<p>In this thesis we discuss different types of regularity for distributions which appear in the theory of pseudo-differential operators and partial differential equations. Partial differential equations often appear in science and technology. For example the Schrödinger equation can be used to describe the change in time of quantum states of physical systems. Pseudo-differential operators can be used to solve partial differential equations.  They are also appropriate to use when modeling different types of problems within physics and engineering. For example, there is a natural connection between pseudo-differential operators and stationary and non-stationary filters in signal processing. Furthermore, the correspondence between symbols and operators when passing from classical mechanics to quantum mechanics essentially agrees with symbols and operators in the Weyl calculus of pseudo-differential operators.</p><p>In this thesis we concentrate on investigating how regularity properties for solutions of partial differential equations are affected under the mapping of pseudo-differential operators, and in particular of the free time-dependent Schrödinger operators.</p><p>The solution of the free time-dependent Schrödinger equation can be expressed as a pseudo-differential operator, with non-smooth symbol, acting on the initial condition. We generalize a result about non-tangential convergence, which was obtained by Sjögren and Sjölin (1989) for the free time-dependent Schrödinger equation.</p><p>Another way to describe regularity for a distribution is to use wave-front sets. They do not only describe where the singularities are, but also the directions in which these singularities appear. The first types of wave-front sets (analytical wave-front sets) were introduced by Sato (1969, 1970). Later on Hörmander introduced ``classical'' wave-front sets (with respect to smoothness) and showed results in the context of pseudo-differential operators with smooth symbols, cf. Hörmander (1985).</p><p>In this thesis we consider wave-front sets with respect to Fourier Banach function spaces. Roughly speaking, we take <em>B</em> as a Banach space, which is invariant under translations and embedded between the space of Schwartz functions and the space of temperated distributions. Then we say that the wave-front set of a distribution contains all points (x₀, ξ₀) such that no localization of the distribution at x₀, belongs to <em>FB</em> in the direction ξ₀. We prove that pseudo-differential operators with smooth symbols shrink the wave-front set and we obtain opposite embeddings by using sets of characteristic points of the operator symbols.</p> / <p>I denna avhandling diskuterar vi olika typer av regularitet för distributioner som uppkommer i teorin för pseudodifferentialoperatorer och partiella differentialekvationer. Partiella differentialekvationer förekommer inom naturvetenskap och teknik. Exempelvis kan Schrödingerekvationen användas för att beskriva förändringen med tiden av kvanttillstånd i fysikaliska system. Pseudodifferentialoperatorer kan användas för att lösa partiella differential\-ekvationer. De användas också för att modellera olika typer av problem inom fysik och teknik. Det finns till exempel en naturlig koppling mellan pseudodifferentialoperatorer och stationära och icke-stationära filter i signalbehandling. Vidare gäller att relationen mellan symboler och operatorer vid övergången från klassisk mekanik till kvantmekanik i huvudsak överensstämmer med symboler och operatorer inom Weylkalkylen för pseudodifferentialoperatorer.</p><p>I den här avhandlingen koncentrerar vi oss på att undersöka hur regularitetsegenskaper för lösningar till partiella differentialekvationer påverkas under verkan av pseudodifferentialoperatorer, och speciellt för de fria tidsberoende Schrödingeroperatorerna.</p><p>Lösningen av den fria tidsberoende Schrödingerekvationen kan uttryckas som en pseudodifferentialoperator, med icke-slät symbol, verkande på begynnelsevillkoret. Vi generaliserar ett resultat om icke-tangentiell konvergens av Sjögren och Sjölin (1989) för den fria tidsberoende Schrödingerekvationen.