Les travaux de cette thèse ont pour but de mettre en œuvre des outils de modélisation et de simulation numériques de mécanismes sous-tendant l’activité neuronale, afin de promouvoir la découverte de médicaments pour le traitement des maladies du système nerveux. Les modèles développés s’inscrivent à différentes échelles : 1) les modèles dits « élémentaires » permettent de simuler la dynamique des récepteurs, des canaux ioniques, et les réactions biochimiques des voies de signalisation intracellulaires ; 2) les modèles de neurones permettent d’étudier l’activité électrophysiologique de ces cellules ; et 3) les modèles de microcircuits permettent de comprendre les propriétés émergentes de ces systèmes complexes, tout en conservant les mécanismes élémentaires qui sont les cibles des molécules pharmaceutiques. À partir d’une synthèse bibliographique des éléments de neurobiologie nécessaires, et d’une présentation des outils mathématiques et informatiques mis en œuvre, le manuscrit décrit les différents modèles développés ainsi que leur processus de validation, allant du récepteur de neurotransmetteur au microcircuit. D’autre part, ces développements ont été appliqués à trois études visant à comprendre : 1) la modulation pharmacologique de la potentialisation à long terme (LTP) dans les synapses glutamatergiques de l’hippocampe, 2) les mécanismes de l'hyperexcitabilité neuronale dans l'épilepsie mésio-temporale (MTLE) à partir de résultats expérimentaux in vitro et in vivo, et 3) la modulation cholinergique de l'activité hippocampique, en particulier du rythme thêta associé à la voie septo-hippocampique. / The work of this thesis aims to apply modeling and simulation techniques to mechanisms underlying neuronal activity, in order to promote drug discovery for the treatment of nervous system diseases. The models are developed and integrated at different scales: 1) the so-called "elementary models" permit to simulate dynamics of receptors, ion channels and biochemical reactions in intracellular signaling pathways; 2) models at the neuronal level allow to study the electrophysiological activity of these cells; and 3) microcircuits models help to understand the emergent properties of these complex systems, while maintaining the basic mechanisms that are the targets of pharmaceutical molecules. After a bibliographic synthesis of necessary elements of neurobiology, and an outline of the implemented mathematical and computational tools, the manuscript describes the developed models, as well as their validation process, ranging from the neurotransmitter receptor to the microcircuit. Moreover, these developments have been applied to three studies aiming to understand: 1) pharmacological modulation of the long-term potentiation (LTP) of glutamatergic synapses in the hippocampus, 2) mechanisms of neuronal hyperexcitability in the mesial temporal lobe epilepsy (MTLE), based on in vitro and in vivo experimental results, and 3) cholinergic modulation of hippocampal activity, particularly the theta rhythm associated with septo-hippocampal pathway.

L'application d'Abel-Jacobi fait le lien entre la forme de Weierstrass d'une courbe elliptique définie sur C et le tore complexe qui lui est associé. Il est possible de la calculer en un nombre d'opérations quasi-linéaire en la précision voulue, c'est à dire en temps O(M(P) log P). Son inverse est donné par la fonction p de Weierstrass, qui s'exprime en fonction de thêta, une fonction importante en théorie des nombres. L'algorithme naturel d'évaluation de thêta nécessite O(M(P) sqrt(P)) opérations, mais certaines valeurs (les thêta-constantes) peuvent être calculées en O(M(P) log P) opérations en exploitant les liens avec la moyenne arithmético-géométrique (AGM). Dans ce manuscrit, nous généralisons cet algorithme afin de calculer thêta en O(M(P) log P). Nous exhibons une fonction F qui a des propriétés similaires à l'AGM. D'une façon similaire à l'algorithme pour les thêta-constantes, nous pouvons alors utiliser la méthode de Newton pour calculer la valeur de thêta. Nous avons implanté cet algorithme, qui est plus rapide que la méthode naïve pour des précisions supérieures à 300 000 chiffres décimaux. Nous montrons comment généraliser cet algorithme en genre supérieur, et en particulier comment généraliser la fonction F. En genre 2, nous sommes parvenus à prouver que la même méthode mène à un algorithme qui évalue thêta