▼ The main idea of this thesis is to define and formulate the role of cognitive control in cognitive dynamic systems and complex networks in order to control the directed flow of information. A cognitive dynamic system is based on Fuster's principles of cognition, the most basic of which is the so-called global perception-action cycle, that the other three build on. Cognitive control, by definition, completes the executive part of this important cycle. In this thesis, we first provide the rationales for defining cognitive control in a way that it suits engineering requirements. To this end, the novel idea of entropic state and thereby the two-state model is first described. Next, on the sole basis of entropic state and the concept of directed information flow, we formulate the learning algorithm as the first process of cognitive control. Most importantly, we show that the derived algorithm is indeed a special case of the celebrated Bellman's dynamic programming. Another significant key point is that cognitive control intrinsically differs from the generic dynamic programming and its approximations (commonly known as reinforcement learning) in that it is stateless by definition. As a result, the main two desired characteristics of the derived algorithm are described as follows: a) it is convergent to optimal policy, and b) it is free of curse of dimensionality. Next, the predictive planning is described as the second process of cognitive control. The planning process is on the basis of shunt cycles (called mutually composite cycles herein) to bypass the environment and facilitate the prediction of future global perception-action cycles. Our results demonstrate predictive planning to have a very significant improvement to the functionality of cognitive control. We also deploy the explore/exploit strategy in order to apply a simplistic form of executive attention. The thesis is then expanded by applying cognitive control into two different applications of practical importance. The first one involves cognitive tracking radar, which is based on a benchmark example and provides the means for testing the theory. In order to have a frame of reference, the results are compared to other cognitive controllers, which use traditional Q-learning and the method of dynamic optimization. In both cases, the new algorithm demonstrates considerable improvement with less computational load. For the second application, the problem of observability in stochastic complex networks has been picked due to its importance in many practical situations. Having known cognitive control theory and its significant performance, the idea here is to view the network as the environment of a cognitive dynamic system; thereby, cognitive dynamic system with the cognitive controller plays a supervisory role over the network. The proposed methodology differs from the state-of-the-art in the literature in two accounts: 1) stochasticity both in modelling as well as monitoring processes, and 2) complexity in terms of edge density. We present several… Advisors/Committee Members: HAYKIN, SIMON, Computational Engineering and Science.

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We propose two efficient automatic differentiation (AD) schemes to compute incrementally Taylor series and System Jacobian for solving differential-algebraic equations (DAEs) by Taylor series. Our schemes are based on topological ordering of a DAE's computational graph and then partitioning the topologically sorted nodes using structural information obtained from the DAE. Solving a DAE by Taylor series is carried out in stages. From one stage to another, partitions of the computational graph are incrementally activated so that we can reuse Taylor coefficients and gradients computed in previous stages. As a result, the computational complexity of evaluating a System Jacobian is independent of the number of stages. We also develop a common subexpression elimination (CSE) method to build a compact computational graph through operator overloading. The CSE method is of linear time complexity, which makes it suitable as a preprocessing step for general operator overloaded computing. By applying CSE, all successive overloaded computation can save time and memory. Furthermore, the computational graph of a DAE reveals its internal sparsity structure. Based on it, we devise an algorithm to propagate gradients in the forward mode of AD using compressed vectors. This algorithm can save both time and memory when computing the System Jacobian for sparse DAEs. We have integrated our approaches into the \daets solver. Computational results show multiple-fold speedups against two popular AD tools, \FAD~and ADOL-C, when solving various sparse and dense DAEs.

Thesis

Master of Science (MSc)

Advisors/Committee Members: Nedialkov, Nedialko, Computational Engineering and Science.

▼ Researchers conduct life testing on objects of interest in an attempt to determine their life distribution as a means of studying their reliability (or survivability). Determining the life distribution of the objects under study helps manufacturers to identify potential faults, and to improve quality. Researchers sometimes conduct accelerated life tests (ALTs) to ensure that failure among the tested units is earlier than what could result under normal operating (or environmental) conditions. Moreover, such experiments allow the experimenters to examine the effects of high levels of one or more stress factors on the lifetimes of experimental units. Examples of stress factors include, but not limited to, cycling rate, dosage, humidity, load, pressure, temperature, vibration, voltage, etc. A special class of ALT is step-stress accelerated life testing. In this type of experiments, the study sample is tested at initial stresses for a given period of time. Afterwards, the levels of the stress factors are increased in agreement with prefixed points of time called stress-change times. In practice, time and resources are limited; thus, any experiment is expected to be constrained to a deadline which is called a termination time. Hence, the observed information may be subjected to Type-I censoring. This study discusses maximum likelihood inferential methods for the parameters of multiple step-stress models from a generalized Birnbaum-Saunders distribution under time constraint alongside other inference-related problems. A couple of general inference frameworks are studied; namely, the observed likelihood (OL) framework, and the expectation-maximization (EM) framework. The last-mentioned framework is considered since there is a possibility that Type-I censored data are obtained. In the first framework, the scoring algorithm is used to get the maximum likelihood estimators (MLEs) for the model parameters. In the second framework, EM-based algorithms are utilized to determine the required MLEs. Obtaining observed information matrices under both frameworks is also discussed. Accordingly, asymptotic and bootstrap-based interval estimators for the model parameters are derived. Model discrimination within the considered generalized Birnbaum-Saunders distribution is carried out by likelihood ratio test as well as by information-based criteria. The discussed step-stress models are illustrated by analyzing three real-life datasets. Accordingly, establishing optimal multiple step-stress test plans based on cost considerations and three optimality criteria is discussed. Since maximum likelihood estimators are obtained by numerical optimization that involves maximizing some objective functions, optimization methods used, and their software implementations in R are discussed. Because of the computational aspects are in focus in this study, the benefits of parallel computing in R, as a high-performance computational approach, are briefly addressed. Numerical examples and Monte Carlo simulations are used to illustrate and to evaluate the… Advisors/Committee Members: Balakrishnan, Narayanaswamy, Computational Engineering and Science.

