The Cayley-Hamilton Theorem is an important result in the study of linear transformations over finite dimensional vector spaces. In this thesis, we show that the Cayley-Hamilton Theorem can be extended to self-adjoint trace-class operators and to closed self-adjoint operators with trace-class resolvent over a separable Hilbert space. Applications of these results include calculating operators resolvents and finding the inverse of a frame operator.

Optimal control problems can in many cases become complicated and difficult to solve. One particular class of difficult control problems to solve are singular control problems. Standard methods for solving optimal control are discussed showing why those methods are difficult to apply to singular control problems. Then standard methods for solving singular control problems are discussed including why the standard methods can be difficult and often impossible to apply without having to resort to numerical techniques. Finally, an alternative method to solving a class of singular optimal control problems is given for a specific class of problems.

The traffic signal affects the life of virtually everyone every day. The effectiveness of signal systems can reduce the incidence of delays, stops, fuel consumption, emission of pollutants, and accidents. The problems related to rapid growth in traffic congestion call for more effective traffic signalization using robust feedback control methodology. Online traffic-responsive signalization is based on real-time traffic conditions and selects cycle, split, phase, and offset for the intersection according to detector data. A robust traffic feedback control begins with assembling traffic demands, traffic facility supply, and feedback control law for the existing traffic operating environment. This information serves the input to the traffic control process which in turn provides an output in terms of the desired performance under varying conditions. Traffic signalization belongs to a class of hybrid systems since the differential equations model the continuous behavior of the traffic flow dynamics and finite-state machines model the discrete state changes of the controller. A complicating aspect, due to the state-space constraint that queue lengths are necessarily nonnegative, is that the continuous-time system dynamics is actually the projection of a smooth system of ordinary differential equations. This also leads to discontinuities in the boundary dynamics of a sort common in queueing problems. The project is concerned with the design of a feedback controller to minimize accumulated queue lengths in the presence of unknown inflow disturbances at an isolated intersection and a traffic network with some signalized intersections. A dynamical system has finite L₂-gain if it is dissipative in some sense. Therefore, the H<SUB>infinity</SUB>-control problem turns to designing a controller such that the resulting closed loop system is dissipative, and correspondingly there exists a storage function. The major contributions of this thesis include 1) to propose state space models for both isolated multi-phase intersections and a class of queueing networks; 2) to formulate H<SUB>infinity</SUB> problems for the control systems with persistent disturbances; 3) to present the projection dynamics aspects of the problem to account for the constraints on the state variables; 4) formally to study this problem as a hybrid system; 5) to derive traffic-actuated feedback control laws for the multi-phase intersections. Though we have mathematically presented a robust feedback solution for the traffic signalization, there still remains some distance before the physical implementation. A robust adaptive control is an interesting research area for the future traffic signalization. / Ph. D.

Purpose: To determine the timing of first ambulation during hospitalization among patients admitted for acute myocardial infarction (AMI) and to identify the predictors of first ambulation. Methods: This retrospective cohort study included 500 AMI patients admitted during 2004 to one of three hospitals that form the Hamilton Health Sciences Corporation in Hamilton, Ontario, Canada. The patients were randomly selected from a total of 1,014 charts from the Hamilton Health Sciences Computerized Health Records (SOVERA). Using a chart abstraction tool, the following data were collected from each patient's chart: demographic information, past medical history, treatment, complications, and patterns of ambulation while in hospital. The primary outcome was first ambulation, defined as the first time patients walked during their hospital stay. Secondary outcomes included heart rate at discharge and mortality during hospitalization. The relationship between patient and care-related factors and the time of first ambulation after AMI was explored through a time to event analysis using Cox regression; the associations were expressed as hazard ratios. The fit for the proportional hazard model was assessed and a stratified proportional hazard model was performed for age. Results: Of the 500 charts, 60 were excluded. Of the 440 patients who were included in the final analysis, 340 (77.3%) walked during hospitalization. One hundred fifteen (26.1 %) walked during the first 48 hours (early walking), 98 (22.3%) walked between 49-96 hours (intermediate walking), and 127 (28.9%) walked after 96 hours (late walking). A total of 100 patients (22.7%) were categorized as non-walkers. Factors that emerged in the survival analysis that were positively associated with early ambulation after AMI and that proved the proportionality on the assessment of the fit of the model were: having a family history of cardiovascular disease (HR 1.33; 95% Cl 1.00, 1.44; p=0.05), receiving thrombolysis (HR 1.47; 95% Cl 1.11, 1.49; p=0.007), receiving nitroglycerin (HR 1.51; 95% Cl 1.19, 1.93; p<0.001 ), and taking calcium channel blockers (HR 1.58; 95% Cl 1.22, 2.05; p<0.001 ). Factors that were negatively associated with early ambulation after AMI were age >59 years (HR 0.98; 95% Cl 0.97, 0.99; p<0.001 ), having an arrhythmia in-hospital (HR 0.48; 95% Cl 0.22, 0.94; p=0.04), taking inotropic drugs (HR 0.72; 95% Cl 0.53, 0.98; p<0.001 ), and undergoing coronary artery bypass surgery (HR 0.51; 95% Cl 0.33, 0.78; p=0.002). Conclusion: There is variability in the timing of first ambulation among patients hospitalized with an AMI. Furthermore, those who walked early were more likely to have a family history of cardiovascular disease, have received thrombolysis, and be taking nitroglycerin or calcium channel blockers. Those least likely to walk early were older (>59 years), were more likely to have had an arrhythmia inhospital, to be taking inotropic drugs, and to have undergone coronary artery bypass surgery. / Thesis / Doctor of Philosophy (PhD)

