Les microalgues, grâce à leur grande biodiversité, présentent une matière première d’intérêt dans différents domaines : nutrition, cosmétique, agrochimie ou énergie. Ces microorganismes sont cultivés dans différents systèmes de culture : soit des systèmes ouverts comme les raceways soit en systèmes fermés comme les photobioréacteurs (PBR). L’objectif général est alors d’apporter les conditions favorables aux microorganismes. La croissance par photosynthèse amène cependant à un dégagement d’oxygène, dont l’accumulation sous forme dissoute dans le système dépend à la fois de la production biologique, mais également de la performance et du transfert gaz-liquide du système de culture. Cette thèse vise à étudier les effets de la concentration en oxygène dissous sur les performances cinétiques des PBRs. Cela sera abordé sur différents géométries de PBRs en lumière continu. L’étude de l’impact d’une fraction sombre pouvant être introduite dans certaines géométries sera également abordée, montrant au final l’interdépendance forte entre paramètres de conception, paramètres opératoires, réponse métabolique et performances cinétiques des PBRs. / Because of their great biodiversity, microalgae can produce an enormous variety of high-value compounds for human needs. These microorganisms are cultivated in different culture systems: either open systems such as raceways or closed systems such as photobioreactors (PBR). The design of these PBRs takes into consideration the various parameters affecting the growth of microalgae such as pH, temperature, nutrients etc. Photosynthesis growth leads to an evolution of oxygen that can build up in dissolved form in the system depending on the biological production and the gas-liquid transfer of the system culture. This thesis aims to study the effects of dissolved oxygen concentration on the kinetic performance of PBRs. This will be tackled on different geometries of PBRs in continuous light. The study of the impact of a dark fraction present in certain geometries will also be discussed, showing finally the strong interdependence between design parameters, operating parameters, metabolic response and the kinetic performances of the PBRs.

The Egyptian Fractions of One problem (EFO), asks the following question: Given a positive integer n, how many ways can 1 be expressed as the sum of n non-increasing unit fractions? In this paper, we verify a result concerning the EFO problem for n=8, and show the computational complexity of the problem can be severely lessened by new theorems concerning the structure of solutions to the EFO problem. / Master of Science / Expressing numbers as fractions has been the subject of one’s education since antiquity. This paper shows how we can write the number 1 as the sum of uniquely behaved fractions called “unit fractions”, that is, fractions with 1 in the numerator and some natural counting number in the denominator. Counting the number of ways this can be done reveals certain properties about the prime numbers, and how they interact with each other, as well as pushes the boundaries of computing power.

No description available.

No description available.

acase@tulane.edu / Multiple sclerosis (MS) is a common neurodegenerative disease and remains an unmet clinical challenge. In MS, an autoimmune response leads to immune cell infiltration, inflammation, demyelination, and lesions in central nervous system (CNS) tissues resulting in tremors, fatigue, and progressive loss of motor function. These pathologic hallmarks are effectively reproduced in the murine experimental autoimmune encephalomyelitis (EAE) model. Using the EAE mouse, we have defined critical time points during the disease progression that have correlative immunopathology with those that occur in MS. As promising therapeutic alternatives to treat MS, we investigated the fresh, heterogeneous population of cells from adipose called the stromal vascular fraction (SVF), which contains adipose-derived stromal/stem cells (ASCs). With these studies, we evaluated the therapeutic efficacies of fresh SVF cells and culture-expanded ASCs at early and late stage EAE disease after intraperitoneal (i.p.) administration. At early stage EAE disease, autoimmune reactions and inflammation are prevalent in the periphery lead to CNS damage by the infiltration of cells that generate inflammatory and demyelinating lesions. We demonstrated that at this time, treatment with SVF cells and ASCs were incapable of attenuating CNS pathology. However, the potency of SVF cells to suppress the autoimmune reactions in the periphery was strong enough to partially ameliorate motor impairments. Furthermore, we revealed the altered gene expressions of the SVF cells and ASCs when exposed to this pathogenic milieu in vitro. Not only did we show that the majority of the helper T (TH) cells contained within the SVF are of the TH2 phenotype, but the most enhanced cytokines in response to the inflammatory milieu were interleukin-10 (IL-10) and transforming growth factor-β (TGFβ) which promote regulatory T cells (Tregs). The most dominant increase detected in ASCs was interleukin-6 (IL-6) which correlates with the inability of ASCs to suppress the activities of the pathogenic T cells at early stage disease. At late stage disease, we showed the greatest improvements in SVF-treated EAE mice that led to amelioration to pathology in CNS tissues and partial restoration of motor function. The most pronounced changes following SVF treatment were the high levels of IL-10 in the peripheral blood, lymphoid and CNS tissues along with the induction of regulatory T cells in the lymph nodes which indicated potent immunomodulatory effects. These effects were not as robust following ASC treatment. A deeper investigation into the potential mechanisms showed phenotypes of T cells and macrophages skewed towards favorable phenotypes. SVF treatment shifted the TH cell subsets away from the effector TH1 and TH2 and toward the Tregs which promote immune tolerance and anti-inflammatory effects. Furthermore, the Treg-associated effects involve the induction of the alternative activation phenotype of macrophages, or M2, which were evidenced in the spleens and CNS tissues of SVF-treated EAE mice. Moreover, we determined that i.p. injected ASCs, and more so, SVF cells were still present in the spleens of EAE mice after 5 days. Together, we investigated a novel modality for treating an inflammatory, autoimmune disease. By comparison with ASC treatment, we demonstrated potential mechanisms of SVF treatment at early and late stage EAE disease that are translational to the inflammatory and demyelinating phases MS disease, respectively. We determined that the timing of administration is most critical, and once active immune activities subside, SVF treatment provides robust and comprehensive effects for improving CNS damage. Additionally, these mechanisms may translate and help explain the favorable effects with current clinical applications such as cell-assisted liposuction that uses SVF cells for improving fat grafting yet mechanisms are still unclear. / 1 / Annie C. Bowles