en O(M(P) log P) opérations ; la même complexité s'applique aussi à l'application d'Abel-Jacobi. Cet algorithme est plus rapide que la méthode naïve pour des précisions plus faibles qu'en genre 1, de l'ordre de 3 000 chiffres décimaux. Nous esquissons également des pistes pour obtenir la même complexité en genre quelconque. Enfin, nous exhibons un nouvel algorithme permettant de calculer une isogénie de courbes elliptiques de noyau donné. Cet algorithme utilise l'application d'Abel-Jacobi, car il est facile d'évaluer l'isogénie sur le tore ; il est sans doute possible de le généraliser au genre supérieur / The Abel-Jacobi map links the short Weierstrass form of a complex elliptic curve to the complex torus associated to it. One can compute it with a number of operations which is quasi-linear in the target precision, i.e. in time O(M(P) log P). Its inverse is given by Weierstrass's p-function, which can be written as a function of theta, an important function in number theory. The natural algorithm for evaluating theta requires O(M(P) sqrt(P)) operations, but some values (the theta-constants) can be computed in O(M(P) log P) operations by exploiting the links with the arithmetico-geometric mean (AGM). In this manuscript, we generalize this algorithm in order to compute theta in O(M(P) log P). We give a function F which has similar properties to the AGM. As with the algorithm for theta-constants, we can then use Newton's method to compute the value of theta. We implemented this algorithm, which is faster than the naive method for precisions larger than 300,000 decimal digits. We then study the generalization of this algorithm in higher genus, and in particular how to generalize the F function. In genus 2, we managed to prove that the same method leads to a O(M(P) log P) algorithm for theta; the same complexity applies to the Abel-Jacobi map. This algorithm is faster than the naive method for precisions smaller than in genus 1, of about 3,000 decimal digits. We also outline a way one could reach the same complexity in any genus. Finally, we study a new algorithm which computes an isogeny of elliptic curves with given kernel. This algorithm uses the Abel-Jacobi map because it is easy to evaluate the isogeny on the complex torus; this algorithm may be generalizable to higher genera

Diese Arbeit untersucht verschiedene Fragen hinsichtlich der birationalen Geometrie der Modulräume $\Mbar_g$ und $\Mbar_{g,n}$, mit besonderem Augenmerk auf der Berechnung effektiver Divisorklassen. In Kapitel 2 definieren wir für jedes $n$-Tupel ganzer Zahlen $\d$, die sich zu $g-1$ summieren, einen geometrisch bedeutsamen Divisor auf $\Mbar_{g,n}$, der durch Zurückziehen des Thetadivisors einer universellen Jacobi-Varietät mittels einer Abel-Jacobi-Abbildung erhalten wird. Er ist eine Verallgemeinerung verschiedener in der Literatur verwendeten Arten von Divisoren. Wir berechnen die Klasse dieses Divisors und zeigen, dass er für bestimmte $\d$ irreduzibel und extremal im effektiven Kegel von $\Mbar_{g,n}$ ist. Kapitel 3 beschäftigt sich mit einem birationalen Modell $X_6$ von $\Mbar_6$, das durch quadrische Hyperebenenschnitte auf der del-Pezzo-Fläche vom Grad $5$ erhalten wird. Wir berechnen die Klasse des großen Divisors, der die birationale Abbildung $\Mbar_6 \dashrightarrow X_6$ induziert, und erhalten so eine obere Schranke an die bewegliche Steigung von $\Mbar_6$. Wir zeigen, dass $X_6$ der letzte nicht-triviale Raum im log-minimalen Modellprogramm für $\Mbar_6$ ist. Weiterhin geben wir einige Resultate bezüglich der Unirationalität der Weierstraßorte auf $\Mbar_{g,1}$. Für $g = 6$ hängen diese mit der del-Pezzo-Konstruktion zusammen, die benutzt wurde, um das Modell $X_6$ zu konstruieren. Kapitel 4 konzentriert sich auf den Fall $g = 0$. Castravet and Tevelev führten auf $\Mbar_{0,n}$ kombinatorisch definierte Hyperbaumdivisoren ein, die für $n = 6$ zusammen mit den Randdivisoren den effektiven Kegel erzeugen. Wir berechnen die Klasse des Hyperbaumdivisors auf $\Mbar_{0,7}$, der bis auf Permutation der markierten Punkte eindeutig ist. Wir geben eine geometrische Charakterisierung für ihn an, die zu der von Keel und Vermeire für den Fall $n = 6$ gegebenen analog ist. / This thesis investigates various questions concerning the birational geometry of the moduli spaces $\Mbar_g$ and $\Mbar_{g,n}$, with a focus on the computation of effective divisor classes. In Chapter 