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S. Johri and R. Bhatt developed a real-space renormalization group approach aimed at extracting the localized single-particle eigenstates of the Anderson model from a large system by identifying clusters of resonant site potentials. E. Campbell generalized this real-space renormalization group approach using standard perturbation theory. Both approaches were intended to approximate the single-particle density of states of the Anderson model. In this thesis, we aimed to test the potential of applying a similar real-space renormalization group approach to calculate the density of states of the interacting Anderson-Hubbard model. Our interest in the density of states of this model is due to a V-shaped zero-bias anomaly in two-dimensional systems. A real-space renormalization group approach is best applied to a one-dimensional system. We found that the zero-bias anomaly is not V-shaped in one-dimension. To test the potential of a real-space renormalization group approach, we used the cluster approach which is the same as the non-interacting renormalization group approach but without the perturbation theory and found that for strong disorder this technique could accurately calculate the density of states over a wide range of energies but deviated from exact results at the band edge, at $\omega=\pm U$ and near $\omega=0$. The first two inaccuracies will be reduced with a proper real-space renormalization group approach. We suspect that the last inaccuracy is associated with long range physics and may be difficult to recover. We also developed a technique that adjusts the identification of clusters in the cluster approach to improve the computation time of the density of states with minimal loss of accuracy in a tunable range around the Fermi level. We found that this technique significantly reduced the computation time and was able to preserve the density of states near the Fermi level, except at the smallest energies near $\omega=0$.

Author Keywords: Anderson-Hubbard model, renormalization group, Strong electron correlations, Zero-bias anomaly

Chultuns are subterranean chambers that are found throughout the Maya area. The purpose of this thesis is to provide further insight into the function of chultuns, specifically within the area of the Southern Maya Lowlands. Within the Northern Lowlands, the Pre-Columbian Maya used chultuns for water storage, but this function does not appear to be as prevalent within the Southern Lowlands Through reviewing published literature and first-hand excavation, a total of 332 chultuns located with the specified area were catalogued into a database. Based on the information obtained from the research, this thesis has identified the most frequent final function of chultuns, if there is chronological change in final functions of chultuns, and if there is regional change in final functions of chultuns.

Author Keywords: burial, chultuns, Maya, ritual, Southern Lowlands, storage

Upland Sandpipers (Bartramia longicauda), like many grassland birds, are undergoing population decline in parts of their range. Habitat fragmentation and change have been hypothesized as potential causes of decline. I used citizen-science occurrence data from Wildlife Preservation Canada's Adopt-A-Shrike Loggerhead Shrike (Lanius ludovicianus) program in conjunction with validation surveys, using similar point-count methods, to examine detectability and determine if landscape level habitat features could predict occupancy of Upland Sandpipers in Southern Ontario. In a single season detectability study, I used Wildlife Preservation Canada's survey protocol to determine detectability in sites that were known to be occupied. Detectability was low, with six surveys necessary to ensure detection using a duration of at least 18 minutes early in the breeding season. The proportion of open habitat did not affect detection on the landscape. Using a larger spatial and temporal scale, with five years of citizen-science data, I showed that Annual Crop Inventory data could not effectively predict Upland Sandpiper occupancy. Model uncertainty could be attributed to survey protocol and life history traits of the Upland Sandpiper, suggesting that appropriate survey methods be derived a priori for maximizing the potential of citizen-science data for robust analyses.

Author Keywords: Bartramia longicauda, citizen-science, detection, landscape, occupancy, Ontario

In 2004 it was discovered that a two-dimensional electron gas (2DEG) forms at the interface between lanthanum aluminate (LAO) and strontium titanate (STO). This 2DEG exhibits a variety of electronic and magnetic phenomena, motivating intense research into its applicability to electronic devices. Over the years several models have been developed in theoretical exploration of this system. Here, the transverse Ising model is applied to the LAO/STO interface for the first time. It is shown that the model as it is traditionally formulated cannot accurately predict the structure of the electron density at the interface. I show that this can be fixed with a simple modification of the model, and discuss how this modification affects both the polarization distribution in ferroelectric thin films and the electron density at the LAO/STO interface. The importance of including the depolarizing field when modelling spatially inhomogeneous ferroelectric systems is also explored.

Author Keywords: ferroelectric thin film, lanthanum aluminate, strontium titanate, transverse Ising model, two-dimensional electron gas

This case study contributes to scholarship surrounding the national conversation on Indigenous language sustainability in North America. Much of this scholarship provides insight on structuring language programs and policies for youth, leaving a tremendous research gap regarding sociolinguistic and cultural research with youth. Youth appear disinterested or otherwise set apart in current research from the development of policies and curriculum concerned with heritage languages. Upon closer inspection; however, youth are engaged and using innovative and different tools than previous generations. This exploration is a foundational case study which builds upon research highlighting the nature of Indigenous language loss in the south as a time sensitive phenomenon as the application of cognitive imperialism and colonial tactics within mainstream schools continue to conceal a large scale cultural and linguistic genocide in Canada.

Although Indigenous language loss may seem of concern to only small groups of linguists and dialectic communities, it should in fact concern anyone who cares about reconciliation or closing the tremendous gap in accessing equitable education. The preservation of Indigenous languages and knowledge systems should also be of interest to those parties who seek to comprehensively understand the Natural World and whom have a vested interest in the survival of the planet and protection of the enviroment. Because of these realities, the viewpoints and experiences of all concerned parties are essential. It follows then, that the youth perspective is significant.

