# Mathematics (Faculty of)

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Item A 2-Approximation for the Height of Maximal Outerplanar Graph Drawings(University of Waterloo, 2016-08-18) Demontigny, PhilippeIn this thesis, we study drawings of maximal outerplanar graphs that place vertices on integer coordinates. We introduce a new class of graphs, called umbrellas, and a new method of splitting maximal outerplanar graphs into systems of umbrellas. By doing so, we generate a new graph parameter, called the umbrella depth (ud), that can be used to approximate the optimal height of a drawing of a maximal outerplanar graph. We show that for any maximal outerplanar graph G, we can create a flat visibility representation of G with height at most 2ud(G) + 1. This drawing can be transformed into a straight-line drawing of the same height. We then prove that the height of any drawing of G is at least ud(G) + 1, which makes our result a 2-approximation for the optimal height. The best previously known approximation algorithm gave a 4-approximation. In addition, we provide an algorithm for finding the umbrella depth of G in linear time. Lastly, we compare the umbrella depth to other graph parameters such as the pathwidth and the rooted pathwidth, which have been used in the past for outerplanar graph drawing algorithms.Item A 2-class maintenance model with dynamic server behavior(Springer, 2019-04-29) Granville, Kevin; Drekic, SteveWe analyze a 2-class maintenance system within a single-server polling model framework. There are C+f machines in the system, where C is the cap on the number of machines that can be turned on simultaneously (and hence, be at risk of failure), and the excess f machines comprise a maintenance float which can be used to replace machines that are taken down for repair. The server’s behavior is dynamic, capable of switching queues upon a machine failure or service completion depending on both queue lengths. This generalized server behavior permits the analysis of several classic service policies, including preemptive resume priority, non-preemptive priority, and exhaustive. More complicated polices can also be considered, such as threshold-based ones and a version of the Bernoulli service rule. The system is modeled as a level-dependent quasi-birth-and-death process and matrix analytic methods are used to find the steady-state joint queue length distribution, as well as the distribution for the sojourn time of a broken machine. An upper bound on the expected number of working machines as a function of C is derived, and Little’s Law is used to find the relationship between the expected number of working machines and the expected sojourn time of a failed machine when f=0 or f≥1. Several numerical examples are presented, including how one might optimize an objective function depending on the mean number of working machines, with penalty costs attributed to increasing C or f.Item 2-crossing critical graphs with a V8 minor(University of Waterloo, 2012-01-17T20:51:50Z) Austin, Beth AnnThe crossing number of a graph is the minimum number of pairwise crossings of edges among all planar drawings of the graph. A graph G is k-crossing critical if it has crossing number k and any proper subgraph of G has a crossing number less than k. The set of 1-crossing critical graphs is is determined by Kuratowski’s Theorem to be {K5, K3,3}. Work has been done to approach the problem of classifying all 2-crossing critical graphs. The graph V2n is a cycle on 2n vertices with n intersecting chords. The only remaining graphs to find in the classification of 2-crossing critical graphs are those that are 3-connected with a V8 minor but no V10 minor. This paper seeks to fill some of this gap by defining and completely describing a class of graphs called fully covered. In addition, we examine other ways in which graphs may be 2-crossing critical. This discussion classifies all known examples of 3-connected, 2-crossing critical graphs with a V8 minor but no V10 minor.Item 2-Semilattices: Residual Properties and Applications to the Constraint Satisfaction Problem(University of Waterloo, 2017-08-22) Payne, IanSemilattices are algebras known to have an important connection to partially ordered sets. In particular, if a partially ordered set $(A,\leq)$ has greatest lower bounds, a semilattice $(A;\wedge)$ can be associated to the order where $a\wedge b$ is the greatest lower bound of $a$ and $b$. In this thesis, we study a class of algebras known as 2-semilattices, which is a generalization of the class of semilattices. Similar to the correspondence between partial orders and semilattices, there is a correspondence between certain digraphs and 2-semilattices. That is, to every 2-semilattice, there is an associated digraph which holds information about the 2-semilattice. Making frequent use of this correspondence, we explore the class of 2-semilattices from three perspectives: (i) Tame Congruence Theory, (ii) the ``residual character" of the class of 2-semilattices, and (iii), the constraint satisfaction problem. Tame Congruence Theory, developed in [29], is a structure theory on finite algebras driven by understanding their prime congruence quotients. The theory assigns to each such quotient a type from 1 to 5. We show that types 3, 4, and 5 can occur in the class of 2-semilattices, but type 4 can not occur