The arithmetic progressions under addition and composition satisfy the usual rules of arithmetic with a modified distributive law. The basic algebra of such mathematical structures is examined; this leads to the consideration of the integers as a metric space under the "factoradic metric", i.e., the integers equipped with a distance function defined by d(n,m)=1/N!, where N is the largest positive integer such that N! divides n-m. Via the process of metric completion, the integers are then extended to a larger set of numbers, the factoradic integers. The properties of the factoradic integers are developed in detail, with particular attention to prime factorization, exponentiation, infinite series, and continuous functions, as well as to polynomials and their extensions. The structure of the factoradic integers is highly dependent upon the distribution of the prime numbers and relates to various topics in algebra, number theory, and non-standard analysis. / Master of Science

Yes / Importance: Myopia is a leading cause of untreatable visual impairment and is increasing in prevalence worldwide. Interventions for slowing childhood myopia progression have shown success in randomized clinical trials; hence, there is a need to identify which children would benefit most from treatment intervention. Objectives: To examine whether genetic information alone can identify children at risk of myopia development and whether including a child’s genetic predisposition to educational attainment is associated with improved genetic prediction of the risk of myopia. Design, Setting, and Participants: Meta-analysis of 3 genome-wide association studies (GWAS) including a total of 711 984 individuals. These were a published GWAS for educational attainment and 2 GWAS for refractive error in the UK Biobank, which is a multisite cohort study that recruited participants between January 2006 and October 2010. A polygenic risk score was applied in a population-based validation sample examined between September 1998 and September 2000 (Avon Longitudinal Study of Parents and Children [ALSPAC] mothers). Data analysis was performed from February 2018 to May 2019. Main Outcomes and Measures: The primary outcome was the area under the receiver operating characteristic curve (AUROC) in analyses for predicting myopia, using noncycloplegic autorefraction measurements for myopia severity levels of less than or equal to −0.75 diopter (D) (any), less than or equal to -3.00 D (moderate), or less than or equal to −5.00 D (high). The predictor variable was a polygenic risk score (PRS) derived from genome-wide association study data for refractive error (n = 95 619), age of onset of spectacle wear (n = 287 448), and educational attainment (n = 328 917). Results: A total of 383 067 adults aged 40 to 69 years from the UK Biobank were included in the new GWAS analyses. The PRS was evaluated in 1516 adults aged 24 to 51 years from the ALSPAC mothers cohort. The PRS had an AUROC of 0.67 (95% CI, 0.65-0.70) for myopia, 0.75 (95% CI, 0.70-0.79) for moderate myopia, and 0.73 (95% CI, 0.66-0.80) for high myopia. Inclusion in the PRS of information associated with genetic predisposition to educational attainment marginally improved the AUROC for myopia (AUROC, 0.674 vs 0.668; P = .02), but not those for moderate and high myopia. Individuals with a PRS in the top 10% were at 6.1-fold higher risk (95% CI, 3.4–10.9) of high myopia. Conclusions and Relevance: A personalized medicine approach may be feasible for detecting very young children at risk of myopia. However, accuracy must improve further to merit uptake in clinical practice; currently, cycloplegic autorefraction remains a better indicator of myopia risk (AUROC, 0.87). / PhD studentship grant from the College of Optometrists (Drs Guggenheim and Williams; supporting Mr Mojarrad) entitled Genetic prediction of individuals at-risk for myopia development) and National Institute for Health Research (NIHR) Senior Research Fellowship award SRF-2015-08-005 (Dr Williams). The UK Medical Research Council and Wellcome grant 102215/2/13/2 and the University of Bristol provide core support for the Avon Longitudinal Study of Parents and Children (ALSPAC). A comprehensive list of grants funding is available on the ALSPAC website (http://www.bristol.ac.uk/alspac/external/documents/grant-acknowledgements.pdf). This research was conducted using the UK Biobank Resource (application 17351). The UK Biobank was established by the Wellcome Trust, the UK Medical Research Council, the Department for Health (London, England), the Scottish government (Edinburgh, Scotland), and the Northwest Regional Development Agency (Warrington, England). It also received funding from the Welsh Assembly Government (Cardiff, Wales), the British Heart Foundation, and Diabetes UK.