2 we define, for any $n$-tuple $\d$ of integers summing up to $g-1$, a geometrically meaningful divisor on $\Mbar_{g,n}$ that is essentially the pullback of the theta divisor on a universal Jacobian variety under an Abel-Jacobi map. It is a generalization of various kinds of divisors used in the literature, for example by Logan to show that $\Mbar_{g,n}$ is of general type for all $g \geq 4$ as soon as $n$ is big enough. We compute the class of this divisor and show that for certain choices of $\d$ it is irreducible and extremal in the effective cone of $\Mbar_{g,n}$. Chapter 3 deals with a birational model $X_6$ of $\Mbar_6$ that is obtained by taking quadric hyperplane sections of the degree $5$ del Pezzo surface. We compute the class of the big divisor inducing the birational map $\Mbar_6 \dashrightarrow X_6$ and use it to derive an upper bound on the moving slope of $\Mbar_6$. Furthermore we show that $X_6$ is the final non-trivial space in the log minimal model program for $\Mbar_6$. We also give a few results on the unirationality of Weierstraß loci on $\Mbar_{g,1}$, which for $g = 6$ are related to the del Pezzo construction used to construct the model $X_6$. Finally, Chapter 4 focuses on the case $g = 0$. Castravet and Tevelev introduced combinatorially defined hypertree divisors on $\Mbar_{0,n}$ that for $n = 6$ generate the effective cone together with boundary divisors. We compute the class of the hypertree divisor on $\Mbar_{0,7}$, which is unique up to permutation of the marked points. We also give a geometric characterization of it that is analogous to the one given by Keel and Vermeire in the $n = 6$ case.

L’épilepsie du lobe temporal (ELT) est la forme d’épilepsie partielle la plus fréquente chez l’adulte. Elle se caractérise par une période de latence pendant laquelle l’ELT se met en place. Cette période est appelée épileptogenèse. L’épileptogenèse reste une période inaccessible chez l’Homme. Cependant, les modèles animaux présentent l’avantage de pouvoir l’étudier, dans le but de prévenir l’ELT. Ainsi, mon travail de thèse a consisté à mettre en évidence des marqueurs prédictifs de l’épileptogenèse, sur le plan cognitif et électrophysiologique in vivo, à partir du modèle pilocarpine. Les résultats ont montré que dès le stade précoce de l’épileptogenèse, des déficits de mémoire spatiale corrélaient avec une diminution de la puissance des oscillations thêta chez les animaux pilocarpine, sans modification jusqu’au stade chronique. Au même stade, une diminution de la puissance et de la fréquence des oscillations thêta lors du comportement d’exploration a été observée. L’activité interictale, activité paroxystique présente chez les patients entre leurs crises et caractéristique du stade épileptogène dans les modèles animaux, ne corrèle pas directement avec les déficits cognitifs mais diminue la puissance des oscillations thêta dans l’onde après la pointe au cours de l’épileptogenèse mais plus au stade chronique, ce qui suggère une importante modification du réseau avant le stade chronique. On a également décrit deux types d’activité interictale dont les propriétés (amplitude, nombre) et la dynamique au cours du temps sont modifiées juste avant la première crise spontanée, ce qui pourrait constituer, comme les déficits spatiaux et l’altération du rythme thêta, un marqueur prédictif de l’épileptogenèse. De plus, une augmentation du couplage entre l’hippocampe et le CE est observée au cours de l’épileptogenèse mais plus au stade chronique, alors qu’une modification du flux de l’information entre ces deux structures au stade épileptogène précoce persiste jusqu’au stade chronique, indépendamment de la présence ou non d’activité interictale. Ces résultats mettent en évidence la construction d’un réseau épileptogène, un changement majeur du réseau avant la première crise spontanée, et des marqueurs qui pourraient être prédictifs de l’épileptogenèse. L’ELT, les oscillations et les fonctions cognitives faisant intervenir des propriétés de réseau, tels les processus de synchronisation, l’enregistrement de 15 structures au sein du lobe temporal a montré, à partir du modèle pilocarpine, un réseau doté de caractéristiques plus « small-world » (SW) qui tendrait à se synchroniser plus localement, avec une perte des connexions longue distance. Ces résultats pourraient expliquer les altérations de réseau observées précédemment au cours de