</p><p>Ett annat sätt att beskriva regularitet hos en distribution är med hjälp av vågfrontsmängder. De beskriver inte bara var singulariteterna finns, utan också i vilka riktningar dessa singulariteter förekommer. De första typerna av vågfrontsmängder (analytiska vågfrontsmängder) introducerades av Sato (1969, 1970). Senare introducerade Hörmander ''klassiska'' vågfrontsmängder (med avseende på släthet) och visade resultat för verkan av pseudodifferentialoperatorer med släta symboler, se  Hörmander (1985).</p><p>I denna avhandling betraktar vi vågfrontsmängder med avseende på Fourier Banach funktionsrum. Detta kan ses som att vi låter <em>B</em> vara ett Banachrum, som är invariant under translationer och är inbäddat mellan rummet av Schwartzfunktioner och rummet av tempererade distributioner. Vågfrontsmängden av en distribution innehåller alla punkter (x₀, ξ₀) så att ingen lokalisering av distributionen kring x₀, tillhör <em>FB</em> i riktningen ξ₀. Vi visar att pseudodifferentialoperatorer med släta symboler krymper vågfrontsmängden och vi får motsatta inbäddningar med hjälp mängder av karakteristiska punkter till operatorernas symboler.</p>

In this thesis we discuss different types of regularity for distributions which appear in the theory of pseudo-differential operators and partial differential equations. Partial differential equations often appear in science and technology. For example the Schrödinger equation can be used to describe the change in time of quantum states of physical systems. Pseudo-differential operators can be used to solve partial differential equations.  They are also appropriate to use when modeling different types of problems within physics and engineering. For example, there is a natural connection between pseudo-differential operators and stationary and non-stationary filters in signal processing. Furthermore, the correspondence between symbols and operators when passing from classical mechanics to quantum mechanics essentially agrees with symbols and operators in the Weyl calculus of pseudo-differential operators. In this thesis we concentrate on investigating how regularity properties for solutions of partial differential equations are affected under the mapping of pseudo-differential operators, and in particular of the free time-dependent Schrödinger operators. The solution of the free time-dependent Schrödinger equation can be expressed as a pseudo-differential operator, with non-smooth symbol, acting on the initial condition. We generalize a result about non-tangential convergence, which was obtained by Sjögren and Sjölin (1989) for the free time-dependent Schrödinger equation. Another way to describe regularity for a distribution is to use wave-front sets. They do not only describe where the singularities are, but also the directions in which these singularities appear. The first types of wave-front sets (analytical wave-front sets) were introduced by Sato (1969, 1970). Later on Hörmander introduced ``classical'' wave-front sets (with respect to smoothness) and showed results in the context of pseudo-differential operators with smooth symbols, cf. Hörmander (1985). In this thesis we consider wave-front sets with respect to Fourier Banach function spaces. Roughly speaking, we take B as a Banach space, which is invariant under translations and embedded between the space of Schwartz functions and the space of temperated distributions. Then we say that the wave-front set of a distribution contains all points (x0, ξ0) such that no localization of the distribution at x0, belongs to FB in the direction ξ0. We prove that pseudo-differential operators with smooth symbols shrink the wave-front set and we obtain opposite embeddings by using sets of characteristic points of the operator symbols. / I denna avhandling diskuterar vi olika typer av regularitet för distributioner som uppkommer i teorin för pseudodifferentialoperatorer och partiella differentialekvationer. Partiella differentialekvationer förekommer inom naturvetenskap och teknik. Exempelvis kan Schrödingerekvationen användas för att beskriva förändringen med tiden av kvanttillstånd i fysikaliska system. Pseudodifferentialoperatorer kan användas för att lösa partiella differential\-ekvationer. De användas också för att modellera olika typer av problem inom fysik och teknik. Det finns till exempel en naturlig koppling mellan pseudodifferentialoperatorer och stationära och icke-stationära filter i signalbehandling. Vidare gäller att relationen mellan symboler och operatorer vid övergången från klassisk mekanik till kvantmekanik i huvudsak överensstämmer med symboler