Background: In recent years, the issue of gender disparities in career progression has gained significant attention, particularly in male-dominated industries. Despite various initiatives aimed at promoting gender equality, women continue to face systemic and personal barriers that hinder their advancement. This study explores these challenges within the context of specific industries, highlighting how societal norms, corporate policies, and personal experiences can shape women's career trajectories.  Purpose: The primary aim of this research is to deepen our understanding of the factors influencing women's careerprogression by identifying the key barriers and opportunities to overcome it.  Method: The thesis was conducted in a qualitative approach. Semi-structured interviews were conducted with 6 femaleCEOs or managers aspiring to become one from 3 companies in Gironde, France.  Conclusion: The findings revealed a complex mix of structural and cultural factors that continue to limit women'scareer progression. Despite some progress, persistent issues such as gender-based discrimination, lack of supportivepolicies, and deeply rooted stereotypes remain significant obstacles. The study underscores the need for sustained efforts to overcome these barriers and foster a truly inclusive professional environment for all women.

No / Accepted definitions and descriptions of advanced practice offer generic ideals for the development of advanced radiographer practitioner roles. However, they fail to specify a development pathway necessary for a clinical practitioner to attain advanced practitioner status and lack of clarity persists around the definition of advanced practice within the context of radiography [Price R. Critical factors influencing the changing scope of practice: the defining periods. Imaging & Oncology 2005;June:6–11.]. This paper will consider the expectations of practitioner and advanced practitioner competencies within the context of radiography practice in the United Kingdom and suggest criteria for an advanced practice development pathway that may be adopted by individual radiographers, or their managers, to assist professional development within any imaging speciality.

La dissémination métastatique est associée à de faibles chances de survie dans les cas de mélanomes humains, comme pour d’autres cancers. Le développement de métastases est un processus qui se fait en plusieurs étapes et nécessite la réorganisation du cytosquelette d’actine pour permettre la migration et l’invasion cellulaire. La protéine Nck2 est un adaptateur protéique principalement impliqué dans la réorganisation du cytosquelette. Une étude préliminaire réalisée dans notre laboratoire avait révélé que les niveaux de la protéine Nck2 et de son ARNm sont augmentés dans les lignées de mélanome métastatiques en comparaison aux lignées primaires. Le but de la présente recherche était donc d’étudier le rôle de l’adaptateur Nck2 dans la progression métastatique. Les résultats obtenus confirment que l’expression de Nck2 augmente de façon marquée au cours de la progression métastatique du mélanome humain. Cette étude révèle en plus que l’expression de hauts niveaux de Nck2 dans les cellules de mélanome primaire stimule la prolifération cellulaire et la migration, n’affecte pas l’invasion d’une matrice de collagène de type I, mais semble affaiblir les contacts cellule-cellule et l’adhésion au substrat. Une étude préliminaire effectuée in vivo révèle que ces phénomènes se traduisent par une légère augmentation de la tumorigenèse et de la croissance tumorale. Dans l’ensemble, les résultats obtenus suggèrent que Nck2 pourrait effectivement jouer un rôle dans la progression métastatique du mélanome en favorisant la prolifération des cellules tumorales et en facilitant leur détachement de la tumeur primaire, les rendant plus aptes à se disperser dans l’organisme et à établir des colonies métastatiques. Au niveau moléculaire, nous proposons que Nck2 est recruté dans les invadopodes pour favoriser la formation de complexes protéiques qui stimulent l’invasion. La mobilisation de Nck2 dans ces structures membranaires diminuerait sa disponibilité pour l’établissent d’autres complexes protéiques, entre autres dans les complexes d’adhésion focaux (FAs) et dans les jonctions adhérentes, diminuant ainsi les contacts des cellules cancéreuses avec la matrice extracellulaire et les cellules avoisinantes. / The metastatic process is highly fatal in many cancers, including human melanoma. Metastatic progression is a multistep process in which cytoskeletal organization allows migration and invasion of cancer cells. Nck2 is an adaptor protein mainly associated with cytoskeletal organization. A preliminary study carried out in our laboratory has shown that Nck2 protein and mRNA levels are increased in metastatic melanoma cell lines compared to primary cell lines. In this study, the role of Nck2 in metastatic progression was further investigated. Results confirmed that Nck2 levels are increased in metastatic melanoma compared to primary cell lines. Nck2 overexpression in primary melanoma induced migration and cell proliferation, did not affect invasion in type I collagen matrix, but decreased cell-cell and cell-substrate adhesion. In addition, a preliminary in vivo study suggested that Nck2 overexpression slightly increased tumorigenesis and tumor growth in primary melanoma. All together, these results indicate that Nck2 may effectively influence metastatic progression of melanoma by increasing cancer cell proliferation and detachment from the primary tumor, allowing them to enter the blood circulation and form distant colonies. At the molecular level, we propose that Nck2 is recruited to invadopodia in order to form molecular complexes that increase cell invasion, and this may results in a decrease in Nck2 levels available to form other molecular complexes in others cell compartments, such as focal adhesions (FA) and adherent cell junctions.

