Universitat de Barcelona Departament de Matemàtiques i Informàtica
Overview
Works:  17 works in 22 publications in 3 languages and 22 library holdings 

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.
Most widely held works by
Universitat de Barcelona
Quantitative equidistribution of Galois orbits of points of small height on the algebraic torus by Marta Narváez Clauss(
)
2 editions published between 2016 and 2017 in English and held by 2 WorldCat member libraries worldwide
El teorema de equidistribución de Bilu establece que, dada una sucesión estricta de puntos en el toro algebraico Ndimensional cuya altura de Weil tiende a cero, las órbitas de Galois de los puntos se equidistribuyen con respecto a la medida de Haar de probabilidad del policírculo unidad. Para el caso unidimensional, versiones cuantitativas de este resultado fueron obtenidas independientemente por Petsche y por Favre y RiveraLetelier. Se presenta en esta tesis una versión cuantitativa del resultado de Bilu para el caso de dimensión cualquiera. Dado un punto en el toro algebraico de dimensión N de altura de Weil menor que 1, se proporciona una cota para la integral de una determinada función test en P1(C)N con respecto a la medida signada definida como la diferencia de la medida discreta de probabilidad asociada a la órbita de Galois del punto y la medida de probabilidad soportada en el policírculo unidad, donde coincide con la medida de Haar normalizada. Esta cota está dada en términos de una constante que depende únicamente de la función test, de la altura de Weil del punto, y de una noción que generaliza a dimensión superior el grado de un número algebraico. Para la demostración de este resultado se utiliza el análisis de Fourier para la descomposición del problema y, a través de proyecciones, se reduce al caso unidimensional donde aplicamos la versión cuantitativa de Favre y RiveraLetelier
2 editions published between 2016 and 2017 in English and held by 2 WorldCat member libraries worldwide
El teorema de equidistribución de Bilu establece que, dada una sucesión estricta de puntos en el toro algebraico Ndimensional cuya altura de Weil tiende a cero, las órbitas de Galois de los puntos se equidistribuyen con respecto a la medida de Haar de probabilidad del policírculo unidad. Para el caso unidimensional, versiones cuantitativas de este resultado fueron obtenidas independientemente por Petsche y por Favre y RiveraLetelier. Se presenta en esta tesis una versión cuantitativa del resultado de Bilu para el caso de dimensión cualquiera. Dado un punto en el toro algebraico de dimensión N de altura de Weil menor que 1, se proporciona una cota para la integral de una determinada función test en P1(C)N con respecto a la medida signada definida como la diferencia de la medida discreta de probabilidad asociada a la órbita de Galois del punto y la medida de probabilidad soportada en el policírculo unidad, donde coincide con la medida de Haar normalizada. Esta cota está dada en términos de una constante que depende únicamente de la función test, de la altura de Weil del punto, y de una noción que generaliza a dimensión superior el grado de un número algebraico. Para la demostración de este resultado se utiliza el análisis de Fourier para la descomposición del problema y, a través de proyecciones, se reduce al caso unidimensional donde aplicamos la versión cuantitativa de Favre y RiveraLetelier
Transport phenomena and anomalous diffusion in conservative systems of low dimension by Narcís Miguel Baños(
Book
)
2 editions published between 2016 and 2017 in English and held by 2 WorldCat member libraries worldwide
2 editions published between 2016 and 2017 in English and held by 2 WorldCat member libraries worldwide
Hankel operators on vectorvalued Bergman spaces by Roc Oliver Vendrell(
Book
)
2 editions published between 2017 and 2018 in English and held by 2 WorldCat member libraries worldwide
The main goal of this work is to study vectorvalued Bergman spaces and to obtain the weak factorization of these spaces. In order to do that we need to study small Hankel operators with operatorvalued holomorphic symbols. We also study the big Hankel operator acting on vectorvalued Bergman spaces. In Chapter 1 we collect all the previous results and notations needed to follow the rest of the manuscript. More concretely, some of the topics covered in this chapter are the Bochner integral, the integral for vectorvalued functions appearing first in Bochner; the Bergman metric, results of the metric used in Bn; harmonic and subharmonic function; basic notions of differentiation, where the differential operators R(a, t) are presented which is important in the next chapters and in the final section we recall some topics on Banach spaces, as the Rademacher type and cotype of a Banach space and some other related results. Having all that in mind, in Chapter 2, the vectorvalued Bergman spaces are presented. The vectorvalued Bloch type spaces play a similar role and therefore we dedícate one full chapter to these spaces. Chapter 3 is devoted to present and characterize the vectorvalued Bloch type spaces. Since we mention Hankel operators, in Chapter 4 we prove the characterization of the boundedness of the small Hankel operator with analytic operatorvalued symbols between vectorvalued Bergman spaces (of different type). We explain what this means in the following. Another very important consequence of the boundedness of the small Hankel operator between vectorvalued Bergman spaces is shown in Chapter 5. We establish the weak factorization of the vectorvalued Bergman spaces. Factorization of analytic functions is a very big topic and many people worked on it during many years and it is known to have many applications. Therefore, in Chapter 6 we fully characterize the boundedness of the big Hankel operator on vectorvalued Bergman spaces in terms of its operatorvalued holomorphic symbol for all cases of p > 1 and q > 1, and so we solve and generalize the previous problem. Finally, in Chapter 7 we discuss some open problems we have not been able to solve, as well as some other interesting problems in the same line as this work in order to look on the future.  TDX