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In this thesis, we study the role of interdiction in the Vehicle Routing Problem (VRP), which naturally arises in humanitarian logistics and military applications. We assume that in a general network, each arc has a chance to be interdicted. When interdiction happens, the vehicle traveling on this arc is lost or blocked and thus unable to continue the trip. We model the occurrence of interdiction as a given probability and consider the multi-period expected delivery. Our objective is to minimize the total travel cost or to maximize the demand fulfillment, depending on the supply quantity. This problem is called the Vehicle Routing Problem with Interdiction (VRPI). We first prove that the proposed VRPI problems are NP-hard. Then we show some key analytical properties pertaining to the optimal solutions of these problems. Most importantly, we examine Dror and Trudeau's property applied to our problem setting. Finally, we present efficient heuristic algorithms to solve these problems and show the effectiveness through numerical studies.

Thesis

Master of Science (MSc)

Advisors/Committee Members: Huang, Kai, Computational Engineering and Science.

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In computational biology, genome sequences are represented as strings of characters defined over a small alphabet. These sequences contain many repeated subsequences, yet most of them are similarities, or approximate repeats. Sequence similarity search is a powerful way of analyzing genome sequences with many applications such as inferring genomic evolutionary events and relationships. The detection of approximate repeats between two sequences is not a trivial problem and solutions generally need large memory space and long processing time. Furthermore, the number of available genome sequences is growing fast along with the sequencing technologies. Hence, designing efficient methods for approximate repeat detection in large sequences is of great importance. In this study, we propose a new method for finding approximate repeats in DNA sequences and develop the corresponding software. A common strategy is to index the locations of short substrings, or seeds, of one sequence and store them in an efficiently searchable structure. Then, scan the other sequence and look up the structure for matches with the stored seeds. A novel feature of our method is its efficient use of spaced seeds, substrings with gaps, to generate approximate repeats. We have designed a new space-efficient hash table for indexing sequences with multiple spaced seeds. The resulting seed-matches are then extended into longer approximate repeats using dynamic programming. Our results indicate that our hash table implementation requires less memory than previously proposed hash table methods, especially when higher similarities between approximate repeats are desired. Moreover, increasing the length of seeds does not significantly increase the space requirement of the hash table, while allowing the same similarities to be computed faster.

Thesis

Master of Science (MSc)

Advisors/Committee Members: Smyth, William F., Computational Engineering and Science.

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Systems of differential-algebraic equations (DAEs) arise in many areas including electrical circuit simulation, chemical engineering, and robotics. The difficulty of solving a DAE is characterized by its index. For index-1 DAEs, there are several solvers, while a high-index DAE is numerically much more difficult to solve. The DAETS solver by Nedialkov and Pryce integrates numerically high-index DAEs. This solver is based on explicit Taylor series method and is efficient on non-stiff to mildly stiff problems, but can have severe stepsize restrictions on highly stiff problems. Hermite-Obreschkoff (HO) methods can be viewed as a generalization of Taylor series methods. The former have smaller error than the latter and can be A- or L- stable. In this thesis, we develop an implicit HO method for numerical solution of stiff high-index DAEs. Our method reduces a given DAE to a system of generally nonlinear equations and a constrained optimization problem. We employ Pryce’s structural analysis to determine the constraints of the problem and to organize the computations of higher-order Taylor coefficients (TCs) and their gradients. Then, we use automatic differentiation to compute these TCs and gradients, which are needed for evaluating the resulting system and its Jacobian. We design an adaptive variable-stepsize and variable-order algorithm and implement it in C++ using literate programming. The theory and implementation are interwoven in this thesis, which can be verified for correctness by a human expert. We report numerical results on stiff DAEs illustrating the accuracy and performance of our method, and in particular, its ability to take large steps on stiff problems.

Thesis

Doctor of Philosophy (PhD)

Advisors/Committee Members: Nedialkov, Nedialko, Computational Engineering and Science.

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Mathematical modeling of ocean waves is based on the formulation and solution of the appropriate equations of continuity, momentum and the choice of proper initial and boundary conditions. Under the influence of gravity, many free surface water waves can be modeled by the shallow water equations (SWE) with the assumption that the horizontal length scale of the wave is much greater than the depth scale and the wave height is much less than the fluid's mean depth. Furthermore, to describe three dimensional flows in the hydrostatic and Boussinesq limits, the multilayer SWE model is used, where the fluid is discretized horizontally into a set of vertical layers, each having its own height, density, horizontal velocity and geopotential. In this study, we used an explicit staggered finite volume method to solve single and multilayer SWE, with and without density stratification and bathymetry, to understand the dynamic of surface waves and internal waves. We implemented a two-dimensional version of the incompressible DYNAMICO method and compare it with a one-dimensional SWE. For multilayer SWE, we considered both two layer and a linear stratification of density, with very small density gradient, consistent with Boussinesq approximation. We used Lagrangian vertical coordinate which doesn't allow mass to flow across vertical layers. Numerical examples are presented to verify multilayer SWE model against single layer SWE, in terms of the phase speed and the steepness criteria of wave profile. In addition, the phase speed of the barotropic and baroclinic mode of two-layer SWE also verified our multilayer SWE model. We found that, for multilayer SWE, waves move slower than single layer SWE and get steeper than normal when they flow across bathymetry. A series of numerical experiment were carried out to compare 1-D shallow water solutions to 2-D solutions with and without density as well as to explain the dynamics of surface wave and internal wave. We found that, a positive fluctuations on free surface causes water to rise above surface level, gravity pulls it back and the forces that acquired during the falling movement causes the water to penetrate beneath it's equilibrium level, influences the generation of internal waves. Internal waves travel considerably more slowly than surface waves. On the other hand, a bumpy or a slicky formation of surface waves is associated with the propagation of internal waves. The interaction between these two waves is therefore demonstrated and discussed.

