions than what are expected under normal operating conditions. Ideally, ALT experiments will induce multiple failures in a short amount of time and provide a basis for statistical modeling to predict failure in the field. The problem with this, however, is that such experiments require many mathematical assumptions which describe the physics of failure. This dissertation challenges one of the most common assumptions used for ALT experiments when specimens are exposed to multiple stress levels. We develop an alternative approach to the analysis of ALT data which drops this assumption (referred to as cumulative exposure) and explore the statistical properties of our method. We find that our approach has many features which will appeal to practitioners who may wish to use our procedures as they seek to understand the data gleaned from ALT experiments. Overall, this work represents an important addition to the reliability practitioner’s toolbox and will allow researchers to avoid potentially dubious assumptions concerning real world behavior.

Une synchronicité existe entre l’apparition de l’atrophie musculaire et osseuse (ostéoporose) mais, très peu de groupes de recherche se sont intéressés à la possibilité qu’une voie de signalisation commune puisse contrôler simultanément ces tissus dans un contexte pathologique. Le but de cette thèse est de caractériser les rôles du sentier signalétique principal du remodelage osseux soit la voie RANK/RANKL/OPG, sur le muscle squelettique sain ou pathologique. Premièrement, nous avons démontré que RANK est exprimé dans le muscle squelettique et que son absence dans ce tissu induit un effet inotropique sur le muscle rapide extensor digitorum longus (EDL), limitant ainsi la perte de force maximale spécifique, tout en augmentant l'atrophie musculaire, la fatigabilité et la proportion de fibres rapides. Ensuite, nous avons montré qu’un blocage pharmacologique de la voie RANKL/RANK par l’OPG atténue la perte de la force musculaire de manière dose-dépendante et préserve l'intégrité musculaire, en particulier des muscles rapides EDL de souris dystrophiques. Cette étude nous a également permis de démontrer que l’OPG-Fc a un effet intéressant mais plus limité sur la préservation de la force du muscle lent soleus (Sol). Par contre, nous avons découvert que l’OPG-Fc potentialise les effets positifs d'une faible dose de formotérol, un membre de la famille des β2-agonistes, et leur combinaison restaure complètement la fonction du Sol des souris dystrophiques. Finalement, nous avons débuté une étude mécanistique sur l’effet protecteur de l’OPG-Fc sur le muscle squelettique dystrophique. Structurellement, l'OPG-Fc pleine longueur contient quatre domaines TNFR (RANKL), deux domaines de la mort cellulaire par apoptose (TRAIL) et un domaine lié à l'héparine. Nos résultats indiquent que les injections d'anti-RANKL, d’anti-TRAIL et d’OPG-Fc tronquée (possédant seulement les domaines TNFR) ou la suppression génétique de RANK dans le muscle sont nettement moins efficaces sur la préservation de la force des muscles dystrophiques que celles d’OPG-Fc pleine longueur. Étonnamment, l'absence de Ca2+ extracellulaire réduit considérablement les effets de l’OPG-Fc pleine longueur sur la force des muscles dystrophiques dans un modèle de contractilité in vitro. Nos analyses en microscopie confocale ont démontré que l’OPG-Fc pleine longueur pourrait se lier à un récepteur présentement non identifié localisé sur les myotubes et que cette liaison entraîne possiblement une activation d’une kinase liée aux intégrines (ILK) et la surexpression d’une pompe calcique ATPase du réticulum sarcoplasmique appelée SERCA-2a, un déterminant clé de la performance musculaire. Les myotubes traités à l'héparinase, une enzyme connue pour cliver les domaines de l'héparine ou encore l’inhibition de l’ILK réduit significativement la surexpression de SERCA-2a induite par l’OPG-Fc. Cette thèse apporte globalement, une meilleure compréhension des fonctions de RANK/RANKL/OPG dans le muscle squelettique dénervé ou dystrophique et s’inscrit dans la liste des travaux pré-cliniques qui pourrait éventuellement contribuer à l’élaboration de nouveaux traitements pour les maladies musculaires et osseuses. / Although there is an obvious dynamic cross-talk between muscle and bone, a common signalling pathway that efficiently and synchronously controls these tissues has barely been investigated in all forms of muscle diseases. The aim of this thesis is to characterize the roles of RANK/RANKL/OPG, key regulators of bone remodeling, on skeletal muscle atrophy, phenotype and dysfunction. Firstly, we show that RANK is expressed in skeletal muscle and that muscle RANK deletion has inotropic effects in denervated fast-twitch extensor digitorum longus (EDL) muscles, preventing on one side the loss of maximum specific force while promoting muscle atrophy and fatigability, and increasing the proportion of fast-twitch fibers. We next demonstrate that a pharmacological treatment of dystrophic mdx mice with recombinant full-length OPG-Fc mitigates the loss of muscle force in a dose-dependent manner and preserves muscle integrity, particularly in EDL muscles. We also found that the full-length OPG-Fc has limited effects on slow-twitch soleus (Sol) muscles. However OPG-Fc potentiates the positive effects of a low dose of formoterol, a member of β2-agonists, and completely restores the function of the Sol dystrophic muscles. Finally, we investigated the mechanism by which the full-length OPGFc protects the dystrophic muscles. Structurally, the OPG protein contains four TNFR domains (RANKL), two death domains ( TRAIL) and a heparin-binding region. Our results indicate that anti-RANKL or anti-TRAIL or truncated OPG treatments (only TNFR domains) or RANK deletion are much less effective in preserving the strength of dystrophic muscles than full-length OPG-Fc. Surprisingly, the absence of extracellular Ca2+ significantly reduces the effects of full-length OPG-Fc on the force production of dystrophic muscles when incubated in a physiological bath in vitro. Confocal microscopy images showed that the full-length OPG-Fc binds directly to myotubes through a receptor that is currently unidentified activating possibly integrin-linked kinase (ILK) which upregulates sarco/endoplasmic calcium ATPase pump (SERCA-2a) expression in C2C12 myotubes. Heparinase, which cleaves heparin and heparin sulphate proteoglycan, or an inhibitor of ILK activity abrogates OPG-induced SERCA-2a expression, suggesting that OPG through ILK upregulates SERCA-2a expression, a key determinant of muscle performance. Overall, this thesis shed some light on RANK/RANKL/OPG functions in skeletal muscle which will potentially contribute to the development of new treatments for several forms of muscle and bone diseases.