och operatorer inom Weylkalkylen för pseudodifferentialoperatorer. I den här avhandlingen koncentrerar vi oss på att undersöka hur regularitetsegenskaper för lösningar till partiella differentialekvationer påverkas under verkan av pseudodifferentialoperatorer, och speciellt för de fria tidsberoende Schrödingeroperatorerna. Lösningen av den fria tidsberoende Schrödingerekvationen kan uttryckas som en pseudodifferentialoperator, med icke-slät symbol, verkande på begynnelsevillkoret. Vi generaliserar ett resultat om icke-tangentiell konvergens av Sjögren och Sjölin (1989) för den fria tidsberoende Schrödingerekvationen. Ett annat sätt att beskriva regularitet hos en distribution är med hjälp av vågfrontsmängder. De beskriver inte bara var singulariteterna finns, utan också i vilka riktningar dessa singulariteter förekommer. De första typerna av vågfrontsmängder (analytiska vågfrontsmängder) introducerades av Sato (1969, 1970). Senare introducerade Hörmander ''klassiska'' vågfrontsmängder (med avseende på släthet) och visade resultat för verkan av pseudodifferentialoperatorer med släta symboler, se  Hörmander (1985). I denna avhandling betraktar vi vågfrontsmängder med avseende på Fourier Banach funktionsrum. Detta kan ses som att vi låter B vara ett Banachrum, som är invariant under translationer och är inbäddat mellan rummet av Schwartzfunktioner och rummet av tempererade distributioner. Vågfrontsmängden av en distribution innehåller alla punkter (x0, ξ0) så att ingen lokalisering av distributionen kring x0, tillhör FB i riktningen ξ0. Vi visar att pseudodifferentialoperatorer med släta symboler krymper vågfrontsmängden och vi får motsatta inbäddningar med hjälp mängder av karakteristiska punkter till operatorernas symboler.

This thesis analyzed the new parameter hydrodynamic demand representing the damage of tsunami waves on structures and coastlines,maximum positive amplitudes and current velocities occurred during tsunami inundation by using the numerical model TUNAMI-N2. Regular shaped basins were used with two different bottom slopes in analyses in order to understand the behaviour of tsunami wave and investigate the change of important tsunami parameters along different slopes during tsunami inundation. In application, different initial conditions were used for wave profiles such as solitary wave, leading elevation single sinusoidal wave and leading depression sinusoidal wave. Three different initial wave amplitudes were used in order to test the change of distribution of the hydrodynamic demand. The numerical results were compared and discussed with each other and with the results of existing analytical and experimental studies.

Diese Dissertation ist dem Studium temperierter Distributionen mittels mikrolokaler Methoden gewidmet. Die fundamentale Größe der mikrolokalen Analysis, die Wellenfrontmenge, wird durch zwei analoge Konzepte ersetzt, die den pseudo-differentiellen SG- und Shubin-Kalkülen zugeordnet sind. Die Eigenschaften dieser globalen Wellenfrontmengen werden studiert und ferner werden unterschiedliche Möglichkeiten, diese globalen Singularitäten zu charakterisieren, untersucht, insbesondere mittels der FBI-Transformation. Zahlreiche Konstruktionen, die den klassischen Wellenfrontmengenbegriff beinhalten, werden in den globalen Kontext übersetzt, insbesondere Rechenoperationen mit temperierten Distributionen wie etwa (getwistete) Produkte, Pull-backs und Paarungen, für die mikrolokale Existenzkriterien angegeben werden. Als eine Anwendung wird eine Klasse von temperierten Oszillatorintegralen eingeführt, welche durch inhomogene Phasenfunktionen und Amplituden aus SG-Symbolklassen parametrisiert werden. Die SG-Wellenfrontmengen dieser Distributionen werden untersucht und es stellt sich heraus, dass diese durch eine Verallgemeinerung der Menge stationärer Punkte der Phasenfunktionen beschränkt werden. In diesem Kontext wird eine Verallgemeinerung des klassischen Begriffs einer konischen Lagrange-Untermannifaltigkeit des T*R^d vorgenommen und diese Objekte werden auf ihre Parametrisierungseigenschaften untersucht. Es stellt sich heraus, dass jedes solche Objekt lokal als die Menge der stationären Punkte einer SG-Phasenfunktion realisiert werden kann. Als weitere Anwendung werden einige Konstruktionen der axiomatischen Quantenfeldtheorie, die Distributionen beinhalten, im temperierten Kontext realisiert.