Thesis

Master of Science (MSc)

In the modelling of ocean wave, the formulation and solution of appropriate equations and proper initial and boundary conditions are required. The shallow water equations (SWE) are derived from the conservation of mass and momentum equations, in the case where the horizontal length scale of the wave is much greater than the depth scale and the wave height is much less than the fluid's mean depth. In multilayer SWE, the fluid is discretized horizontally into a set of vertical layers, each having its own…

Advisors/Committee Members: Kevlahan, Nicholas, Computational Engineering and Science.

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There have been several infamous incidences where world-renowned corporations have been caught by surprise when a low-tier downstream supplier has been publicly found to be non-compliant with basic corporate social responsibilities (CSR) codes. In such instances, the company reputation, and consequently financial health, suffer greatly. Motivated by the advances in predictive modeling, we present a predictive analytics model for detecting possible supplier deviations before they become a corporate liability. The model will be built based on publicly available data such as news and online content. We apply text mining and machine learning tools to design a corporate social responsibility "early warning system" on the upstream side of the supply chain. In our literature review we found that there is a lack of studies that focus on the social aspect of sustainability. Our research will help fill this gap by providing performance measures that can be used to build prescriptive analytics models to help in the selection of suppliers. To this end, we use the output of the predictive model to create a supplier selection optimization model that takes into account CSR compliance in global supply chain context. We propose a heuristic to solve the problem and computationally study its effectiveness as well as the impact of introducing CSR on procurement costs as well as ordering and supplier selection patterns. Our models provide analytics tools to companies to detect supplier deviance behaviour and act upon it so as to contain its impact and possible disruptions that can shake the whole supply chain.

Thesis

Master of Science (MSc)

Advisors/Committee Members: Hassini, Elkafi, Computational Engineering and Science.

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A balanced double square in a string x consists of two squares starting in the same position and of comparable lengths. We present a unique fac- torization of the longer square into primitive components refereed to as the canonical factorization and analyze its properties. In particular, we examine the inversion factors and the right and left inversion subfactors. All three substrings are collectively referred to as rare factors as they occur only twice in a signi cant portion of the larger square. The inversion factors were es- sential for determining the classi cation of mutual con gurations of double squares and thus providing the best-to-date upper bound of 11n=6 for the number of distinct squares in a string of length n by Deza, Franek, and Thierry. The right and left inversion subfactors have the advantage of being half the length of the inversion factors, thus providing a stronger dis- crimination property for a possible third square. This part of the thesis was published by Bai, Franek, and Smyth. The canonical factorization and the right and left inversion subfactors are used to formulate and prove a signi cantly stronger version of the New Periodicity Lemma by Fan, Puglisi, Smyth, and Turpin, 2006, that basically restricts what kind of a third square can exists in a balanced double square. This part of the thesis was published by Bai, Franek, and Smyth. The canonical factorization and the inversion factors are applied to for- mulate and prove a stronger version of the Three Squares Lemma by Crochemore and Rytter. This part of the thesis was published by Bai, Deza, and Franek.

Thesis

Doctor of Philosophy (PhD)

Advisors/Committee Members: Deza, Antoine, Franek, Frantisek, Computational Engineering and Science.

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In recent years, emotion classification using electroencephalography (EEG) has attracted much attention with the rapid development of machine learning techniques and various applications of brain-computer interfacing. In this study, a general model for emotion recognition was created using a large dataset of 116 participants' EEG responses to happy and fearful videos. We compared discrete and dimensional emotion models, assessed various popular feature extraction methods, evaluated the efficacy of feature selection algorithms, and examined the performance of 2 classification algorithms. An average test accuracy of 76% was obtained using higher-order spectral features with a support vector machine for discrete emotion classification. An accuracy of up 79% was achieved on the subset of classifiable participants. Finally, the stability of EEG patterns in emotion recognition was examined over time by evaluating consistency across sessions.

Thesis

Master of Science (MSc)

Advisors/Committee Members: Sonnadara, Ranil, Becker, Suzanna, Computational Engineering and Science.

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In manufacturing, metrological inspection is a time-consuming process. The higher the required precision in inspection, the longer the inspection time. This is due to both slow devices that collect measurement data and slow computational methods that process the data. The goal of this work is to propose methods to speed up some of these processes. Conventional measurement devices like Coordinate Measuring Machines (CMMs) have high precision but low measurement speed while new digitizer technologies have high speed but low precision. Using these devices in synergy gives a significant improvement in the measurement speed without loss of precision. The method of synergistic integration of an advanced digitizer with a CMM is discussed. Computational aspects of the inspection process are addressed next. Once a part is measured, measurement data is compared against its model to check for tolerances. This comparison is a time-consuming process on conventional CPUs. We developed and benchmarked some GPU accelerations. Finally, naive data fitting methods can produce misleading results in cases with non-uniform data. Weighted total least-squares methods can compensate for non-uniformity. We show how they can be accelerated with GPUs, using plane fitting as an example.

Thesis

Doctor of Philosophy (PhD)

Advisors/Committee Members: Spence, Allan, Anand, Christopher, Computational Engineering and Science.

