No description available.

<p>The primary somatosensory cortex (SI) is important for hand function and influences motor circuitry in the primary motor cortex (M1). Areas 3a, 1 and 2 of SI have direct connectivity with M1. Much of our present knowledge of this connectivity and its relevance to hand function is based on animal research. However, less is known about the neural mechanisms that underpin hand function in humans. The present study investigated the influence of SI on corticospinal excitability as well as inhibitory and excitatory neural circuitry within M1 before and after continuous theta-burst stimulation (cTBS). Additionally, stimulation parameters influence the direction and magnitude of cTBS after-effects. Thus, current direction and frequency of cTBS were manipulated. Two experiments were performed. In Experiment 1, motor-evoked potentials (MEPs) were recorded from the first-dorsal interosseous (FDI) muscle bilaterally before and after 50 Hz cTBS over left SI. In a second condition, the orientation of cTBS was reversed. Experiment 2 measured MEPs, short-latency intracortical inhibition (SICI) and intracortical facilitation (ICF) from the right FDI following a modified 30 Hz cTBS over left SI or M1. The results of Experiment 1 and 2 demonstrate that SI influences M1 circuitry such that MEPs are facilitated following cTBS over SI. However, MEPs are suppressed when the current direction is reversed. CTBS at 30 Hz delivered over M1 suppressed excitatory circuitry that generates MEPs and ICF. The findings from the thesis suggest that SI influences hand motor circuitry and is likely a mechanism by which somatosensory information modulates hand motor function.</p> / Bachelor of Science (BSc)

