<p> This thesis investigates the application of multiple model estimation algorithms to the problem of channel equalization for digital data transmission and channel tracking for space-time block coded systems with non-Gaussian additive noise. Recently, a network of Kalman filters (NKF) has been reported for the equalization of digital communication channels based on the approximation of the a posteriori probability density function of a sequence of delayed symbols by a weighted Gaussian sum. A serious drawback of this approach is that the number of Gaussian terms in the sum increases exponentially through iterations. In this thesis, firstly, we have shown that the NKF-based equalizer can be further improved by considering the interactions between the parallel filters in an efficient way. To this end, we take resort to the Interacting Multiple Model (IMM) estimator widely used in the area of multiple target tracking. The IMM is a very effective approach when the system exhibits discrete uncertainties in the dynamic or measurement model as well as continuous uncertainties in state values. A computationally feasible implementation based on a weighted sum of Gaussian approximation of the density functions of the data signals is introduced. Next, we present an adaptive multiple model blind equalization algorithm based on the IMM estimator to estimate the channel and the transmitted sequence corrupted by intersymbol interference and noise. It is shown through simulations that the proposed IMM-based equalizer offers substantially improved performance relative to the blind equalizer based on a (static or non-interacting) network of extended Kalman filters. It obviates the exponential growth of the state complexity caused by increasing channel memory length. The proposed approaches avoid the exponential growth of the number of terms used in the weighted Gaussian sum approximation of the plant noise making it practical for real-time processing.</p> <p> Finally, we consider the problem of channel estimation and tracking for space-time block coded systems contaminated by additive non-Gaussian noise. In many practical wireless channels in which space-time block coding techniques may be applied, the ambient noise is likely to have an impulsive component that gives rise to larger tail probabilities than is predicted by the Gaussian model. Although Kalman filters are often used in practice to track the channel variation, they are notoriously sensitive to heavy-tailed outliers and model mismatches resulting from the presence of impulsive noise. Non-Gaussian noise environments require the modification of standard filters to perform acceptably. Based on the coding/decoding technique, we propose a robust IMM algorithm approach in estimating time-selective fading channels when the measurements are perturbed by the presence of impulsive noise. The impulsive noise is modeled by a two terms Gaussian mixture distribution. Simulations demonstrate that the proposed method yields substantially improved performance compared to the conventional Kalman filter algorithm using the clipping or localization approaches to handle impulses in the observation. It is also shown that IMM-based approach performs robustly even when the prior information about the impulsive noise is not known exactly.</p> / Thesis / Master of Applied Science (MASc)

Fiscal capacity is some type of quantifiable measure of economic resources existing within a political subdivision, jurisdiction, or governmental unit which may be utilized to support a wide array of public functions. Measures commonly used throughout the United States as indicators of economic capacity are tax bases and personal income. The most commonly used measure for fiscal capacity is equalized assessed value of property within the governmental units in question. Once the fiscal capacity is determined, relative capacity among governmental units may be calculated by dividing the aggregated capacity measure by total population or total pupils. The equalization of educational opportunity is dependent partially upon accurately measuring a locality's ability to pay taxes. Prior to the 1971 establishment of the Standards of Quality in Virginia, the public school funding formula relied exclusively on equalized (true) valuation per pupil to measure the fiscal capacities of the several school divisions. Unfortunately, by employing only true valuation per pupil as the sale measure of fiscal capacity approximately fifty percent of the ability to pay was ignored. As a consequence, the Commonwealth developed and implemented a index of fiscal capacity composed of several measures of fiscal capacity. / Ed. D.

Blind equalization schemes are used to cancel the effects of a channel on the received signal when the transmission of a training sequence in a predefined time slot is not possible. In the absence of a training sequence, blind equalization schemes can also increase the throughput of the overall system. A general problem with blind adaptation techniques is that they have poor convergence properties compared to the traditional techniques using training sequences. Having a multi-modal cost surface, blind adaptation techniques may force the equalizer to converge to a false minimum, depending on the initialization. The most commonly used blind adaptation algorithm is the Constant Modulus Algorithm (CMA). It is shown by simulation that a logarithmic error equation can make CMA converge to a global minimum, if a differential encoding scheme is used. The performance of CMA with different error equations is also investigated for different channel conditions. For a time varying channel, the performance of an equalizer not only depends on the convergence behavior but also on the tracking property, which indicates the ability of an equalizer to track changes in the channel. The tracking property of a blind equalizer with CMA has been investigated under different channel conditions. It is also shown that the tracking property of a blind equalizer can be improved by using a recursive linear predictor at the output of the equalizer to predict the amplitude of the equalizer output. The predicted value of the amplitude is then used to adjust the instantaneous gain of the overall system. A recursive linear predictor is designed to predict a colored signal without having a priori knowledge about the correlation function of the input sequence. The performance of the designed predictor is also investigated by predicting the envelope of a flat fading channel under constant mobile velocity and constant acceleration conditions. / Master of Science