l’épileptogenèse. L’analyse SW et de cohérence, à l’échelle de ce réseau de structures, lors de différents états (comportementaux, processus cognitifs), mettent en évidence des changements de la dynamique lors de ces états, en conditions normales et pathologiques. Toutes ces modifications de réseau doivent être sûrement recrutées dans la mise en place d’un cerveau épileptique et des altérations cognitives associées. / Temporal lobe epilepsy (TLE) is the most common form of partial epilepsy in adults. TLE is characterized by a latent period during which TLE takes place. This period is called epileptogenesis. In TLE patients, epileptogenesis is unexplored. However, the use of animal models, like pilocarpine model, allows the study of epileptogenic processes, in order to try to prevent TLE. Thus, my PhD work tries to yield some predictive markers of epileptogenesis, in the pilocarpine model. We studied cognitive and electrophysiological in vivo alterations in this model. We showed that there are early and persistent spatial deficits that correlate with a decrease of the power of theta oscillations, i.e. during the early stage of epileptogenesis and the chronic stage. At the same time, there is also a decrease of power and frequency of theta rhythm during exploratory behaviors. Interictal-like activity (ILA) is a pathological activity present during epileptogenesis in experimental models. ILA does not correlate with cognitive deficits, but decreases theta power after the spike, i.e. in its wave, during epileptogenesis but not during the chronic stage anymore. This suggests an important network alteration before the chronic stage. Indeed, we described two types of ILA, whose properties (number, amplitude) and dynamics evolved during epileptogenesis with a major switch just before the first spontaneous seizure. All together, these results may constitute, with spatial deficits and theta rhythm alterations, predictive markers of epileptogenesis. Moreover, we showed an increase in the coupling, ILA-dependent, between the hippocampus and the entorhinal cortex, during epileptogenesis but not during the chronic stage, whereas a reversal of the information flow between these two structures occurs at the early stage of epileptogenesis and persists without any modification till the chronic stage. These results suggest the build-up of an epileptogenic network, a major switch of network properties just before the first spontaneous seizure, and some markers that could be predictive of epileptogenesis. TLE, oscillations and cognition involved processes at the network level, in particular synchronization processes. These processes could be possible via oscillations, which allow information transfer between structures of the network, in order to provide behavioral and cognitive processing. Recordings performed in 15 different structures of the temporal lobe showed, in pilocarpine animals, a network with more “small-world” (SW) features, with a higher local clustering and a loss of long-range connections. These results could explain cognitive and oscillatory alterations observed previously during epileptogenesis. SW and coherence analysis, at the network level, between signals during different brain-states (behaviors and cognitive processes) showed changes in dynamics occurring during these states, in normal and epileptogenic conditions. All these modifications in network activities may be involved in the construction of an epileptic brain and in associated cognitive deficits.

<p>The topic of this thesis is computation of Mass waveforms, and we consider a number of different cases: Congruence subgroups of the modular group and Dirichlet characters (chapter 1); congruence subgroups and general multiplier systems and real weight (chapter 2); and noncongruence subgroups (chapter 3). In each case we first discuss the necessary theoretical background. We then outline the algorithm and display some of the results obtained by it.</p>

The topic of this thesis is computation of Mass waveforms, and we consider a number of different cases: Congruence subgroups of the modular group and Dirichlet characters (chapter 1); congruence subgroups and general multiplier systems and real weight (chapter 2); and noncongruence subgroups (chapter 3). In each case we first discuss the necessary theoretical background. We then outline the algorithm and display some of the results obtained by it.