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Mathematical models applied to epidemiology are useful tools that help understand how infectious diseases spread in populations, and hence support public-health decisions. Over the last 250 years, these modelling tools have have developed at an increasing rate, both on the theoretical and computational sides. This thesis explores various modelling techniques to address debated or unanswered questions about the transmission dynamics of infectious diseases, in particular sexually transmitted ones. The role of sero-discordant couples (when only one partner is infected) in the HIV epidemic in Sub-Saharan Africa is controversial. Their importance compared to other sexual transmission routes is critical when designing intervention policies. In chapter 2, I used a compartmental model with an original partnership process to show that infection of uncoupled individuals is usually the predominant route, while transmission within discordant couples is also important, but to a lesser extent. Despite the availability of inexpensive antimicrobial treatment, syphilis remains prevalent worldwide, affecting millions of individuals. Development of a syphilis vaccine would be a potentially promising step towards control, but the value of dedicating resources to vaccine development should be evaluated in the context of the anticipated benefits. In chapter 3, I explored the potential impact of a hypothetical syphilis vaccine on morbidity from both syphilis and HIV using an agent-based model. My results suggest that an efficacious vaccine has the potential to sharply reduce syphilis under a wide range of scenarios, while expanded treatment interventions are likely to be substantially less effective. General concepts in epidemic modelling, that could be applied to any disease, are still debated. In particular, a rigorous definition and analysis of the generation interval – the interval between the time that an individual is infected by an infector and the time this infector was infected – needed clarification. Indeed, the generation interval is a fundamental quantity when modelling and forecasting epidemics. Chapter 4 clarifies its theoretical framework, explains how its distribution changes as an epidemic progresses and discuss how empirical generation-interval data can be used to correctly inform mathematical models.

Thesis

Doctor of Philosophy (PhD)

Advisors/Committee Members: Dushoff, Jonathan, Earn, David, Computational Engineering and Science.

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In this thesis we explore three applications of chance constrained optimization in operations management. We first investigate the effect of consumer demand estimation error on new product production planning. An inventory model is proposed, whereby demand is influenced by price and advertising. The effect of parameter misspecification of the demand model is empirically examined in relation to profit and service level feasibility, and conservative approaches to estimating their effect on consumer demand is determined. We next consider optimization in Internet advertising by introducing a chance constrained model for the fulfillment of guaranteed display Internet advertising campaigns. Lower and upper bounds using Monte Carlo sampling and convex approximations are presented, as well as a branching heuristic for sample approximation lower bounds and an iterative algorithm for improved convex approximation upper bounds. The final application is in risk management for parimutuel horse racing wagering. We develop a methodology to limit potential losing streaks with high probability to the given time horizon of a gambler. A proof of concept was conducted using one season of historical race data, where losing streaks were effectively contained within different time periods for superfecta betting.

Thesis

Doctor of Philosophy (PhD)

Advisors/Committee Members: Deza, Antoine, Huang, Kai, Computational Engineering and Science.

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This thesis is a numerical investigation of two-dimensional steady flows past a circular obstacle. In the fluid dynamics research there are few computational results concerning the structure of the steady wake flows at Reynolds numbers larger than 100, and the state-of-the-art results go back to the work of Fornberg (1980) Fornberg (1985). The radial velocity component approaches its asymptotic value relatively slowly if the solution is ``physically reasonable''. This presents a difficulty when using the standard approach such as domain truncation. To get around this problem, in the present research we will develop a spectral technique for the solution of the steady Navier-Stokes system. We introduce the ``bootstrap" method which is motivated by the mathematical fact that solutions of the Oseen system have the same asymptotic structure at infinity as the solutions of the steady Navier-Stokes system with the same boundary conditions. Thus, in the ``bootstrap" method, the streamfunction is calculated as a perturbation to the solution to the Oseen system. Solutions are calculated for a range of Reynolds number and we also investigate the solutions behaviour when the Reynolds number goes to infinity. The thesis compares the numerical results obtained using the proposed spectral ``bootstrap" method and a finite – difference approach for unbounded domains against previous results. For Reynolds numbers lower than 100, the wake is slender and similar to the flow hypothesized by Kirchoff (1869) and Levi-Civita (1907). For large Reynolds numbers the wake becomes wider and appears more similar to the Prandtl-Batchelor flow, see Batchelor (1956).

Doctor of Science (PhD)

Advisors/Committee Members: Protas, Bartosz, Computational Engineering and Science.

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Today's highly integrated supply chains are exposed to various types of risks which disrupt the normal flow of goods or services within a supply chain network. Since most of these individual risks are interconnected, a mitigation strategy to tackle one risk may result in the exacerbation of another. Risk dependencies have been modelled using two approaches in the financial insurance literature : (i) random variables, and (ii) copulas. In this dissertation these studies are reviewed and extended. Also, applications for these models for different supply chain network configurations are presented. Then, a Poisson process model for risk propagation is proposed. Unlike the existing models, the transition rate of the proposed model not only expresses the time dependency, but also captures other possible dependencies in the network. Finally, the thesis is summarized and general directions and suggestions for future research on risk dependency and propagation modelling are provided.

Master of Science (MSc)

Advisors/Committee Members: Hassini, Elkafi, Computational Engineering and Science.

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Recent developments in signal processing called Compressive Sampling (CS) show that the measurement and reconstruction of sparse signals often requires fewer samples than is estimated by the sampling theorem. CS is a combination of a linear sampling scheme and a reconstruction method and, typically, the signal is assumed to be sparse, compressible, or having a prior distribution, with the reconstruction error measured in the ℓ² norm. This thesis investigates the application of CS to turbulence signals, particularly for estimating some statistics or nonlinear functions of the signals. The main original research result of the thesis is a proposed method, Spectrum Estimation by Sparse Optimization (SpESO), which uses a priori information about isotropic homogeneous turbulent flows and the multilevel structure of wavelet transforms to reconstruct energy spectra from compressive measurements, with errors measured on a logarithmic scale. The method is tested numerically on a variety of 1D and 2D turbulence signals, and is able to approximate energy spectra with an order of magnitude fewer samples than with traditional fixed rate sampling. The results demonstrate that SpESO performs much better than Lumped Orthogonal Matching Pursuit (LOMP), and as well or better than wavelet-based best M-term methods in many cases, even though these methods require complete sampling of the signal before compression.