[ES] En esta tesis estudiamos operadores pseudodiferenciales, que son operadores integrales de la forma f 7→ ∫ Rd (∫ Rd ei(x−y)·ξa(x,y,ξ)f(y)dy)dξ, en las clases globales de funciones ultradiferenciables de tipo Beurling Sω(Rd) introducidas por Björck, cuando la función peso ω viene dada en el sentido de Braun, Meise y Taylor. Desarrollamos el cálculo simbólico para estos operadores, tratando además el cambio de cuantización, la existencia de paramétrix pseudodiferencial y aplicaciones al frente de ondas global. La tesis consta de cuatro capítulos. En el Capítulo 1 introducimos los símbolos y amplitudes globales, y demostramos que los correspondientes operadores pseudodiferenciales están bien definidos y son continuos en en Sω(Rd). Estos resultados son extendidos en el Capítulo 2 para cuantizaciones arbitrarias, lo que conduce al estudio del traspuesto de cualquier cuantización de un operador pseudodiferencial y a la composición de dos cuantizaciones distintas de operadores pseudodiferenciales. En el Capítulo 3, desarrollamos el método de la paramétrix, dando condiciones suficientes para la existencia de paramétrix por la izquierda de un operador pseudodiferencial, que motiva en el Capítulo 4 la definición de un nuevo frente de ondas global para ultradistribuciones en S′ω(Rd) dada en términos de cuantizaciones de Weyl. Comparamos este frente de ondas con el frente de ondas de Gabor definido mediante la STFT y damos aplicaciones a la regularidad de las cuantizaciones de Weyl. / [CAT] En aquesta tesi estudiem operadors pseudodiferencials, que són operadors integrals de la forma f 7→ ∫ Rd (∫ Rd ei(x−y)·ξa(x,y,ξ)f(y)dy)dξ, en les classes globals de funcions ultradiferenciables de tipus Beurling Sω(Rd) introduïdes per Björck, quan la funció pes ω ve donada en el sentit de Braun, Meise i Taylor. Desenvolupem el càlcul simbòlic per aquestos operadors, tractant, a més a més, el canvi de quantització, l'existència de paramètrix pseudodiferencial i aplicacions al front d'ones global. La tesi consisteix de quatre capítols. Al Capítol 1 introduïm els símbols i amplituds globals, i demostrem que els corresponents operadors pseudodiferencials estan ben definits i són continus en Sω(Rd). Aquestos resultats són estesos al Capítol 2 per a quantitzacions arbitràries, que condueix a l'estudi del transposat de qualsevol quantització d'un operador pseudodiferencial i a la composició de dues quantitzacions distintes d'operadors pseudodiferencials. Al Capítol 3 desenvolupem el mètode de la paramètrix, donant condicions suficients per a l'existència de paramètrix per l'esquerra d'un operador pseudodiferencial donat, que motiva al Capítol 4 la definició d'un nou front d'ones global per a ultradistribucions en S′ω(Rd) mitjançant quantitzacions de Weyl. Comparem aquest front d'ones amb el front d'ones de Gabor definit mitjançant la STFT i donem aplicacions a la regularitat de les quantitzacions de Weyl. / [EN] In this thesis we study pseudodifferential operators, which are integral operators of the form f 7→ ∫ Rd (∫ Rd ei(x−y)·ξa(x,y,ξ)f(y)dy)dξ, in the global class of ultradifferentiable functions of Beurling type Sω(Rd) as introduced by Björck, when the weight function ω is given in the sense of Braun, Meise, and Taylor. We develop a symbolic calculus for these operators, treating also the change of quantization, the existence of pseudodifferential parametrices and applications to global wave front sets. The thesis consists of four chapters. In Chapter 1 we introduce global symbols and amplitudes and show that the corresponding pseudodifferential operators are well defined and continuous in Sω(Rd). These results are extended in Chapter 2 for arbitrary quantizations, which leads to the study of the transpose of any quantization of a pseudodifferential operator, and the composition of two different quantizations of pseudodifferential operators. In Chapter 3 we develop the method of the parametrix, providing sufficient conditions for the existence of left parametrices of a pseudodifferential operator, which motivates in Chapter 4 the definition of a new global wave front set for ultradistributions in S′ω(Rd) given in terms of Weyl quantizations. Then, we compare this wave front set with the Gabor wave front set defined by the STFT and give applications to the regularity of Weyl quantizations. / Asensio López, V. (2021). Global pseudodifferential operators in spaces of ultradifferentiable functions [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/174847