2 editions published between 2017 and 2018 in English and held by 2 WorldCat member libraries worldwide
The main goal of this work is to study vectorvalued Bergman spaces and to obtain the weak factorization of these spaces. In order to do that we need to study small Hankel operators with operatorvalued holomorphic symbols. We also study the big Hankel operator acting on vectorvalued Bergman spaces. In Chapter 1 we collect all the previous results and notations needed to follow the rest of the manuscript. More concretely, some of the topics covered in this chapter are the Bochner integral, the integral for vectorvalued functions appearing first in Bochner; the Bergman metric, results of the metric used in Bn; harmonic and subharmonic function; basic notions of differentiation, where the differential operators R(a, t) are presented which is important in the next chapters and in the final section we recall some topics on Banach spaces, as the Rademacher type and cotype of a Banach space and some other related results. Having all that in mind, in Chapter 2, the vectorvalued Bergman spaces are presented. The vectorvalued Bloch type spaces play a similar role and therefore we dedícate one full chapter to these spaces. Chapter 3 is devoted to present and characterize the vectorvalued Bloch type spaces. Since we mention Hankel operators, in Chapter 4 we prove the characterization of the boundedness of the small Hankel operator with analytic operatorvalued symbols between vectorvalued Bergman spaces (of different type). We explain what this means in the following. Another very important consequence of the boundedness of the small Hankel operator between vectorvalued Bergman spaces is shown in Chapter 5. We establish the weak factorization of the vectorvalued Bergman spaces. Factorization of analytic functions is a very big topic and many people worked on it during many years and it is known to have many applications. Therefore, in Chapter 6 we fully characterize the boundedness of the big Hankel operator on vectorvalued Bergman spaces in terms of its operatorvalued holomorphic symbol for all cases of p > 1 and q > 1, and so we solve and generalize the previous problem. Finally, in Chapter 7 we discuss some open problems we have not been able to solve, as well as some other interesting problems in the same line as this work in order to look on the future.  TDX
Evolutionary Bags of SpaceTime Features for Human Analysis by Víctor Ponce López(
Book
)
2 editions published in 2016 in English and held by 2 WorldCat member libraries worldwide
L'aprenentatge de la representació (o de característiques) ha estat un concepte emergent en els darrers anys, ja que recopila un conjunt de tècniques que són presents en qualsevol metodologia teòrica o pràctica referent a la intel·ligència artifcial. En la visió per computador, una representació molt comuna ha adoptat la forma de la ben coneguda Bossa de Paraules Visuals (BdPV). Aquesta representació apareix implícitament en la majoria d'aproximacions per descriure imatges, i és també present en un enorme nombre d'àrees i dominis: recuperació de contingut en imatges, detecció de vianants, interacció humàordinador, vigilància, esalut, i la computació social, entre d'altres. Les fases inicials d'aquesta dissertació proporcionen una aproximació per aprendre representacions visuals dins d'algorismes evolutius, que consisteix en evolucionar esquemes de pesat per millorar les representacions BdPV en la tasca de reconèixer les categories de vídeos i imatges. Per tant, demostrem l'aplicabilitat dels esquemes de pesat més comuns, que s'usen sovint en la mineria de textos però es troben amb menys freqüència en tasques de visió per computador. Més enllà d'aprendre representacions visuals, proporcionem una aproximació basada en estratègies de fusió per a l'aprenentatge de representacions espai temporals, a partir de dades multimodals obtingudes per sensors de profunditat. A més, el nostre objectiu és especialment el modelatge evolutiu i dinàmic, on el factor temporal és present en la naturalesa de les dades, com les seqüències de gestos i accions. De fet, explorem els efectes del modelatge probabilístic per aquelles aproximacions basades en programació dinàmica per a gestionar la deformació temporal i variància entre seqüències de vídeo de categories diferents. Finalment, integrem la programació dinàmica i els models generatius en un marc de computació evolutiva, amb l'objectiu d'aprendre representacions en Bosses de SubGestos i, per tant, millorar la capacitat de generalització de les aproximacions estàndards pel reconeixement de gestos. Els resultats obtinguts en l'experimentació demostra, en primer lloc, que els algorismes evolutius són útils per millorar la representació d'aproximacions BdPV en diverses bases de dades pel reconeixement de categories en imatges fxes i seqüències de vídeo. Per altra banda, la nostra experimentació revela que, tant l'ús de la programació dinàmica i els models generatius per alinear seqüències de vídeos, com les representacions obtingudes d'aplicar estratègies de fusió en dades multimodals, comporten una millora en el rendiment a l'hora de reconèixer algunes categories de gestos. A més a més, la combinació d'algorismes evolutius amb models basats en programació dinàmica i aproximacions generatives resulten, a l'hora de classifcar categories de vídeos de bases de dades grans, en una millora considerable sobre les aproximacions estàndards de reconeixement de gestos i accions. Finalment, demostrem les aplicacions d'aquestes representacions en varis dominis per a l'anàlisi humà: classifcació d'imatges on els humans poden serhi presents, el reconeixement d'accions i gestos per aplicacions en general, i en particular per entorns conversacionals dins del camp de la justícia restaurativa
