Thesis (Ph.D.)--McMaster University, 2005. / Supervisor: John C. Wilson. Includes bibliographical references (leaves 299-310).

Computational gene regulation models provide a means for scientists to draw biological inferences from large-scale gene expression data. The expression data used in the models usually are obtained in a time series in response to an initial perturbation. The common objective is to reverse engineer the internal structure and function of the genetic network from observing and analyzing its output in a time-based fashion. In many studies (Wang [39], Resendis-Antonio [31]), each gene is considered to have a regulatory effect on another gene. A network association is created based on the correlation of expression data. Highly correlated genes are thought to be co-regulated by similar (if not the same) mechanism. Gene co-regulation network models disregard the cascading effects of regulatory genes such as transcription factors, which could be missing in the expression data or are expressed at very low concentrations and thus undetectable by the instrument. As an alternative to the former methods, some authors (Wu et al. [40], Rangel et al. [28], Li et al. [20]) have proposed treating expression data solely as observation values of a state-space system and derive conceptual internal regulatory elements, i.e. the state-variables, from these measurements. This approach allows one to model unknown biological factors as hidden variables and therefore can potentially reveal more complex regulatory relations.<p>In a preliminary portion of this work, two state-space models developed by Rangel et al. and Wu et al. respectively were compared. The Rangel model provides a means for constructing a statistically reliable regulatory network. The model is demonstrated on highly replicated Tcell activation data [28]. On the other hand, Wu et al. develop a time-delay module that takes transcriptional delay dynamics into consideration. The model is demonstrated on non-replicated yeast cell-cycle data [40]. Both models presume time-invariant expression data. Our attempt to use the Wu model to infer small gene regulatory network in yeast was not successful. Thus we develop a new modeling tool incorporating a time-lag module and a novel method for constructing regulatory networks from non-replicated data. The latter involves an alternative scheme for determining network connectivity. Finally, we evaluate the networks generated from the original and extended models based on a priori biological knowledge.

Computational gene regulation models provide a means for scientists to draw biological inferences from large-scale gene expression data. The expression data used in the models usually are obtained in a time series in response to an initial perturbation. The common objective is to reverse engineer the internal structure and function of the genetic network from observing and analyzing its output in a time-based fashion. In many studies (Wang [39], Resendis-Antonio [31]), each gene is considered to have a regulatory effect on another gene. A network association is created based on the correlation of expression data. Highly correlated genes are thought to be co-regulated by similar (if not the same) mechanism. Gene co-regulation network models disregard the cascading effects of regulatory genes such as transcription factors, which could be missing in the expression data or are expressed at very low concentrations and thus undetectable by the instrument. As an alternative to the former methods, some authors (Wu et al. [40], Rangel et al. [28], Li et al. [20]) have proposed treating expression data solely as observation values of a state-space system and derive conceptual internal regulatory elements, i.e. the state-variables, from these measurements. This approach allows one to model unknown biological factors as hidden variables and therefore can potentially reveal more complex regulatory relations.<p>In a preliminary portion of this work, two state-space models developed by Rangel et al. and Wu et al. respectively were compared. The Rangel model provides a means for constructing a statistically reliable regulatory network. The model is demonstrated on highly replicated Tcell activation data [28]. On the other hand, Wu et al. develop a time-delay module that takes transcriptional delay dynamics into consideration. The model is demonstrated on non-replicated yeast cell-cycle data [40]. Both models presume time-invariant expression data. Our attempt to use the Wu model to infer small gene regulatory network in yeast was not successful. Thus we develop a new modeling tool incorporating a time-lag module and a novel method for constructing regulatory networks from non-replicated data. The latter involves an alternative scheme for determining network connectivity. Finally, we evaluate the networks generated from the original and extended models based on a priori biological knowledge.

Thesis (Ph. D.)--University of Texas at Austin, 2001. / Vita. Includes bibliographical references (leaves 117-128). Available also in a digital version from Dissertation Abstracts.

No description available.