This thesis discusses a theorem on the convergence of a continued fraction.

Thirty years ago, Effros and Shen classified the simple dimension groups with rank two. Every such group is parametrized by an irrational number, and can be constructed as an inductive limit using that number's continued fraction expansion. There is a natural generalization of continued fractions to higher dimensions, and this invites the following question: What dimension groups correspond to multidimensional continued fractions? We describe this class of groups and show how some properties of a continued fraction are reflected in the structure of its dimension group. We also consider a related issue: an Effros-Shen group has been shown to arise in a natural way from the tail equivalence relation on a certain sequence space. We describe a more general class of sequence spaces to which this construction can be applied to obtain other dimension groups, including dimension groups corresponding to multidimensional continued fractions.

Thirty years ago, Effros and Shen classified the simple dimension groups with rank two. Every such group is parametrized by an irrational number, and can be constructed as an inductive limit using that number's continued fraction expansion. There is a natural generalization of continued fractions to higher dimensions, and this invites the following question: What dimension groups correspond to multidimensional continued fractions? We describe this class of groups and show how some properties of a continued fraction are reflected in the structure of its dimension group. We also consider a related issue: an Effros-Shen group has been shown to arise in a natural way from the tail equivalence relation on a certain sequence space. We describe a more general class of sequence spaces to which this construction can be applied to obtain other dimension groups, including dimension groups corresponding to multidimensional continued fractions.