Encoding and consolidation of memories are two processes within the hippocampus, and connected cortical networks, that recruit different circuit level dynamics to effectively process and pass information from brain region to brain region. In the hippocampal CA1 pyramidal layer local field potential (LFP), these processes take the form of theta and sharp wave ripples (SPW-Rs) for encoding and consolidation, respectively. As an animal runs through an environment, neurons become active at specific locations in the environment (place cells) increasing their firing rate, functionally representing these specific locations. These firing rate increases are organized within the local theta oscillations and sequential activation of many place cells creates a map of the environment. Once the animal stops moving and begins consummatory behaviors, such as eating, drinking, or grooming, theta activity diminishes, and large irregular activity (LIA) begins to dominate the LFP. Spontaneously, with the LIA, the place cells active during the experience are replayed during SPW-Rs in the same spatial order they were encountered in the environment. Both theta and SPW-R oscillations and their associated neuronal firing are necessary for effective place recognition as well as learning and memory. As such, interruption or termination of SPW-R events results in decreased learning performance over days. During exploration, the associated theta and sequential place cell activity is thought to encode the experience. During quiet restfulness or slow wave sleep (SWS), SPW-R events, that replay experience specific place sequences, are thought to be the signal by which systems consolidation progresses and the hippocampus guides cortical synaptic reorganization. The granular retrosplenial cortex (gRSC) is an associational area that exhibits high frequency oscillations (HFOs) during both hippocampal theta and SPW-Rs, and is potentially a period when the gRSC interprets incoming content from the hippocampus during encoding and systems consolidation. However, the precise laminar organization of synaptic currents supporting HFOs, whether the local gRSC circuitry can support HFOs without patterned input, and the precise coupling of hippocmapla oscillations to gRSC HFOs across brain states remains unknown. We aimed to answer these questions using in vivo, awake electrophysiological recordings in head-fixed mice that were trained to run for water rewards in a 1D virtual environment. We show that gRSC synaptic currents supporting HFOs, across all awake brain states, are exclusively localized to layer 2/3 (L2/3), even when events are detected within layer 5 (L5). Using focal optogenetics, both L2/3 and L5 can generate induced HFOs given a strong enough broad stimulation. Spontaneous gRSC HFOs occurring outside of SPW-Rs are highly comodulated with medial entorhinal cortex (MEC) generated high gamma in hippocampal stratum lacunosum moleculare. gRSC HFOs may serve a necessary role in communication between the hippocampus during SPW-Rs states and between the hippocampus, gRSC, and MEC during theta states to support memory consolidation and memory encoding, respectively. / Doctor of Philosophy / As an animal moves through an environment, individual neurons in the hippocampus, known as place cells, increase and decrease their firing rate as the animal enters and exits specific locations in the environment. Within an environment, multiple neurons become active in different locations, this cooperation of spiking in various locations creates a place map of the environment. Now let's say when the animal moved from one corner of the environment to another, place cells 'A', 'C', 'B', 'E', and 'D' became active in that order. This means, at any given point in the environment, the animal is standing in a venn-diagram-esque overlap of place fields, or locations individual place cells represent. A key question that entranced researchers for many years was how do these neurons know when to be active to not impinge on their neighbor's locations? The answer to this question rested with population electrical activity, known as the local field potential (LFP), that place cell activity is paced to. During active navigation through an environment, place cells activity is coupled to the phase of a slow ~8 hertz (Hz) theta oscillation. Within one theta cycle, or peak to peak, multiple place cells are active, representing the venn diagram of location the animal is in. Importantly, this theta activity and encoding of place cell activity is largely seen during active running or rapid eye movement (REM) sleep. During slow wave sleep (SWS), after an animal has experienced a specific environment and has created a place map, place cells are reactivated in the same order the animal experienced them in. From our previous example, the content of this reactivation would be the place cells 'A', 'C', 'B', 'E', and 'D' which all would be reactivated in that same order. These reactivations or replays occur during highly synchronous and fast LFP oscillations known as sharp wave-ripples (SPW-Rs). SPW-Rs are thought to be a key LFP event that drives memory consolidation and the eventual conversion of short-term memory into long-term memory. However, for consolidation to occur, connected cortical regions need to be able to receive and interpret the information within SPW-Rs. The granular retrosplenial cortex (gRSC) is one proposed region that serves this role. During SPW-Rs the superficial gRSC has been shown to exhibit high frequency oscillations (HFOs), which potentially serve the purpose for interpreting SPW-R content. However, HFOs have been reported during hippocampal theta, suggesting HFOs serve multiple purposes in interregional communication across different states. In this study, we found that naturally occurring gRSC HFOs occur exclusively in layer 2/3 across all awake brain states. Using focal optogenetic excitation we were able to evoke HFOs in both layer 2/3 and 5. Spontaneous gRSC HFOs occurring without SPW-Rs were highly comodulated with medial entorhinal cortex (MEC) generated high gamma in hippocampal stratum lacunosum moleculare. gRSC HFOs may serve a general role in supporting hippocampo-cortical dialogue during SPW-R and theta brain states to support memory consolidation and encoding, respectively.