Master of Science (MSc)

Advisors/Committee Members: Kevlahan, Nicholas, Computational Engineering and Science.

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The proposed aim of this thesis, inspired by the human brain, is to improve on the performance of a perceptual processing algorithm, referred to as a “perceptor”. This is done by trying to bridge the gap between neuroscience and engineering. To this end, we build on localized perception-action cycle in cognitive neuroscience by categorizing it under the umbrella of perceptual attention, which lends itself to increase gradually the contrast between relevant information and irrelevant information. Stated in another way, irrelevant information is filtered away while relevant information about the environment is enhanced from one cycle to the next. Accordingly, we propose to improve on the performance of a perceptor by modifying it to operate under the influence of perceptual attention. For this purpose, we first start with a single-layered perceptor and investigate the impact of perceptual attention on its performance through two computer experiments: The first experiment uses simulated (real-valued) data that are generated to purposely make the problem challenging. The second experiment uses real-life radar data that are complex-valued, hence the proposal to introduce Wirtinger calculus into derivation of our proposed method. We then take one step further and extend our proposed method to the case where a perceptor is hierarchical. In this context, every constitutive component of a hierarchical perceptor is modified to operate under the influence of perceptual attention. Then, another experiment is carried out to demonstrate the positive impact of perceptual attention on the performance of that hierarchical perceptor, just described.

Dissertation

Doctor of Philosophy (PhD)

Advisors/Committee Members: Haykin, Simon, Computational Engineering and Science.

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In this study we develop a computational approach to the solution of an inverse modelling problem concerning the material properties of electrolytes used in Lithium-ion batteries. The dependence of the diffusion coefficient and the transference number on the concentration of Lithium ions is reconstructed based on the concentration data obtained from an in-situ NMR imaging experiment. This experiment is modelled by a 1D time-dependent PDE describing the evolution of the concentration of Lithium ions with prescribed initial concentration and fluxes at the boundary. The material properties that appear in this model are reconstructed by solving a variational optimization problem in which the least-square error between the experimental and simulated concentration values is minimized. This optimization problem is solved using an innovative gradient-based method in which the gradients are obtained with adjoint analysis. In the thesis we develop and validate a computational framework for this reconstruction problem. Reconstructed material properties are presented for a lab-manufactured and a commercial battery electrolyte providing insights which complement available experimental results.

Thesis

Master of Science (MSc)

Advisors/Committee Members: Protas, Bartosz, Computational Engineering and Science.

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The main idea of this thesis is to de ne and formulate the role of bias estimation in multitarget{multisensor scenarios as a general framework for various measurement types. After a brief introduction of the work that has been done in this thesis, three main contributions are explained in detail, which exercise the novel ideas. Starting with radar measurements, a new bias estimation method that can estimate o set and scaling biases in large network of radars is proposed. Further, Cram er{Rao Lower Bound is calculated for the bias estimation algorithm to show the theoretical accuracy that can be achieved by the proposed method. In practice, communication loss is also part of the distributed systems, which sometimes can not be avoided. A novel technique is also developed to accompany the proposed bias estimation method in this thesis to compensate for communication loss at di erent rates by the use of tracklets. Next, bearing{only measurements are considered. Biases in this type of measurement can be di cult to tackle because the measurement noise and systematic biases are normally larger than in radar measurements. In addition, target observability is sensitive to sensor{target alignment and can vary over time. In a multitarget{ multisensor bearing{only scenario with biases, a new model is proposed for the biases that is decoupled form the bearing{only measurements. These decoupled bias measurements then are used in a maximum likelihood batch estimator to estimate the biases and then be used for compensation. The thesis is then expanded by applying bias estimation algorithms into video sensor measurements. Video sensor measurements are increasingly implemented in distributed systems because of their economical bene ts. However, geo{location and geo{registration of the targets must be considered in such systems. In last part of the thesis, a new approach proposed for modeling and estimation of biases in a two video sensor platform which can be used as a standalone algorithm. The proposed algorithm can estimate the gimbal elevation and azimuth biases e ectively. It is worth noting that in all parts of the thesis, simulation results of various scenarios with di erent parameter settings are presented to support the ideas, the accuracy, mathematical modelings and proposed algorithms. These results show that the bias estimation methods that have been conducted in this thesis are viable and can handle larger biases and measurement errors than previously proposed methods. Finally, the thesis conclude with suggestions for future research in three main directions.

Thesis

Doctor of Philosophy (PhD)

Advisors/Committee Members: Kirubarajan, Thia, Computational Engineering and Science.

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In this paper, a two-stage stochastic facility location problem integrated with inven- tory and recourse decisions is studied and solved. This problem is inspired by an industrial supply chain design problem of a large retail chain with slow-moving prod- ucts. Uncertainty is expressed by a discrete and finite set of scenarios. Recourse actions can be taken after the realization of random demands. Location, inventory, transportation, and recourse decisions are integrated into a mixed-integer program with an objective minimizing the expected total cost. A dual heuristic procedure is studied and embedded into the sample average approximation (SAA) method. The computation experiments demonstrate that our combined SAA with dual heuristic algorithm has a similar performance on solution quality and a much shorter compu- tational time.

Thesis

Master of Applied Science (MASc)

Advisors/Committee Members: Huang, Kai, Computational Engineering and Science.