2 editions published in 2016 in English and held by 2 WorldCat member libraries worldwide
L'aprenentatge de la representació (o de característiques) ha estat un concepte emergent en els darrers anys, ja que recopila un conjunt de tècniques que són presents en qualsevol metodologia teòrica o pràctica referent a la intel·ligència artifcial. En la visió per computador, una representació molt comuna ha adoptat la forma de la ben coneguda Bossa de Paraules Visuals (BdPV). Aquesta representació apareix implícitament en la majoria d'aproximacions per descriure imatges, i és també present en un enorme nombre d'àrees i dominis: recuperació de contingut en imatges, detecció de vianants, interacció humàordinador, vigilància, esalut, i la computació social, entre d'altres. Les fases inicials d'aquesta dissertació proporcionen una aproximació per aprendre representacions visuals dins d'algorismes evolutius, que consisteix en evolucionar esquemes de pesat per millorar les representacions BdPV en la tasca de reconèixer les categories de vídeos i imatges. Per tant, demostrem l'aplicabilitat dels esquemes de pesat més comuns, que s'usen sovint en la mineria de textos però es troben amb menys freqüència en tasques de visió per computador. Més enllà d'aprendre representacions visuals, proporcionem una aproximació basada en estratègies de fusió per a l'aprenentatge de representacions espai temporals, a partir de dades multimodals obtingudes per sensors de profunditat. A més, el nostre objectiu és especialment el modelatge evolutiu i dinàmic, on el factor temporal és present en la naturalesa de les dades, com les seqüències de gestos i accions. De fet, explorem els efectes del modelatge probabilístic per aquelles aproximacions basades en programació dinàmica per a gestionar la deformació temporal i variància entre seqüències de vídeo de categories diferents. Finalment, integrem la programació dinàmica i els models generatius en un marc de computació evolutiva, amb l'objectiu d'aprendre representacions en Bosses de SubGestos i, per tant, millorar la capacitat de generalització de les aproximacions estàndards pel reconeixement de gestos. Els resultats obtinguts en l'experimentació demostra, en primer lloc, que els algorismes evolutius són útils per millorar la representació d'aproximacions BdPV en diverses bases de dades pel reconeixement de categories en imatges fxes i seqüències de vídeo. Per altra banda, la nostra experimentació revela que, tant l'ús de la programació dinàmica i els models generatius per alinear seqüències de vídeos, com les representacions obtingudes d'aplicar estratègies de fusió en dades multimodals, comporten una millora en el rendiment a l'hora de reconèixer algunes categories de gestos. A més a més, la combinació d'algorismes evolutius amb models basats en programació dinàmica i aproximacions generatives resulten, a l'hora de classifcar categories de vídeos de bases de dades grans, en una millora considerable sobre les aproximacions estàndards de reconeixement de gestos i accions. Finalment, demostrem les aplicacions d'aquestes representacions en varis dominis per a l'anàlisi humà: classifcació d'imatges on els humans poden serhi presents, el reconeixement d'accions i gestos per aplicacions en general, i en particular per entorns conversacionals dins del camp de la justícia restaurativa
Integración de técnicas de personalización basadas en el comportamiento colaborativo del ser humano con interfaces de usuario
inteligentes by David Contreras Aguilar(
Book
)
2 editions published in 2017 in Spanish and held by 2 WorldCat member libraries worldwide
Esta tesis está enfocada en la problemática asociada a la personalización de información para usuarios que interactúan con grandes volúmenes de información. En concreto, la tesis se centra en el estudio de los sistemas de recomendación conversacionales basados en críticas como herramientas para ayudar a los usuarios en la búsqueda de productos o servicios. Los sistemas de recomendación basados en críticas permiten recoger información asociada a las preferencias del usuario a través de un proceso conversacional, en el cual el usuario puede realizar una retroalimentación a las recomendaciones recibidas. La retroalimentación recibida desde el usuario, permite al recomendador adquirir conocimiento acerca de las preferencias que tiene el usuario respecto del producto que desea y generar un perﬁl asociado al usuario. Este tipo de técnica de recomendación en forma de diálogo cíclico, que caracteriza a los sistemas de recomendación basados en críticas, ha demostrado resultados satisfactorios en estudios previos orientados principalmente al dominio de comercio electrónico. Sin embargo, cuando un usuario en el mundo real se encuentra en una tienda física, tiene la posibilidad de interactuar y comunicarse con otros compradores. Aún más, hoy en día existen entornos virtuales colaborativos, la mayoría en tres dimensiones, donde los usuarios se pueden comunicar con otras personas y sentirse inmersos en un mundo virtual. Considerando todo lo anterior, esta tesis se focaliza en aprovechar el comportamiento colaborativo de las personas para mejorar las recomendaciones de productos o servicios. En concreto, el objetivo de la tesis es deﬁnir e