L'obésité est associée à une augmentation de la morbidité et de la mortalité liée à de nombreuses maladies, y compris le diabète de type 2, l'hypertension et des pathologies hépatiques menant à une surcharge lipidique d’origine non alcoolique. Récemment, l’imagerie par résonance magnétique (IRM) est devenue la méthode de choix pour la quantification non invasive de la graisse. Dans cette thèse, les méthodes d'IRM ont été étudiées sur un scanner préclinique de 4.7T in vitro (fantômes MR) et in vivo (souris). Deux algorithmes de quantifications de la graisse -la méthode de Dixon et l’algorithme IDEAL- ont été considérés. Les performances de l'algorithme IDEAL ont été analysées en fonction de propriétés des tissus (T2*, fraction de graisse et modèle spectral de la graisse), de paramètres d'acquisition IRM (temps d’écho, nombre d'échos) et de paramètres expérimentaux (SNR et carte de champ). Sur les fantômes, l'approche standard single-T2* IDEAL a montré certaines limites qui pourraient être surmontées en optimisant le nombre d'échos. Une nouvelle méthode, pour déterminer les valeurs de vérité terrain pour T2* de l'eau et pour T2* de la graisse, a été proposée. Pour les mesures in vivo, différentes analyses ont été effectuées en utilisant l'algorithme IDEAL sur le foie et les muscles. L'analyse statistique sur les mesures de ROI a montré que le choix optimal du nombre d'échos est égal à trois pour la quantification de la graisse et six ou plus pour la quantification du T2*. Les valeurs de la fraction de graisse, calculées avec l'algorithme IDEAL, étaient statistiquement comparables aux valeurs obtenues avec la méthode de Dixon. Enfin, un procédé pour générer des signaux de référence mimant les systèmes eau-graisse (Fat Virtual Phantom MRI), sans l'aide d'objets physiques, a été proposé. Ces fantômes virtuels, qui présentent des caractéristiques de bruit réalistes, représentent une alternative intéressante aux fantômes physiques pour fournir un signal de référence dans les mesures IRM. / Obesity is associated with increased morbidity and mortality linked to many diseases, including type 2 diabetes, hypertension and disease nonalcoholic fatty liver. Recently, 1H magnetic resonance imaging (MRI) has emerged as the method of choice for non-invasive fat quantification. In this thesis, MRI methodologies were investigated for in vitro (MR phantoms) and in vivo (mice) measurements on a 4.7T preclinical scanner. Two algorithms of fat quantifications – the Dixon’s method and IDEAL algorithm – were considered. The performances of the IDEAL algorithm were analyzed as a function of tissue properties (T2*, fat fraction and fat spectral model), MRI acquisition parameters (echo times, number of echoes) and experimental parameters (SNR and field map). In phantoms, the standard approach of single-T2* IDEAL showed some limitations that could be overcome by optimizing the number of echoes. A novel method to determine the ground truth values of T2* of water and T2* of fat was here proposed. For in vivo measurements, different analyses were performed using the IDEAL algorithm in liver and muscle. Statistical analysis on ROI measurements showed that the optimal choice of the number of echoes was equal to three for fat quantification and six or more for T2* quantification. The fat fraction values, calculated with IDEAL algorithm, were statistically similar to the values obtained with Dixon’s method. Finally, a method for generating reference signals mimicking fat-water systems (Fat Virtual Phantom MRI), without using physical objects, was proposed. These virtual phantoms, which display realistic noise characteristics, represent an attractive alternative to physical phantoms for providing a reference signal in MRI measurements.