My dissertation examines the unique contribution of school district boundaries – over and above municipal boundaries – in the suburban context, which can tell us more about how today’s multiracial suburbs came to be structured and stagnated in such residentially and educationally segregated ways. Specifically, this dissertation aims to provide insight into how school districts are a compelling structural force in social and spatial hierarchies and explain why we need to build a deeper understanding of their unique role in the self-perpetuating segregation we find in suburban spaces. This study focuses on Westchester County, NY at key inflection points from the 1800s to 2023, including phases of suburbanization, diversification, and legal contention over housing access. This suburb north of New York City is a study of contrasts in many ways, as it has evolved into a profoundly racially and economically stratified county with extreme differences in wealth and demographics across its highly spatially fragmented landscape. This study is informed by a theoretical framework that takes a critical spatial approach to the study of local bordering practices. This dissertation demonstrates the need to take seriously the spatial dimensions of education, which point toward systems of power that shape our understanding of “good” and “bad” schools. Utilizing GIS mapping, municipal and school demographic data, legal documents, and real estate marketing data, I analyze the unique spatial impact of school districts on housing policy in a range of spatial contexts. Focusing specifically on publicly subsidized affordable housing, this research highlights the unique history of debates over segregated housing in Westchester, making it an ideal case study for understanding the relationship between school district boundaries, affordable housing access, and social reputation. I contextualize my analysis throughout with historical archival and demographic materials demonstrating how educational spaces have shifted through time. Centering the interconnected spatial relationships of educational and residential boundaries fills the gap in our understanding of the unique contribution of educational borders as powerful spatial structures that can create, reproduce, and interrupt society through their influence on collective individual action. The findings throughout this research shed light on the complexities of the relationship between school districts and municipalities in diversifying suburban spaces and emphasize the critical need for a more spatially aware research agenda in the study of the school-housing nexus. This dissertation demonstrates that school district boundaries shape children’s educational opportunities in a number of profound ways. My findings on next-door inequality emphasize how living on one side of a school district boundary or another can mean tens of thousands of dollars in difference in per-student spending and vastly different demographics in student populations. The racial and economic separation that is happening between school district neighbors in Westchester is only exacerbated by the extensive fragmentation of small districts that have been treated as sacrosanct for decades without consideration of any broader benefit to their reorganization.

In the present era of inclusion, special schools increasingly serve as spaces for the delivery of supplementary education and rehabilitation services for mainstreamed disabled children. A history of segregation and institutionalization weigh heavily on the sector, prompting many special educators to advocate for students' continued mainstreaming (often against students' wishes) through mastery of the necessary compensatory techniques and technologies that promise to help them attain equality with their non-disabled peers in mainstream schools. Drawing on 14 months of ethnographic research, including bi-weekly in-person participant observation and semi-structured interviews with educators and parents, in a public special school for the blind and visually impaired in southern France, this dissertation explores the narratives and practices that maintain educators in a deficit mindset vis-à-vis disabled lives, a mindset from which it becomes difficult to see the potential of visual impairment to contribute to an enacted, non-representational epistemology in an education system based on ocular-centric objectivism. Nevertheless, students harness being together disabled at the school to make sense of the world through their unique phenomenologies in which sight often plays a surprisingly important part. Engaging anthropology, embodied cognitive science, and critical disability studies, I argue that sight shows up for the children as a tool of playful curiosity for learning in an always emergent present, a disposition I call "sight as question" that stands in contrast to the objectivist "sight as power" standard in mainstream schools. In re-conceptualizing the special school as understated space of embodied knowledge creation, my dissertation makes three primary contributions. First, I show how the French state's race to mainstream all students has exacerbated reactionary approaches to educating disabled children, a reality now hidden behind an innovative facade of assistive technology. Second, I document how such situation continues with the full compliance of otherwise progressive-minded educators because of a historical cultural context wherein national public education is instilled with the status of meritocratic authority responsible for vetting all children for epistemic conformity as a matter of égalité. Finally, I offer an alternative perspective for repurposing special schools to spaces of phenomenological potential led by members of the disabled community and explore what, as such, they might contribute to teaching and learning in an age of artificial intelligence.