L’atrophie et les dysfonctions musculaires sont des problèmes courants et d’origines variées. À titre d’exemple l’alitement prolongé, le SIDA, les cancers, l’hypogravité et le vieillissement peuvent tous entraîner une perte de masse et de force musculaire. Malgré les coûts économiques et sociaux élevés, relativement peu d’efforts ont été investis dans la caractérisation des processus qui gouvernent l’atrophie/dysfonction musculaire et dans le développement de traitements plus efficaces. Conséquemment, cette thèse vise à approfondir les connaissances actuelles sur les mécanismes qui régulent l’atrophie/dysfonction et la récupération des muscles atrophiés par sous-utilisation. Tout d’abord, nous avons caractérisé l’impact des leucocytes impliqués lors de la remise en charge du muscle soléaire atrophié par hypogravité. Ainsi, nous avons démontré que les mastocytes étaient activés par la remise en charge et que leur dégranulation orchestrait le recrutement des neutrophiles et des monocytes/macrophages. Ensuite, nos recherches ont indiqué que l’activité des neutrophiles pouvait être régulée en fonction de leur microenvironnement et que leur présence dans les muscles atrophiés et inflammés n’était pas nécessairement associée à l’induction de dommages secondaires. Par la suite, nous avons établi que la présence des macrophages était importante pour permettre la récupération optimale de la force des muscles atrophiés. Nous avons également démontré que l’activité myogénique des macrophages pouvait être optimisée en favorisant leur phénotype anti-inflammatoire avec le facteur de croissance hématopoïétique « macrophage-colony stimulating factor » (M-CSF). Finalement, nous avons caractérisé l’impact du « receptor activator of NF-kB » (RANK) et de son ligand RANKL, une voie signalétique impliquée dans le remodelage osseux et l’ostéoporose, sur l’atrophie/dysfonction musculaire. Nous avons démontré qu’une déficience de RANK ou le blocage de RANKL par l’ostéoprotégérine protègent contre la perte de force des muscles dénervés ou dystrophiques. Ce phénomène est associé à des modifications dans l’expression des protéines favorisant une recaptation plus efficace du calcium. De plus, RANK participe à la reconversion des fibres rapides vers lentes durant la période de remise charge. Globalement, nos travaux permettent de mieux comprendre les mécanismes entourant l’atrophie, la croissance et les dysfonctions musculaires et ouvrent la voie à de nouvelles pistes de traitement pour plusieurs maladies neuro-musculaires. / Muscle atrophy and dysfunction are characterized by a loss of muscle mass and force, which are commonly found in many pathologies or conditions such as AIDS, cancers, chronic obstructive pulmonary diseases, cast immobilization, hypogravity, bed rest or aging, to name a few. Muscle atrophy/dysfunction have also very high social and economic costs, but very few laboratories have investigated the cellular and molecular mechanisms behind these muscular problems. The aim of this thesis is therefore to enhance our understanding of different mechanisms governing muscle atrophy/dysfunction and regrowth by using different models of disuse and dystrophy. Thus, we have initially explored the roles of different leucocytes in atrophied and reloaded soleus muscle. Firstly, we looked at the role of mast cells and showed that the mechanical stress associated with muscle reloading is able to stimulate mast cell degranulation, which orchestrates the recruitment of neutrophils and monocytes/macrophages. Secondly, our experiments revealed that neutrophil activity is adaptable and that neutrophil-induced tissue damage is dependent on the microenvironment. In atrophied and reloaded muscles, the presence of neutrophils is not associated with secondary damage or promotion of muscle recovery. Thirdly, we demonstrated that the presence of macrophages is essential for optimal muscle force recovery from atrophy. Fourthly, we showed that the macrophage-colony stimulating factor (M-CSF) promote the myogenic activity of macrophages by stimulating their anti-inflammatory phenotype. Finally, we investigated the impact of the receptor activator of NF-kB (RANK) and its ligand RANKL, a signalling pathway involved in bone remodelling and osteoporosis, on muscle atrophy and dysfunction. Our results showed that the specific deletion of RANK in the muscle or the blockage of RANKL with osteoprotegerin increased significantly force production in denervated and dystrophic muscles. These results were associated with various modifications in calcium handling protein expression favouring efficient calcium uptake. Moreover, we also demonstrated that RANK activation gives preference to the reconversion from fast-to-slow muscle fibers following hindlimb unloading/reloading. Overall, our results bring a better understanding of different mechanisms related to muscle atrophy, dysfunction and regrowth and potentially open new avenues for the treatment of several debilitating skeletal muscle conditions.