O ganho crescen te de desempenho nos computadores modernos tem impulsionado os trabalhos científicos nas áreas de simulação computacional. Muitos autores utilizam em suas pesquisas ferramentas comerciais que limitam seus trabalhos ao esconder os algoritmos internos destas ferramentas e dificultam a adição de dados in-vivo nestes trabalhos. Este trabalho explora esta lacuna deixada por aqueles autores. Elaboramos um arcabouço computacional capaz de reproduzir os fenômenos óticos e fisiológicos do sistema visual. Construímos com superfícies quádricas os modelos esquemáticos do olho humano e propomos um algoritmo de traçado de raio realístico. Então realizamos um estudo nos modelos esquemáticos e a partir deles mais a adição de dados in-vivo obtidos de um topógrafo de córnea extraímos informações óticas destes modelos. Calculamos os coeficientes e Zernike dos modelos para tamanhos diversos de pupila e obtivemos medidas de aberração do olho humano. Os resultados encontrados estão de acordo com os trabalhos relacionados e as simulações com dados in-vivo estão consoantes com as produzidas por um aparelho de frente de onda comerciais. Este trabalho é um esforço em aproveitar as informações adquiridas pelos equipamentos modernos de oftalmologia, além de auxiliar o entendimento de sistemas visuais biológicos acabam também em auxiliar a elaboração de sistemas de visão artificial e os projetistas de sistemas óticos / The increase in performance of the modern computers has driven scientific work in the areas of computer simulation. Many authors use in their research commercial tools that use embedding algorithms, which sources are not provided, and it makes harder and sometimes impossible, the development of novel theories or experiments. This work explores this gap left for those authors. We present a computational framework capable to reproduce the optical and physiological phenomena of the human visual system. We construct schematical models of the human eye from quadrics surfaces and consider an algorithm of realistic ray tracing. Afterward, we performed a study on schematics models and in addition we introduce, in these models, in-vivo data obtained from corneal topography machine and extract optical information. We calculate the Zernike coefficients in the models for different sizes of pupil and measures of aberration of the human eye. The results are in agreement with related work and simulations with in-vivo data are according with the produced by a commercial wave-front device. This work is an effort in using to advantage the information acquired for the modern equipment of ophthalmology, besides assisting the understanding of biological visual systems, it also helps the development of artificial vision systems and the designing of optical systems

Las lentes progresivas (LP) para gafas es una solución muy extendida para la presbicia, ya que proporcionan una visión continua a todas las distancias debido a un cambio progresivo de potencia. En este trabajo se han medido las aberraciones de frente de onda espacialmente resueltas y la calidad visual en estas lentes. Además del astigmatismo que aumenta periféricamente, también se han encontrado pequeños valores de aberraciones de tercer orden, coma y trefoil, que producen un bajo deterioro de la calidad óptica y visual. El logaritmo de métricas sobre la PSF del sistema lente con ojo son las que mejor predicen la agudeza visual. Durante la primera semana de adaptación, no se aprecia una mejora significativa de la agudeza visual a través de distintas zonas de las LPs. Al comparar diferentes LPs, las aberraciones, principalmente el astigmatismo, se comporta como un colchón de agua, que se puede mover pero no eliminar. / Progressive lenses (PL) are designed to provide continuous vision at all distances by means a progressive change in spherical power from upper to lower zones. In this thesis, we measure the spatially resolved aberrations and the visual quality of PLs. In addition to astigmatism, third order aberrations, coma and trefoil, are also found in the PLs, but the impact of these aberrations on visual performance is limited. The logarithm of metrics on the PSF of the entire system eye plus PL are the parameters that best predict the visual acuity. There is not a significant improvement of visual acuity through the different zones of the PLs during the first week of adaptation. The current designs of PLs are somehow similar to a waterbed, with the aberrations, mainly astigmatism, being the water: they can be moved but they cannot be eliminated.

