VictorJuiz/thesis huggingface dataset:
Topics in Multiplicative and Probabilistic Number Theory

A heuristic in analytic number theory stipulates that sets of positive integers cannot simultaneously be additively and multiplicatively structured. The practical verification of this heuristic is the source of a great number of difficult problems, including the well-known Hardy-Littlewood tuples conjecture. Conjectures of this type are also at least morally equivalent to the expectation that a generic multiplicative function behaves randomly on additively structured sets. In this thesis, we consider several problems involving the behaviour of multiplicative functions interacting with additively structured sets. First, we prove quantitative versions of mean value theorems due to Wirsing and Halász for multiplicative functions that often take values outside of the unit disc, and provide some applications of this result to probabilistic number theory. In a different direction, we refine a quantitative mean value theorem for multiplicative functions, and thereby significantly improve the existing upper bounds on the maximum size of partial sums of odd order non-principal Dirichlet characters, both unconditionally and assuming the Generalized Riemann Hypothesis, and show that our conditional results are nearly best possible unconditionally. We also prove a quantitative bivariate Erdo&huml;s-Kac theorem on the joint distribution of pairs of values of certain additive functions, and use this probabilistic result to derive a weak version of Chowla's conjecture on binary correlations of the Möbius function, among other applications. Solving a 60-year-old open problem of N.G. Chudakov, we show that a completely multiplicative function that only takes finitely many values, vanishes at only finitely many primes and whose partial sums are uniformly bounded, must be a non-principal Dirichlet character. We also solve a folklore conjecture due to Elliott, Ruzsa and others on the gaps between consecutive values of a unimodular completely multiplicative function, showing that these gaps cannot be uniformly large. This latter result is a corollary of several stronger results that are proved regarding the distribution of consecutive values of multiplicative functions. Finally, we make some progress on some natural variants of Chowla's conjecture on sign patterns of the {+1, –1}-valued multiplicative functions. Some of the aforementioned results are joint work with O. Klurman, or with Y. Lamzouri.

Keywords: Correlations
Dirichlet Characters
Mean Value Theorems
Multiplicative Functions
Probabilistic Number Theory
Advisor: Friedlander, John B
Star Cluster Formation and Radiative Feedback

In this dissertation, I begin by exploring star-cluster forming regions undergoing both mass accretion and stellar feedback. I consider the interplay between accretion, star formation, stellar feedback, turbulent energy-driving, and turbulent decay. The resulting analytical model predicts that the feedback mechanisms are not powerful enough to reverse the flow of accreting matter onto low mass clusters and terminate star cluster formation. Moreover, low-mass clusters will have outflow feedback that significantly drives turbulence. However, as this model makes several assumptions and analytical approximations about the nature of feedback, including radiation feedback in clumpy dust envelopes, I turn my attention to exploring this problem for the remainder of the dissertation. I start from the simpler case of a spherical envelope and address numerical solutions for the radiation forces, relating these to analytical estimates. Radiation reprocessing is important to these models, as infrared radiation escapes from dust more easily than starlight. I conduct these models with the Monte Carlo code Hyperion and the scaling solution code DUSTY. I show that Monte Carlo methods underestimate temperatures and radiation forces when the mean free path of starlight is poorly resolved. I then introduce clumping into these envelopes to study its effects on the captured forces. I find power-law fits to the scaling of three summary parameters (a normalized radial force (ɸ), a force-averaged radius, 〈r〉F, and a radiative virial term, R) with the intensity of clumping in the envelopes. R is the least stochastic across multiple realizations of imposed inhomogeneity. I conclude by further exploring the dependence of Monte Carlo solutions with resolution in the context of AMR density data, varying an imposed level of grid refinement. Coarser grids suppress channels that helped photon leakage, but also underestimate the temperature, yielding two opposing effects that may partially cancel against each other.

Keywords: ISM: dust
extinction
methods: numerical
radiative transfer
star clusters
stars: formation
Advisor: Matzner, Christopher D
Resolving Macrophages Block Osteolysis Through Anabolic Actions on Bone Cells