Les principaux objets étudiés dans cette thèse sont les équations décrivant le morphisme de groupe sur une variété abélienne, plongée dans un espace projectif, et leurs applications en cryptographie. Notons g sa dimension et k son corps de définition. Ce mémoire est composé de deux parties. La première porte sur l'étude des courbes d'Edwards, un modèle pour les courbes elliptiques possédant un sous-groupe de points k-rationnels cyclique d'ordre 4, connues en cryptographie pour l'efficacité de leur loi d'addition et la possibilité qu'elle soit définie pour toute paire de points k-rationnels (loi d'addition k-complète). Nous en donnons une interprétation géométrique et en déduisons des formules explicites pour le calcul du couplage de Tate réduit sur courbes d'Edwards tordues, dont l'efficacité rivalise avec les modèles elliptiques couramment utilisés. Cette partie se conclut par la génération, spécifique au calcul de couplages, de courbes d'Edwards dont les tailles correspondent aux standards cryptographiques actuellement en vigueur. Dans la seconde partie nous nous intéressons à la notion de complétude introduite ci-dessus. Cette propriété est cryptographiquement importante car elle permet d'éviter des attaques physiques, comme les attaques par canaux cachés, sur des cryptosystèmes basés sur les courbes elliptiques ou hyperelliptiques. Un précédent travail de Lange et Ruppert, basé sur la cohomologie des fibrés en droite, permet une approche théorique des lois d'addition. Nous présentons trois résultats importants : tout d'abord nous généralisons un résultat de Bosma et Lenstra en démontrant que le morphisme de groupe ne peut être décrit par strictement moins de g+1 lois d'addition sur la clôture algébrique de k. Ensuite nous démontrons que si le groupe de Galois absolu de k est infini, alors toute variété abélienne peut être plongée dans un espace projectif de manière à ce qu'il existe une loi d'addition k-complète. De plus, l'utilisation des variétés abéliennes nous limitant à celles de dimension un ou deux, nous démontrons qu'une telle loi existe pour leur plongement projectif usuel. Finalement, nous développons un algorithme, basé sur la théorie des fonctions thêta, calculant celle-ci dans P^15 sur la jacobienne d'une courbe de genre deux donnée par sa forme de Rosenhain. Il est désormais intégré au package AVIsogenies de Magma. / The main objects we study in this PhD thesis are the equations describing the group morphism on an abelian variety, embedded in a projective space, and their applications in cryptograhy. We denote by g its dimension and k its field of definition. This thesis is built in two parts. The first one is concerned by the study of Edwards curves, a model for elliptic curves having a cyclic subgroup of k-rational points of order 4, known in cryptography for the efficiency of their addition law and the fact that it can be defined for any couple of k-rational points (k-complete addition law). We give the corresponding geometric interpretation and deduce explicit formulae to calculate the reduced Tate pairing on twisted Edwards curves, whose efficiency compete with currently used elliptic models. The part ends with the generation, specific to pairing computation, of Edwards curves with today's cryptographic standard sizes. In the second part, we are interested in the notion of completeness introduced above. This property is cryptographically significant, indeed it permits to avoid physical attacks as side channel attacks, on elliptic -- or hyperelliptic -- curves cryptosystems. A preceeding work of Lange and Ruppert, based on cohomology of line bundles, brings a theoretic approach of addition laws. We present three important results: first of all we generalize a result of Bosma and Lenstra by proving that the group morphism can not be described by less than g+1 addition laws on the algebraic closure of k. Next, we prove that if the absolute Galois group of k is infinite, then any abelian variety can be projectively embedded together with a k-complete addition law. Moreover, a cryptographic use of abelian varieties restricting us to the dimension one and two cases, we prove that such a law exists for their classical projective embedding. Finally, we develop an algorithm, based on the theory of theta functions, computing this addition law in P^15 on the Jacobian of a genus two curve given in Rosenhain form. It is now included in AVIsogenies, a Magma package.

No description available.

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)