O ganho crescen te de desempenho nos computadores modernos tem impulsionado os trabalhos científicos nas áreas de simulação computacional. Muitos autores utilizam em suas pesquisas ferramentas comerciais que limitam seus trabalhos ao esconder os algoritmos internos destas ferramentas e dificultam a adição de dados in-vivo nestes trabalhos. Este trabalho explora esta lacuna deixada por aqueles autores. Elaboramos um arcabouço computacional capaz de reproduzir os fenômenos óticos e fisiológicos do sistema visual. Construímos com superfícies quádricas os modelos esquemáticos do olho humano e propomos um algoritmo de traçado de raio realístico. Então realizamos um estudo nos modelos esquemáticos e a partir deles mais a adição de dados in-vivo obtidos de um topógrafo de córnea extraímos informações óticas destes modelos. Calculamos os coeficientes e Zernike dos modelos para tamanhos diversos de pupila e obtivemos medidas de aberração do olho humano. Os resultados encontrados estão de acordo com os trabalhos relacionados e as simulações com dados in-vivo estão consoantes com as produzidas por um aparelho de frente de onda comerciais. Este trabalho é um esforço em aproveitar as informações adquiridas pelos equipamentos modernos de oftalmologia, além de auxiliar o entendimento de sistemas visuais biológicos acabam também em auxiliar a elaboração de sistemas de visão artificial e os projetistas de sistemas óticos / The increase in performance of the modern computers has driven scientific work in the areas of computer simulation. Many authors use in their research commercial tools that use embedding algorithms, which sources are not provided, and it makes harder and sometimes impossible, the development of novel theories or experiments. This work explores this gap left for those authors. We present a computational framework capable to reproduce the optical and physiological phenomena of the human visual system. We construct schematical models of the human eye from quadrics surfaces and consider an algorithm of realistic ray tracing. Afterward, we performed a study on schematics models and in addition we introduce, in these models, in-vivo data obtained from corneal topography machine and extract optical information. We calculate the Zernike coefficients in the models for different sizes of pupil and measures of aberration of the human eye. The results are in agreement with related work and simulations with in-vivo data are according with the produced by a commercial wave-front device. This work is an effort in using to advantage the information acquired for the modern equipment of ophthalmology, besides assisting the understanding of biological visual systems, it also helps the development of artificial vision systems and the designing of optical systems

Dans cette thèse, on considère plusieurs problèmes issus de la modélisation macroscopique des mouvements de foule. Le premier modèle consiste en une loi de conservation avec un flux discontinu, le second est un système mixte hyperbolique-elliptique et le dernier est une équation non-locale. D'abord, on utilise le modèle de Hughes une dimension pour décrire l'évacuation d'un couloir avec deux sorties. Ce modèle couple une loi de conservation avec un flux discontinu à une équation eikonale. On implémente la méthode de suivi de fronts, qui traite explicitement le comportement de la solution non-classique au point de rebroussement, afin d'obtenir des solutions de référence. Elles serviront à tester numériquement la convergence de schémas aux volumes finis classiques. Ensuite, on modélise le croisement de deux groupes marchant dans des directions opposées avec un système de lois de conservation mixte hyperbolique-elliptique dont le flux dépend des deux densités. Le système perd son hyperbolicité pour certainement valeurs de densité. On assiste à l'apparition d'oscillations persistantes mais bornées, ce qui conduit à la reformulation du problème associé dans le cadre des mesures de probabilités. Finalement, on étudie un modèle non-local de trafic piétonnier en deux dimensions. Le modèle consiste en une loi de conservation dont le flux dépend d'une convolution de la densité. Avec ce modèle, on résout un problème d'optimisation pour une évacuation d'une salle avec une méthode de descente, évaluant l'impact du calcul explicite du gradient de la fonction coût avec la méthode de l'état adjoint plutôt que son approximation par différences finies. / In this thesis, we consider nonclassical problems brought out by the macroscopic modeling of pedestrian flow. The first model consists of a conservation law with a discontinuous flux, the second is a mixed hyperbolic-elliptic system of conservation laws and the last one is a nonlocal equation. In the first chapter, we use the Hughes model in one space-dimension to represent the evacuation of a corridor with two exits. The model couples a conservation law with discontinuous flux to an eikonal equation. We implement the wave front tracking scheme, treating explicitly the solution nonclassical behavior at the turning point, to provide a reference solution, which is used to numerically test the convergence of classical finite volume schemes. In the second chapter, we model the crossing of two groups of pedestrians walking in opposite directions with a system of conservation laws whose flux depends on the two densities. This system loses its hyperbolicity for certain density values. We assist to the rising of persistent but bounded oscillations, that lead us to the recast of the problem in the framework of measure-valued solutions. Finally we study a nonlocal model of pedestrian flow in two space-dimensions. The model consists of a conservation law whose flux depends on a convolution of the density. With this model, we solve an optimization problem for a room evacuation with a descent method, evaluating the impact of the explicit computation of the cost function gradient with the adjoint state method rather than approximating it with finite differences.

