VictorJuiz/thesis huggingface dataset:
Topics on Based Loop Groups

We prove two generalizations of localization formulae for finite-dimensional spaces to the infinite-dimensional based loop group ΩG. The Atiyah-Bott-Lefschetz Formula is a well-known formula for computing the equivariant index of an elliptic operator on a compact smooth manifold. We provide an analogue of this formula for the based loop group ΩSU(2) with respect to the natural (T × S1)-action. This is accomplished by computing certain equivariant multiplicities in the K-theory of affine Schubert varieties. From this result we also derive an effective formula for computing characters of certain Demazure modules. The based loop group for a compact Lie group G has been studied intensively since the work of Atiyah and Pressley and the book of Pressley and Segal. It is an infinite-dimensional symplectic manifold equipped with a Hamiltonian torus action, where the torus is the product of a circle and the maximal torus of G. When G = SU(2), the fixed points for this action are in bijective correspondence with the integers. Our final result is a Duistermaat-Heckman type oscillatory integral over the based loop group, expanded around the fixed points of the torus action. To accomplish this we use Frenkel’s results (1984) on pinned Wiener measure for orbital integrals on the affine Lie algebra, as well as the results of Urakawa (1975) on the heat kernel for a compact Lie group and Fegan’s inversion formula (1978) for orbital integrals.

Keywords: Equivariant Multiplicity
Kac-Moody
Localization
Loop Groups
Oscillatory Integral
Advisor: Jeffrey, Lisa
Selick, Paul
Modularity in Somatic Cell Reprogramming

Reprogramming relies on the concept that cellular fate is plastic, and therefore a considerable effort has been made to develop molecular strategies that reset the epigenome to achieve distinct cell fates, including stem cells. Deriving induced pluripotent stem (iPS) cells has thus emerged as a critical approach in personalized regenerative medicine that provides an exclusive platform to study human development ex utero, engineer complex tissues, and build new models of human disease. However, reprogramming human somatic cells is an inefficient and nebulous, ill-defined process, and thus to benefit from the potential of iPS cell technology, it is essential to understand the mechanisms underlying cell fate transitions. Here, I explored the transcriptome dynamics of human cells as they acquire pluripotency and propose a novel model of modular-based reprogramming. My observations suggest that numerous common pathways observed during reprogramming are implemented in varying temporal orders across distinct systems, and show that disparate/opposing developmental programs can co-exist within individual cells. By applying a barcoded, single cell-tracing platform, I further identified a subpopulation of highly plastic cells that can access multiple cell fates, of which iPS cells is one of them. Moreover, I show that these cells elicit an elite gene signature that is shared with another highly plastic cell type shed from the kidneys that has elite reprogramming features. These results provide a new perspective on reprogramming as a non-linear process that requires a highly plastic intermediary cell state to achieve pluripotency. By applying this philosophy of reprogramming I propose that we can achieve a better understanding of cell fate control and propel more effective translation of stem cell biology.

Keywords: iPS cells
Pluripotency
Reprogramming
Stem cells
Advisor: Wrana, Jeff
Equivariant Localization in Factorization Homology and Vertex Algebras from Supersymmetric Gauge Theory

We develop a theory of equivariant factorization algebras on varieties with an action of a connected algebraic group G, extending the definitions of Francis-Gaitsgory and Beilinson-Drinfeld to the equivariant setting. We define an equivariant analogue of factorization homology, valued in modules over H•G(pt), and in the case G = (ℂ×)n we prove an equivariant localization theorem for factorization homology, analogous to the classical localization theorem. We establish a relationship between ℂ× equivariant factorization algebras and filtered quantizations of their restrictions to the fixed point subvariety. These results provide a model for predictions from the physics literature about the Ω-background construction introduced in, interpreting factorization En algebras as observables in mixed holomorphic-topological quantum field theories. We give an account of the theory of factorization spaces, categories, functors, and algebras, following the approach of. We apply these results to give geometric constructions of factorization En algebras describing mixed holomorphic-topological twists of supersymmetric gauge theories in low dimensions. We formulate and prove several recent predictions from the physics literature in this language: We recall the Coulomb branch construction of from this perspective. We prove a conjecture from [CosG] that the Coulomb branch factorization E1 algebra 퓐(G,N) acts on the factorization algebra of chiral differential operators 퓓ch(Y) on the quotient stack Y=N/G. We identify the latter with the semi-infinite cohomology of 퓓ch(N) with respect to g, following the results of [Ras3]. Both these results require the hypothesis that Y admits a Tate structure, or equivalently that 퓓ch(N) admits an action of g at level κ = -Tate. We construct an analogous factorization E2 algebra ℱ(Y) describing the local observables of the mixed holomorphic-B twist of four dimensional 풩 = 2 gauge theory. We identify S1 equivariant structures on ℱ(Y) with Tate structures on Y=N/G, and prove that the corresponding filtered quantization of ι!ℱ(Y) is given by the two-periodic Rees algebra of chiral differential operators on Y. This gives a mathematical account of the results of [Beem4]. Finally, we apply the equivariant cigar reduction principle to explain the relationship between these results and our account of the results of [CosG] described above.