Progression of inflammatory osteolytic diseases, including rheumatoid arthritis and periodontitis, is characterized by increased production of pro-inflammatory mediators and matrix degrading enzymes by macrophages, and increased osteoclastic activity. Phenotypic changes in macrophages are central to the healing process in virtually all tissues. In the present study, we assessed the timing of macrophage phenotypic changes and the impact of anti-inflammatory pro-resolving activation during inflammatory osteolysis and healing, using a murine model of periodontitis. Pro-inflammatory macrophage activation and TNF-α overproduction within three weeks after induction of periodontitis was associated with progressing bone loss. Pro-resolving activation within one week of stimulus removal and markers of resolving macrophages, IL-10, TGF-β and CD206 correlated strongly with bone levels. In vivo macrophage depletion with clodronate liposomes prevented bone resorption but impaired regeneration. Induction of resolving macrophages with rosiglitazone, a PPAR-γ agonist, led to reduced bone resorption during inflammatory stimulation and increased bone formation during healing. In vitro assessment of primary bone marrow-derived macrophages activated with either IFN-γ and LPS (pro-inflammatory activation) or IL-4 (pro-resolving activation) showed that IL-4-activated cells have enhanced resolving functions (production of anti-inflammatory cytokines, migration and phagocytosis of aged neutrophils), and exert direct anabolic actions on bone cells. Cystatin C secreted by resolving but not inflammatory macrophages explained, in part, the macrophage actions on osteoblasts and osteoclasts. This study supports the concept that therapeutic induction of pro-resolving functions in macrophages can re-couple bone resorption and formation in inflammatory osteolytic diseases.

Keywords: bone regeneration
inflammation resolution
innate immunity
osteoblast
osteoclast
periodontitis
Advisor: Glogauer, Michael
Hinz, Boris
Nicotine Metabolism and Smoking Behaviour in Vulnerable Populations

The rate of nicotine metabolic inactivation varies widely among different populations, influencing smoking behaviors and associated disease risk. African American smokers metabolize nicotine more slowly and report lower cigarette consumption compared to Caucasian smokers, but suffer disproportionately from lung cancer risk. In addition to ethnic/racial differences, altered physiological states, for example during pregnancy, may lead to variation in the rate of nicotine metabolism, smoking behaviors, and reproductive toxicity in pregnant smokers. We sought to characterize sources of variability in the rate of nicotine metabolism, and resultant influences on smoking behaviors in these vulnerable populations. We demonstrate variation in UDP-glucuronosyltransferase 2B10 and 2B17 (UGT2B10 and UGT2B17) and flavincontaining monooxigenase 3 (FMO3) do not substantially alter nicotine metabolism or tobacco consumption in African Americans. We further demonstrate the metabolism of cotinine, the primary metabolite of nicotine, is influenced by variation in UGT2B10 altering the utility of cotinine as a biomarker of nicotine intake in African American smokers. Most analytical methods for measuring nicotine’s urinary metabolites involve enzymatic or chemical deglucuronidation for quantification of the glucuronide-conjugated metabolites. We developed a direct liquid chromatography-tandem mass spectrometry (LCMS/MS) assay that provides more accurate estimates of the nicotine metabolism rate, intake and impact of genetic variation in smokers. We then utilized this direct LCMS/MS approach to evaluate nicotine metabolism during pregnancy and postpartum. We identified distinct patterns of nicotine metabolites, and an overall faster rate of nicotine metabolism during pregnancy. We demonstrate nicotine metabolism was accelerated likely through induction of CYP2A6 and UGT2B10 activity leading to faster nicotine C-oxidation and N-glucuronidation, respectively. We further biochemically characterized the level of nicotine intake, and thus tobacco exposure, during pregnancy and postpartum. We demonstrate the intake of nicotine was higher during pregnancy and postpartum than is suggested by self-reported cigarettes per day. Lastly, we found cotinine underestimated nicotine intake during pregnancy compared to postpartum. Overall, our findings provide insight into the patterns of nicotine metabolism, CYP2A6 and UGT2B10 genetic variation, and tobacco exposure in two vulnerable, biologically and physiologically distinct, populations, and expand on our knowledge of genetic and non-genetic sources of variation in the rate of nicotine metabolism.

Keywords: Biomarkers
Drug Metabolism
Ethnicity
Nicotine
Pharmacogenetics
Smoking
Advisor: Tyndale, Rachel F
Using a Neighbourhood Measure of School Readiness to Predict Academic Achievement in a Population of Children

This study investigates whether academic achievement in individual children can be predicted by the proportion of children with school readiness vulnerabilities within the school neighbourhood. The data analyzed came from: 1) an extensive administrative database on the EDI (Early Development Instrument) (Janus Offord, 2007), which provided the measure of school readiness vulnerability; and 2) a large study of academic achievement and associated factors conducted in Latin American and Caribbean countries (SERCE, UNESCO/LLECE, 2008), which provided the measure of individual child achievement and demographics at the school level. These data were collected in 2006 (SERCE) and 2008 (EDI) in Nuevo Leon, Mexico. A two-level Hierarchical Linear Modeling (HLM) approach was conducted to analyze the data, with individual SERCE student level predictors at level-1, and average EDI school neighbourhood vulnerability scores as predictors at level-2. The EDI records (n=50,400) were nested within a total of 116 school neighbourhoods comprised of 151 schools. Results indicate that the level-2 predictors (EDI) accounted for a small but significant proportion of between school variance in third (13.8%) and sixth (17.2%) grade reading. However, the level-2 predictors (EDI) did not account for significant variance in third and sixth grade mathematics. These results provide further evidence for the influence that average school or neighbourhood readiness variations have on academic achievement. The study findings add to the conceptualization of the EDI as a marker of school and neighbourhood influences and suggest an enriched perspective on trajectories in learning for the UNESCO/LLECE research initiative.