integrar nuevas técnicas de personalización con interfaces de usuario inteligentes, basadas en el comportamiento colaborativo del ser humano y en la información recogida de las interacciones de las personas tanto con la interfaz como con otros usuarios. La tesis se divide en dos partes. En la primera parte, describo las nuevas técnicas de recomendación que incorporan información colaborativa. En la segunda parte, presento nuevas interfaces de usuario inteligentes implementadas en diferentes entornos de visualización y que integran las técnicas de recomendación propuestas en esta tesis. Las nuevas técnicas de recomendación que propongo integran, por un lado, opiniones de los usuarios acerca de los productos, por otro lado, integran recomendaciones históricas de otros usuarios que han utilizado el sistema de recomendación previamente y ﬁnalmente integran avances de estudios previos que han demostrado mejorar los procesos de recomendación. Adicionalmente, propongo otras técnicas basadas en información colaborativa instantánea que se puede obtener de parte del sistema de recomendación, como también de otros usuarios que están utilizando el sistema en el mismo momento. Las interfaces de usuario inteligentes que propongo se basan en entornos de visualización en 2D y 3D. En primer lugar, propongo un framework ba sado en un entorno web en dos dimensiones que permite integrar técnicas basadas en información proveniente de opiniones y recomendaciones histó ricas de otros usuarios. En segundo lugar, propongo un framework basado en un entorno virtual colaborativo en tres dimensiones que permite integrar técnicas basadas en información colaborativa que se genera por la interacción de los usuarios dentro del entorno virtual. Es necesario destacar, que ambos frameworks son modulares y escalables, permitiendo integrar diferentes algoritmos de recomendación basados en críticas. Para validar las técnicas de recomendación y las interfaces de usuario propuestas en esta tesis, deﬁno dos metodologías de evaluación. En concreto, para la evaluación de las técnicas de recomendación utilizo un simulador que por medio de un "usuario artiﬁcial" permite evaluar el funcionamiento de las técnicas de recomendación simulando varias pruebas con usuarios reales de forma automática. Adicionalmente, para los frameworks que imple mentan las interfaces de usuario inteligentes, he realizado evaluaciones con usuarios reales. El análisis de los resultados obtenidos mediante las evaluaciones con el simulador y con los usuarios reales, revela que tanto las nuevas técnicas propuestas, como las interfaces de usuario inteligentes obtienen resultados muy satisfactorios, los cuales superan signiﬁcativamente a los resultados obtenidos con técnicas de recomendación de estudios previos. Es necesario destacar, que todos los resultados han sido corroborados por métodos estadísticos. De acuerdo a los resultados obtenidos, puedo concluir que la incorporación de información colaborativa en nuevas técnicas de recomendación favorece la eﬁciencia y eﬁcacia de los sistemas de recomendación basados en críticas. Además, las nuevas y novedosas interfaces de usuario inteligentes propuestas en esta tesis, representan un avance en el desarrollo de interfaces de usuario para sistemas de recomendación basados en críticas. Estas interfaces aparte de favorecer la integración de técnicas de recomendación colaborativa, mejoran la experiencia de los usuarios durante las sesiones de recomendación, lo cual es corroborado por los usuarios que participaron en los experimentos
2 editions published in 2017 in Spanish and held by 2 WorldCat member libraries worldwide
Esta tesis está enfocada en la problemática asociada a la personalización de información para usuarios que interactúan con grandes volúmenes de información. En concreto, la tesis se centra en el estudio de los sistemas de recomendación conversacionales basados en críticas como herramientas para ayudar a los usuarios en la búsqueda de productos o servicios. Los sistemas de recomendación basados en críticas permiten recoger información asociada a las preferencias del usuario a través de un proceso conversacional, en el cual el usuario puede realizar una retroalimentación a las recomendaciones recibidas. La retroalimentación recibida desde el usuario, permite al recomendador adquirir conocimiento acerca de las preferencias que tiene el usuario respecto del producto que desea y generar un perﬁl asociado al usuario. Este tipo de técnica de recomendación en forma de diálogo cíclico, que caracteriza a los sistemas de recomendación basados en críticas, ha demostrado resultados satisfactorios en estudios previos orientados principalmente al dominio de comercio electrónico. Sin embargo, cuando un usuario en el mundo real se encuentra en una tienda física, tiene la posibilidad de interactuar y comunicarse con otros compradores. Aún más, hoy en día existen entornos virtuales colaborativos, la mayoría en tres dimensiones, donde los usuarios se pueden comunicar con otras personas y sentirse inmersos en un mundo virtual. Considerando todo lo anterior, esta tesis se focaliza en aprovechar el comportamiento colaborativo de las personas para mejorar las recomendaciones de productos o servicios. En concreto, el objetivo de la tesis es deﬁnir e integrar nuevas técnicas de personalización con interfaces de usuario inteligentes, basadas en el comportamiento colaborativo del ser humano y en la información recogida de las interacciones de las personas tanto con la interfaz como con otros usuarios. La tesis se divide en dos partes. En la primera parte, describo las nuevas técnicas de recomendación que incorporan información colaborativa. En la segunda parte, presento nuevas interfaces de usuario inteligentes