Magister Scientiae - MSc (Biotechnology) / The vaginal mucosa is dominated by Gram positive, rod shaped lactobacilli which serve as a natural barrier against infection. In both healthy and BV infected women Lactobacillus crispatus and Lactobacillus jensennii has been found to be the predominant Lactobacillus species. Many studies have been conducted to assess factors influencing lactobacilli dominance in the vaginal microbiome. However, no study has evaluated the impact of plasmids on the vaginal lactobacilli. In the present study two plasmids, pLc17 and pLc4, isolated from vaginal Lactobacillus species of both healthy and BV infected women were characterized. pLc4 was present in both Lactobacillus crispatus and Lactobacillus jensennii while pLc17 was only present in Lactobacillus crispatus. pLc17 (16663 bp in size) encoded a ribonucleotide diphosphate reductase (RNR), a filamentation induced by cAMP-like (FIC-like) protein and numerous mobile elements. The FIC-like protein may assist pLc17 to persist within the bacterial population, while RNR is commonly associated with phages and may indicate phage infection. pLc4 (4224 bp in size) encodes for a replication initiator protein and a plasmid partitioning protein. The replication protein on pLc4 shows 44% identity with the replication initiation protein of pSMQ173b_03. On further phylogenetic and sequence analysis with other Rolling Circle Replication (RCR) plasmids, pLc4 appears to be novel as the plasmid shows a low degree of similarity to these RCR plasmids. pLc17 appears to carry both a RCR replicon as well as a theta replicon, similar to pIP501, the broad-host-range plasmid from Bacillus subtilis. The relative Plasmid Copy Number (PCN) for pLc4 and pLc17 was analysed using quantitative polymerase chain reaction (qPCR) for the healthy state relative to the disease state from twentyeight vaginal swab samples obtained from the National Institute for Communicable Diseases (NICD). The relative PCN for pLc4 and pLc17 had a fold increase of ~2.803 and ~1.693, respectively in the healthy patient samples relative to BV infected patient samples. However, there were not found to be significant differences when taking the standard error into account Due to the novelty of these plasmids further analysis and characterisation is required for both plasmids, to establish what role they may play in the health of the vaginal milieu.

This study focuses on the predicate argument structure (PAS) of a sub-class of verbs in Xitsonga - verbs of change of possession: give, contribute, future having, providing, obtaining and verbs of exchange. It is shown that these verbs select various theta roles to form their PAS in the different alternations allowed in this language. The effects of the applicative {-el-} and causative {-is-} verbal affixes on the PAS of such verbs are also considered. The study confirms the fact that the ordering of objects in ditransitive verbs is determined by an interplay of syntactic and semantic factors. Ambiguity arises in the case of two animate objects. In this case the object with a definite reading will appear adjacent to the verb. / African Languages / M. A. (Arican Languages)

Nous considérons certaines séries de Fourier liées à la théorie des formes modulaires. Nous étudions leurs propriétés analytiques : la dérivabilité, le module de continuité et l'exposant de Hölder. Nous utilisons deux méthodes différentes. La première revient à trouver et itérer une équation fonctionnelle de la fonction étudiée (méthode d'Itatsu) et la deuxième provient de l'analyse en ondelettes (méthode de Jaffard). L'étape essentielle de chacune dépend de la modularité sous-jacente. Nous trouvons que les propriétés analytiques de ces séries aux points irrationnels sont liées aux propriétés diophantiennes de ces points. Ce travail a été motivé par l'étude de la fonction de Riemann. / We consider certain Fourier series which arise from modular or automorphicforms. We study their analytic properties: differentiability, modulus of continuity and theH¨older regularity exponent. We use two different methods. One is based on finding anditerating a functional equation for the function studied (Itatsu’s method), the second onecomes from wavelet analysis (Jaffard’s method). The crucial steps in both of them arebased on the underlined modularity. We find that the analytic properties of these seriesat an irrational x are related to the fine diophantine properties of x, in a very precise way.The work was motivated by the study of the Riemann series.