in a finite simple 2-semilattice. Classes of algebras contain ``subdirectly irreducible" members which hold information about the class. Specifically, the size of these members has been of interest to many authors. We show for certain subclasses of the class of 2-semilattices that there is no cardinal bound on the size of the irreducible members in that subclass. The ``fixed template constraint satisfaction problem" can be identified with the decision problem hom$(\mathbb{A})$ where $\mathbb{A}$ is a fixed finite relational structure. The input to hom$(\mathbb{A})$ is a finite structure $\mathbb{B}$ similar to $\mathbb{A}$. The question asked is ``does there exist a homomorphism from $\mathbb{B}$ to $\mathbb{A}$?" Feder and Vardi [22] conjectured that for fixed $\mathbb{A}$, this decision problem is either NP-complete or solvable in polynomial time. Bulatov [15] confirmed this conjecture in the case that $\mathbb{A}$ is invariant under a 2-semilattice operation. We extend this result.Item 3-D Reconstruction from Single Projections, with Applications to Astronomical Images(University of Waterloo, 2013-08-23T18:52:01Z) Cormier, MichaelA variety of techniques exist for three-dimensional reconstruction when multiple views are available, but less attention has been given to reconstruction when only a single view is available. Such a situation is normal in astronomy, when a galaxy (for example) is so distant that it is impossible to obtain views from significantly different angles. In this thesis I examine the problem of reconstructing the three-dimensional structure of a galaxy from this single viewpoint. I accomplish this by taking advantage of the image formation process, symmetry relationships, and other structural assumptions that may be made about galaxies. Most galaxies are approximately symmetric in some way. Frequently, this symmetry corresponds to symmetry about an axis of rotation, which allows strong statements to be made about the relationships between luminosity at each point in the galaxy. It is through these relationships that the number of unknown values needed to describe the structure of the galaxy can be reduced to the number of constraints provided by the image so the optimal reconstruction is well-defined. Other structural properties can also be described under this framework. I provide a mathematical framework and analyses that prove the uniqueness of solutions under certain conditions and to show how uncertainty may be precisely and explicitly expressed. Empirical results are shown using real and synthetic data. I also show a comparison to a state-of-the-art two-dimensional modelling technique to demonstrate the contrasts between the two frameworks and show the important advantages of the three-dimensional approach. In combination, the theoretical and experimental aspects of this thesis demonstrate that the proposed framework is versatile, practical, and novel---a contribution to both computer science and astronomy.Item 3D Online Multi-Object Tracking for Autonomous Driving(University of Waterloo, 2019-08-29) Balasubramanian, VenkateshwaranThis research work focuses on exploring a novel 3D multi-object tracking architecture: 'FANTrack: 3D Multi-Object Tracking with Feature Association Network' for autonomous driving, based on tracking by detection and online tracking strategies using deep learning architectures for data association. The problem of multi-target tracking aims to assign noisy detections to a-priori unknown and time-varying number of tracked objects across a sequence of frames. A majority of the existing solutions focus on either tediously designing cost functions or formulating the task of data association as a complex optimization problem that can be solved effectively. Instead, we exploit the power of deep learning to formulate the data association problem as inference in a CNN. To this end, we propose to learn a similarity function that combines cues from both image and spatial features of objects. The proposed approach consists of a similarity network that predicts the similarity scores of the object pairs and builds a local similarity map. Another network formulates the data association problem as inference in a CNN by using the similarity scores and spatial information. The model learns to perform global assignments in 3D purely from data, handles noisy detections and a varying number of targets, and is easy to train. Experiments on the challenging Kitti dataset show competitive results with the state of the art. The model is finally implemented in ROS and deployed on our autonomous vehicle to show the robustness and online tracking capabilities. The proposed tracker runs alongside the object detector utilizing the resources efficiently.Item 3D Pointing with Everyday Devices: Speed, Occlusion, Fatigue(University of Waterloo, 2015-07-24) Pietroszek, KrzysztofIn recent years, display technology has evolved to the point where displays can be both non-stereoscopic and stereoscopic, and 3D environments can be rendered realistically on many types of displays. From movie theatres and shopping malls to conference rooms and research labs, 3D information can be deployed seamlessly. Yet, while 3D environments are commonly displayed in desktop settings, there are virtually no examples of interactive 3D environments deployed within ubiquitous environments, with the