implementadas en diferentes entornos de visualización y que integran las técnicas de recomendación propuestas en esta tesis. Las nuevas técnicas de recomendación que propongo integran, por un lado, opiniones de los usuarios acerca de los productos, por otro lado, integran recomendaciones históricas de otros usuarios que han utilizado el sistema de recomendación previamente y ﬁnalmente integran avances de estudios previos que han demostrado mejorar los procesos de recomendación. Adicionalmente, propongo otras técnicas basadas en información colaborativa instantánea que se puede obtener de parte del sistema de recomendación, como también de otros usuarios que están utilizando el sistema en el mismo momento. Las interfaces de usuario inteligentes que propongo se basan en entornos de visualización en 2D y 3D. En primer lugar, propongo un framework ba sado en un entorno web en dos dimensiones que permite integrar técnicas basadas en información proveniente de opiniones y recomendaciones histó ricas de otros usuarios. En segundo lugar, propongo un framework basado en un entorno virtual colaborativo en tres dimensiones que permite integrar técnicas basadas en información colaborativa que se genera por la interacción de los usuarios dentro del entorno virtual. Es necesario destacar, que ambos frameworks son modulares y escalables, permitiendo integrar diferentes algoritmos de recomendación basados en críticas. Para validar las técnicas de recomendación y las interfaces de usuario propuestas en esta tesis, deﬁno dos metodologías de evaluación. En concreto, para la evaluación de las técnicas de recomendación utilizo un simulador que por medio de un "usuario artiﬁcial" permite evaluar el funcionamiento de las técnicas de recomendación simulando varias pruebas con usuarios reales de forma automática. Adicionalmente, para los frameworks que imple mentan las interfaces de usuario inteligentes, he realizado evaluaciones con usuarios reales. El análisis de los resultados obtenidos mediante las evaluaciones con el simulador y con los usuarios reales, revela que tanto las nuevas técnicas propuestas, como las interfaces de usuario inteligentes obtienen resultados muy satisfactorios, los cuales superan signiﬁcativamente a los resultados obtenidos con técnicas de recomendación de estudios previos. Es necesario destacar, que todos los resultados han sido corroborados por métodos estadísticos. De acuerdo a los resultados obtenidos, puedo concluir que la incorporación de información colaborativa en nuevas técnicas de recomendación favorece la eﬁciencia y eﬁcacia de los sistemas de recomendación basados en críticas. Además, las nuevas y novedosas interfaces de usuario inteligentes propuestas en esta tesis, representan un avance en el desarrollo de interfaces de usuario para sistemas de recomendación basados en críticas. Estas interfaces aparte de favorecer la integración de técnicas de recomendación colaborativa, mejoran la experiencia de los usuarios durante las sesiones de recomendación, lo cual es corroborado por los usuarios que participaron en los experimentos
Social Signal Processing from Egocentric PhotoStreams by Maedeh Aghaei(
)
1 edition published in 2018 in English and held by 1 WorldCat member library worldwide
Wearable photocameras offer a handsfree way to record images from the camera wearer perspective of daily experiences as they are lived, without the necessity to interrupt recording due to the device battery or storage limitations. This stream of images, known as egocentric photostreams, contains important visual data about the living of the user, where social events among them are of special interest. Social interactions are proven to be a key to longevity and having too few interactions equates the same risk factor as smoking regularly. Considering the importance of the matter, there is no wonder that automatic analysis of social interactions is largely attracting the interest of the scientific community. Analysis of unconstrained photostreams however, imposes novel challenges to the social signal processing problem with respect to conventional videos. Due to the free motion of the camera and to its low temporal resolution, abrupt changes in the field of view, in illumination condition and in the target location are highly frequent. Also, since images are acquired under realworld conditions, occlusions occur regularly and appearance of the people undergoes intensive variations from one event to another. Given a user wearing a photocamera during a determined period, this thesis, driven by the social signal processing paradigm presents a framework for comprehensive social pattern characterization of the user. In social signal processing, the second step after recording the scene is to track the appearance of multiple people who are involved in the social events. Hence, our proposal begins by introducing a multiface tracking which holds certain characteristics to deal with challenges imposed by the egocentric photostreams. Next step forward in social signal processing, is to extract the socalled social signals from the tracked people. In this step, besides the conventionally studied social signals, clothing as a novel social signal is proposed for further studies within the social signal processing. Finally, the last step is social signal analysis, itself. In this thesis, social signal analysis is essentially defined as reaching an understanding of social patterns of a wearable photocamera user by reviewing captured photos by the worn camera over a period of time. Our proposal for social signal analysis is comprised of first, to detect social interactions of the user where the impact of several social signals on the task is explored. The detected social events are inspected in the second step for categorization into different social meetings. The last step of the framework is to characterize social patterns of the user. Our goal is to quantify the duration, the diversity and the frequency of the user social relations in various social situations. This goal is achieved by the discovery of recurrences of the same people across the whole set of social events related to the user. Each step of our proposed pipeline is validated over relevant datasets, and the obtained results are reported quantitatively and qualitatively. For each section of the pipeline, a comparison with related stateoftheart models is provided. A discussion section over the obtained results is also given which is dedicated to highlighting the advantages, shortcomings, and differences of the proposed models, and with regards to the stateoftheart