Advisor: Costello, Kevin
Emotions in Emerging Readers: Results from Automatic Facial Expression Analyses

Emotions significantly impact classroom experiences, as emotions can shape a student’s academic self-concept and achievement. In the early elementary years, learning to read is a highly salient objective for students. As a result, reading can elicit strong emotions that influence students’ enjoyment and perceived efficacy in reading. Previous research in reading has overlooked the effects of emotions. The majority of emotion research has focused on adolescent and undergraduate students and overlooked students in the early elementary years. The impact of emotions on students learning to read (i.e., emerging readers) has not been extensively studied. The work presented within this dissertation attempted to address this gap in the literature by examining how emotions affect scores on two different literacy tasks in a sample of emerging readers. In three separate studies, a computer-generated automatic facial expression coding software was used to measure individual emotions such as joy, anger, confusion and frustration. The first study examined students’ emotional reactions during a word recognition task and whether they affect word recognition scores. The results demonstrated that increases in the negative affective valence of a word were related to increases in anger and frustration. Further, increases in negative affective valence and increased confusion and anger were related to decreases in word recognition scores. The second study sought to examine how emotions affect scores on the various measures within a narrative storytelling task. The results demonstrated that confusion was related to decreases in complex sentences and evaluative devices. Additionally, frustration fully mediated the effects of confusion on complex sentences. Finally, the third study examined how emotions affect Self-Regulated Learning (SRL) strategies and narrative storytelling scores. The results demonstrated that frustration was related to decreases in narrative storytelling scores, joy was related to increases in monitoring strategies, frustration was related to decreases in planning strategies, and planning fully mediated the effect of frustration on narrative storytelling scores. Taken together, the results from these three studies provide a novel contribution to the current research in emotions and literacy development in emerging readers.

Keywords: Emotions
Narratives
Reading
Advisor: Woodruff, Earl
Leibniz's Modal Metaphysics

Modality plays an important role in Leibniz's philosophy. One of Leibniz's major philosophical concerns was with formulating a theory of contingency with which to resist the threat of necessitarianism. In this dissertation I argue that Leibniz developed a theory—the inclination theory of contingency—according to which a truth is contingent if it depends on reasons that incline without necessitating, while necessary truths depend on reasons that necessitate. The inclination theory has so far been overlooked by Leibniz scholars. I argue that it was Leibniz's preferred theory of contingency from the 1680s, when he developed it, until the end of his life. The inclination theory has much to recommend it. It provides a better defense against the threat of necessitarianism than Leibniz's other theories and, moreover, it is far more philosophically plausible. I argue that the inclination theory supersedes the earlier, well-known per se possible theory, which many interpreters consider unsatisfactory. The inclination theory also provides a way of making sense of the later infinite analysis theory of contingency, which otherwise faces serious technical and philosophical problems, and which has also been regarded as unsatisfactory. I argue that the infinite analysis theory is best understood not as an independent theory of contingency, but as an aspect of the inclination theory. Finally, I argue that the inclination theory enables Leibniz to deny counterfactual identity without relying on a necessary connection between an individual and its predicates. Another important piece of Leibniz's philosophy is his doctrine of possible worlds. I argue that Leibniz developed an account of possible worlds—the laws-first account—according to which possible worlds are structured by laws of the general order that determine everything in them. Like the inclination theory, the laws-first account has so far been overlooked by Leibniz scholars, but it has certain advantages over the received the compossibility interpretation of Leibnizian possible worlds.