Understanding fractions is fundamental for expanding number knowledge from the whole number system to the rational number system. According to the National Council of Teachers of Mathematics (NCTM) Principles and Standards for School Mathematics (2000), learning fractions is an important mathematical goal for students in grades three through five in the U.S. Moreover, the NCTM suggests that fraction instruction start in Pre-K and continue through 8th grade. At the same time, the Common Core State Standards for Mathematics (CCSSM) suggests that fraction instruction should occur from Grade 3 to 7. In contrast to the time spent on learning fractions in the U.S., students in China spend a relatively short time learning fractions (Zhang and Siegler, 2022). According to the Chinese national curriculum standards, the Chinese National Mathematics Curriculum Standards (CNMCS) for five-four system, the fundamental fraction concepts are taught in grades 3 and 5 only. However, Chinese students continue to have higher performance on fraction items in international assessments when compared with American students (Fan and Zhu, 2004). Consequently, over the last several years, researchers have investigated subject content knowledge and pedagogical content knowledge of Chinese in-service teachers and pre-service teachers via fraction division (e.g., Li and Huang, 2008; Ma, 1999). There are also studies exploring Chinese written curricula of fraction division (e. g., Li, Zhang, and Ma, 2009). Recently, a quantitative study from Norton, Wilkins, and Xu (2018) investigated the process of Chinese students' construction of fraction knowledge through the lens of fraction schemes, a model established by western scholars Steffe (2002) and his colleague Olive (Steffe and Olive, 2010). However, there is a lack of qualitative research that attempts to use fraction schemes as an explanatory framework to interpret the process of Chinese students' construction of fraction knowledge. The main purpose of this study was to investigate Chinese students' understanding of the fundamental fraction knowledge in terms of their understanding of the "fraction unit," referred to as a "unit fraction" in the U.S., using Steffe and Olive's (2010) fraction schemes as the conceptual framework. A sequential mixed methods design was used in this study. The design included two consecutive phases, namely a quantitative phase followed by a qualitative phase (Creswell and Plano Clark, 2011). During the quantitative phase, five hundred and thirty-four Chinese fourth and fifth grade students were administered an assessment. The quantitative data was first analyzed using a Cochran's Q test to determine if the Chinese participants in this study follow the same progression of fraction schemes as their American peers. Results indicate that the development of fractional schemes among Chinese 4th and 5th grade participants in this study is similar to their U.S. counterparts and the Chinese participants in Norton et al.'s (2018) study regardless of the curricula differences across countries or areas in the same country, the textbook differences, and the language differences. Next, two different analysis of variances (ANOVA), a three-way mixed ANOVA and a two-way repeated measures ANOVA were conducted. The three-way mixed ANOVA was used to inform the researcher as to the fraction schemes these students had constructed before the concept of fraction unit is formally introduced and after the concept of fraction unit is formally introduced. The results showed that the fraction knowledge of the students in this study developed from 4th grade to 5th grade. The analysis of clinical interview data confirmed this conclusion. The two-way repeated measures ANOVA was used to determine which model (i.e., linear, circular, or rectangular) is more or less problematic for Chinese students when solving fraction tasks. The results suggest that generally students' performance on linear model tasks was better than their performance on circular model tasks, but there was no statistically significant difference between performance on circular model and its corresponding rectangular model tasks. The results from the quantitative analyses were also used to screen students to form groups based on their highest available fraction scheme for a clinical interview in the second phase, the qualitative phase. In the qualitative phase, a clinical interview using a think-aloud method was used to gain insight into the role of students' conceptual understanding of the fraction unit in their construction of fraction knowledge. In this phase, students were asked to solve the tasks in the clinical interview protocol using the think aloud method. Two main findings were revealed analyzing the clinical interview data. First, a conceptual understanding of fraction units as well as a conceptual understanding of a unit whole play a critical role in the construction of Chinese students' fraction knowledge. Second, the lack of the understanding of a fraction unit as an iterable unit may be one of the reasons that obstructs students move from part-whole concept of fractions to the measurement concept of fractions. This study also demonstrates that a conceptual understanding of fraction units and the unit whole are a necessary condition for constructing of a conceptual understanding of fraction knowledge. Thus, implications of this study suggest that teachers not only should help students build a conceptual understanding of fraction units, but also need to confirm that students have constructed the concept of what the unit whole is before asking students to identify the fraction units for the referent whole. On the other hand, the tasks used in the present study only include continuous but not discrete wholes. Therefore, future research may focus on investigating how students identify fraction units and in what way the iterating operation could be used when students encounter a discrete whole. / Doctor of Philosophy / Understanding fractions is fundamental for expanding number knowledge from the whole number system to the rational number system. According to the National Council of Teachers of Mathematics (NCTM) Principles and Standards for School Mathematics (2000), learning fractions is an important mathematical goal for students in grades three through five in the U.S. At the same time, the Common Core State Standards for Mathematics (CCSSM), suggests that fraction instruction should occur from Grade 3 to 7. In contrast to the time spent on learning fractions in the U.S., students in China spend a relatively short time learning fractions (Zhang and Siegler, 2022). According to the Chinese national curriculum standards, the Chinese National Mathematics Curriculum Standards (CNMCS) for five-four system, the fundamental fraction concepts are taught in grades 3 and 5 only. However, Chinese students continue to have higher performance on fraction items in international assessments when compared with American students (Fan and Zhu, 2004). Consequently, over the last several years, researchers have investigated fraction knowledge of Chinese in-service teachers and pre-service teachers via fraction division (e.g., Li and Huang, 2008; Ma, 1999). There are also studies exploring Chinese written curricula of fraction division (e. g., Li, Zhang, and Ma, 2009). Recently, Norton, Wilkins, and Xu (2018) collected and analyzed numerical data from Chinese students and investigated the process of how Chinese students learn fraction knowledge through a model established by western scholars Steffe (2002) and his colleague Olive (Steffe and Olive, 2010). However, there is a lack of research study that attempts to seek an in-depth understanding of how Chinese students learn their fraction knowledge. This study used both numerical data and data gathering from interviewing 29 4th and 5th grade Chinese students. It aimed to investigate Chinese students' understanding of the fundamental fraction knowledge in terms of their understanding of the "fraction unit," referred to as a "unit fraction" in the U.S., using Steffe and Olive's (2010) fraction schemes as the conceptual framework. This study demonstrates that a comprehensive and practical understanding of fraction units and the whole of a given fraction are a necessary condition for building a comprehensive understanding of fraction knowledge. The implications of this study suggest that teachers not only should help students build a comprehensive understanding of fraction units, but also need to confirm that students have built the concept of what the whole of a given fraction is before asking students to identify the fraction units for the referent whole.