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Systems of differential-algebraic equations (DAEs) arise in many areas including chemical engineering, electrical circuit simulation, and robotics. Such systems are routinely generated by simulation and modeling environments, like MapleSim, Matlab/Simulink, and those based on the Modelica language. Before a simulation starts and a numerical solution method is applied, some kind of structural analysis (SA) is performed to determine the structure and the index of a DAE system. Structural analysis methods serve as a necessary preprocessing stage, and among them, Pantelides's graph-theory-based algorithm is widely used in industry. Recently, Pryce's Σ-method is becoming increasingly popular, owing to its straightforward approach and capability of analyzing high-order systems. Both methods are equivalent in the sense that (a) when one succeeds, producing a nonsingular Jacobian, the other also succeeds, and that (b) the two give the same structural index in the case of either success or failure. When SA succeeds, the structural results can be used to perform an index reduction process, or to devise a stage-by-stage solution scheme for computing derivatives or Taylor coefficients up to some order. Although such a success occurs on fairly many problems of interest, SA can fail on some simple, solvable DAEs with an identically singular Jacobian, and give incorrect structural information that usually includes the index. In this thesis, we focus on the Σ-method and investigate its failures. Aiming at making this SA more reliable, we develop two conversion methods for fixing SA failures. These methods reformulate a DAE on which the Σ-method fails into an equivalent problem on which SA is more likely to succeed with a nonsingular Jacobian. The implementation of our methods requires symbolic computations. We also combine our conversion methods with block triangularization of a DAE. Using a block triangular form of a Jacobian sparsity pattern, we identify which diagonal block(s) of the Jacobian is identically singular, and then perform a conversion on each singular block. This approach can reduce the computational cost and improve the efficiency of finding a suitable conversion for fixing SA's failures.

Thesis

Doctor of Philosophy (PhD)

Advisors/Committee Members: Nedialkov, Ned, Computational Engineering and Science.

▼ A string is a sequence of symbols, usually called letters, drawn from some alphabet. It is one of the most fundamental and important structures in computing, bioinformatics and mathematics. Computer files, contents of a computer memory, network and satellite signals are all instances of strings. The genome of every living thing can be represented by a string drawn from the alphabet {a, c, g, t}. The algorithms processing strings have a wide range of applications such as information retrieval, search engines, data compression, cryptography and bioinformatics. In a DNA sequence the indeterminate symbol {a, c} is used when it is unclear whether a given nucleotide is a or c, We could then say that {a, c} matches another symbol {c, g} which in turn matches {g, t}, but {a, c} certainly does not match {g, t}. The processing of indeterminate strings is much more difficult because of this nontransitivity of matching. Thus a combinatorial understanding of indeterminate strings becomes essential to the development of efficient methods for their processing. With indeterminate strings, as with ordinary ones, the main task is the recognition/computation of patterns called regularities . We are particularly interested in regularities called repeats, whether tandem such as acgacg or nontandem (acgtacg). In this thesis we focus on newly-discovered regularities in strings, especially the enhanced cover array and the Lyndon array, with attention paid to extending the computations to indeterminate strings. Much of this work is necessarily abstract in nature, because the intention is to produce results that are applicable over a wide range of application areas. We will focus on finding algorithms to construct different data structures to represent strings such as cover arrays and Lyndon arrays. The idea of cover comes from strings which are not truly periodic but "almost" periodic in nature. For example abaababa is covered by aba but is not periodic. Similarly the Lyndon array describes the string in another unique way and is used in many fields of string algorithms. These data structures will help us in the field of string processing. As one application of these data structures we will work on "Reverse Engineering"; that is, given data structures derived from of a string, how can we get the string back. Since DNA, RNA and peptide sequences are effectively "strings" with unique properties, we will adapt our algorithms for regular or indeterminate strings to these sequences. Sequence analysis can be used to assign function to genes and proteins by observing the similarities between the compared sequences. Identifying unusual repetitive patterns will aid in the identification of intrinsic features of the sequence such as active sites, gene-structures and regulatory elements. As an application of periodic strings we investigate microsatellites which are short repetitive DNA patterns where repeated substrings are of length 2 to 5. Microsatellites are used in a wide range of studies due to their small size and… Advisors/Committee Members: Smyth, William F, Golding, Brian, Computational Engineering and Science.

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One of the key open problems in the field of theoretical fluid mechanics concerns the possibility of the singularity formation in solutions of the 3D Navier-Stokes system in finite time. This phenomenon is associated with the behaviour of the enstrophy, which is an L2 norm of the vorticity and must become unbounded if such a singularity occurs. Although there is no blow-up in the 2D Navier-Stokes equation, we would like to investigate how much enstrophy can a planar incompressible flow in a bounded domain produce given certain initial enstrophy. We address this issue by formulating an optimization problem in which the time derivative of the enstrophy serves as the objective functional and solve it using tools of the optimization theory and calculus of variations. We propose an efficient computational approach which is based on the iterative steepest-ascent procedure. In addition, we introduce an easy-to-implement method of computing the gradient of the objective functional. Finally, we present computational results addressing the key question of this project and provide numerical evidence that the maximum enstrophy growth exhibits the scaling dE/dt ~ C*E*E for C>0 and very small E. All computations are performed using the Chebyshev spectral method.

Thesis

Master of Science (MSc)

For many decades, scientists have been investigating fundamental aspects of the Navier-Stokes equation, a central mathematical model arising in fluid mechanics. Although the equation is widely used by engineers to describe numerous flow phenomena, it is still an open question whether the Navier-Stokes system always admits physically meaningful solutions. To address this issue, we want to explore its mathematical aspects deeper by analyzing the behaviour of the enstrophy, which is a quantity associated with the vorticity of the flow and a convenient measure of the regularity of the solution. In this study, we consider a planar and incompressible flow bounded by solid walls. Using basic tools of mathematical analysis and optimization theory, we propose a computational method enabling us to find out how much enstrophy can such a flow produce instantaneously. We present numerical evidence that this instantaneous growth of enstrophy has a well-defined asymptotic behavior, which is consistent with physical assumptions.

