Croissance et ensemble nodal de fonctions propres du laplacien sur des surfaces

Dans cette thèse, nous étudions les fonctions propres de l'opérateur de Laplace-Beltrami - ou simplement laplacien - sur une surface fermée, c'est-à-dire une variété riemannienne lisse, compacte et sans bord de dimension 2. Ces fonctions propres satisfont l'équation $\Delta_g \phi_\lambda + \lambda \phi_\lambda = 0$ et les valeurs propres forment une suite infinie. L'ensemble nodal d'une fonction propre du laplacien est celui de ses zéros et est d'intérêt depuis les expériences de plaques vibrantes de Chladni qui remontent au début du 19ème siècle et, plus récemment, dans le contexte de la mécanique quantique. La taille de cet ensemble nodal a été largement étudiée ces dernières années, notamment par Donnelly et Fefferman, Colding et Minicozzi, Hezari et Sogge, Mangoubi ainsi que Sogge et Zelditch. L'étude de la croissance de fonctions propres n'est pas en reste, avec entre autres les récents travaux de Donnelly et Fefferman, Sogge, Toth et Zelditch, pour ne nommer que ceux-là. Notre thèse s'inscrit dans la foulée du travail de Nazarov, Polterovich et Sodin et relie les propriétés de croissance des fonctions propres avec la taille de leur ensemble nodal dans l'asymptotique $\lambda \nearrow \infty$. Pour ce faire, nous considérons d'abord les exposants de croissance, qui mesurent la croissance locale de fonctions propres et qui sont obtenus à partir de la norme uniforme de celles-ci. Nous construisons ensuite la croissance locale moyenne d'une fonction propre en calculant la moyenne sur toute la surface de ces exposants de croissance, définis sur de petits disques de rayon comparable à la longueur d'onde. Nous montrons alors que la taille de l'ensemble nodal est contrôlée par le produit de cette croissance locale moyenne et de la fréquence $\sqrt{\lambda}$. Ce résultat permet une reformulation centrée sur les fonctions propres de la célèbre conjecture de Yau, qui prévoit que la mesure de l'ensemble nodal croît au rythme de la fréquence. Notre travail renforce également l'intuition répandue selon laquelle une fonction propre se comporte comme un polynôme de degré $\sqrt{\lambda}$. Nous généralisons ensuite nos résultats pour des exposants de croissance construits à partir de normes $L^q$. Nous sommes également amenés à étudier les fonctions appartenant au noyau d'opérateurs de Schrödinger avec petit potentiel dans le plan. Pour de telles fonctions, nous obtenons deux résultats qui relient croissance et taille de l'ensemble nodal.

Théorème de Pleijel pour l'oscillateur harmonique quantique

L'objectif de ce mémoire est de démontrer certaines propriétés géométriques des fonctions propres de l'oscillateur harmonique quantique. Nous étudierons les domaines nodaux, c'est-à-dire les composantes connexes du complément de l'ensemble nodal. Supposons que les valeurs propres ont été ordonnées en ordre croissant. Selon un théorème fondamental dû à Courant, une fonction propre associée à la $n$-ième valeur propre ne peut avoir plus de $n$ domaines nodaux. Ce résultat a été prouvé initialement pour le laplacien de Dirichlet sur un domaine borné mais il est aussi vrai pour l'oscillateur harmonique quantique isotrope. Le théorème a été amélioré par Pleijel en 1956 pour le laplacien de Dirichlet. En effet, on peut donner un résultat asymptotique plus fort pour le nombre de domaines nodaux lorsque les valeurs propres tendent vers l'infini. Dans ce mémoire, nous prouvons un résultat du même type pour l'oscillateur harmonique quantique isotrope. Pour ce faire, nous utiliserons une combinaison d'outils classiques de la géométrie spectrale (dont certains ont été utilisés dans la preuve originale de Pleijel) et de plusieurs nouvelles idées, notamment l'application de certaines techniques tirées de la géométrie algébrique et l'étude des domaines nodaux non-bornés.