Land value capture (LVC) has been used to capitalize on the symbiotic relationship between rapid transit and its potential land value uplift (LVU) benefits for more than a century. For the public sector in particular, the rationale to engage in LVC to recapture the ‘unearned increment’ is strong. While interest in LVC has wavered over this time, planners and policymakers in Ontario and around the world are increasingly looking to value capture as a potential solution for raising more revenue to fund the construction and operation of rapid transit projects. However, significant theoretical, conceptual, and practical gaps remain in our knowledge of LVU and LVC that prevent the wider adoption of value capture as a strategy. First, a fundamental flaw in applications of LVC is that the value increment caused by rapid transit must to some degree be known a priori to set benchmark levels and ensure LVC tools capture the actual changes in land values caused by the project. Yet despite a rich history of research into the LVU benefits of rapid transit in cities around the world, a method for arriving at more empirical predictions of future LVU beyond simple approximation remains elusive. This leads to a second issue. Previous research into the LVU effects of rapid transit has produced a body of work that exhibits significant heterogeneity in results. Such diversity in research outcomes is due to a singular focus on expectations of LVU from rapid transit accessibility, which has led previous research to ignore the potential for additional land value impacts from sorting into different bundles of transit-oriented development (TOD) based on individual preferences. As such, the results of previous studies consider the value placed on a bundle of transit and TOD characteristics. This context-dependency makes them unsuitable for extensions to estimate the potential for LVC in future transit corridors. To overcome these issues, the present dissertation develops a value planning framework for rapid transit. This is accomplished through five objectives. First, Chapter 2 establishes a theoretical framework for understanding the LVU effects of rapid transit accessibility and TOD. Second, Chapter 3 develops a typology of station area TOD to reduce the complexity of station area heterogeneity and control for such contextual factors in further research. Third, Chapter 4 applies the TOD typology to unbundle the LVU effects of existing rapid transit in the City of Toronto. Fourth, Chapter 5 develops the value planning framework to better conceptualize the drivers of LVU benefits and capturable revenues, the policy interventions to maximize them, and the beginnings of a model to utilize unbundled estimates of LVU in other study areas to derive context-sensitive predictions of LVU in future transit station areas. Finally, Chapter 6 conducts a theoretical application of the value planning framework to the case of a light rail transit line in Hamilton, Ontario, to demonstrate a rationale for engaging in value planning to promote value capture. In accomplishing these objectives, the present dissertation makes a number of contributions to research and practice. However, it also raises a number of questions for future research. Nevertheless, this work presents a significant first step towards realizing research on rapid transit’s LVU effects that is more theoretically comprehensive and practical for better informing LVC planning and policy around the world. / Dissertation / Doctor of Philosophy (PhD)