La progression tumorale est caractérisée par deux processus clés, la prolifération et l’invasion cellulaires. Les nAChRs, activés par la nicotine et ses nitrosamines dérivées (NNN et NNK), modulent les concentrations calciques intracellulaires et activent in vitro la prolifération, l’apoptose, la migration et l’invasion de lignées cellulaires tumorales. Dans cette étude, nous montrons, en utilisant des cultures primaires de cellules dérivées de cancers pulmonaires non à petites cellules (carcinomes épidermoïdes et adénocarcinomes), que les nAChRs α7 régulent différemment la prolifération cellulaire en fonction du stade de différenciation des tumeurs. Le nAChR α7 agit comme répresseur de la prolifération cellulaire dans les tumeurs bien différenciées et dans l’épithélium respiratoire normal, alors que dans les tumeurs peu différenciées, il stimule la prolifération cellulaire en réponse à la nicotine. A l’inverse, le nAChR α3α5β2 n’est que partiellement impliqué dans la régulation de la prolifération cellulaire aussi bien dans les tumeurs pulmonaires que dans l’épithélium respiratoire normal. Les nAChRs α7 et nAChRs α3α5β2 sont tous les deux impliqués dans la stimulation de l’invasion des cellules tumorales des carcinomes épidermoïdes et adénocarcinomes. Le polymorphisme non-synonyme rs16969968 de la sous-unité α5 induit une mutation au niveau d’un acide aminé hautement conservé (D398N). De nombreuses études d’association pangénomiques lient ce polymorphisme au développement des cancers pulmonaires. Dans cette étude nous montrons que les nAChRs exprimant la sous-unité α5 mutée (D398N) altèrent la prolifération et la différenciation des cellules respiratoires et modulent l’invasion des cellules tumorales, en synergie avec les nAChRs α7. / Tumor progression is characterized by two key processes, cell proliferation and invasion. Nicotinic receptors, activated by nicotine and its derived nitrosamines (NNK and NNN) modulate intracellular calcium concentrations and activate in vitro proliferation, apoptosis, migration and invasion of tumor cell lines. In this study, we show, by using primary cell cultures from lung cancer tumors, adenocarcinoma and squamous cell carcinoma, that nAChR α7 differently regulates cell proliferation according to the state of tumor differentiation. The α7 nAChRs acts as a repressor of cell proliferation in differentiated lung cancer tissues and in the normal respiratory epithelium, while it stimulates cell proliferation in response to nicotine, in poorly differentiated tumors. Conversely, the α3α5β2 nAChR is only partially involved in the regulation of cell proliferation in lung cancers and in the normal respiratory epithelium. The α7 and α3α5β2 nAChRs are both involved in the in vitro invasion process of adenocarcinoma and squamous cell carcinoma. Non-synonymous polymorphism rs16969968 in the CHRNA5 gene induces a mutation in a highly conserved amino acid (D398N). Many genome-wide association studies have demonstrated the relationship between this polymorphism and the incidence of lung cancer. In this study, we show that nAChRs, expressing the mutated α5 subunit (D398N), are in involved in the alteration of the proliferation and the differentiation state of respiratory epithelial cells, and also modulate tumor cell invasion, in synergy with the α7 nAChRs.

