How can we evaluate and design integrated photonic circuit performance systematically? Can active photonic circuits be controlled for optimized performance? This work uses control theory to analyze, design, and optimize photonic integrated circuits based on versatile semiconductor optical amplifiers (SOAs). Control theory provides a mathematically robust set of tools for system analysis, design, and control. Although control theory is a rich and well-developed field, its application to the analysis and design of photonic circuits is not widespread. Following control theoretic methods already used for fibreline systems we derive three interrelated state-space models: a core photonic model, a photonic model with gain compression, and a equivalent circuit optoelectronic model. We validate each model and calibrate the gain compression model by pump/probe experiments. We then linearize the state-space models to design and analyze SOA controllers. We apply each linearized model to proof-of-concept SOA control applications such as suppressing interchannel crosstalk and regulating output power. We demonstrate the power of linearized state-space models in controller design and stability analysis. To illustrate the importance of using the complete equivalent circuit model in controller design, we demonstrate an intuitive bias-current controller that fails due to the dynamics of the intervening parasitic circuitry of the SOA. We use the linearized state-space models to map a relationship between feedback delay and controller strength for stable operation, and demonstrate that SOAs pose unusual control difficulties due to their ultrafast dynamics. Finally, we leverage the linearized models to design a novel and successful hybrid controller that uses one SOA to control another via feedback (for reliability) and feedforward (for speed) control. The feedback controller takes full advantage of the equivalent circuit modelling by sampling the voltage of the controlled SOA and using the error to drive the bias current of the controller SOA. Filtering in the feedback path is specified by transfer function analysis. The feedforward design uses a novel application of the linearized models to set the controller bias points correctly. The modelling and design framework we develop is entirely general and opens the way to the robust optoelectronic control of integrated photonic circuits.

Research in the areas of target detection, tracking, and geo-location is most important for enabling an unmanned aerial vehicle (UAV) platform to autonomously execute a mission or task without the need for a pilot or operator. Small-class UAVs and video camera sensors complemented with "soft sensors" realized only in software as a combination of a priori knowledge and sensor measurements are called upon to replace the cumbersome precision sensors on-board a large class UAV. The objective of this research is to develop a geo-location solution for use on-board multiple UAVs with mounted video camera sensors only to accurately geo-locate and track a target. This research introduces an estimation solution that combines the power of the particle filter with the utility of the video sensor as a general solution for passive target geo-location on-board multiple UAVs. The particle filter is taken advantage of, with its ability to use all of the available information about the system model, system uncertainty, and the sensor uncertainty to approximate the statistical likelihood of the target state. The geo-location particle filter is tested online and in real-time in a simulation environment involving multiple UAVs with video cameras and a maneuvering ground vehicle as a target. Simulation results show the geo-location particle filter estimates the target location with a high accuracy, the addition of UAVs or particles to the system improves the location estimation accuracy with minimal addition of processing time, and UAV control and trajectory generation algorithms restrict each UAV to a desired range to minimize error.

Model diagnostics for normal and non-normal state space models is based on recursive residuals which are defined from the one-step ahead predictive distribution. Routine calculation of these residuals is discussed in detail. Various tools of diagnostics are suggested to check e.g. for wrong observation distributions and for autocorrelation. The paper also covers such topics as model diagnostics for discrete time series, model diagnostics for generalized linear models, and model discrimination via Bayes factors. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