Network alignment is the problem of finding a common subgraph between two graphs, and more generally <i>k </i>graphs. The results of network alignment are often used for information transfer, which makes it a powerful tool for deducing information or insight about networks. Network alignment is tightly related to the subgraph isomorphism problem which is known to be NP-hard, this makes the network alignment problem supremely hard in practice. Some algorithms have been devised to approach it via solving a form of a relaxed version of the NP-hard problem or by defining certain heuristic measures. These algorithms normally work well for problems when there is some form of prior known similarity between the nodes of the graphs to be aligned. The absence of such information makes the problem more challenging. In this scenario, these algorithms would often require much more time to finish executing, and even fail sometimes. The version of network alignment that this thesis tackles is the one when such prior similarity measures are absent. In this thesis, we address three versions of network alignment: (i) multimoal network alignment, (ii) standard pairwise network alignment, and (iii) multiple network alignment. A key common component of the algorithms presented in this thesis is exploiting a low rank structure in the network alignment problem and thus producing algorithms that run much faster than classic network alignment algorithms.

Neste trabalho propomos gráficos de controle tipo CUSUM para monitoramento de tempos de sobrevivência. Nossa proposta é desenvolver diferentes estatísticas para o escore do gráfico CUSUM de forma prospectiva. Inicialmente propomos um gráfico CUSUM não paramétrico para monitoramento de populações homogêneas que avalia a variação na estatística log-rank como forma de identificar se há uma mudança significativa no risco de falha ao longo do tempo. Algumas abordagens diferentes foram consideradas e em destaque colocamos o gráfico ZDiff CUSUM, que tem como escore o incremento na estatística Z do teste log-rank em relação à inspeção anterior. Foi constatado, via simulação, que este método é eficiente. Posteriormente investigamos abordagens que levam em conta heterogeneidade na população por meio do modelo de Cox, considerando medidas baseadas na razão de verossimilhanças e em resíduos martingal e deviance. Através de simulações, verificou-se que o método com base na razão de verossimilhanças se mostrou ágil para detectar alteração na taxa de falha, quando se conhece a intensidade da mudança e este valor é informado na construção do teste. Por outro lado, os gráficos CUSUM com base em resíduos são mais simples e se mostraram eficazes para identificar aumentos no padrão da sobrevivência. Estes três métodos e o ZDiff CUSUM foram aplicados a dados de um estudo conduzido no Instituto do Coração (InCor) envolvendo pacientes com insuficiência cardíaca. Foi detectado que ao longo do tempo estes pacientes apresentam sobrevida maior, o que pode estar ligado à melhoria no tratamento e procedimentos realizados no hospital. Como conclusão, sugerimos que os gráficos tipo CUSUM com resíduos do modelo de Cox e o método não paramétrico com teste log-rank podem ser alternativas para utilização na prática em monitoramento de dados de sobrevivência. / In this work we propose CUSUM control charts to monitor survival times. Our proposal is to develop different statistics for the CUSUM chart score in a prospective way, to take into account SA approaches. We initially consider a non-parametric approach to monitor homogeneous populations. This CUSUM evaluates the variation on the log-rank test statistics as a way to identify significant changes in the risk of failure. Some different expressions for this have been considered and, in particular, we propose a ZDiff CUSUM chart computed as the increment on the log-rank test statistics Z at each inspection point in relation to the previous one. Based on simulation studies it was found that this method is efficient. Subsequently we investigated approaches that take into account heterogeneity in the population through the Cox model, considering measures based on the likelihood ratio and on martingal and deviance residuals. Through simulations, it was verified that the method based on the likelihood ratio was agile to detect a change in the hazard rate, when the intensity of the change is known and this value is informed in the construction of the test. On the other hand, CUSUM methods based on residuals are simpler and have been shown to be effective in identifying increases in survival pattern. These three methods and the ZDiff CUSUM were applied to a dataset from a study conducted at the Heart Institute (InCor) on patients with heart failure. It has been found that, over time, these patients have greater survival, which may be linked to improved treatment and procedures performed at the hospital. As a conclusion, we suggest that the CUSUM methods based on Cox model residuals and the nonparametric method on the log-rank test may be alternatives for practice in monitoring survival data.