<p>High density sampling (n=50) was conducted in Cootes Paradise, a shallow wetland on the western shoreline of Lake Ontario near the city of Hamilton. Cootes Paradise is an urban wetland that has been affected by pollutants and nutrients and invasive carp. Thecamoebian analyses paired with site specific environmental measurements (depth, sp. conductivity, temperature, DO and pH) and substrate characteristics (textural and organic content -LOI) show relationships (R² = 0.6) with depth (0-1m) and corresponding sp. conductivity (0.5 to 0.65 mS/cm) and temperature (26.5 to 30.5 °C). Q-mode cluster analysis recognized two biofacies. Biofacies 1 samples (n= 26) are found in the deeper areas (0.70 ± 0.27 m) and dominated by <em>C. tricuspis</em> 36 ± 8% (1 std), <em>L. vas</em> 18 ± 13% and <em>D. protaeiformis “claviformis”</em> 14 ± 6%. Mean water temperature is 28.0 ± 0.6 °C and conductivity at 0.56 ± 0.04 mS/cm. This assemblage has low species diversity (SDI=1.9 ± 0.3) which indicates a transitional environment. Biofacies 2 contains samples (n= 24) which are found in shallower areas (0.38 ± 0.15 m) and the assemblage is characterized by <em>C. constricta “aerophila”</em> 25 ± 8%, <em>C. tricuspis</em> 18 ± 5%, <em>Cyclopyxis sp.</em> 9 ± 6 % and <em>L. vas</em> 9 ± 4 %. The SDI for Biofacies 2 is 2.2 ± 0.2 and like Biofacies 1 shows a transitional environment. The average temperature is and 29.0 ± 1.0 °C with mean sp. conductivity also slightly higher than Biofacies 1 at 0.6 ± 0.04 mS/cm.</p> / Master of Science (MSc)

<p>While there are numerous studies of the police, few have addressed the changes in policing that have occurred since the turn of century. Prior studies address issues such as police effectiveness, social control, the military model of police organization, police socialization, and the relationship between crime rates and the size of police forces. Although these studies have provided insight into different aspects of policing, they have not established a comprehensive understanding of the police as an institution. In other words, we have little understanding of what has caused the police to change. Further, we know little about the substance and consequences of change.</p> <p>My goal is to conduct an exploratory study of changes in policing by examining the main trends in the Hamilton, Ontario, Police Department between 1900 and 1973. Trends in economics, organization and work are considered. The study provides significant findings, which can be understood in relation to the existing literature, and can provide new questions to serve as the basis for future research.</p> <p>I explain trends in policing in relation to larger social and historical factors including population growth, the changing distribution of crime, and the role of the automobile. Change was pluralistic; different factors contributed to major changes in policing. Often, change was the result of external circumstances -the larger social context provided both the motivation for change and the possible range of alternatives that could be implemented. In Hamilton, the twentieth century was a period of considerable population growth. At the same time, the city was being transformed by the automobile, a revolution that redefined urban space, patterns of social interaction and the mobility of citizens. Over the course of the century, there was a substantial shift in the distribution of criminal offenses. It is within this context that significant changes to policing occurred.</p> <p>The police responded to the changing times by changing themselves. The growth of the Department paralleled that of the city. The police adopted cars and motorcycles for patrols to cope with traffic problems and to provide a quick response to citizens in need. The Department was completely reorganized and became more professional. At the same time, the costs of policing were rising. Police chiefs continually struggled to find ways to cope with rising wages and declining work weeks. Citizens would be hired, technology employed, patrol strategies changed to cope with declining productivity.</p> <p>The findings of my research suggest that changes to the Hamilton Police can be understood in terms of diffusion theory. The larger social milieu provided not only the motivation for change: it limited the range of possible solutions at any given point in time. I argue that changes to the Police Department were a direct result of their ability to adopt innovations. Ultimately, to understand the police we must view them as social and historical products.</p> / Doctor of Philosophy (PhD)

There has been an increase in reactionary racial violence in the past eight years following the presidency of Barack Obama, and in response to perceived threats to the racial and cultural order posed by movements for racial justice and the refugee crisis. Complicit to the spate of organized racial violence are passive white bystanders, who, through their inaction, have tolerated and given free reign to a resurgence of racial violence. Only a minority of whites have responded to calls for solidarity from Black, Indigenous and People of Color (BIPOC). This study set out to uncover how these minority of whites respond to racism. Drawing on narratives and questionnaires of thirty-eight white persons, I begin with an exploration of the frames that shape participants’ understanding of antiracism. Three frames are discussed: the (a) equality and human rights frame, (b) anti-oppression frame, and (c) whiteness-centered frame. The core of this study is on antiracism praxis. I discuss two categories of praxis: quotidian antiracism and organizational antiracism. In the former category are three types of antiracism strategies: (a) confrontation, (b) counterclaiming, and (c) covert and clandestine antiracism. The latter category consists of equality and equity focused strategies in education that I distinguish based on setting: (a) classroom antiracism and (b) administrative antiracism. This discussion is enriched by an investigation of the enablers and obstacles of antiracism and what respondents consider when deciding to engage in bystander action. In conversation with Frankenberg’s (1993) ‘race-cognizance’ concept, I present a subsidiary antiracism awareness that I call self-implication cognizance. I detail five ways participants stop themselves from ‘racing to innocence’ by implicating themselves in the hegemonic order of whiteness. This study contributes a typological model of frames and praxis and a situated picture of enablers of antiracism to the scholarship of white antiracism. It also offers insights for progressive whites and organizations interested in racial justice, equality and equity. Subject keywords: antiracism, activism, whiteness, white racial identity, racial awareness, frames, enablers, obstacles, racism / Dissertation / Doctor of Philosophy (PhD)