The State Space Model (SSM) encompasses the class of multivariate linear models, in particular, regression models with fixed, time-varying and random parameters, time series models, unobserved components models and combinations thereof. The well-known Kalman Filter (KF) provides a unifying tool for conducting statistical inferences with the SSM. A major practical problem with the KF concerns its initialization when either the initial state or the regression parameter (or both) in the SSM are diffuse. In these situations, it is common practice to either apply the KF to a transformation of the data which is functionally independent of the diffuse parameters or else initialize the KF with an arbitrarily large error covariance matrix. However neither approach is entirely satisfactory. The data transformation required in the first approach can be computationally tedious and furthermore it may not preserve the state space structure. The second approach is theoretically and numerically unsound. Recently however, De Jong (1991) has developed an extension of the KF, called the Diffuse Kalman Filter (DKF) to handle these diffuse situations. The DKF does not require any data transformation. The thesis contributes further to the theoretical and computational aspects of con ducting statistical inferences using the DKF. First, we demonstrate the appropriate initialization of the DKF for the important class of time-invariant SSM’s. This result is useful for maximum likelihood statistical inference with the SSM. Second, we derive and compare alternative pseudo-likelihoods for the diffuse SSM. We uncover some interesting characteristics of the DKF and the diffuse likelihood with the class of ARMA models. Third, we propose an efficient implementation of the DKF, labelled the collapsed DKF (CDKF). The latter is derived upon sweeping out some columns of the pertinent matrices in the DKF after an initial number of iterations. The CDKF coincides with the KF in the absence of regression effects in the SSM. We demonstrate that in general the CDKF is superior in practicality and performance to alternative algorithms proposed in the literature. Fourth, we consider maximum likelihood estimation in the SSM using an EM (Expectation-Maximization) approach. Through a judicious choice of the complete data, we develop an CDKF-EM algorithm which does not require the evaluation of lag one state error covariance matrices for the most common estimation exercise required for the SSM, namely the estimation of the covariance matrices of the disturbances in the SSM. Last we explore the topic of diagnostic testing in the SSM. We discuss and illustrate the recursive generation of residuals and the usefulness of the latters in pinpointing likely outliers and points of structural change.

The State Space Model (SSM) encompasses the class of multivariate linear models, in particular, regression models with fixed, time-varying and random parameters, time series models, unobserved components models and combinations thereof. The well-known Kalman Filter (KF) provides a unifying tool for conducting statistical inferences with the SSM. A major practical problem with the KF concerns its initialization when either the initial state or the regression parameter (or both) in the SSM are diffuse. In these situations, it is common practice to either apply the KF to a transformation of the data which is functionally independent of the diffuse parameters or else initialize the KF with an arbitrarily large error covariance matrix. However neither approach is entirely satisfactory. The data transformation required in the first approach can be computationally tedious and furthermore it may not preserve the state space structure. The second approach is theoretically and numerically unsound. Recently however, De Jong (1991) has developed an extension of the KF, called the Diffuse Kalman Filter (DKF) to handle these diffuse situations. The DKF does not require any data transformation. The thesis contributes further to the theoretical and computational aspects of con ducting statistical inferences using the DKF. First, we demonstrate the appropriate initialization of the DKF for the important class of time-invariant SSM’s. This result is useful for maximum likelihood statistical inference with the SSM. Second, we derive and compare alternative pseudo-likelihoods for the diffuse SSM. We uncover some interesting characteristics of the DKF and the diffuse likelihood with the class of ARMA models. Third, we propose an efficient implementation of the DKF, labelled the collapsed DKF (CDKF). The latter is derived upon sweeping out some columns of the pertinent matrices in the DKF after an initial number of iterations. The CDKF coincides with the KF in the absence of regression effects in the SSM. We demonstrate that in general the CDKF is superior in practicality and performance to alternative algorithms proposed in the literature. Fourth, we consider maximum likelihood estimation in the SSM using an EM (Expectation-Maximization) approach. Through a judicious choice of the complete data, we develop an CDKF-EM algorithm which does not require the evaluation of lag one state error covariance matrices for the most common estimation exercise required for the SSM, namely the estimation of the covariance matrices of the disturbances in the SSM. Last we explore the topic of diagnostic testing in the SSM. We discuss and illustrate the recursive generation of residuals and the usefulness of the latters in pinpointing likely outliers and points of structural change. / Business, Sauder School of / Graduate

A six-degree-ofreedom piecewise simulation of aircraft motion is developed in SIMULINK. Using a mathematical model of fixed-wing aircraft, the simulation is used to observe the longitudinal and lateral-directional motions of the aircraft following a pilot input. The mathematical model is in state-space form and uses aircraft stability and control derivatives calculated from the aircraft geometric and aerodynamic characteristics. The simulation takes into account the changed speed and altitude due to pilot input and demonstrates the non-linearity of the aircraft motion due to change in speed and altitude. The results from the simulation are compared with the known results to validate the mathematical model used. The simulation is carried out for a number of airspeed and altitude combinations to examine the effect of changing speed and altitude on the aircraft dynamic response.