1 edition published in 2018 in English and held by 1 WorldCat member library worldwide
Wearable photocameras offer a handsfree way to record images from the camera wearer perspective of daily experiences as they are lived, without the necessity to interrupt recording due to the device battery or storage limitations. This stream of images, known as egocentric photostreams, contains important visual data about the living of the user, where social events among them are of special interest. Social interactions are proven to be a key to longevity and having too few interactions equates the same risk factor as smoking regularly. Considering the importance of the matter, there is no wonder that automatic analysis of social interactions is largely attracting the interest of the scientific community. Analysis of unconstrained photostreams however, imposes novel challenges to the social signal processing problem with respect to conventional videos. Due to the free motion of the camera and to its low temporal resolution, abrupt changes in the field of view, in illumination condition and in the target location are highly frequent. Also, since images are acquired under realworld conditions, occlusions occur regularly and appearance of the people undergoes intensive variations from one event to another. Given a user wearing a photocamera during a determined period, this thesis, driven by the social signal processing paradigm presents a framework for comprehensive social pattern characterization of the user. In social signal processing, the second step after recording the scene is to track the appearance of multiple people who are involved in the social events. Hence, our proposal begins by introducing a multiface tracking which holds certain characteristics to deal with challenges imposed by the egocentric photostreams. Next step forward in social signal processing, is to extract the socalled social signals from the tracked people. In this step, besides the conventionally studied social signals, clothing as a novel social signal is proposed for further studies within the social signal processing. Finally, the last step is social signal analysis, itself. In this thesis, social signal analysis is essentially defined as reaching an understanding of social patterns of a wearable photocamera user by reviewing captured photos by the worn camera over a period of time. Our proposal for social signal analysis is comprised of first, to detect social interactions of the user where the impact of several social signals on the task is explored. The detected social events are inspected in the second step for categorization into different social meetings. The last step of the framework is to characterize social patterns of the user. Our goal is to quantify the duration, the diversity and the frequency of the user social relations in various social situations. This goal is achieved by the discovery of recurrences of the same people across the whole set of social events related to the user. Each step of our proposed pipeline is validated over relevant datasets, and the obtained results are reported quantitatively and qualitatively. For each section of the pipeline, a comparison with related stateoftheart models is provided. A discussion section over the obtained results is also given which is dedicated to highlighting the advantages, shortcomings, and differences of the proposed models, and with regards to the stateoftheart
Learning to recognize human actions : from handcrafted to deeplearning based visual representations by Albert Clapés i Sintes(
)
1 edition published in 2019 in English and held by 1 WorldCat member library worldwide
"Action recognition is a very challenging and important problem in computer vision. Researchers working on this field aspire to provide computers with the ability to visually perceive human actions  that is, to observe, interpret, and understand humanrelated events that occur in the physical environment merely from visual data. The applications of this technology are numerous: humanmachine interaction, ehealth, monitoring/surveillance, and contentbased video retrieval, among others. Handcrafted methods dominated the field until the apparition of the first successful deep learningbased action recognition works. Although earlier deepbased methods underperformed with respect to handcrafted approaches, these slowly but steadily improved to become stateoftheart, eventually achieving better results than handcrafted ones. Still, handcrafted approaches can be advantageous in certain scenarios, specially when not enough data is available to train very large deep models or simply to be combined with deepbased methods to further boost the performance. Hence, showing how handcrafted features can provide extra knowledge the deep networks are not able to easily learn about human actions. This Thesis concurs in time with this change of paradigm