Analysis of the regulation of Nodal function by SPC-mediated cleavage during early mammalian development

RÉSUMÉ Après implantation dans l'utérus, le foetus de mammifère est composé de trois populations différentes de cellules: l'epiblast, l'ectoderme extraembryonnaire et l'endoderme viscéral. Pendant la gastrulation, les cellules de l'epiblast donnent naissance aux trois lignées germinales: l'ectoderme, le mésoderme et l'endodermes. Les lignées germinales produisent par la suite les différents tissus et organes du corps embryonnaire et adulte. Les cellules de l'ectoderme extraembryonnaire donnent par la suite le composant foetal du placenta qui est essentiel à la survie de l'embryon dans l'utérus. L'épiblast et l'ectoderme extraembryonnaire sont entourés par l'endoderme viscéral et forment une structure connue sous le nom de bouton embryonnaire. L'endoderme viscéral joue un rôle important dans l'embryogenèse car il comporte une sous-population de cellules appelées l'endoderme viscéral antérieur dont les signaux influencent l'épiblast adjacent et déterminent le futur axe antéro-postérieur de l'embryon. La protéine de signalisation Nodal de la famille des TGFß est essentielle dans l'épiblast pour spécifier le mésendoderme, l'endoderme viscéral antérieur, ainsi que pour maintenir les cellules souche de l'ectoderme extraembryonnaire. Ainsi, dans les embryons mutants pour Nodal, aucun axe antéro-postérieur n'est établi, les lignées germinales ne sont pas spécifiés et le placenta ne se développe pas. Au niveau moléculaire, comme pour les protéines de la famille des TGFß, Nodal est initialement synthétisée sous forme de précurseur avant d'être clivée de façon endoproteolytique par des protéanes sécrétées, les proprotéines convertases du type subtilisin (SPC), qui suppriment la partie inhibitrice N-terminale du pro peptide. Dans ce contexte, le projet de ma thèse a été d'analyser l'influence des SPC sur la fonction de Nodal en employant une combinaison d'approches génétiques et biochimiques. Premièrement, nous avons constaté que le clivage du précurseur par les protéases active Nodal, mais en même temps augmente son turn-over et diminue la portée de son action. Deuxièmement, dans l'embryon, il apparaît que Nodal est activé par l'action combinée de Furin et de PACE4, deux protéases sécrétées qui sont spécifiquement exprimées dans les cellules de l'ectoderme extraembryonnaire, donc adjacentes au domaine d'expression de Nodal. De manière similaire aux mutants de Nodal, les embryons mutants pour les deux protéases ne forment pas d'endoderme viscéral antérieur et ne gastrulent pas. Cependant, certains gènes cible de Nodal restent exprimés, suggérant que toutes les activités de Nodal ne sont pas dépendent du clivage par les SPCs. En effet, la génération et l'analyse de mutants portant un allèle knock-in qui code pour une forme mutante de Nodal résistante aux SPC, ont montré que ces mutants ont les caractères phénotypique des mutants de Nodal seulement de façon partielle. La formation de mésoderme est partiellement induite, et de façon remarquable, la forme de Nodal résistante aux SPC est capable d'agir à une distance de sa source, maintenant l'expression de ses propres protéases et d'autres gènes essentiels pour la spécification de l'ectoderme extraembryonnaire. Ensemble, ces résultats prouvent que par leur action directe les protéases extraembryonnaire modulent la signalisation de Nodal pendant le développement mammifère précoce. SUMMARY : Early after implantation in the uterus, the mammalian conceptus is composed of three different cell populations: the epiblast, the extraembryonic ectoderm and the visceral endoderm. During gastrulation, epiblast cells give rise to the three embryonic germ layers: the ectoderm, the mesoderm and the endoderm. These germ layers then generate the different tissues and organs of the embryonic and adult bodies. In parallel, extraembryonic ectoderm cells give rise to the fetal component of the placenta, which is essential for the survival of the embryo in the uterus. Both the epiblast and extraembryonic ectoderm are surrounded by the visceral endoderm to form a structure known as the egg cylinder. The visceral endoderm plays an important role as it harbours a subpopulation of cells called the anterior visceral endoderm, from which signals influence the adjacent epiblast and determine the future antero-posterior embryonic axis. The TGFß-related signalling protein Nodal is required within the epiblast to specify the mesoderm, the endoderm,the anterior visceral endoderm and is also essential to maintain stem cells in the extraembryonic ectoderm. Thus, in Nodal null conceptuses, no antero-posterior axis is established, the germ layers are not specified and the placenta does not develop. At the molecular level, Nodal, like related proteins of the TGFß family, is initially synthesized as a precursor and undergoes endoproteolytic cleavage by secreted proteases of the subtilisin-like proprotein convertases (SPC) to remove an inhibitory N-terminal pro peptide. In the embryo, Nodal is activated by the combined action of Furin and PACE4, two secreted SPCs that are specifically expressed in cells of the extraembryonic ectoderm, thus adjacent to the Nodal expression domain. Similar to Nodal null .embryos, mutant embryos lacking both these proteases fail to specify the anterior visceral endoderm and to undergo gastrulation. However, these mutants still express a subset of Nodal target genes, suggesting that part of Nodal activity is independent on cleavage by SPCs. Indeed, by generating and analyzing mutants with a knock-in allele that encodes an SPC-resistant mutant form of Nodal, I could show that they retain a subset of Nodal activities. Mesoderm formation is partially induced, but most remarkably, SPC-resistant Nodal form is able to act at a distance from its source, maintaining the expression of its proteases and of other genes essential for maintenance of the extraembryonic ectoderm.