Keywords: academic achievement
early childhood development
EDI
HLM
neighbourhood
trajectories in learning
Advisor: Corter, Carl
The Ethical, Social, and Cultural Dimensions of Screening for Mental Health of Children and Adolescents in the Developing World

This thesis formally and systematically identifies and prioritizes, for the first time, the most pressing ethical, social, and cultural challenges related to the screening for mental, neurological, and substance abuse disorders (MNSDs) in children and adolescents (C&A) living in the developing world, and proposes targeted strategies to address them. C&A mental health has been sadly neglected despite the severe life-long burden of C&A MNSDs and the large and growing number of C&A living in low- and middle-income countries. I carried out a three-round international Delphi survey completed by 135 experts from 37 countries. This multi- and inter-disciplinary panel selected and ranked 39 challenges, organized into eight themes, and 32 related solutions, arranged into seven topics. A 100% response rate was attained in Round 3. Near consensus was achieved in several areas, and a high degree of correlation was found between the challenges and their proposed solutions. The experts recommended integrating screening into primary health care; addressing potential sociocultural dissonances by designing and implementing accessible, affordable, cost-effective, and culturally and socially appropriate screening tools and programs, and post-screening follow-up; addressing resource issues by securing long-term programs funding, strengthening education and training for mental health, and incorporating well-supervised local non-specialists and lay individuals in the screening programs; increasing trust and decreasing stigmatization of at-risk C&A, their families, and their communities by engaging stakeholders throughout the screening initiatives, protecting the rights of the C&A screened, guaranteeing privacy, confidentiality, and free, uncoerced informed consent and assent, and determining the baseline acceptance, motivation, and support for screening programs in target populations; and regularly implementing empowering, culturally sensitive public and community engagement initiatives. My findings encompass all MNSDs, focus on developing countries, and represent the combined global wisdom of the leading authorities in C&A mental health. They can become a guide for policy- and decision-making, resource allocation, and international cooperation in global mental health, offering a novel approach to reduce the burden of C&A MNSDs by encouraging timely and context-sensitive prevention and management of MNSDs, and helping to mitigate the lifelong suffering that they inflict on C&A and their families in the developing world.

Keywords: children and adolescents
developing world
ethical
social
and cultural issues
mental health
screening
Advisor: Upshur, Ross E. G.
Investigating Adult Stem Cell Lineage Specification in the Freshwater Flatworm Schmidtea mediterranea

Adult stem cells (ASCs) serve to facilitate tissue turnover during the lifespan of an organism. The goal of my research has been to deepen our understanding of how ASCs become specified towards differentiation to produce physiologically functional cell types. To this end, I have chosen to use the freshwater planarian Schmidtea mediterranea, which possess a large pool of ASCs that supports the constant cell turnover of all their tissues. A transcriptomic approach was used to identify a set of candidate genes to screen for potential regulators and markers of ASC progeny. Using gene expression characterization and RNAi functional analysis, I have identified a MEX3 homolog (Smed-mex3-1) and a putative MYB-type transcription factor (Smed-myb-1) as regulators of ASC differentiation. This body of work demonstrates that (A) mex3-1 is a critical factor broadly required for ASC differentiation, and (B) myb-1 is a regulator of the early temporal window of epidermal lineage progression.

Advisor: Pearson, Bret J
Factors Influencing the Effectiveness of Mass Distribution of Free Nicotine Replacement Therapy