La méiose est la division cellulaire qui aboutit à la production de gamètes haploïdes. Lors de la méiose, un unique évènement de réplication est suivi de deux divisions afin de réduire la ploïdie. Lors de ces deux divisions, la cohésion entre chromatides sœurs est éliminée de façon séquentielle pour permettre la succession de deux ségrégations de chromosomes équilibrées. La progression du ‘’cycle méiotique’’ est contrôlée par des régulateurs communs à la mitose et à la méiose mais également par des mécanismes nécessitant des protéines spécifiques à la méiose. L’objectif de de mon travail de thèse était de décrypter les mécanismes moléculaires permettant l’enchainement de deux divisions équilibrées pour la production de gamètes haploïdes. Nous avons pu montrer que la protéine OSD1 inhibait l’APC/C pour permettre la progression méiotique. Nous avons également mis en évidence un réseau fonctionnel, comprenant OSD1, CYCA1;2/TAM et TDM, indispensable à trois étapes clés de la progression méiotique chez Arabidopsis ; la transition prophase-méiose I, la transition méiose I-méiose II et la sortie de méiose. Ces travaux ont également permis de caractériser chez Arabidopsis les deux paralogues de Shugoshin, qui sont des protéines conservées et impliquées dans la protection de la cohésion centromérique. Nous avons également identifié Patronus comme un nouveau protecteur de la cohésion centromérique en méiose. Les résultats obtenus suggèrent que Patronus est un régulateur de l’APC/C qui permet d’empêcher l’élimination de la cohésion centromérique en interkinèse méiotique. / Meiosis is a specialized type of cell division that generates haploid gametes. At meiosis, two divisions follow a single DNA replication event leading to ploidy halving. A stepwise sister chromatids cohesion release also occurs to allow the two successive balanced rounds of chromosome segregation. In addition to general cell-cycle regulators, meiosis requires specific proteins. The aim of this thesis was to understand the molecular mechanisms leading to two successive balanced chromosome segregations. We show that OSD1 promotes meiotic progression through APC/C inhibition and we identified a functional network between OSD1, CYCA1;2/TAM and TDM in Arabidopsis. This functional network controls three key steps of meiotic progression; the prophase-meiosis I transition, the meiosis I-meiosis II transition and the meiosis exit. In addition, we characterized the two Arabidopsis thaliana Shugoshin paralogs, which are conserved proteins involved in sister chromatid cohesion protection. We also identified Patronus, an uncharacterized protein, as a novel protector of meiotic centromeric cohesion. We suggest that Patronus is a novel APC/C regulator that prevents cohesins release during meiotic interkinesis. This work identified two APC/C regulators essential for meiosis in Arabidopsis thaliana.