Probabilistic models are dominant in many research areas. To learn those models we need to find a way to determine parameters of distributions over variables which are included in the model. The main focus of my research is related to continuous variables. Thus, Gaussian distribution over variables is the most dominant factor in all models used in this document. I have been working on different and important real-life problems such as Uncertainty of Neural Network Based Aerosol Retrieval, Regression Learning with Multiple Noise Oracles and Model Predictive Control (MPC) for Sepsis Treatment, Clustering Causes of Action in Federal Courts. These problems will be discussed in the following chapters. Aerosols, small particles emanating from natural and man-made sources, along with green house gases have been recognized as very important factors in ongoing climate changes. Accurate estimation of aerosol composition and concentration is one of the main challenges in current climate research. Algorithm for prediction of aerosol designed by domain scientists does not provide quantitative information about aerosol estimation uncertainty. We deployed algorithm which uses neural networks to determine both uncertainty and the estimation of the aerosol. The uncertainty estimator has been built under an assumption that uncertainty is a function of variables used for aerosol prediction. Also, the uncertainty of predictions has been computed as the variance of the conditional distribution of targets given the input data. In regression learning, it is often difficult to obtain the true values of the label variables, while multiple sources of noisy estimates of lower quality are readily available. To address this problem, I propose a new Bayesian approach that learns a regression model from a data with noisy labels which are provided by multiple oracles. This method gives closed form solution for model parameters and it is applicable to both linear and nonlinear regression problems. Sepsis is a medical condition characterized as a systemic inflammatory response to an infection. High mortality rate (30-35%) of septic patients is usually caused by inadequate treatment. Thus, development of tools that can aid clinicians in designing optimal strategies for inflammation treatments is of utmost importance. Towards this objective I developed a data driven approach for therapy optimization where a predictive model for patients' behavior is learned directly from historical data. As such, the predictive model is incorporated into a model predictive control optimization algorithm to find optimal therapy, which will lead the patient to a healthy state. A more careful targeting of specific therapeutic strategies to more biologically homogeneous groups of patients is essential to developing effective sepsis treatment. We propose a kernel-based approach to characterize dynamics of inflammatory response in a heterogeneous population of septic patients. The method utilizes Linear State Space Control (LSSC) models to take into account dynamics of inflammatory response over time as well as the effect of therapy applied to the patient. We use a similarity measure defined on kernels of LSSC models to find homogeneous groups of patients. In addition to clustering of dynamics of inflammatory response we also explored a clustering of civil litigation from its inception by examining the content of civil complaints. We utilize spectral cluster analysis on a newly compiled federal district court dataset of causes of action in complaints to illustrate the relationship of legal claims to one another, the broader composition of lawsuits in trial courts, and the breadth of pleading in individual complaints. Our results shed light not only on the networks of legal theories in civil litigation but also on how lawsuits are classified and the strategies that plaintiffs and their attorneys employ when commencing litigation. / Computer and Information Science

Harmonic domain models have been developed for Thyristor Controller Reactors (TCR) and other power electronic devices. Recently, these models have been extended to describe not just the steady-state harmonic interactions but harmonic transients as well. However, these dynamic models consistently do not incorporate models for controls. On the other hand, for the TCR as a FACTS Controller, dynamic models are available in which only the fundamental frequency component of the Controller is included; excluding harmonic interactions presumes that these do not affect the dynamics of the Controller. This thesis describes the development of a Harmonic State Space (HSS) model of a three phase TCR. As an extended state space description, this model describes the dynamics of the Controller while capturing harmonic interactions. It also includes the effect of switching instant variation which significantly improves the effectiveness of the model and allows the controller feedback characteristics to be included. The result of this model was validated with a purely time-domain simulation in PSCAD/EMTDC. Using the HSS to model a power system with TCR, it is illustrated that harmonic interactions play a significant role in the dynamics of the system. It is observed that for the specific system analysed, the least-damped pole-pair which dominates the dynamics of the system is associated with the 5th harmonic. Failure to include interactions with this specific harmonic produces an inaccurate dynamic description. Preliminary to the development of HSS model, a linearised harmonic domain model of a TCR which establishes the harmonic interactions across the device is also developed. Results of this model are validated with a time-domain simulation. This characterisation paves the way for a reduced harmonic state space model that is used in the HSS model. The principles and procedures established in this thesis can be applied to the development of models for other FACTS Controllers or HVDC links.