Chez l’humain, différents protocoles de stimulation magnétique transcrânienne répétée (SMTr) peuvent être utilisés afin de manipuler expérimentalement la plasticité cérébrale au niveau du cortex moteur primaire (M1). Ces techniques ont permis de mieux comprendre le rôle du sommeil dans la régulation de la plasticité cérébrale. Récemment, une étude a montré que lorsqu’une première session de stimulation SMTr au niveau de M1 est suivie d’une nuit de sommeil, l’induction subséquente de la plasticité par une deuxième session SMTr est augmentée. La présente étude a investigué si ce type de métaplasticité pouvait également bénéficier d’une sieste diurne. Quatorze sujets en santé ont reçu deux sessions de intermittent theta burst stimulation (iTBS) connue pour son effet facilitateur sur l’excitabilité corticale. Les sessions de stimulation étaient séparées par une sieste de 90 minutes ou par une période équivalente d’éveil. L’excitabilité corticale était quantifiée en terme d’amplitude des potentiels évoqués moteurs (PEM) mesurés avant et après chaque session de iTBS. Les résultats montrent que la iTBS n’est pas parvenue à augmenter de manière robuste l’amplitude des PEMs lors de la première session de stimulation. Lors de la deuxième session de stimulation, la iTBS a produit des changements plastiques variables et ce peu importe si les sujets ont dormi ou pas. Les effets de la iTBS sur l’excitabilité corticale étaient marqués par une importante variabilité inter et intra-individuelle dont les possibles causes sont discutées. / In humans, various repetitive transcranial magnetic stimulation (rTMS) protocols can be used to modulate motor cortical plasticity. These techniques have shed light on the role of sleep in neural plasticity regulation. Recent work has demonstrated that when a night of sleep follows one session of rTMS over the hand motor cortex (M1), the capacity to induce subsequent plasticity by another rTMS session in M1 is enhanced. The present study investigated whether such metaplasticity could also benefit from a day nap. Fourteen healthy participants received two sessions of intermittent theta burst stimulation (iTBS) known for its excitatory effects on cortical excitability over M1 spaced by either a 90-minute nap or an equivalent amount of wake. Motor cortical excitability was measured in terms of amplitude of motor evoked potentials (MEP), which were assessed before iTBS and after the stimulation. Results show that the first iTBS session did not induce significant change in MEP amplitude. The second iTBS session induced variable plastic changes regardless of whether participants slept or stayed awake. The effects of iTBS on motor cortical excitability were highly variable within and between individuals. The possible causes of such variability are discussed.

Chez l’humain, différents protocoles de stimulation magnétique transcrânienne répétée (SMTr) peuvent être utilisés afin de manipuler expérimentalement la plasticité cérébrale au niveau du cortex moteur primaire (M1). Ces techniques ont permis de mieux comprendre le rôle du sommeil dans la régulation de la plasticité cérébrale. Récemment, une étude a montré que lorsqu’une première session de stimulation SMTr au niveau de M1 est suivie d’une nuit de sommeil, l’induction subséquente de la plasticité par une deuxième session SMTr est augmentée. La présente étude a investigué si ce type de métaplasticité pouvait également bénéficier d’une sieste diurne. Quatorze sujets en santé ont reçu deux sessions de intermittent theta burst stimulation (iTBS) connue pour son effet facilitateur sur l’excitabilité corticale. Les sessions de stimulation étaient séparées par une sieste de 90 minutes ou par une période équivalente d’éveil. L’excitabilité corticale était quantifiée en terme d’amplitude des potentiels évoqués moteurs (PEM) mesurés avant et après chaque session de iTBS. Les résultats montrent que la iTBS n’est pas parvenue à augmenter de manière robuste l’amplitude des PEMs lors de la première session de stimulation. Lors de la deuxième session de stimulation, la iTBS a produit des changements plastiques variables et ce peu importe si les sujets ont dormi ou pas. Les effets de la iTBS sur l’excitabilité corticale étaient marqués par une importante variabilité inter et intra-individuelle dont les possibles causes sont discutées. / In humans, various repetitive transcranial magnetic stimulation (rTMS) protocols can be used to modulate motor cortical plasticity. These techniques have shed light on the role of sleep in neural plasticity regulation. Recent work has demonstrated that when a night of sleep follows one session of rTMS over the hand motor cortex (M1), the capacity to induce subsequent plasticity by another rTMS session in M1 is enhanced. The present study investigated whether such metaplasticity could also benefit from a day nap. Fourteen healthy participants received two sessions of intermittent theta burst stimulation (iTBS) known for its excitatory effects on cortical excitability over M1 spaced by either a 90-minute nap or an equivalent amount of wake. Motor cortical excitability was measured in terms of amplitude of motor evoked potentials (MEP), which were assessed before iTBS and after the stimulation. Results show that the first iTBS session did not induce significant change in MEP amplitude. The second iTBS session induced variable plastic changes regardless of whether participants slept or stayed awake. The effects of iTBS on motor cortical excitability were highly variable within and between individuals. The possible causes of such variability are discussed.

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