and, hence, reflects it into two distinguished parts. In the first part, we focus on improving current successful handcrafted approaches for action recognition and we do so from three different perspectives. Using the dense trajectories framework as a backbone: first, we explore the use of multimodal and multiview input data to enrich the trajectory descriptors. Second, we focus on the classification part of action recognition pipelines and propose an ensemble learning approach, where each classifier learns from a different set of local spatiotemporal features to then combine their outputs following an strategy based on the DempsterShaffer Theory. And third, we propose a novel handcrafted feature extraction method that constructs a midlevel feature description to better model longterm spatiotemporal dynamics within action videos. Moving to the second part of the Thesis, we start with a comprehensive study of the current deeplearning based action recognition methods. We review both fundamental and cutting edge methodologies reported during the last few years and introduce a taxonomy of deeplearning methods dedicated to action recognition. In particular, we analyze and discuss how these handle the temporal dimension of data. Last but not least, we propose a residual recurrent network for action recognition that naturally integrates all our previous findings in a powerful and promising framework."  TDX
1 edition published in 2019 in English and held by 1 WorldCat member library worldwide
"Action recognition is a very challenging and important problem in computer vision. Researchers working on this field aspire to provide computers with the ability to visually perceive human actions  that is, to observe, interpret, and understand humanrelated events that occur in the physical environment merely from visual data. The applications of this technology are numerous: humanmachine interaction, ehealth, monitoring/surveillance, and contentbased video retrieval, among others. Handcrafted methods dominated the field until the apparition of the first successful deep learningbased action recognition works. Although earlier deepbased methods underperformed with respect to handcrafted approaches, these slowly but steadily improved to become stateoftheart, eventually achieving better results than handcrafted ones. Still, handcrafted approaches can be advantageous in certain scenarios, specially when not enough data is available to train very large deep models or simply to be combined with deepbased methods to further boost the performance. Hence, showing how handcrafted features can provide extra knowledge the deep networks are not able to easily learn about human actions. This Thesis concurs in time with this change of paradigm and, hence, reflects it into two distinguished parts. In the first part, we focus on improving current successful handcrafted approaches for action recognition and we do so from three different perspectives. Using the dense trajectories framework as a backbone: first, we explore the use of multimodal and multiview input data to enrich the trajectory descriptors. Second, we focus on the classification part of action recognition pipelines and propose an ensemble learning approach, where each classifier learns from a different set of local spatiotemporal features to then combine their outputs following an strategy based on the DempsterShaffer Theory. And third, we propose a novel handcrafted feature extraction method that constructs a midlevel feature description to better model longterm spatiotemporal dynamics within action videos. Moving to the second part of the Thesis, we start with a comprehensive study of the current deeplearning based action recognition methods. We review both fundamental and cutting edge methodologies reported during the last few years and introduce a taxonomy of deeplearning methods dedicated to action recognition. In particular, we analyze and discuss how these handle the temporal dimension of data. Last but not least, we propose a residual recurrent network for action recognition that naturally integrates all our previous findings in a powerful and promising framework."  TDX
Equacions algebraiques : 274 exercicis resolts by
Olga Lavila Vidal(
Book
)
1 edition published in 2020 in Catalan and held by 1 WorldCat member library worldwide
1 edition published in 2020 in Catalan and held by 1 WorldCat member library worldwide
Periodic time dependent Hamiltonian systems and applications by Marc JorbaCuscó(
)
1 edition published in 2019 in English and held by 1 WorldCat member library worldwide
A dynamical system is one that evolves with time. This definition is so diffuse that seems to be completely useless, however, gives a good insight of the vast range of applicability of this field of Mathematics has. It is hard to track back in the history of science to find the origins of this discipline. The works by Fibonacci, in the twelfth century, concerning the population growth rate of rabbits can be already considered to belong to the above mentioned field. Newton's legacy changed the prism through the humankind watched the universe and established the starting shot of several areas of knowledge including the study of difierential equations. Newton's second law relates the acceleration, the second derivative of the position of a body with the net force acting upon it. The formulation of the law of universal gravitation settled the many body problem, the fundamental question around the field of celestial mechanics has grown. Newton itself solved the two body problem, providing an analytical proof of Kepler's laws. In the subsequent years a number of authors, among of them Euler and Lagrange, exhausted Newton's powerful ideas but none of them