Educational and psychological tests are critical for measuring latent traits, yet their fairness can be compromised by Differential Item Functioning (DIF), where individuals of similar abilities across demographic groups have unequal probabilities of correct responses. To address these challenges, this study introduces the Fair Rasch Model (FRM) and Generalized Fair Rasch Model (GFRM), which integrate fairness regularization into the Rasch model framework to mitigate DIF effects during parameter estimation without requiring prior DIF detection. These models use adjustable hyperparameters to balance fairness and estimation accuracy. Simulation studies demonstrate that FRM and GFRM outperform existing methods in ability estimation, especially under conditions with high DIF magnitude or prevalence. In real data analysis using TIMSS 2015 mathematics assessments, the models minimized gender disparities in ability estimates more effectively than existing approaches. This study advances equitable testing practices, offering a novel approach to addressing DIF in psychometric assessments.

This study examined different funding methods for financing public education in order to solve the problems associated with large numbers of school districts and great disparities in property wealth without abandonment of property tax as the major revenue source. Using enrollment and State Property Tax Board data for the 1,061 school districts in Texas in 1986-87, four alternative funding plans were studied to compare the equity and fiscal impact of each on public school finance in Texas. The state and local shares of the total cost of education were computed using a combination of three per-pupil expenditure levels and four funding formulas. The per-pupil expenditure levels used were $3,850, $4,200, and $4,580. The formulas used were representative of a full state funding plan, a percentage equalization plan, a power equalization plan, and a foundation school program plan. Since each of the four plans used significantly higher per-pupil expenditure values, all required a greater monetary investment on the part of the state. However, all plans were found to be equalizing in nature if set per-pupil expenditure values were maintained and no local enrichment was permitted. In addition, each of the four plans, as studied, met the fiscal neutrality standard of the 1987 Edqewood v. Kirbv case. The percentage and power equalization plans required less monetary investment on the part of the state than either full state funding or the foundation school program. As a result of the study, it is recommended that the state consider a combination of plans. For example, the state could employ a full state funding model up to the $3,850 per-pupil expenditure level with added permissible local millage being limited and power equalized. In addition, while each of the plans studied reduces inequity, the increased cost of an adequate public school education suggests that the state consider other sources of revenue to fund public education. These could include personal or corporate income taxes.

The use of optical fiber is of great interest in developing extensive, high-speed networking infrastructures. Optical fiber provide many advantages over traditional copper cables and wireless links. Among them are high security, low electromagnetic interference, extremely low loss and high bandwidths, light weight and manageability. However, the very small wavelengths associated with optical radiation requires very small waveguide dimensions. Waveguide dimension of single mode fiber (SMF) are < 10µm, resulting in relatively poor yield in device manufacturing. For residential and other last-mile networks topologies, cost constraints limit the appeal of SMF. Multimode fiber (MMF) allow for less restrictive manufacturing tolerances; however, the distortion that results from the dispersion in propagation among the many modes can be prohibitively large for data rates approaching and exceeding 1 Gb/s. To improve the deployability of MMF, a method of dispersion compensation that maintains the ease-of-use characteristic of MMF is required This dissertation demonstrates an opto-electronic method of dispersion compensation by the use of a multisegment photodetector. It is shown the modes of the fiber can be seperated such that when the individual photodetector signals are combined, the resulting temporal response of the fiber link is improved from that of a conventional fiber link. This method is extremely robust to system variation and is independent of data rate and transmission format, allowing it to be employed in a wide variety of optical links. More importantly, the implementation demonstrated is comparable, in simplicity and alignment tolerance, to a conventional photodetector. System performance is shown using both temporal and frequency response as well as real bit error rate and eye diagram measurements.

Thesis (M.A.)--University of Toronto, 2004. / Adviser: Kathy Bickmore.

Diabetic retinopathy (DR) is becoming a global health concern, which causes the loss of vision of most patients with the disease. Due to the vast prevalence of the disease, the automated detection of the DR is needed for quick diagnoses where the progress of the disease is monitored by detection of exudates changes and their classifications in the fundus retina images. Today in the automated system of the disease diagnoses, several image enhancement methods are used on original Fundus images. The primary goal of this thesis is to make a comparison of three of popular enhancement methods of the Mahalanobis Distance (MD), the Histogram Equalization (HE) and the Contrast Limited Adaptive Histogram Equalization (CLAHE). By quantifying the comparison in the aspect of the ability to detect and classify exudates, the best of the three enhancement methods is implemented to detect and classify soft and hard exudates. A graphical user interface is also adopted, with the help of MATLAB. The results showed that the MD enhancement method yielded better results in enhancement of the digital images compared to the HE and the CLAHE. The technique also enabled this study to successfully classify exudates into hard and soft exudates classification. Generally, the research concluded that the method that was suggested yielded the best results regarding the detection of the exudates; its classification and management can be suggested to the doctors and the ophthalmologists.