Pour croître et proliférer, les cellules cancéreuses de la prostate activent des voies de signalisation dépendantes des androgènes. L'intervention thérapeutique en première ligne du cancer de la prostate (CaP) s'appuie donc d’abord sur le blocage de l'axe androgènes-récepteur aux androgènes (RA) mais rapidement, les patients développent des tumeurs résistantes (CRPC, Castration Resistant Prostate Cancer).Les récepteurs à activité tyrosine kinase de la famille ErbB semblent jouer un rôle dans cette résistance, en particulier le récepteur ErbB3. En effet, l'inactivation des voies en aval d'ErbB1 et ErbB2, en association avec les anti-androgéniques n'empêche pas la progression vers l'hormono-indépendance, et une accumulation nucléaire d'ErbB3 est observée dans les CRPC en même temps que la voie PI3K-Akt est réactivée.Dans ce contexte, nous avons validé l'expression d'une isoforme nucléaire ErbB380kDa chez les patients et dans des lignées hormono-sensible (LNCaP) et hormono-résistante (PC3). Par ChIP-on-chip, nous avons isolé 353 promoteurs cibles communs aux deux lignées, 245 spécifiques à la lignée LNCaP et 925 à la lignée PC3, et montré qu'ErbB380kDa est un co-régulateur transcriptionnel des gènes étudiés, parmi lesquels GATA2. L'analyse in silico de ces promoteurs révèle des sites de liaison pour les facteurs de transcription GATA2 et MZF1 au niveau des régions liant ErbB380kDa. Un complexe nucléaire GATA2-MZF1-ErbB380kDa est retrouvé dans les cellules LNCaP et PC3.Des travaux récents montrent que GATA2 s'associe au RA pour réguler l'expression de gènes et qu'il pourrait être participer à la dissémination métastatique dans le CaP.Nos résultats suggèrent qu'ErbB380kDa pourrait jouer un rôle régulateur, en amont de GATA2, dans les processus de résistance et l'apparition de métastases. Cette isoforme nucléaire insensible aux traitements actuels apparaît donc comme une cible privilégiée pour le ciblage thérapeutique. / Prostate cancer (PCa) is dependent on androgens and functional androgen-receptor (AR) for growth and proliferation. Androgen-directed therapy is used at the first stages of the disease but cancer cells frequently become resistant (CRPC) by inappropriate reactivation of AR activity. As ErbB receptors are expressed in PCa cells, therapies aiming at inactivate the pathways downstream have been tested in advanced prostate cancers alongside hormone-based therapy. Still, a significant proportion of CRPC treated by ErbB1/2 inhibitors resist to treatment. ErbB3 could be responsible for this failure through both its unexpected nuclear localization and the reactivation of the PI3K-Akt pathway in those advanced tumors.We have described a nuclear ErbB380kDa isoform, expressed in hormone-sensitive (LNCaP) and hormone-resistant (PC3) PCa cell lines that accumulates in the nucleus of tumor cells during cancer progression. ChIP-on-chip experiments led us to characterize 353 target promoters binding ErbB380kDa in both cell lines; 245 promoters specific to LNCaP and 925 specific to PC3 cells, among which the promoter of GATA2. We show that ErbB380kDa functions as a transcriptional co-regulator for the studied genes, potentially through its interaction with transcription factors. In silico analysis revealed binding sites for GATA2 and MZF1 transcription factors on the target promoters, and a complex GATA2-MZF1-ErbB380kDa has been found in LNCaP and PC3 cells. Recent publications have reported a role for GATA2 in the regulation of RA responsive-genes and in metastatic spreading. We propose that ErbB380kDa could act, upstream of GATA2, to induce resistance mechanisms and facilitate cancer progression. Thus, ErbB380kDa emerges as a putative target for the development of new therapies in prostate cancer.

Neste trabalho são apresentadas duas propostas de sequências didáticas para ensino de logaritmos. A primeira delas é destinada ao aperfeiçoamento de professores de Matemática e a outra, para alunos de Ensino Médio. Tais sequências foram desenvolvidas com base em pesquisas realizadas pelo Prof. João Pedro da Ponte sobre o processo de investigação matemática. A sequência didática para professores foi aplicada no Centro de Aperfeiçoamento do Ensino de Matemática do Instituto de Matemática e Estatística da Universidade de São Paulo (CAEM IME USP). Já a sequência para alunos foi aplicada em uma escola da rede estadual situada no município de São Paulo. Ambas foram analisadas sob os pontos de vista da eficiência e adequação, bem como da clareza das ideias apresentadas. As sequências didáticas têm como ponto de partida a observação das propriedades comuns a várias tabelas, cada uma contendo uma progressão geométrica ao lado de uma progressão aritmética. Tais propriedades caracterizam o que virá a ser definido como logaritmo. Essa introdução ao conceito de logaritmo é diferente da usual, que se baseia na solução de uma equação exponencial. O processo de investigação matemática visa a um aprendizado eficaz por parte do aluno, proporcionado por atividades que conduzam o aluno, de forma gradual, a fazer descobertas, formular conjecturas e buscar validações. Tais investigações são coordenadas e supervisionadas pelo professor, cujo papel é fundamental no processo de construção do conhecimento. / This dissertation presents two didactic sequences for teaching and learning logarithms. One of them aims at Mathematics teachers and is designed for improving their knowledge. The other sequence is meant to be used on high school students. Both didactic sequences were developed based upon research carried out by Professor João Pedro da Ponte on Mathematical Investigations. The didactic sequence for teachers was applied at CAEM IME USP. The one for students was applied at a state school in the city of São Paulo. They were analysed from the points of view of efficiency and of adequacy, as well as of the clarity of the presented ideas. The didactic sequences start with the observation of properties common to multiple tables, each containing a geometric progression side by side with an arithmetic progression. The observed properties characterize what will be later defined as logarithm. Such introduction to the concept of logarithm is different from the usual, which is based on the solution of an exponential equation. The Mathematical Investigation process aims at an effective learning by the students, which is provided by activities that lead the student to gradually make discoveries, formulate conjectures, and search for validations. These investigations are coordinated and supervised by the teacher, whose role in the knowledge construction process is fundamental.