Advisor: Rozemond, Marleen
Saccadic Eye Movement Event-related Potentials and the Effects of Subsequent Phase-based Stimulation on Memory in Humans

With the ageing population comes an increase in dementia and memory-related disorders. Investigations of memory formation can facilitate insights into more effective treatments for this growing problem. Deep brain stimulation (DBS), the delivery of electrical stimulation to modulate brain activity, presents an exciting opportunity to investigate mechanisms of memory formation and potentially alleviate memory loss. One critical question with regards to DBS is when and where to stimulate. Treatment for individuals with epilepsy who require resection surgery usually involves the implantation of electrodes in mesial temporal lobe structures (MTL), locations known to be involved in memory formation. This provides a unique opportunity for researchers, in a controlled setting, to record and stimulate the brain to investigate memory formation. Episodic memory, our recollection of personal experiences, can be tested through visual cues (presenting a stimulus and saccadic eye movements (SEM) during memory task). We used a model of how the brain can separate encoding and retrieval states to inspire our approach to try and optimize DBS timing delivery. Our objectives were to 1. Determine which visual stimulus is most relevant for timing stimulation, and 2. Determine the effects of such stimulation. In this thesis, we identified that eye movement in response to a visual stimulus is a more appropriate timing cue than image presentation. In fact, through work with single-unit activity, we found inhibition of activity during the SEM. Our results suggest the SEM in MTL results from an internally generated movement not previously probed in mnemonic structures. Finally, we were able to investigate the effects of contingent stimulation on the SEM. This stimulation resulted in memory impairment. By customizing stimulation delivery contingent on an individual’s timing of the electrophysiological response post saccade, we saw no difference in memory performance between stimulation and no stimulation We successfully established eye movements as an important timing mechanism in MTL structures. Furthermore, stimulation contingent on eye movements can modify memory. These contributions support the potential to look at eye movements as a window on stimulation for investigating, modifying, and hopefully improving memory formation.

Keywords: Corollary discharge
Deep brain stimulation
Human intracranial electroencephalography
Medial temporal lobe
Memory
Saccades
Advisor: Valiante, Taufik A.
Zariffa, José
Play Like a Champion, Post Like a Champion: Investigating Adolescent Female Identity and Social Media

This intersectional feminist research project critically explores the experiences and identity constructions of adolescent female athletes through social media. Specifically, this research project studies how adolescent female athletes use social media as a possible tool to confront and disrupt current media discourses of female athletes. Grounded in feminist sports media scholarship and intersectional fourth-wave feminism, I engaged in a qualitative virtual ethnography, conducting surveys, collecting and analyzing digital artifacts, and interviewing adolescent female athletes aged 13-18. Findings included four significant themes: 1) Creating Narratives on Social Media, 2) “Legitimate” Athletes and the Female/Athlete Paradox, 3) Gendered Spaces in Sports and Sports Media, and 4) Female Athleticism and Social Justice Participation. Overall, each participant discussed how their identity constructions on social media were intentional and deliberate. Results demonstrate that participants are extremely conscientious social media experts, questioning and working through ideas about where, how and what to post on social media, as they negotiate identities of female athletes. This work provides further insights into the gender inequities and discourses in Canada’s sports and sports media climate, and how these inequities are mediated through social media technologies. This work aims to contribute to the body of intersectional feminist sports media scholarship in ways that legitimize, value and hold true to girls’ experiences and understandings. The overall impact of these studies is significant because this research addresses the challenges of being an adolescent female athlete in the 21st century and how this phenomenon contributes to gender inequities in sports and sports media. Using existing literature and scholarship, I contextualize, expand, and consider the findings, explain theoretical and methodological considerations, and discuss future research projects stemming from this work.

Keywords: female athlete
feminism
gender
postfeminism
social media
sports media
Advisor: Brett, Clare
Regulating Lactation: Defining Key Players in the Lactogenic Process for the Development of an In Vitro Model of Drug Transfer into Breast Milk