exception of console gaming. At the same time, immersive 3D environments remain - in users' minds - associated with professional work settings and virtual reality laboratories. An excellent opportunity for 3D interactive engagements is being missed not because of economic factors, but due to the lack of interaction techniques that are easy to use in ubiquitous, everyday environments. In my dissertation, I address the lack of support for interaction with 3D environments in ubiquitous settings by designing, implementing, and evaluating 3D pointing techniques that leverage a smartphone or a smartwatch as an input device. I show that mobile and wearable devices may be especially beneficial as input devices for casual use scenarios, where specialized 3D interaction hardware may be impractical, too expensive or unavailable. Such scenarios include interactions with home theatres, intelligent homes, in workplaces and classrooms, with movie theatre screens, in shopping malls, at airports, during conference presentations and countless other places and situations. Another contribution of my research is to increase the potential of mobile and wearable devices for efficient interaction at a distance. I do so by showing that such interactions are feasible when realized with the support of a modern smartphone or smartwatch. I also show how multimodality, when realized with everyday devices, expands and supports 3D pointing. In particular, I show how multimodality helps to address the challenges of 3D interaction: performance issues related to the limitations of the human motor system, interaction with occluded objects and related problem of perception of depth on non-stereoscopic screens, and user subjective fatigue, measured with NASA TLX as perceived workload, that results from providing spatial input for a prolonged time. I deliver these contributions by designing three novel 3D pointing techniques that support casual, "walk-up-and-use" interaction at a distance and are fully realizable using off-the-shelf mobile and wearable devices available today. The contributions provide evidence that democratization of 3D interaction can be realized by leveraging the pervasiveness of a device that users already carry with them: a smartphone or a smartwatch.Item 5-Choosability of Planar-plus-two-edge Graphs(University of Waterloo, 2018-01-02) Mahmoud, AmenaWe prove that graphs that can be made planar by deleting two edges are 5-choosable. To arrive at this, first we prove an extension of a theorem of Thomassen. Second, we prove an extension of a theorem Postle and Thomas. The difference between our extensions and the theorems of Thomassen and of Postle and Thomas is that we allow the graph to contain an inner 4-list vertex. We also use a colouring technique from two papers by Dvořák, Lidický and Škrekovski, and independently by Compos and Havet.Item 5G RAN/MEC Slicing and Admission Control using Deep Reinforcement Learning(University of Waterloo, 2023-01-19) Moayyedi, ArashThe 5G RAN functions can be virtualized and distributed across the radio unit (RU), distributed unit (DU), and centralized unit (CU) to facilitate flexible resource management. Complemented by multi-access edge computing (MEC), these components create network slices tailored for applications with diverse quality of service (QoS) requirements. However, as the requests for various slices arrive dynamically over time and the network resources are limited, it is non-trivial for an infrastructure provider (InP) to optimize its long-term revenue from real-time admission and embedding of slice requests. Prior works have leveraged Deep Reinforcement Learning (DRL) to address this problem, however, these solutions either do not scale to realistic topologies, require re-training of the DRL agents when facing topology changes, or do not consider the slice admission and embedding problems jointly. In this thesis, we use multi-agent DRL and Graph Attention Networks (GATs) to address these limitations. Specifically, we propose novel topology-independent admission and slicing agents that are scalable and generalizable to large and different metropolitan networks. Results show that the proposed approach converges faster and achieves up to 35.2% and 20% gain in revenue compared to heuristics and other DRL-based approaches, respectively. Additionally, we demonstrate that our approach is generalizable to scenarios and substrate networks previously unseen during training, as it maintains superior performance without re-training or re-tuning. Finally, we extract the attention maps of the GAT, and analyze them to detect potential bottlenecks and efficiently improve network performance and InP revenue through eliminating them.Item A+ Indexes: Highly Flexible Adjacency Lists in Graph Database Management Systems(University of Waterloo, 2019-09-17) Khaliq, ShahidAdjacency lists are the most fundamental storage structure in existing graph database management systems (GDBMSs) to index input graphs. Adjacency lists are universally linked-list like per-vertex structures that allow access to a set of edges that are all adjacent to a vertex. In several systems, adjacency lists can also allow efficient access to subsets of a vertex’s adjacent edges that satisfy a fixed set of predicates, such as those that have the same label, and support a fixed set of ordering criteria, such as sorting