As the demographics of faculty in American higher are fast changing and more foreign-born faculty entering the system, more information about this new group of entrants needs to be scrutinized. This research is aiming to answer some issues related the foreign-born professors overlooked by the mainstream studies about faculty in American postsecondary education. In the first half of this dissertation, related issues such as highly skilled immigrants and their importance to the economy, national strategy and smart power have been discussed. In the second half of this paper, some empirical research and statistical results revealed significant differences between the foreign-born and native-born faculty in terms of salary, working hours, time allocations and variances of above factors in different fields. This research suggested that foreign-born faculty is treated fairly in American academia and they enjoyed neither salary advantage nor disadvantage in comparison to their native counterparts. However, this author found empirical evidence that foreign-born did emphasize more on research by allocating more share of their work time on research and publications. This study shed some light on the researches about faculty salary, time allocation and some other aspects of employment for the foreign-born faculty. The author hopes to raise the academic interests of this topic and would like to see more detailed studies and researches in this direction.

Criticism of J.K. Rowling’s Harry Potter series has maintained that its popularity stems from a well-marketed, repetitive and simple structure. However, this essay considers that this success derives from recognizable mythological heroic structures. The essay traces the protagonist’s development from the perspective of two different theories that contrast and complement each other in various ways, Otto Rank’s theory of the myth of the birth of the hero and Joseph Campbell’s theory of the monomyth. Campbell and Rank both hypothesize that hero myths are repetitive because they emerge from the subconscious of human kind. It can be seen in the tracing of the heroic development in Harry Potter that— although various aspects and features in the hero’s journey are followed in the narrative — the series does not strictly fit these theories. The result is a combination of different features from both theories, which modernizes the heroic myth that has pervaded human culture and history since time immemorial.

Model theory can express properties of algebraic subsets of complex n-space. The constructible subsets are precisely the first order definable subsets, and varieties correspond to maximal consistent collections of formulas, called types. Moreover, the topological dimension of a constructible set is equal to the Morley rank of the formula which defines it.

Finding the maximum size of a matching in an undirected graph and finding the maximum size of branching in a directed graph can be formulated as matrix rank problems. The Tutte matrix, introduced by Tutte as a representation of an undirected graph, has rank equal to the maximum number of vertices covered by a matching in the associated graph. The branching matrix, a representation of a directed graph, has rank equal to the maximum number of vertices covered by a branching in the associated graph. A mixed graph has both undirected and directed edges, and the matching forest problem for mixed graphs, introduced by Giles, is a generalization of the matching problem and the branching problem. A mixed graph can be represented by the matching forest matrix, and the rank of the matching forest matrix is related to the size of a matching forest in the associated mixed graph. The Tutte matrix and the branching matrix have indeterminate entries, and we describe algorithms that evaluate the indeterminates as rationals in such a way that the rank of the evaluated matrix is equal to the rank of the indeterminate matrix. Matroids in the context of graphs are discussed, and matroid formulations for the matching, branching, and matching forest problems are given.

The evaluation of the product of two matrices can be very computationally expensive. The multiplication of two n×n matrices, using the “default” algorithm can take O(n3) field operations in the underlying field k. It is therefore desirable to find algorithms to reduce the “cost” of multiplying two matrices together. If multiplication of two n × n matrices can be obtained in O(nα) operations, the least upper bound for α is called the exponent of matrix multiplication and is denoted by ω. A bound for ω < 3 was found in 1968 by Strassen in his algorithm. He found that multiplication of two 2 × 2 matrices could be obtained in 7 multiplications in the underlying field k, as opposed to the 8 required to do the same multiplication previously. Using recursion, we are able to show that ω ≤ log2 7 < 2.8074, which is better than the value of 3 we had previously. In chapter 1, we look at various techniques that have been found for reducing ω. These include Pan’s Trilinear Aggregation, Bini’s Border Rank and Sch¨onhage’s Asymptotic Sum inequality. In chapter 2, we look in detail at the current best estimate of ω found by Coppersmith and Winograd. We also propose a different method of evaluating the “value” of trilinear forms. Chapters 3 and 4 build on the work of Coppersmith and Winograd and examine how cubing and raising to the fourth power of Coppersmith and Winograd’s “complicated” algorithm affect the value of ω, if at all. Finally, in chapter 5, we look at the Group-Theoretic context proposed by Cohn and Umans, and see how we can derive some of Coppersmith and Winograd’s values using this method, as well as showing how working in this context can perhaps be more conducive to showing ω = 2.