In this study, we have developed a dense La0.85Sr0.15MnO3-δ (LSM) Ce0.9Gd0.1O1.95 (GDC) composite electrode system for studying the surface modification of cathodes. The LSM and GDC grains in the composite were well defined and distinguished using energy dispersive x-ray (EDX) analysis. The specific three-phase boundary (TPB) length per unit electrode surface area was systematically controlled by adjusting the LSM to GDC volume ratio of the composite from 40% up to 70%. The TPB length for each tested sample was determined through stereological techniques and used to correlate the cell performance and degradation with the specific TPB length per unit surface area. An overlapping spheres percolation model was developed to estimate the activity of the TPB lines on the surface of the dense composite electrodes developed. The model suggested that the majority of the TPB lines would be active and the length of those lines maximized if the volume percent of the electrolyte material was kept in the range of 47 57%. Additionally, other insights into the processing conditions to maximize the amount of active TPB length were garnered from both the stereology calculations and the percolation simulations. Steady-state current voltage measurements as well as electrochemical impedance measurements on numerous samples under various environmental conditions were completed. The apparent activation energy for the reduction reaction was found to lie somewhere between 31 kJ/mol and 41 kJ/mol depending upon the experimental conditions. The exchange current density was found to vary with the partial pressure of oxygen differently over two separate regions. At relatively low partial pressures, i0 had an approximately dependence and at relatively high partial pressures, i0 had an approximately dependence. This led to the conclusion that a change in the rate limiting step occurs over this range. A method for deriving the electrochemical properties from proposed reaction mechanisms was also presented. State-space modeling was used as it is a robust approach to addressing these particular types of problems due to its relative ease of implementation and ability to efficiently handle large systems of differential algebraic equations. This method combined theoretical development with experimental results obtained previously to predict the electrochemical performance data. The simulations agreed well the experimental data and allowed for testing of operating conditions not easily reproducible in the lab (e.g. precise control and differentiation of low oxygen partial pressures).

Despite their success and widespread usage in industry and business, ES methods have received little attention from the statistical community. We investigate three types of statistical models that have been found to underpin ES methods. They are ARIMA models, state space models with multiple sources of error (MSOE), and state space models with a single source of error (SSOE). We establish the relationship among the three classes of models and conclude that the class of SSOE state space models is broader than the other two and provides a formal statistical foundation for ES methods. To better understand ES methods, we investigate the behaviors of ES methods for time series generated from different processes. We mainly focus on time series of ARIMA type. ES methods forecast a time series using only the series own history. To include covariates into ES methods for better forecasting a time series, we propose a new forecasting method, Exponential Smoothing with Covariates (ESCov). ESCov uses an ES method to model what left unexplained in a time series by covariates. We establish the optimality of ESCov, identify SSOE state space models underlying ESCov, and derive analytically the variances of forecasts by ESCov. Empirical studies show that ESCov outperforms ES methods and regression with ARIMA errors. We suggest a model selection procedure for choosing appropriate covariates and ES methods in practice. Computer models have been commonly used to investigate complex systems for which physical experiments are highly expensive or very time-consuming. Before using a computer model, we need to address an important question ``How well does the computer model represent the real system?" The process of addressing this question is called computer model validation that generally involves the comparison of computer outputs and physical observations. In this thesis, we propose a Bayesian approach to computer model validation. This approach integrates together computer outputs and physical observation to give a better prediction of the real system output. This prediction is then used to validate the computer model. We investigate the impacts of several factors on the performance of the proposed approach and propose a generalization to the proposed approach.

In this study, neutral real interest rate gap and output gap are estimated jointly under two different multivariate unobserved components models with the motivation to provide empirical measures that can be used to analyze the amount of stimulus that monetary policy is passing on to the economy, and to understand historical macroeconomic developments. In the analyses, Kalman filter technique is applied to a small-scale macroeconomic model of the Turkish economy to estimate the unobserved variables for the period 1989-2005. In addition, two alternative specifications for neutral real interest rate are used in the analyses. The first model uses a random walk model for the neutral real interest rate, whereas the second one employs more structural specification, which specifically links the neutral real rate with the trend growth rate and the long-term course of the risk premium. Comparison of the models developed by using various performance criteria clearly indicates the use of more structural specification against random walk specification. Results suggest that though there is relatively high uncertainty surrounding the neutral real interest rate estimates to use them directly in the policy-making process, estimates appear to be very useful for ex-post monetary policy evaluations.

We study two classes of stochastic systems, the limited processor sharing system and the multi-server system. They share the common feature that multiple jobs/customers are being processed simultaneously, which makes the study of them intrinsically difficult. In the limited processor sharing system, a limited number of jobs can equally share a single server, and the excess ones wait in a first-in-first-out buffer. The model is mainly motivated by computer related applications, such as database servers and packet transmission over the Internet. This model is studied in the first part of the thesis. The multi-server queue is mainly motivated by call centers, where each customer is handled by an agent. The number of customers being served at any time is limited by number of agents employed. Customers who can not be served upon arrival wait in a first-in-first-out buffer. This model is studied in the second part of the thesis.