by the ID of destination vertices of the edges. This thesis describes a highly-flexible indexing subsystem for GDBMSs, which consists of two components. The primary component called A+ indexes store adjacency lists, which compared to existing adjacency lists, provide flexibility to users in three aspects: (1) in addition to per-vertex adjacency lists, users can define per-edge adjacency lists; (2) users can define adjacency lists for sets of edges that satisfy a wide range of predicates; and (3) provide flexible sorting criteria. Indexes in existing GDBMS, such as adjacency list, B+ tree, or hash indexes, index as elements the vertices or edges in the input graph. The second component of our indexing sub-system is secondary B+ tree and bitmap indexes that index aggregate properties of adjacency lists in A+ indexes. Therefore, our secondary indexes effectively index adjacency lists as elements. We have implemented our indexing sub-system on top of the Graphflow GDBMS. We describe our indexes, the modifications we had to do to Graphflow’s optimizer, and our implementation. We provide extensive experiments demonstrating both the flexibility and efficiency of our indexes on a large suite of queries from several application domains.Item Abelian, amenable operator algebras are similar to C∗ -algebras(Duke University Press, 2016-12) Marcoux, Laurent W.; Popov, Alexey I.Suppose that H is a complex Hilbert space and that ℬ(H) denotes the bounded linear operators on H. We show that every abelian, amenable operator algebra is similar to a C∗-algebra. We do this by showing that if 𝒜⊆ℬ(H) is an abelian algebra with the property that given any bounded representation ϱ:𝒜→ℬ(Hϱ) of 𝒜 on a Hilbert space Hϱ, every invariant subspace of ϱ(𝒜) is topologically complemented by another invariant subspace of ϱ(𝒜), then 𝒜 is similar to an abelian C∗-algebra.Item Abstract and Explicit Constructions of Jacobian Varieties(University of Waterloo, 2018-08-10) Urbanik, DavidAbelian varieties, in particular Jacobian varieties, have long attracted interest in mathematics. Their influence pervades arithmetic geometry and number theory, and understanding their construction was a primary motivator for Weil in his work on developing new foundations for algebraic geometry in the 1930s and 1940s. Today, these exotic mathematical objects find applications in cryptography and computer science, where they can be used to secure confidential communications and factor integers in subexponential time. Although in many respects well-studied, working in concrete, explicit ways with abelian varieties continues to be difficult. The issue is that, aside from the case of elliptic curves, it is often difficult to find ways of modelling and understanding these objects in ways amenable to computation. Often, the approach taken is to work ``indirectly'' with abelian varieties, in particular with Jacobians, by working instead with divisors on their associated curves to simplify computations. However, properly understanding the mathematics underlying the direct approach --- why, for instance, one can view the degree zero divisor classes on a curve as being points of a variety --- requires sophisticated mathematics beyond what is usually understood by algorithms designers and even experts in computational number theory. A direct approach, where explicit polynomial and rational functions are given that define both the abelian variety and its group law, cannot be found in the literature for dimensions greater than two. In this thesis, we make two principal contributions. In the first, we survey the mathematics necessary to understand the construction of the Jacobian of a smooth algebraic curve as a group variety. In the second, we present original work with gives the first instance of explicit rational functions defining the group law of an abelian variety of dimension greater than two. In particular, we derive explicit formulas for the group addition on the Jacobians of hyperelliptic curves of every genus g, and so give examples of explicit rational formulas for the group law in every positive dimension.Item Accelerating and Privatizing Diffusion Models(University of Waterloo, 2023-08-17) Dockhorn, TimDiffusion models (DMs) have emerged as a powerful class of generative models. DMs offer both state-of-the-art synthesis quality and sample diversity in combination with a robust and scalable learning objective. DMs rely on a diffusion process that gradually perturbs the data towards a normal distribution, while the neural network learns to denoise. Formally, the problem reduces to learning the score function, i.e., the gradient of the log-density of the perturbed data. The reverse of the diffusion process can be approximated by a differential equation, defined by the learned score function, and can therefore be used for generation when starting from random noise. In this thesis, we give a thorough and beginner-friendly introduction to DMs and discuss their history starting from early work on score-based generative models. Furthermore, we discuss connections to other statistical models and lay out applications of DMs, with a focus on image generative modeling. We then present CLD: a new DM based on critically-damped Langevin dynamics. CLD can be interpreted as running a joint diffusion in an extended space, where the auxiliary variables can be considered "velocities" that are coupled to the data variables as in Hamiltonian dynamics. We derive a novel score matching objective for CLD-based DMs and introduce a fast solver for the reverse diffusion process which is inspired by methods from the statistical mechanics literature. The CLD framework provides new insights into DMs and generalizes many existing DMs which are based on overdamped Langevin dynamics. Next, we present GENIE, a novel higher-order numerical solver for DMs. Many existing higher-order solvers for DMs built on finite difference schemes which break down in the large step size limit as approximations become too crude. GENIE, on the other hand, learns neural network-based models for higher-order derivatives whose precision do not depend on the step size. The additional networks in GENIE are implemented as small output heads on top of the neural backbone of the original DM, keeping the computational overhead minimal. Unlike recent sampling distillation methods that fundamentally alter the generation process in DMs, GENIE still solves the true generative differential equation, and therefore naturally enables applications such as encoding and guided sampling. The fourth chapter presents differentially private diffusion models (DPDMs), DMs trained with strict differential privacy guarantees. While modern machine learning models rely on increasingly large training datasets, data is often limited in privacy-sensitive domains. Generative models trained on sensitive data with differential privacy guarantees can sidestep this challenge, providing access to synthetic data instead. DPDMs enforce privacy by using differentially private stochastic gradient descent for training. We thoroughly study the design space of DPDMs and propose noise multiplicity, a simple yet powerful modification of the DM training objective tailored to the differential privacy setting. We motivate and show numerically why DMs are better suited for differentially private generative modeling than one-shot generators such as generative adversarial networks or normalizing flows. Finally, we propose to distill the knowledge of large pre-trained DMs into smaller student DMs. Large-scale DMs have achieved unprecedented results across several domains, however, they generally require a large amount of GPU memory and are slow at inference time, making it difficult to deploy them in real-time or on resource-limited devices. In particular, we propose an approximate score matching objective that regresses the student model towards predictions of the teacher DM rather than the clean data as is done in standard DM training. We show that student models outperform the larger teacher model for a variety of compute budgets. Additionally, the student models may also be deployed on GPUs with significantly less memory than was required for the original teacher model.Item Accelerating the Training of Convolutional Neural Networks for Image Segmentation with Deep Active Learning(University of Waterloo, 2020-01-23) Chen, Wei TaoImage semantic segmentation is an important problem in computer vision. However, Training a deep neural network for semantic segmentation in supervised learning requires expensive manual labeling. Active learning (AL) addresses this problem by automatically selecting a subset of the dataset to label and iteratively improve the model. This minimizes labeling costs while maximizing performance. Yet, deep active learning for image segmentation has not been systematically studied in the literature. This thesis offers three contributions. First, we compare six different state-of-the-art querying methods, including uncertainty, Bayesian, and out-of-distribution methods, in the context of active learning for image segmentation. The comparison uses the standard dataset Cityscapes, as well as randomly generated data, and the state-of-the-art image segmentation architecture DeepLab. Our results demonstrate subtle but robust differences between the querying methods, which we analyze and explain. Second, we propose a novel way to query images by counting the number of pixels with acquisition values above a certain threshold. Our counting method outperforms the standard averaging method. Lastly, we demonstrate that the previous two findings remain consistent for both whole images and image crops. Furthermore, we provide an in-depth discussion of deep active learning and results from supplementary experiments. First, we studied active learning in the context of image classification with the MNIST dataset. We observed an interesting phenomenon where active learning querying methods perform worse than random sampling in the early cycles but overtake random sampling at a break-even point. This break-even point can be controlled by varying model capacity, sample diversity, and temperature scaling. The difference in performances of the six querying methods is larger than in the case of image segmentation. Second, we attempt to explore the theoretical optimal query by querying samples with the lowest accuracy and querying with a trained expert model. Although they turned out to be suboptimal, their results would hopefully shed light on the subject. Lastly, we present the experiment results from using SegNet and FCN. With these architectures, our querying methods did not perform any better than random sampling. Nevertheless, those negative