Deformed Gaussian-orthogonal-ensemble description of small-world networks

The study of spectral behavior of networks has gained enthusiasm over the last few years. In particular, random matrix theory (RMT) concepts have proven to be useful. In discussing transition from regular behavior to fully chaotic behavior it has been found that an extrapolation formula of the Brody type can be used. In the present paper we analyze the regular to chaotic behavior of small world (SW) networks using an extension of the Gaussian orthogonal ensemble. This RMT ensemble, coined the deformed Gaussian orthogonal ensemble (DGOE), supplies a natural foundation of the Brody formula. SW networks follow GOE statistics until a certain range of eigenvalue correlations depending upon the strength of random connections. We show that for these regimes of SW networks where spectral correlations do not follow GOE beyond a certain range, DGOE statistics models the correlations very well. The analysis performed in this paper proves the utility of the DGOE in network physics, as much as it has been useful in other physical systems.

Nodal solutions for nonlinear eigenvalue problems

We are concerned with determining values of, for which there exist nodal solutions of the boundary value problems u" + ra(t) f(u) = 0, 0 < t < 1, u(O) = u(1) = 0. The proof of our main result is based upon bifurcation techniques.

Influence of the interaction between nodal fibroblast and breast cancer cells on gene expression

Our aim was to evaluate the interaction between breast cancer cells and nodal fibroblasts, by means of their gene expression profile. Fibroblast primary cultures were established from negative and positive lymph nodes from breast cancer patients and a similar gene expression pattern was identified, following cell culture. Fibroblasts and breast cancer cells (MDA-MB231, MDA-MB435, and MCF7) were cultured alone or co-cultured separated by a porous membrane (which allows passage of soluble factors) for comparison. Each breast cancer lineage exerted a particular effect on fibroblasts viability and transcriptional profile. However, fibroblasts from positive and negative nodes had a parallel transcriptional behavior when co-cultured with a specific breast cancer cell line. The effects of nodal fibroblasts on breast cancer cells were also investigated. MDA MB-231 cells viability and migration were enhanced by the presence of fibroblasts and accordingly, MDA-MB435 and MCF7 cells viability followed a similar pattern. MDA-MB231 gene expression profile, as evaluated by cDNA microarray, was influenced by the fibroblasts presence, and HNMT, COMT, FN3K, and SOD2 were confirmed downregulated in MDA-MB231 co-cultured cells with fibroblasts from both negative and positive nodes, in a new series of RT-PCR assays. In summary, transcriptional changes induced in breast cancer cells by fibroblasts from positive as well as negative nodes are very much alike in a specific lineage. However, fibroblasts effects are distinct in each one of the breast cancer lineages, suggesting that the inter-relationships between stromal and malignant cells are dependent on the intrinsic subtype of the tumor.

Lymph Node Size in Rectal Cancer Following Neoadjuvant Chemoradiation-Can We Rely on Radiologic Nodal Staging After Chemoradiation?