Advisors/Committee Members: Protas, Bartosz, Computational Engineering and Science.

▼ Brain-computer interfaces (BCIs) create a new form of communication and control for humans by translating brain activity directly into actions performed by a computer. This new field of research, best known for its breakthroughs in enabling fully paralyzed or locked-in patients to communicate and control simple devices, has resulted in a variety of remarkable technological developments. However, the field is still in its infancy, and facilitating control of a computer application via thought in a broader context involves a number of a challenges that have not yet been met. Advancing BCIs beyond the experimental phase continues to be a struggle. End-users have rarely been reached, except for in the case of a few highly specialized applications which require continual involvement of BCI experts. While these applications are profoundly beneficial for the patients they serve, the potential for BCIs is much broader in scope and powerful in effect. Unfortunately, the current approaches to brain-computer interfacing research have not been able to address the primary limitations in the field: the poor reliability of most BCIs and the highly variable performance across individuals. In addition to this, the modes of control available to users tend to be restrictive and unintuitive (\emph{e.g.}, imagining complex motor activities to answer ``Yes" or ``No" questions). This thesis presents a novel approach that addresses both of these limitations simultaneously. Brain-computer interfacing is currently viewed primarily as a machine learning problem, wherein the computer must learn the patterns of brain activity associated with a user's mental commands. In order to simplify this problem, researchers often restrict mental commands to those which are well characterized and easily distinguishable based on \emph{a priori} knowledge about their corresponding neural correlates. However, this approach does not fully recognize two properties of a BCI which makes it unique to other human-computer interfaces. First, individuals can vary widely with respect to the patterns of activation associated with how their brains generate similar mental activity and with respect to which kinds of mental activity have been most trained due to life experience. Thus, it is not surprising that BCIs based on predefined neural correlates perform inconsistently for different users. Second, for a BCI to perform well, the human and the computer must become a cohesive unit such that the computer can adapt as the user's brain naturally changes over time and while the user learns to make their mental commands more consistent and distinguishable given feedback from the computer. This not only implies that BCI use is a skill that must be developed, honed, and maintained in relation to the computer's algorithms, but that the human is the fundamental component of the system in a way that makes human learning just as important as machine learning. In this thesis it is proposed that, in the long term, a generalized BCI that can discover the appropriate neural… Advisors/Committee Members: Becker, Suzanna, Computational Engineering and Science.

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Modern numerical ordinary differential equation initial-value problem (ODE-IVP) solvers compute a piecewise polynomial approximate solution to the mathematical problem. Evaluating the mathematical problem at this approximate solution defines the defect. Corless and Corliss proposed rigorous defect control of numerical ODE-IVP. This thesis automates rigorous defect control for explicit, first-order, nonlinear ODE-IVP. Defect control is residual-based backward error analysis for ODE, a special case of Wilkinson's backward error analysis. This thesis describes a complete software implementation of the Corless and Corliss algorithm and extensive numerical studies. Basic time-stepping software is adapted to defect control and implemented. Advances in software developed for validated computing applications and advances in programming languages supporting operator overloading enable the computation of a tight rigorous enclosure of the defect evaluated at the approximate solution with Taylor models. Rigorously bounding a norm of the defect, the Corless and Corliss algorithm controls to mathematical certainty the norm of the defect to be less than a user specified tolerance over the integration interval. The validated computing software used in this thesis happens to compute a rigorous supremum norm. The defect of an approximate solution to the mathematical problem is associated with a new problem, the perturbed reference problem. This approximate solution is often the product of a numerical procedure. Nonetheless, it solves exactly the new problem including all errors. Defect control accepts the approximate solution whenever the sup-norm of the defect is less than a user specified tolerance. A user must be satisfied that the new problem is an acceptable model.

Thesis

Master of Science (MSc)

Many processes in our daily lives evolve in time, even the weather. Scientists want to predict the future makeup of the process. To do so they build models to model physical reality. Scientists design algorithms to solve these models, and the algorithm implemented in this project was designed over 25 years ago. Recent advances in mathematics and software enabled this algorithm to be implemented. Scientific software implements mathematical algorithms, and sometimes there is more than one software solution to apply to the model. The software tools developed in this project enable scientists to objectively compare solution techniques. There are two forces at play; models and software solutions. This project build software to automate the construction of the exact solution of a nearby model. That's cool.

Advisors/Committee Members: Nedialkov, Nedialko, Computational Engineering and Science.

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Target tracking refers to the process of estimating the state of a moving object from remote and noisy measurements. In this thesis we consider the Bayesian filtering framework to perform target tracking under nonlinear models, a target moving in continuous time, and measurements that are available in discrete time intervals (known as continuous-discrete). The Bayesian filtering theory establishes the mathematical basis to obtain the posterior probability density function of the state, given the measurement history. This probability density function contains all the information required about the state of the target. It is well documented that there is no exact solution for posterior density under the models mentioned. Hence, the approximation of such density functions have been studied for over four decades. The literature demonstrates that this has led to the development of multiple filters. In target tracking, due to the remote sensing performed, an additional complication emerges. The measurements received are not always from the desired target and could have originated from unknown sources, thus making the tracking more difficult. This problem is known as a measurement origin uncertainty. Additionally to the filters, different methods have been proposed to address the measurement origin uncertainty due to its negative impact, which could cause a false track. Unfortunately, a final solution has yet to be achieved. The first proposal of this thesis is a new approximate Bayesian filter for continuous-discrete systems. The new filter is a higher accuracy version of the cubature Kalman filter. This filter is developed using a fifth-degree spherical radial cubature rule and the Ito-Taylor expansion of order 1.5 for dealing with stochastic differential equations. The second proposal is an improved version of the probabilistic data association method. The proposed method utilizes the maximum likelihood values for selecting the measurements that are used for the data association. In the first experiment, the new filter is tested in a challenging 3-dimensional turn model, demonstrating superiority over other existing filters. In a second and third experiments, the proposed data association method is tested for target tracking in a 2-dimensional scenarios under heavy measurement origin uncertainty conditions. The second and third experiments demonstrate the superiority of the proposed data association method compared to the probabilistic data association.