Despite over 50 years of tobacco control efforts, tobacco use remains the leading preventable cause of disease and premature death in Canada. The mailed distribution of free nicotine replacement therapy (NRT) has been shown to be a promising population-level approach for promoting smoking cessation, increasing accessibility to efficacious treatment, and helping smokers quit. The present body of research aimed to gain a comprehensive understanding of factors that may mediate the effectiveness of the mailed free distribution of NRT approach via a large, single blinded, randomized controlled trial of mailed free nicotine patches to adult smokers across Canada, in absence of behavioural support. The mailed provision of 5-weeks of free nicotine patches was found to increase the odds of smoking cessation irrespective of lifetime history of depression or anxiety, both highly prevalent comorbidities that are well established moderators of cessation success. Evaluating demographic and smoking history predictors of nicotine patch use and cessation, only those who were unemployed, previously used NRT, and expressed greater intent for change at baseline were more likely to take advantage of and use at least some of the freely provided nicotine patches to make a quit attempt. Past NRT use and use of all provided nicotine patches were the only predictors of smoking cessation at a 6-month follow-up. In general, the conscientiousness personality trait and attitudes towards smoking cessation aids were found to be predictive of whether smokers quit using formal assistance or unassisted. Further, compared to a control cohort, receipt and use of nicotine patches corresponded to higher prevalence of primary care support, suggesting that the provision of free NRT particularly to those who are likely to use it may facilitate opportunities for benefits beyond the direct pharmacological effects of the medication. In summary, the research outlined the benefit of the mass distribution approach even among those with presumed difficulty in quitting smoking, delineated predictors of treatment utilization and cessation, as well as developed insights on the impact of the approach in harnessing additional smoking cessation support, thus strengthening support for the inclusion of free NRT provision as part of a comprehensive tobacco control strategy.

Keywords: Free Distribution
Nicotine Replacement Therapy
Smoking
Smoking Cesastion
Tobacco
Advisor: Sproule, Beth A
Understanding and Predicting the Stress Relaxation Behavior of Short-Fiber Composites

The viscoelastic properties of short-fiber composites are complex and not well-understood. Previous experimental work has shown that the viscoelastic properties of short-fiber composites are affected by both elastic fibers and the matrix, which is baffling since elastic fibers do not exhibit any time-dependence of their own. The goal of this study was to understand why and how elastic fibers can alter time-dependent behavior when contained in a composite. In this thesis, conventional shear-lag theory was adapted to include a time-dependent matrix and a novel analytical model was used to predict the tensile relaxation modulus of short-fiber composites. The model highlighted the importance of incorporating both the time-dependent tensile modulus of the matrix as well as its time-dependent shear modulus. Investigations using the model showed that since stress transfer in a short-fiber composite occurs through interfacial shearing, the time-dependent shear modulus of the matrix results in time-varying stress transfer the fiber. Since the stress in the fiber is time-dependent, it exhibits an apparent stress relaxation stemming from the relaxing shear modulus of the matrix. The model predictions were validated using finite-element simulations and experimental data. Comparison to real data confirmed the hypothesis that the time-dependency observed in elastic fibers stemmed from the indirect time-dependency imposed by the time-varying stress transfer from the matrix. The model was also used to determine the effect of various parameters including fiber aspect ratio and fiber volume fraction. For the first time, a critical aspect ratio for viscoelasticity was introduced. This was defined as the aspect ratio at which the contribution to composite stress relaxation by the fiber is maximized. The effect of fiber orientation was also examined, and an analytical model was developed to predict the stress relaxation of composites containing randomly-oriented fibers. It was found that random orientation in the plane would shrink the effect of fibers by one-third of what would be observed in oriented composites. In the last part of the thesis, we investigated the strain rate-dependence of short fiber-reinforced foams. The study highlighted a potential area where knowledge of the stress relaxation behavior of the short-fiber composites could prove useful.

Keywords: Composites
Creep
Finite Element Modelling
Mechanics
Stress Relaxation
Viscoelasticity
Advisor: Kortschot, Mark T
Sain, Mohini
Dynamic Corticomuscular Coherence during Cyclical Ankle Movements: Effects of Aging and Parkinson’s Disease

Parkinson’s disease (PD) is a progressive neurodegenerative disease with diverse motor and non- motor symptoms. Although the primary neuropathology and symptoms of PD have been well established, the physiological mechanisms behind specific kinematic abnormalities are not well understood. Many such abnormalities (e.g., gait disturbances) can significantly impact a person’s quality of life. One way that PD may affect movement is through its connection with the motor cortex. In a series of experimental studies, I have examined whether the communication between the cortex and active muscles (corticomuscular communication) is affected by PD during anti- phasic cyclical ankle movements. To quantify such communication, coherence was calculated between cortical and muscle activities (corticomuscular coherence). The results from these studies suggest that i) the midline cortical areas are functionally involved in the cyclical ankle movements, ii) the corticomuscular communication may be affected by compensation against aging-related neuromuscular changes, and iii) the performance of the cyclical ankle movements is impaired by PD although the kinematic abnormalities were not accompanied by changes in the corticomuscular communication. To better understand how aging and PD affect the corticomuscular communication, future studies should examine the relevant neural correlates of movement in a more comprehensive manner (i.e., including subcortical structures). To my knowledge, these studies are the first to demonstrate that simple cyclical ankle movements are accompanied by dynamic changes in corticomuscular coherence and to examine how such coherence is affected by aging and PD.

Advisor: Popovic, Milos R.
Chen, Robert