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Master of Science / Department of Statistics / James J. Higgins / A simulation study was done to compare the Type I error and power of standard analysis of variance (ANOVA), the aligned rank transform procedure (ART), and the aligned rank transform procedure where alignment is done using medians (ART + Median). The methods were compared in the context of a balanced two-way factorial design with interaction when errors have a normal distribution and outliers are present in the data and when errors have the Cauchy distribution. The simulation results suggest that the nonparametric methods are more outlier-resistant and valid when errors have heavy tails in comparison to ANOVA. The ART + Median method appears to provide greater resistance to outliers and is less affected by heavy-tailed distributions than the ART method and ANOVA.

Um dos principais problemas em testes de hipóteses para a homogeneidade de curvas de sobrevivência ocorre quando as taxas de falha (ou funções de intensidade) não são proporcionais. Apesar do teste de Log-rank ser o teste não paramétrico mais utilizado para se comparar duas ou mais populações sujeitas a dados censurados, este teste apresentada duas restrições. Primeiro, toda a teoria assintótica envolvida com o teste de Log-rank, tem como hipótese o fato das populações envolvidas terem distribuições contínuas ou no máximo mistas. Segundo, o teste de Log-rank não apresenta bom comportamento quando as funções intensidade cruzam. O ponto inicial para análise consiste em assumir que os dados são contínuos e neste caso processos Gaussianos apropriados podem ser utilizados para testar a hipótese de homogeneidade. Aqui, citamos o teste de Renyi e Cramér-von Mises para dados contínuos (CCVM), ver Klein e Moeschberger (1997) [15]. Apesar destes testes não paramétricos apresentar bons resultados para dados contínuos, esses podem ter problemas para dados discretos ou arredondados. Neste trabalho, fazemos um estudo simulação da estatística de Cramér von-Mises (CVM) proposto por Leão e Ohashi [16], que nos permite detectar taxas de falha não proporcionais (cruzamento das taxas de falha) sujeitas a censuras arbitrárias para dados discretos ou arredondados. Propomos também, uma modificação no teste de Log-rank clássico para dados dispostos em uma tabela de contingência. Ao aplicarmos as estatísticas propostas neste trabalho para dados discretos ou arredondados, o teste desenvolvido apresenta uma função poder melhor do que os testes usuais / One of the main problems in hypothesis testing for homogeneity of survival curves occurs when the failure rate (or intensity functions) are nonproportional. Although the Log-rank test is a nonparametric test most commonly used to compare two or more populations subject to censored data, this test presented two constraints. First, all the asymptotic theory involved with the Log-rank test, is the hypothesis that individuals and populations involved have continuous distributions or at best mixed. Second, the log-rank test does not show well when the intensity functions intersect. The starting point for the analysis is to assume that the data is continuous and in this case suitable Gaussian processes may be used to test the assumption of homogeneity. Here, we cite the Renyi test and Cramér-von Mises for continuous data (CCVM), and Moeschberger see Klein (1997) [15]. Despite these non-parametric tests show good results for continuous data, these may have trouble discrete data or rounded. In this work, we perform a simulation study of statistic Cramér-von Mises (CVM) proposed by Leão and Ohashi [16], which allows us to detect failure rates are nonproportional (crossing of failure rates) subject to censure for arbitrary data discrete or rounded. We also propose a modification of the test log-rank classic data arranged in a contingency table. By applying the statistics proposed in this paper for discrete or rounded data, developed the test shows a power function better than the usual testing