OBJECTIVES: Local excision is currently being considered as an alternative strategy for ypT0-2 rectal cancer. However, patient selection is crucial to rule out nodal disease and is performed by radiologic studies that consider size as a surrogate marker for positive nodes. The purpose of this study was to determine the difference in size between metastatic and nonmetastatic nodes and the critical lymph node size after neoadjuvant chemoradiation therapy. METHODS: The 201 lymph nodes available from 31 patients with ypT0-2 rectal cancer were reviewed and measured. Lymph nodes were compared according to the presence of metastases and size. RESULTS: There was a mean of 6.5 lymph nodes per patient and 12 positive nodes of the 201 recovered (6%). Ninety-five percent of all lymph nodes were <5 mm, whereas 50% of positive lymph nodes were <3 mm. Metastatic lymph nodes were significantly greater in size (5.0 vs. 2.5mm; P = 0.02). Lymph nodes >4.5 mm had a greater risk of harboring metastases (P = 0.009). CONCLUSIONS: Patients with ypT0-2 rectal cancer following neoadjuvant chemoradiation have very small perirectal nodes. Individual metastatic lymph nodes are significantly larger. However, a significant number of lymph nodes after neoadjuvant chemoradiation (negative and positive) are <3 mm. Individual lymph node size is not a good predictor of nodal metastases and may lead to inaccurate radiologic staging.

Individual risk prediction of nodal and distant metastasis for patients with typical bronchial carcinoid tumors

Objective: Bronchial typical carcinoid tumors are tow-grade malignancies. However, metastases are diagnosed in some patients. Predicting the individual risk of these metastases to determine patients eligible for a radical lymphadenectomy and patients to be followed-up because of distant metastasis risk is relevant. Our objective was to screen for predictive criteria of bronchial typical carcinoid tumor aggressiveness based on a logistic regression model using clinical, pathological and biomolecular data. Methods: A multicenter retrospective cohort study, including 330 consecutive patients operated on for bronchial typical carcinoid tumors and followed-up during a period more than 10 years in two university hospitals was performed. Selected data to predict the individual risk for both nodal and distant metastasis were: age, gender, TNM staging, tumor diameter and location (central/peripheral), tumor immunostaining index of p53 and Ki67, Bcl2 and the extracellular density of neoformed microvessels and of collagen/elastic extracellular fibers. Results: Nodal and distant metastasis incidence was 11% and 5%, respectively. Univariate analysis identified all the studied biomarkers as related to nodal metastasis. Multivariate analysis identified a predictive variable for nodal metastasis: neo angiogenesis, quantified by the neoformed pathological microvessels density. Distant metastasis was related to mate gender. Discussion: Predictive models based on clinical and biomolecular data could be used to predict individual risk for metastasis. Patients under a high individual risk for lymph node metastasis should be considered as candidates to mediastinal lymphadenectomy. Those under a high risk of distant metastasis should be followed-up as having an aggressive disease. Conclusion: Individual risk prediction of bronchial typical carcinoid tumor metastasis for patients operated on can be calculated in function of biomolecular data. Prediction models can detect high-risk patients and help surgeons to identify patients requiring radical lymphadenectomy and help oncologists to identify those as having an aggressive disease requiring prolonged follow-up. (C) 2008 European Association for Cardio-Thoracic Surgery. Published by Elsevier B.V. All rights reserved.

Growth of papaya nodal and rooted shoot cultures as affected by ACC, STS, culture vessel size and incubation conditions

Nodal shoot cultures of 'Clone 003', a selected Australian papaya cultivar, were cultured on modified De Fossard medium supplemented with chemicals that either promote ethylene evolution or inhibit action while in culture. Nodal shoot cultures grown in the presence of 1-aminocyclopropane carboxylic acid (ACC, 1.0 mM) resulted in a significant reduction in percent fresh and dry weights, shoot length, leaf area, petiole length and chlorophyll content, but leaf development was significantly increased. In contrast, nodal cultures grown in the presence of silver thiosulphate (STS, 0.5 mM) significantly produced the highest percentage of fresh and dry weights, shoot length, leaf production, leaf area expansion, petiole length and leaf chlorophyll content. Nodal cultures and rooted whole plantlets placed in medium-sized (125 mL) culture vessels had significantly better growth than those cultures placed in small (70 mL) or in large (250 mL) vessels. Cultures grown in medium-sized vessels had higher fresh and dry weights, longer shoots, more leaves and larger leaf area than those cultures placed in smaller or larger vessels. Similarly, values for said growth parameters and for chlorophyll content of the nodal and rooted whole plantlets were higher when they were incubated under high light intensity of 120 mumol m(-2)s(-1) at a prevailing temperature of either 20+/-1 C or 25+/-1 C.