To address this gap, participatory narrative inquiry was used as a theoretical framework to conduct a foundational case study in which detailed consideration was given to exploring the lived narratives of three Anishnaabeg participants to establish the value of Indigenous youth voice in alternative forms of sociolinguistic and culturally sustainable language learning in the 21st century, and, to strengthen the argument that more research is needed in the field of first-person youth studies.

The results of this case study will be useful, specifically, to localized communities of Anishnaabe youth with and for whom much of the research was conducted, and, more generally to youth resistance work focused on media and technology in globalized and contemporary language and cultural ecologies. Research outcomes indicated potential directions for future research in different contexts and localities by presenting commonalities within the fields of social and political engagement and their connection to language and new media in youth populations. It is hoped that this initial material pinpointing a research gap in Indigenous youth language studies will be used to investigate future research in this field.

Author Keywords: Anishnaabe, Decolonization, Language, Sociolinguistics, Technology, Youth Studies

The parasitic protist Giardia intestinalis has five heme proteins: a flavohemoglobin and several isotypes of cytochrome b5. While the flavohemoglobin has a role in counteracting nitric oxide, the functions of the cytochromes (gCYTb5s) are unknown. In this study, the protein level and cellular localization of three gCYTB5 isotypes (gCYTb5-I, II and III) and flavohemoglobin were examined in Giardia trophozoites exposed to three nitrosative stressors at two different concentrations: nitrite (20 mM, 0.5 mM); GSNO (2 mM, 0.25 mM) and DETA-NONOate (2 mM, 0.05 mM). An increase in protein levels was observed for gCYTb5-II with all stressors at both concentrations. However, the effects of these nitrosative stressors on gCYTb5-I and III were inconclusive due to the variation among the replicates and the poor detection of gCYTb5- III on western blots. The protein level of the flavohemoglobin also increased in response to the three stressors at the low concentrations of stressors that were tested. Only the cellular localization of gCYTb5-I changed in response to nitrosative stress, where it moved from the nucleolus to the nucleus and cytoplasm. This response was extremely sensitive and occurred at the lower doses of the three stressors, suggesting that gCYTb5-I may be involved in a nucleolar- based stress response.

Support Vector Machines (SVMs) are a deterministic, supervised machine learning algorithm that have been successfully applied to many areas of research. They are heavily grounded in mathematical theory and are effective at processing high-dimensional data. This thesis models a variety of galaxy classification tasks using SVMs and data from the Galaxy Zoo 2 project. SVM parameters were tuned in parallel using resources from Compute Canada, and a total of four experiments were completed to determine if invariance training and ensembles can be utilized to improve classification performance. It was found that SVMs performed well at many of the galaxy classification tasks examined, and the additional techniques explored did not provide a considerable improvement.

Author Keywords: Compute Canada, Kernel, SDSS, SHARCNET, Support Vector Machine, SVM

Environmental DNA (eDNA) is rapidly becoming an established method for the detection of species in aquatic systems and has been suggested as a promising tool to estimate species abundance. However, the strength of the relationship between eDNA concentrations and taxon abundance (density/biomass) can vary widely between species. I investigated the relationship between eDNA concentration and species abundance using two common and closely-related amphibians in eastern North America, the wood frog (Rana sylvatica) and northern leopard frog (Rana pipiens). I manipulated tadpole density in 80 L mesocosms and documented the relationship between tadpole density, biomass, and eDNA concentration. Species were comparable in biomass but differed in the amount of detectible genetic material produced; density and biomass were the superior abundance metric correlated with eDNA concentration for wood frogs and leopard frogs, respectively. However, increases in eDNA concentration reflected increasing tadpole biomass, therefore biomass is likely a better metric of abundance than density. Overall my findings support that eDNA concentration can be used as an index of species abundance, but that species-specific calibration may be needed before eDNA concentration can be effectively translated to an abundance metric. Future research should refine our understanding of how biotic and abiotic factors influence eDNA production, degradation, and recovery across species, before the method can receive widespread use as a monitoring tool in natural settings.

Author Keywords: abundance estimates, environmental DNA, mesocosm, Rana pipiens, Rana sylvatica

Recent developments at an aluminum (Al) smelter in Kitimat, BC resulted in a permitted increase of 27 to 42 tonnes of sulphur dioxide (SO2) emissions per day. Gaseous SO2 is a pollutant known to contribute to acidic deposition through processes of wet and dry deposition and can additionally react in-atmosphere to form particulate sulphate (pSO42-). Between June 2017 to October 2018, an extensive network consisting of ion exchange resin (IER) column, passive-diffusive, and active filter-pack samplers was established to provide an estimate of total annual S deposition and pSO42- variation throughout the Kitimat Valley. Filter-pack sampling determined the relative concentration of pSO42- increased downwind of the smelter. Comparison of observation-based and modelled total annual deposition suggested CALPUFF was accurate in representing the spatial viability of S deposition (R2 = > 0.85). However, the model appeared to overpredict near-field deposition suggesting the potential of underestimation further downwind of the smelter.

Author Keywords: aluminum smelter, atmospheric deposition, filter-pack sampler, ion-exchange column sampler, pSO42-, SO2