results demonstrate some of the difficulties of active learning for image segmentation.Item Access Control Administration with Adjustable Decentralization(University of Waterloo, 2007-09-12T15:50:52Z) Chinaei, Amir HosseinAccess control is a key function of enterprises that preserve and propagate massive data. Access control enforcement and administration are two major components of the system. On one hand, enterprises are responsible for data security; thus, consistent and reliable access control enforcement is necessary although the data may be distributed. On the other hand, data often belongs to several organizational units with various access control policies and many users; therefore, decentralized administration is needed to accommodate diverse access control needs and to avoid the central bottleneck. Yet, the required degree of decentralization varies within different organizations: some organizations may require a powerful administrator in the system; whereas, some others may prefer a self-governing setting in which no central administrator exists, but users fully manage their own data. Hence, a single system with adjustable decentralization will be useful for supporting various (de)centralized models within the spectrum of access control administration. Giving individual users the ability to delegate or grant privileges is a means of decentralizing access control administration. Revocation of arbitrary privileges is a means of retaining control over data. To provide flexible administration, the ability to delegate a specific privilege and the ability to revoke it should be held independently of each other and independently of the privilege itself. Moreover, supporting arbitrary user and data hierarchies, fine-grained access control, and protection of both data (end objects) and metadata (access control data) with a single uniform model will provide the most widely deployable access control system. Conflict resolution is a major aspect of access control administration in systems. Resolving access conflicts when deriving effective privileges from explicit ones is a challenging problem in the presence of both positive and negative privileges, sophisticated data hierarchies, and diversity of conflict resolution strategies. This thesis presents a uniform access control administration model with adjustable decentralization, to protect both data and metadata. There are several contributions in this work. First, we present a novel mechanism to constrain access control administration for each object type at object creation time, as a means of adjusting the degree of decentralization for the object when the system is configured. Second, by controlling the access control metadata with the same mechanism that controls the users’ data, privileges can be granted and revoked to the extent that these actions conform to the corporation’s access control policy. Thus, this model supports a whole spectrum of access control administration, in which each model is characterized as a network of access control states, similar to a finite state automaton. The model depends on a hierarchy of access banks of authorizations which is supported by a formal semantics. Within this framework, we also introduce the self-governance property in the context of access control, and show how the model facilitates it. In particular, using this model, we introduce a conflict-free and decentralized access control administration model in which all users are able to retain complete control over their own data while they are also able to delegate any subset of their privileges to other users or user groups. We also introduce two measures to compare any two access control models in terms of the degrees of decentralization and interpretation. Finally, as the conflict resolution component of access control models, we incorporate a unified algorithm to resolve access conflicts by simultaneously supporting several combined strategies.Item Accurate viscous free surfaces for buckling, coiling, and rotating liquids(Association for Computing Machinery, 2008-07) Batty, Christopher; Bridson, RobertWe present a fully implicit Eulerian technique for simulating free surface viscous liquids which eliminates artifacts in previous approaches, efficiently supports variable viscosity, and allows the simulation of more compelling viscous behaviour than previously achieved in graphics. Our method exploits a variational principle which automatically enforces the complex boundary condition on the shear stress at the free surface, while giving rise to a simple discretization with a symmetric positive definite linear system. We demonstrate examples of our technique capturing realistic buckling, folding and coiling behavior. In addition, we explain how to handle domains whose boundary comprises both ghost fluid Dirichlet and variational Neumann parts, allowing correct behaviour at free surfaces and solid walls for both our viscous solve and the variational pressure projection of Batty et al. [BBB07].Item Achieving Performance Objectives for Database Workloads(University of Waterloo, 2010-08-30T21:22:49Z) Mallampalli, AnushaIn this thesis, our goal is to achieve customer-specified performance objectives for workloads in a database management system (DBMS). Competing workloads in current DBMSs have detrimental effects on performance. Differentiated levels of