Durant ma thèse, j’ai étudié l’implication d’un variant du récepteur aux œstrogènes α, ERα36, dans l’initiation et la progression du cancer du sein. Au laboratoire, son expression dans les cancers testiculaires avait été montrée comme étant inductrice de la prolifération cellulaire in vitro et in vivo après une exposition à un mélange de polluants environnementaux, considérés comme perturbateurs endocriniens oestrogéno-mimétique : les alkylphénols. Une analyse rétrospective d’échantillons de tumeurs mammaires a montré, par la modélisation de réseaux d’interactions géniques, que l’expression d’ERα36 était corrélée avec l’expression de marqueurs de migration cellulaire, caractéristiques de la progression tumorale. La surexpression d’ERα36 par transfection in vitro et dans un modèle unique de souris Knocked In exprimant ERalpha36 dans la glande mammaire ont montré qu’ERα36 est suffisant pour altérer le phénotype épithélial des cellules mammaires saines. Une exposition aux alkylphénols qui stimulent son expression endogène accentue les altérations cellulaires observées et contribue à l’acquisition transgénérationnelle de propriétés relatives à une transformation tumorale. Les analyses de ce projet pluridisciplinaire se sont appuyées sur des expertises biologiques, mathématiques et bioinformatiques et ont permis de mettre en évidence pour la première fois le rôle potentiel d’ERα36 dans l’initiation tumorale et de confirmer son implication dans la progression du cancer du sein. Enfin, nous avons montré que l’exposition à des doses environnementales d’alkylphénols lors de la période de périnatalité peut conduire à une modification transgénérationnelle de la différenciation de la glande mammaire sous le contrôle d’ERα36 et ainsi augmenter le risque de cancer mammaire / This work was dedicated to study how a variant of estrogen receptor α, ERα36, acts in initiation and progression of breast cancer. In the laboratory, his expression in testicular cancer was shown to stimulate cell proliferation in vitro and in vivo after environmental pollutant exposure. The compounds studied, the alkylphenols, are endocrine disruptors, interfering with normal estrogen signaling. Gene interaction network modelling from retrospective analysis of breast cancer samples showed that ERα36 expression was correlated with the expression of cell migration markers, typical of tumor progression. In vitro ERα36 overexpression and in a unique mouse Knocked In model, expressing ERα36 in the mammary gland, showed that ERα36 is sufficient to alter epithelial phenotype of normal breast cells. Alkylphenols exposure, that stimulated ERα36 endogenous expression, increased cellular alterations and contributed to transgenerational acquisition of properties related to neoplastic transformation. Analysis of this multidisciplinary project were based on biological expertise, mathematics and bioinformatic tools. These results enabled to highlight for the first time the potential role of ERα36 in tumor initiation and confirmed his involvement in breast cancer progression. Finally, we showed that exposure to environmental doses of alkylphenols during the perinatal period can lead to transgenerational modification of mammary gland differentiation under ERα36 control and eventually may increase breast cancer risk