Made available in DSpace on 2014-12-17T15:28:49Z (GMT). No. of bitstreams: 1 RobsonST_DISSERT.pdf: 350196 bytes, checksum: eaf6055553dc1f6cec39e0f754c20635 (MD5) Previous issue date: 2011-12-02 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / Brain oscillation are not completely independent, but able to interact with each other through cross-frequency coupling (CFC) in at least four different ways: power-to-power, phase-to-phase, phase-to-frequency and phase-to-power. Recent evidence suggests that not only the rhythms per se, but also their interactions are involved in the execution of cognitive tasks, mainly those requiring selective attention, information flow and memory consolidation. It was recently proposed that fast gamma oscillations (60 150 Hz) convey spatial information from the medial entorhinal cortex to the CA1 region of the hippocampus by means of theta (4-12 Hz) phase coupling. Despite these findings, however, little is known about general characteristics of CFCs in several brain regions. In this work we recorded local field potentials using multielectrode arrays aimed at the CA1 region of the dorsal hippocampus for chronic recording. Cross-frequency coupling was evaluated by using comodulogram analysis, a CFC tool recently developted (Tort et al. 2008, Tort et al. 2010). All data analyses were performed using MATLAB (MathWorks Inc). Here we describe two functionally distinct oscillations within the fast gamma frequency range, both coupled to the theta rhythm during active exploration and REM sleep: an oscillation with peak activity at ~80 Hz, and a faster oscillation centered at ~140 Hz. The two oscillations are differentially modulated by the phase of theta depending on the CA1 layer; theta-80 Hz coupling is strongest at stratum lacunosum-moleculare, while theta-140 Hz coupling is strongest at stratum oriens-alveus. This laminar profile suggests that the ~80 Hz oscillation originates from entorhinal cortex inputs to deeper CA1 layers, while the ~140 Hz oscillation reflects CA1 activity in superficial layers. We further show that the ~140 Hz oscillation differs from sharp-wave associated ripple oscillations in several key characteristics. Our results demonstrate the existence of novel theta-associated high-frequency oscillations, and suggest a redefinition of fast gamma oscillations / As oscila??es cerebrais n?o s?o completamente independentes, mas capazes de interagir umas com as outras atrav?s de acoplamentos entre frequ?ncias (cross-frequency coupling, doravante CFC) em pelo menos quatro diferentes modalidades: amplitudeamplitude, fase-fase (coer?ncia), fase-frequ?ncia e fase-amplitude. Evid?ncias recentes sugerem que n?o somente os ritmos per se, mas tamb?m as intera??es entre eles est?o envolvidas na execu??o de tarefas cognitivas, principalmente aquelas que requerem aten??o seletiva, transmiss?o de informa??es e consolida??o de mem?rias. Estudos recentes prop?em que oscila??es gama alto (60 150 Hz) transferem informa??es espaciais do c?rtex entorrinal medial para a regi?o CA1 do hipocampo atrav?s do acoplamento com a fase de teta (4 12 Hz). Apesar destas descobertas, entretanto, pouco se sabe sobre as caracter?sticas gerais dos CFCs em diversas regi?es cerebrais. Neste trabalho, registramos potenciais de campo local usando matrizes de multieletrodos implantadas no hipocampo dorsal para registro neural cr?nico. O acoplamento fase-amplitude foi avaliado por meio da an?lise de comodulogramas, uma ferramenta de CFC desenvolvida recentemente (Tort et al. 2008, Tort et al. 2010). Todas as an?lises de dados foram realizadas em MATLAB (MathWorks Inc). Descrevemos duas oscila??es funcionalmente distintas dentro da faixa de frequ?ncia de gama, ambas acopladas ao ritmo teta durante explora??o ativa e sono REM: uma oscila??o com um pico de atividade em ~80 Hz e uma mais r?pida centrada em ~140 Hz. As duas oscila??es s?o diferencialmente moduladas pela fase de teta conforme a camada de CA1; o acoplamento teta-80 Hz ? mais forte no stratum lacunosum-moleculare, enquanto que o acoplamento teta-140 Hz ? mais forte no stratum oriens-alveus. Este perfil laminar sugere que a oscila??o de 80 Hz origina-se das entradas do c?rtex entorrinal para as camadas profundas de CA1, e que a oscila??o de 140 Hz reflete a atividade de CA1 em camadas superficiais. Ademais, n?s mostramos que a oscila??o de 140 Hz difere-se das oscila??es ripples associadas com sharp-waves em diversos aspectos chave. Nossos resultados demonstram a exist?ncia de novas oscila??es de alta frequ?ncia associadas ? teta e sugerem uma redefini??o das oscila??es gama alto