service become important to ensure that critical work takes priority. We design a feedback-based admission differentiation framework, which consists of three components: workload classifier, workload monitor and adaptive admission controller. The adaptive admission controller uses the workload management capabilities of IBM DB2’s Workload Manager (WLM) to achieve the performance objectives of the most important workload by applying admission control on the rest of the work, which is less important and may or may not have performance objectives. The controller uses a feedback-based technique to automatically adjust the admission control on the less important work to achieve performance objectives for the important workload. The adaptive admission controller is implemented on an instance of DB2 to the test the effectiveness of the controller.Item Action of degenerate Bethe operators on representations of the symmetric group(University of Waterloo, 2018-05-24) Rahman, SifatDegenerate Bethe operators are elements defined by explicit sums in the center of the group algebra of the symmetric group. They are useful on account of their relation to the Gelfand-Zetlin algebra and the Young-Jucys-Murphy elements, both of which are important objects in the Okounkov-Vershik approach to the representation theory of the symmetric group. We examine all of these results over the course of the thesis. Degenerate Bethe operators are a new, albeit promising, topic. Therefore, we include proofs for previously-unproven basic aspects of their theory. The primary contribution of this thesis, however, is the computation of eigenvalues and eigenvectors of all the degenerate Bethe operators in sizes 4 and 5, as well as many in size 6. For each partition $\bld{\lambda} \vdash k$ we compute the operators $B_{\ell j}$, where $\ell + j \leq k$, and give the eigenvalues and their corresponding eigenvectors in terms of standard Young tableaux of shape $\bld{\lambda}$. The number of terms in the degenerate Bethe operators grows very rapidly so we used a program written in the computer algebra system \texttt{SAGE} to compute the eigenvalue-eigenvector pair data. From this data, we observed a number of patterns that we have formalized and proven, although others remain conjectural. All of the data computed is collected in an appendix to this thesis.Item Active Learning with Semi-Supervised Support Vector Machines(University of Waterloo, 2007-05-22T16:23:10Z) Chinaei, LeilaA significant problem in many machine learning tasks is that it is time consuming and costly to gather the necessary labeled data for training the learning algorithm to a reasonable level of performance. In reality, it is often the case that a small amount of labeled data is available and that more unlabeled data could be labeled on demand at a cost. If the labeled data is obtained by a process outside of the control of the learner, then the learner is passive. If the learner picks the data to be labeled, then this becomes active learning. This has the advantage that the learner can pick data to gain specific information that will speed up the learning process. Support Vector Machines (SVMs) have many properties that make them attractive to use as a learning algorithm for many real world applications including classification tasks. Some researchers have proposed algorithms for active learning with SVMs, i.e. algorithms for choosing the next unlabeled instance to get label for. Their approach is supervised in nature since they do not consider all unlabeled instances while looking for the next instance. In this thesis, we propose three new algorithms for applying active learning for SVMs in a semi-supervised setting which takes advantage of the presence of all unlabeled points. The suggested approaches might, by reducing the number of experiments needed, yield considerable savings in costly classification problems in the cases when finding the training data for a classifier is expensive.Item Active Sensing for Partially Observable Markov Decision Processes(University of Waterloo, 2013-01-21T19:46:56Z) Koltunova, VeronikaContext information on a smart phone can be used to tailor applications for specific situations (e.g. provide tailored routing advice based on location, gas prices and traffic). However, typical context-aware smart phone applications use very limited context information such as user identity, location and time. In the future, smart phones will need to decide from a wide range of sensors to gather information from in order to best accommodate user needs and preferences in a given context. In this thesis, we present a model for active sensor selection within decision-making processes, in which observational features are selected based on longer-term impact on the decisions made by the smart phone. This thesis formulates the problem as a partially observable Markov decision process (POMDP), and proposes a non-myopic solution to the problem using a state of the art approximate planning algorithm Symbolic Perseus. We have tested our method on a 3 small example domains, comparing different policy types, discount factors and cost settings. The experimental results proved that the proposed approach delivers a better policy in the situation of costly sensors, while at the same time provides the advantage of faster policy computation with less memory usage.