Resumo: O sistema OPG, RANK e RANKL é uma das mais importantes descobertas da biologia óssea. Essas proteínas regulam as atividades celulares na remodelação do tecido ósseo e na literatura há diversas investigações nos tecidos dentários. No entanto, no reimplante dentário, ainda não foram encontrados relatos. Foi objetivo deste trabalho, avaliar a imunomarcação das proteínas OPG, RANK e RANKL em dentes reimplantados de rato. Um grupo controle foi formado com quatro ratos no qual o reimplante dentário não foi realizado. Vinte e quatro ratos (Rattus norvegicus, albinus) tiveram seu incisivo superior extraído e depois reimplantado formando os seguintes grupos: grupo I - reimplante imediato; grupo II - reimplante tardio sem tratamento e grupo III - reimplante tardio com tratamento endodôntico (ressecção da papila dentária e preenchimento do canal com pasta de hidróxido de cálcio) e tratamento da superfície radicular (raspagem mecânica do ligamento periodontal necrosado e imersão em solução de flúor fosfato acidulado de sódio a 2,5%). Ao final dos períodos experimentais (10 e 60 dias) os ratos foram eutanasiados. Foram obtidos cortes longitudinais parafinados com 6μm de espessura. Os cortes foram submetidos à reação imunoístoquímica mediante a utilização de anticorpos primários para OPG, RANK e RANKL. Os resultados mostraram que a imunomarcação de OPG e RANKL ocorreu em todos os grupos e períodos estudados, muito embora RANKL não tenha sido observada no grupo reimplante imediato aos 60 dias. RANK foi observada somente aos 10 dias de todos os grupos no qual o reimplante foi realizado. A análise qualitativa dos resultados demonstrou que o sistema OPG, RANK e RANKL apresentou marcação evidente no reimplante tardio, sugerindo a efetiva participação no início do processo de reabsorção radicular, uma vez que aos 60 dias a imunomarcação foi discreta. / Abstract: The OPG, RANK and RANKL system is one of the most important discoveries in bone biology. These proteins are key regulators of bone remodeling and in the literature there are several studies of tooth resorption. However, in tooth replantation, reports have not been found. The purpose of this study was to determine the immunolabeling of OPG, RANK and RANKL in replanted teeth in rats, using immunohistochemistry methodology. A control group (no replanted teeth) was formed by four rats. Twenty-four rats (Rattus norvegicus, albinus) were submitted to the extraction of their upper right incisors. The replantation was performed according to the groups below: group I - immediate replantation; group II - delay replantation without treatment and group III - delay replantation with endodontic treatment (extirpation of papilla and the root canal filled with calcium hydroxide) and root surface treatment (periodontal ligament was removed with scalpel and teeth were immersed in 2% acidulated phosphate sodium fluoride). The animals were euthanized at the end of the experimental periods (10 and 60 days). Longitudinal 6μm slices embedded in paraffin were obtained. The slices were submitted to immunohistochemistry reaction by means of the primary antibodies for OPG, RANK and RANKL proteins. The results showed the expression of OPG in all groups and periods. RANKL expression was observed in all groups, except in the immediate replanted teeth group (60 days). RANK expression was observed only at 10 days in all groups which replantation was performed. The qualitative analysis of our findings indicated that the system OPG, RANK and RANKL presented strong expression in delayed replantation, suggesting effective participation at the beginning of root resorption, since at 60 days the immunostained cells were discreet. / Orientador: Wilson Roberto Poi / Coorientador: Roberta Okamoto / Banca: Sônia Regina Panzarini Barioni / Banca: Celso Koogi Sonoda / Banca: Luiz Guilherme Brentegani / Banca: Mirian Marubayashi Hidalgo / Doutor