The study of xenobiotic transfer into breast milk remains an unresolved and difficult task, as clinical trials involving the administration of drugs to breastfeeding mothers to measure milk levels mostly remain unethical and unsafe. Although prediction of drug excretion into milk using physiologically based pharmacokinetic (PBPK) modeling coupled with in vitro-in vivo extrapolation is becoming an important alternative, in vitro experimental approaches remain to be fully developed. This thesis attempted to enrich the knowledge required for the development of in vitro approaches and PBPK models of lactation in 4 domains: the identification of gene expression profiles of the lactating mammary gland; the elucidation of the role of ELF5 in ABCG2 expression; the 3D visualization of milk and vascular compartments of the lactating mammary gland and development of a microfluidic mammary gland-on-chip as an experimental platform in vitro; and the exploration of methotrexate mammary gland transport. First, a gene expression profile in the lactating mouse mammary gland was identified through GEO2R analysis of published microarray data, which was then used to examine hormone responses of the CIT3 mammary epithelial (MEC) line. Second, ELF5, an identified lactogenic marker, was found to be a transcription factor for ABCG2 expression, a transporter marker of the lactating mammary gland, upon prolactin stimulation in vitro. Third, the 3D imaging of the milk and vascular compartments of the lactating mouse mammary gland by 2-photon microscopy revealed dimensional characteristics of milk compartments interspersed by attenuated epithelia and a network of microvasculature. Further, a microfluidic chip was developed as an in vitro platform of the mammary gland, composed of poly(methylmethacrylate) pieces with channels accommodating media flow on either side of a porous membrane. Lastly, in order to gain mechanistic insight into the influx of methotrexate into MECs as a potential target pathway for riboflavin-associated reduction of methotrexate excretion into milk, folate receptor alpha (FRα) was tested for its capacity to mediate methotrexate influx into FRα-overexpressing HEK293 cells. A known methotrexate receptor highly upregulated in the lactating mammary gland, data reveal FRα to be a mediator of methotrexate influx into MECs, however riboflavin interference of methotrexate uptake was not detected.

Advisor: Ito, Shinya
Teaching and Learning for Historical Justice: A Comparative Case Study of Four Sites of History Education in Canada

Recently, Canadian governments and public institutions have initiated a wide range of symbolic gestures and policy reforms aimed at reconciling historical injustices. Reforming history education to teach Canada’s difficult past has been a key priority in this movement, leading to curricular changes and the development of new resources across the country. This dissertation explores four case studies that consider history education’s role in making sense of past injustice and pursuing historical justice and redress in Canada. The four case studies include a curriculum reform process in British Columbia, two grade 9 social studies classrooms engaging with the difficult past, a university field school and bus tour, and a temporary exhibit at the Royal Ontario Museum focused on a difficult history. Drawing on theories of settler colonialism, multidirectional memory, and historical consciousness, this comparative case study illustrates the relationship between teaching and learning difficult history amid a culture of redress in Canada. This dissertation argues that history education’s new roles and responsibilities for helping to right historical wrongs present specific challenges and opportunities for teachers and learners. In particular, this dissertation argues that issues of identity, group memory, and collective responsibility are all brought into focus when educators and learners engage the difficult past. This dissertation raises questions and makes suggestions about the possible roles and limitations for social studies and history education in pursuit of reconciliation and redress in post-conflict and settler colonial contexts.

Keywords: Difficult history
Historical injustice
History education
Memory
Settler colonialism
Social studies education
Advisor: Sandwell, Ruth
Fate of Food Cooking Emissions in the Atmosphere

Food cooking emissions represent an important source of particulate matter in urban areas, contributing 10-35% of total organic aerosol. Cooking emissions also contribute significant levels of volatile organic compounds (VOCs) such as carbonyls which are important precursors to formation of secondary organic aerosol (SOA). In this work, I use heated cooking oils as a model to investigate the reaction pathways that drive formation of VOCs and cooking organic aerosol (COA), and their evolution in physicochemical properties. I demonstrate that VOCs and primary COA emissions are driven by autoxidation reactions involving radical species, and the composition of cooking oils strongly influences the reaction mechanisms. Antioxidants, routinely employed in food industry to delay oil oxidation have complex effects on autoxidation reaction mechanisms. Furthermore, in this work, physicochemical properties and chemistry of COA are investigated. I demonstrate that evaporation of oxidized cooking oil particles is much slower than unoxidized oil particles, despite containing a higher fraction of volatile reaction products than unoxidized cooking oil particles. Additionally, a new analytical approach was developed to characterize the chemical composition of SOA. It is shown that SOA formed from cooking oil vapors undergo fragmentation reactions with increasing atmospheric oxidative aging. Moreover, detailed chemical speciation and total production of SOA from heated cooking oils are explained from aldehydes and its oxidation products which are significant contributors to VOCs from cooking emissions. Overall, knowledge about both oxidation pathways provide useful insights into the importance of fragmentation reactions during evolution of cooking emissions in the atmosphere.

Keywords: Cooking emissions
Evaporation rates
Primary organic aerosol
Secondary organic aerosol
Volatile organic compounds
Advisor: Chan, Arthur