According to the literature, youth experiencing with either homelessness or disabilities face severe barriers throughout their life-time which would negatively impact their physical development, psychological development, and mental health, but also contribute to a vicious circle of homeless and poverty. However, the intersection between homeless youth with learning, developmental and/or intellectual disabilities (LD/DD/ID) in the school system has rarely been explored. This population is invisible to the school system which indicates an urgency in identifying and understanding their experience at school. This research, as a part of the Partnering for Change initiative, aimed to provide some insight into the socially constructed problems which cause barriers for this invisible population. In this study, an interpretive lens and a critical approach were adopted as a guide to data analysis and as a means to identify constructed barriers based on the interviews with homeless youth with LD/DD/ID in Hamilton, Ontario, Canada. The data on homeless youth with LD/DD/ID was analysed for impacts on relationships, academic performance, and the effects of invisibility on multiple levels of their school life. The data also revealed the way schools respond to disabilities and homelessness. In the discussion I investigate the way policy, funding structure and implementation of support are significantly affected by the neoliberal context with its emphasis on market-driven pedagogy and individuals conceptualized as agents of self- capitalization. This thesis argues for a better alternative, as referenced from Finland. The Finnish approach emphasizes human rights, equality, and inclusion, and aims to demonstrate how changes in fundamental beliefs and values can construct a barrier-free and supportive education system for everyone. / Thesis / Master of Social Work (MSW)

This work examines British inquiry into the human mind in the early nineteenth century using a multivalent structural analysis of ideas and practices within traditions established by Hume, Hartley, and Reid. While these traditions were propagated into the nineteenth century by such figures as Thomas Brown, James Mill, Sir William Hamilton, and Alexander Bain, this later period has received a dearth of attention in the history of psychology, the history of philosophy, and the history of ideas in general. This conspicuous lacuna forms the basis for two simple questions: What was the situated significance of work on the human mind in nineteenth century Britain? What was it supposed to accomplish, or be about? In particular, I focus on the differentiation of science from philosophy as a particular kind of non-science, investigating a set of existing formulations of the respective characters of the two. Using this historiographic survey as a springboard, I establish an analytical apparatus based upon four structural dimensions that I term conceptual, expository, iconic, and genealogical. Taken together, these four elements form an historical problematic, a set of persistent features and issues that structured work on mental subjects. With respect to conceptual structure, I propose a set of a dozen persistently central, but fluid, concept clusters involved in the study of mind. Regarding texts themselves, I situate my subject in terms of specific audience groups, patterns of expository development, and topical scope. I also examine the limiting influence of authorial and editorial practices on the appearance of the conceptual systems these texts convey. Iconic structural patterns focus even more closely on textual content, demonstrating shifts in the density, nature, and extent of citation within the intellectual community. These four dimensions interact significantly, reflecting the complex character of an active community of intellectual discussion. Having established this analytical space, I return to the basic terminological distinction between science and philosophy to investigate what was at stake in distinguishing these two fields in the nineteenth century. The dichotomy was far from definitive: British mental inquiry from the time of Hume's Treatise to that of Bain's first two major works never established a firm division of science from philosophy, but the evidence suggests several directions of tension along which this split would subsequently emerge. As demonstrated by evidence from the first volume of the journal, Mind, founded by Bain in 1876, discussions among students of the human mind in the nineteenth century established a position for mental philosophy itself as arbiter of the new science-philosophy dipole. In this light, the establishment of Mind can be viewed as the creation of a boundary-object that itself constituted this distinction in psychological terms. / Ph. D.