Desenvolvimento de algoritmos para a determinação da máxima injeção nodal em redes de energia elétrica

A presente dissertação apresenta um conjunto de algoritmos, cujo objetivo é a determinação da capacidade máxima de energia que é possível integrar numa rede de energia elétrica, seja num único nó ou em vários nós simultaneamente. Deste modo, obtém-se uma indicação dos locais mais adequados à nova instalação de geração e quais os reforços de rede necessários, de forma a permitirem a alocação da nova energia. Foram estudados e identificados os fatores que influenciam o valor da capacidade máxima nodal, assim como as suas consequências no funcionamento da rede, em particular o carácter simultâneo associado às referidas injeções nodais. Nesse sentido, são apresentados e desenvolvidos algoritmos que têm em consideração as características técnicas da geração a ligar e as restrições físicas impostas pela rede elétrica existente. Os algoritmos desenvolvidos apresentados baseiam-se em busca gaussiana, tendo sido igualmente implementada uma heurística que tem em consideração a proximidade de outras injeções em nós adjacentes e finalmente, dada a natureza combinatória do problema, propõe-se a aplicação de algoritmos genéticos especificamente adaptados ao problema Conclui-se que os algoritmos genéticos encerram características que lhes permitem ser aplicados em qualquer topologia com resultados superiores a todos os algoritmos desenvolvidos. Os métodos apresentados foram desenvolvidos e implementados usando a linguagem de programação Python, tendo-se desenvolvido ainda um interface visual ao utilizador, baseado em wxPython, onde estão implementadas diversas ferramentas que possibilitam a execução dos algoritmos, a configuração dos seus parâmetros e ainda o acesso à informação resultante dos algoritmos em formato Excel.

Nodal price simulation in competitive electricity markets

Locational Marginal Prices (LMP) are important pricing signals for the participants of competitive electricity markets, as the effects of transmission losses and binding constraints are embedded in LMPs [1],[2]. This paper presents a software tool that evaluates the nodal marginal prices considering losses and congestion. The initial dispatch is based on all the electricity transactions negotiated in the pool and in bilateral contracts. It must be checked if the proposed initial dispatch leads to congestion problems; if a congestion situation is detected, it must be solved. An AC power flow is used to verify if there are congestion situations in the initial dispatch. Whenever congestion situations are detected, they are solved and a feasible dispatch (re-dispatch) is obtained. After solving the congestion problems, the simulator evaluates LMP. The paper presents a case study based on the the 118 IEEE bus test network.

Ensemble: an e-learning framework

E-Learning frameworks are conceptual tools to organize networks of elearning services. Most frameworks cover areas that go beyond the scope of e-learning, from course to financial management, and neglects the typical activities in everyday life of teachers and students at schools such as the creation, delivery, resolution and evaluation of assignments. This paper presents the Ensemble framework - an e-learning framework exclusively focused on the teaching-learning process through the coordination of pedagogical services. The framework presents an abstract data, integration and evaluation model based on content and communications specifications. These specifications must base the implementation of networks in specialized domains with complex evaluations. In this paper we specialize the framework for two domains with complex evaluation: computer programming and computer-aided design (CAD). For each domain we highlight two Ensemble hotspots: data and evaluations procedures. In the former we formally describe the exercise and present possible extensions. In the latter, we describe the automatic evaluation procedures.

O jazz e a música do mediterrâneo: modos e ritmos de influência árabe num contexto de escrita para Large Ensemble

Dissertação para obtenção do grau de Mestre em Música - Interpretação Artística

Ensemble: an innovative approach to practice computer programming

Currently, the teaching-learning process in domains, such as computer programming, is characterized by an extensive curricula and a high enrolment of students. This poses a great workload for faculty and teaching assistants responsible for the creation, delivery, and assessment of student exercises. The main goal of this chapter is to foster practice-based learning in complex domains. This objective is attained with an e-learning framework—called Ensemble—as a conceptual tool to organize and facilitate technical interoperability among services. The Ensemble framework is used on a specific domain: computer programming. Content issues are tacked with a standard format to describe programming exercises as learning objects. Communication is achieved with the extension of existing specifications for the interoperation with several systems typically found in an e-learning environment. In order to evaluate the acceptability of the proposed solution, an Ensemble instance was validated on a classroom experiment with encouraging results.