The present work introduces a methodology to obtain a discrete time state space representation of an electrical network using the nodal [G] matrix of the Electromagnetic Transients Program (EMTP) solution. This is the first time the connection between the EMTP nodal analysis solution and a corresponding state-space formulation is presented. Compared to conventional state space solutions, the nodal EMTP solution is computationally much more efficient. Compared to the phasor solutions used in transient stability analysis, the proposed approach captures a much wider range of eigenvalues and system operating states. A fundamental advantage of extracting the system eigenvalues directly from the EMTP solution is the ability of the EMTP to follow the characteristics of nonlinearities. The system's trajectory can be accurately traced and the calculated eigenvalues and eigenvectors correctly represent the system's instantaneous dynamics. In addition, the algorithm can be used as a tool to identify network partitioning subsystems suitable for real-time hybrid power system simulator environments, including the implementation of multi-time scale solutions. The proposed technique can be implemented as an extension to any EMTP-based simulator. Within our UBC research group, it is aimed at extending the capabilities of our real-time PC-cluster Object Virtual Network Integrator (OVNI) simulator.

In recent years, trade activity in stock markets has increased substantially. This is mainly attributed to the development of powerful computers and intranets connecting traders to markets across the globe. The trades have to be carried out almost instantaneously and the systems in place that handle trades are burdened with millions of transactions a day, several thousand a minute. With increasing transactions the time to execute a single trade increases, and this can be seen as an impact on the performance. There is a need to model the performance of these systems and provide forecasts to give a heads up on when a system is expected to be overwhelmed by transactions. This was done in this study, in cooperation with Cinnober Financial Technologies, a firm which provides trading solutions to stock markets. To ensure that the models developed weren‟t biased, the dataset was cleansed, i.e. operational and other transactions were removed, and only valid trade transactions remained. For this purpose, a descriptive analysis of time series along with change point detection and LOESS regression were used. State space model with Kalman Filtering was further used to develop a time varying coefficient model for the performance, and this model was applied to make forecasts. Wavelets were also used to produce forecasts, and besides this high pass filters were used to identify low performance regions. The State space model performed very well to capture the overall trend in performance and produced reliable forecasts. This can be ascribed to the property of Kalman Filter to handle noisy data well. Wavelets on the other hand didn‟t produce reliable forecasts but were more efficient in detecting regions of low performance.

To understand the processes affecting the abundance of wild populations is a fundamental goal of ecology and a prerequisite for the management of living resources. Variable abundance, however, makes the investigation of ecological processes challenging. Recruitment, the process whereby new individuals enter a given stage of a ?sh population, is a highly variable entity. I have confronted this issue by developing methodologies speci?cally designed to account for, and ecologically interpret, patterns of variability in recruitment. To provide the necessary context, Chapter 2 begins with a review of the history of recruitment science. I focus on the major achievements as well as present limitations, particularly regarding environmental drivers. Approaches that include explicit environmental information are contrasted with time-varying parameter techniques. In Chapter 3, I ask what patterns of variability in pre-recruit survival can tell us about the strength of density-dependent mortality. I provide methods to investigate the presence of density-dependent mortality where this has previously been hindered by highly variable data. Stochastic density-independent variability is found to be attenuated via density dependence. Sources of recruitment variability are further partitioned in Chapter 4. Using time-varying parameter techniques, signi?cant temporal variation in the annual reproductive rate is found to have occurred in many Atlantic cod populations. Multivariate state space models suggest that populations in close proximity typically have a shared response to environmental change whereas marked differences occur across latitude. Hypotheses that could result in consistent changes in productivity of cod populations are tested in Chapter 5. I focus on a meta-analytical investigation of potential interactions between Atlantic cod and small pelagic species, testing aspects of the cultivation-depensation hypothesis. The ?ndings suggest that predation or competition by herring and mackerel on egg and larval cod could delay recovery of depleted cod populations. Chapter 6 concludes with a critical re?ection on: the suitability of the theories employed, the underlying assumptions of the empirical approaches, and the quality of the data used in my thesis. Application of ecological insights to ?sheries management is critically evaluated. I then propose future work on recruitment processes based on methods presented herein.