Bone metastases are a major cause of morbidity in patients of advanced breast cancer. Development of osteolytic bone metastasis depends on the interaction between malignant tumour cells and bone microenvironment. Receptor Activator of Nuclear Factor Kappa B (RANK) is a member of tumour necrosis factor (TNF) superfamily that is expressed by osteoclasts (the bone resorbing cells) and primary breast tumour cells. Previous studies demonstrated that RANK receptor and its ligand (RANKL) play an important role in bone remodelling, mammary gland development and immune system. RANKL was also found to serve as a chemotactic factor that facilitates breast tumour metastasis to bone. However, the role of the RANK receptor in breast cancer cell metastatic behaviour in bone is not fully understood. Therefore, the aim of this thesis was to explore the role of the RANK receptor in parental and bone-tropic breast cancer cell growth, motility and invasion, and assess these cells influence on breast cancer cell induced osteoclastogenesis. Functional studies in breast cancer cells showed that RANKL (100 - 300 ng/ ml) significantly enhanced parental human MDA-231 (MDA-231P) and mouse 4T1 breast cancer cell spreading within minutes. RANKL induced chemotactic cell migration of MDA-231P cells in vitro. I also found that RANKL significantly stimulated random and directional 2D and 3D cell migration of parental MDA-231P and bone-tropic (MDA-231BT) breast cancer cells in vitro. These effects were observed at concentrations (100 – 300 ng/ml) that were sufficient to induce osteoclast formation in the presence and absence of breast cancer cells in vitro. In contrast, high concentrations of RANKL (1000 ng/ ml) dramatically suppressed human MDA-231P breast cancer cell invasion in vitro. These data indicate that the RANK receptor in the breast cancer cell lines tested influences cancer cell spreading, migration and invasion in vitro. Thus, targeting RANK in tumour cells may be of value in the prevention of tumour burden associated with breast cancer bone metastasis. Mechanistic studies revealed that RANKL stimulated the phosphorylation of p38 kinase in human and mouse breast cancer cells. Interestingly, RANKL had no effect on NFᴋB, JNK and AKT pathways in parental human MDA-231 and mouse 4T1 breast cancer cells at concentrations up to 300 ng/ ml. These data implies that the RANK receptor modulates human and mouse breast cancer cell metastatic behaviour via p38 activation and independently of the NFᴋB and PI3K/AKT pathways. Silencing of the RANK receptor in the bone-tropic human breast cancer cells MDA- 231BT2 reduced directional cell migration without affecting cell viability and growth. Functional studies in osteoclast and breast cancer cell revealed that knockdown of RANK expression in both parental and bone-tropic human breast cancer cells significantly inhibited the ability of these cells to stimulate osteoclast formation. Although, I cannot exclude the possibility of the involvement of other signalling pathways downstream of the RANK receptor, these studies suggest that the RANK/P38 signalling in osteoclast and breast cancer cells contributes significantly to breast cancer cell behaviour in bone. Genetic analysis of the RANK gene in human parental and bone-tropic MDA-231 breast cancer cells showed a number of polymorphisms. One variant detected was found to be deleterious for the RANK protein. This variant changes the amino acid sequence from alanine to threonine (Ala ˃ Thr) and only appeared in the RANK gene in the parental human MDA-231P breast cancer cells. Moreover, of the four known RANK isoforms that were detected in the parental and bone-tropic breast cancer cells tested, two lacked the TRAF6 binding motifs associated with NFκB activation. All RANK isoforms detected on the bone-tropic MDA-231BT breast cancer cells expressed the P38 binding motifs. Altogether, these findings support the role of the RANK/P38 signalling pathway in breast cancer cell behaviour in bone. Epigenetic analysis in parental human MDA-231P breast cancer cells showed that continuous and long-term exposure to RANKL (10 and 100 ng/ ml) for up to 50 passages (approximately 120 days) did not induce epigenetic changes, particularly DNA methylation, in the RANK gene. However, I found DNA methylation changes in a set of genes that are known to be involved in cell development and regulation. The methylation status of the altered CpG loci either hypermethylated or hypomethylated are located at different parts in the CpG islands. Whole genome DNA methylation pattern of the bone-tropic breast cancer cells showed a number of genes that appeared in both bone-tropic variants are correlated with different biological function of the cells. I also found that long-term exposure of human MDA-231P to RANKL (100 ng/ ml) enhanced the ability of these cells to stimulate osteoclastogenesis in vitro. These data together indicate that long-term exposure to RANKL induces “boney” epigenetic changes in a set of genes that enhances breast cancer cell behaviour in bone. Overall, this thesis illustrated that the RANK receptor on human parental and bone-tropic breast cancer cells plays an important role in cell motility and ability of these cells to influence osteoclastogenesis and ultimately osteolysis. Therefore, agents that selectively target the RANK receptor may be of value in the treatment of both tumour burden and osteolytic bone disease associated with breast cancer. However, the role of the RANK receptor in bone metastasis will require further in vivo investigation.