Thesis

Doctor of Philosophy (PhD)

Advisors/Committee Members: Haykin, Simon, Computational Engineering and Science.

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Anticipations of personalized medicine are primarily attributed to the recent advances in computational science and high-throughput technologies that enable the ever-more realistic modeling of complex diseases. These diseases result from the interplay between genes and environment that have limited our ability to predict, prevent, or treat them. While many envision the utility of integrated high-dimensional patient-specific information, basic research towards developing accurate and reliable frameworks for personalized medicine is relatively slow in progress. This thesis provides a state-of-the-art review of current challenges towards personalized medicine. There is a need for global investment in basic research that includes 1) cost-effective generation of high-quality high-throughput data, 2) hybrid education and multidisciplinary teams, 3) data storage and processing, 4) data integration and interpretation, and 5) individual and global economic relevance; to be followed by global investments into public health to adopt routine personalized medicine. This review also highlights that unknown or unadjusted interactions result in true heterogeneity in the effect and relevance of patient data. This limits our ability to integrate and reliably utilize high-dimensional patient-specific data. This thesis further investigates the true heterogeneity in marginal effects of known BMI genetic variants. This involved the development of the novel statistical method, meta-quantile regression (MQR), to identify variants with potential gene-gene / gene-environment interactions. Applying MQR on public and local data (75,230 European adults) showed that FTO, PCSK1, TCF7L2, MC4R, FANCL, GIPR, MAP2K5, and NT5C2 have potential interactions on BMI. In addition, a gene score of 37 BMI variants shows that the genetic architecture of BMI is shaped by gene-gene and gene-environment interactions. The computational cost of fitting MQR models was greatly reduced using unconditional quantile regression. The utility of MQR was further compared to variance heterogeneity tests in identifying variants with potential interactions. MQR tests were found to have a higher power of detecting synergetic and antagonistic interactions for skewed quantitative traits while maintaining nominal Type I error rates compared to variance heterogeneity tests. Overall, MQR is a valuable tool to detect potential interactions without imposing assumptions on the nature of interactions.

Thesis

Doctor of Philosophy (PhD)

The anticipations of personalized medicine are largely due to the recent advances in computational science and our capabilities to rapidly measure and generate biological data. These developments have enhanced our understanding of complex diseases, and should theoretically enable us to predict, prevent and treat such cases in a proactive personalized context. This thesis provides a state-of-the-art review of the challenges and opportunities that explain the relatively slow progress towards personalized medicine. It identifies data integration and…

Advisors/Committee Members: Meyre, David, Computational Engineering and Science.

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Standard MRI is used to image objects at rest. In addition to standard MRI images, which measure tissues at rest, Phase Contrast MRI can be used to quantify the motion of blood and tissue in the human body. The current method used in Phase Contrast MRI is time consuming. The development of new trajectories has minimized imaging time, but creates sub-sampling errors. The proposed method uses regularization of velocities and proton densities to eliminate errors arising from k-space under-sampling.

Master of Applied Science (MASc)

Advisors/Committee Members: Anand, Christopher, Computational Engineering and Science.

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In this work we propose and validate a computational method for reconstructing constitutive relations (material properties) in complex multiphysics phenomena based on incomplete and noisy measurements which is applicable to different problems arising in nonequilibrium thermodynamics and continuum mechanics. The parameter estimation problem is solved as PDE–constrained optimization using a gradient–based technique in the optimize–then–discretize framework. The reconstructed material properties taken as an example here are the transport coefficients characterizing diffusion processes such as the viscosity and the thermal conductivity, and we focus on problems in which these coefficients depend on the state variables in the system. The proposed method allows one to reconstruct a smooth constitutive relation defined over a broad range of the dependent variable. This research is motivated by questions arising in the computational analysis and optimization of advanced welding processes which involves modelling complex alloys in the liquid phase at high temperatures.

Doctor of Philosophy (PhD)

Advisors/Committee Members: Protas, Bartosz, Computational Engineering and Science.

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The promotion of Electric Vehicles (EV) has become a key measure of the governments to reduce greenhouse gas emissions. However, range anxiety is a big barrier for drivers to choose EVs over traditional vehicles. Installing more charging stations in appropriate locations can relieve EV drivers’ range anxiety. To help decide the location and number of public charging stations, we propose two optimization models for two different charging modes - fast and slow charging, which aim at minimizing the total cost while satisfying certain spatial coverage goals. Instead of using discrete points we employ network and polygons to represent charging demands. Importantly, we resolve the partial coverage problem (PCP) by segmenting the geometric objects into smaller ones using Geographic Information System (GIS) functions. We compare the geometric segmentation method (GS) and the complementary partial coverage method (CP) developed by Murray (2005) to solve the PCP. After applying the models to Greater Toronto and Hamilton Area (GTHA) and to Downtown Toronto, we show that that the proposed models are practical and effective in determining the locations and number of required charging stations. Moreover, comparison of the two methods shows that GS can fully eliminate PCP and provide much more accurate result than CP.

Thesis

Master of Science (MSc)

Advisors/Committee Members: Huang, Kai, Computational Engineering and Science.