La révolution en cours des outils optogénétiques - des protéines photosensibles génétiquement induites qui peuvent activer, inhiber et enregistrer l'activité neuronale - a permis d'ouvrir une nouvelle voie pour relier l'activité neuronale et la cognition. Néanmoins, pour profiter au mieux de ces outils nous avons besoin de méthodes optiques qui peuvent projeter des schémas d'illumination complexes dans le cerveau. Pendant mon doctorat, j'ai travaillé sur deux nouveaux systèmes complémentaires pour la stimulation de l'activité neuronale. Le premier système combine des déflecteurs acousto-optiques et une illumination Gaussienne à faible ouverture numérique pour produire une photo activation rapide des outils optogénétiques. La capacité d'accès aléatoire du système permet de délivrer des séquences d'illumination spatialement et temporellement complexes qui simulent avec succès les schémas physiologiques de l'activité des fibres moussues dans des tranches de cerveaux. Ces résultats démontrent que les schémas de stimulation optogénétique peuvent être utilisés pour recréer l'activité en cours et étudier les microcircuits du cerveau dans un environnement physiologique. Alternativement, l'holographie générée par ordinateur (HGO) permet d'améliorer grandement les stimulations optogénétiques en répartissant efficacement la lumière sur plusieurs cibles cellulaires simultanément. Néanmoins, le confinement axial se dégrade pour des schémas d'illuminations larges. Afin de d'améliorer ce point, l’HGO peut être combinée avec une technique de focalisation temporelle qui confine axialement la fluorescence sans dépendre de l'allongement latéral. Les précédentes configurations maintiennent l'excitation non linéaire à un unique plan focal spatiotemporel. Dans cette thèse, je décris deux méthodes différentes qui permettent de dépasser ces limitations et de permettre la génération de schémas focalisés tridimensionnellement, à la fois spatialement et temporellement. / The ongoing revolution of optogenetic tools – genetically encoded light-sensitive proteins that can activate, silence and monitor neural activity – has opened a new pathway to bridge the gap between neuronal activity and cognition. However, to take full advantage of these tools we need optical methods that can deliver complex light patterns in the brain. During my doctorate, I worked on two novel and complementary optical systems for complex spatiotemporally neural activity stimulation. The first system combined acousto-optic deflectors and low numerical aperture Gaussian beam illumination for fast photoactivation of optogenetic tools. The random-access capabilities of the system allowed to deliver complex spatiotemporal illumination sequences that successfully emulated physiological patterns of cerebellar mossy fiber activity in acute slices. These results demonstrate that patterned optogenetic stimulation can be used to recreate ongoing activity and study brain microcircuits in a physiological activity context. Alternatively, Computer Generated Holography (CGH) can powerfully enhance optogenetic stimulation by efficiently shaping light onto multiple cellular targets simultaneously. Nonetheless, the axial confinement degrades for laterally extended illumination patterns. To address this issue, CGH can be combined with temporal focusing that axially confines fluorescence regardless of lateral extent. However, previous configurations restricted nonlinear excitation to a single spatiotemporal focal plane. In this thesis, I describe two alternative methods to overcome this limitation and enable three-dimensional spatiotemporal focused pattern generation.