was able to find a closed solution of the many body problem. By the end of the nineteenth century, Poincaré changed again the point of view: The French mathematician realized that the many body problem could not be solved in the sense his predecessors expected, however, many other fundamental questions could be addressed by studying the solutions of not quantitatively but by means of their geometrical and topological properties. The ideas that bloomed in Poincaré's mind are nowadays a source of inspiration for modern scientist facing problems located along all the spectrum of human knowledge. Poincaré understood that invariant structures organize the long term behaviour of the solutions of the system. Invariant objects are, therefore, the skeleton of the dynamics. These invariant structures and their linear normal behaviour are to be analyzed carefully and this shall lead to a good insight on global aspects of the phase space. For nonintegrable systems the task of studying invariant objects and their stability is, in general, a problem which is hard to be handled rigorously. Usually, the hypotheses needed to prove specific statements on the solutions of the systems reduce the applicability of the results. This is especially relevant in physical problems: Indeed, we cannot, for instance, choose the mass of Sun to be suficiently small. The advent of the computers changed the way to undertake studies of dynamical systems. The task of writing programs for solving, numerically, problems related to specific examples is, at the present time, as important as theoretical studies. This has two main consequences: On the first hand, more involved models can be chosen to study real problems and this allow us to understand better the relation between abstract concepts and physical phenomena. Secondly, even when facing fundamental questions on dynamics, the numerical studies give us data from which build our theoretical developments. Nowadays, a large number of commercial (or public) software packages helps scientist to study simple problems avoiding the tedious work to master numerical algorithms and programming languages. These programs are coded to work in the largest possible number of different situations, therefore, they do not have the eficiency that programs written specifically for a certain purpose have. Some of the computations presented in this dissertation cannot be performed by using commercial software or, at least, not in a reasonable amount of time. For this reason, a large part of the work presented here has to do with coding and debugging programs to perform numerical computations. These programs are written to be highly eficient and adapted to each problem. At the same time, the design is done so that specific blocks of the code can be used for other computations, that is, there exist a commitment between eficiency and reusability which is hard to achieve without having full control on the code. Under these guiding principles we undertake the study of applied dynamical systems according to the following stages: From a particular problem we get a simple model, then perform a number of numerical experiments that permits us to understand the invariant objects of the system, with that information, we can isolate the relevant phenomena and identify the key elements playing a role on it. Next, we try to find an even simpler model in which we can develop theoretical arguments and produce theorems that, with more effort, can be generalized or related to other problems which, in principle, seem to be difierent to the original one. Paraphrasing Carles Simó, from a physical problem we can take the lift to the abstract world, use theoretical arguments, come out with conclusions and, finally, lift down to the real world and apply these conclusions to specific problems (maybe not only the original one). This methodology has been developed in the last decades over the world when it turned out to outstand among the most powerful approaches to cope with problems in applied mathematics. The group of Dynamical Systems from Barcelona has been one of the bulwarks of this development from the late seventies to the present days. Following the guidelines presented in the previous section, we concern with several problems, mostly from the field of celestial mechanics but we also deal with a phenomenon coming from high energy physics. All these situations can be modeled by means of periodically time dependent Hamiltonian systems. To cope with those investigations, we develop software which can be used to perform computations in any periodically perturbed Hamiltonian system. We split the contents of this dissertation in two parts. The first one is devoted to general tolos to handle periodically time dependent Hamiltonians, even though we fill this first part with a number of illustrating examples, the goal is to keep the exposition in the abstract setting. Most of the contents of Part I deal with the development of software used to be applied in the second part. Some of the software has not been applied to the specific contents of Part II, this is left for future work. We also devote a whole chapter to some theoretical issues that, while are motivated by physical problems, they fall out of the category of periodic time dependent Hamiltonians. This splitting of contents has the intention of reecting, somehow, the basic methodological principles presented in the previous paragraph, keeping separated the abstract and the physical world but keeping in mind the lift
1 edition published in 2019 in English and held by 1 WorldCat member library worldwide
A dynamical system is one that evolves with time. This definition is so diffuse that seems to be completely useless, however, gives a good insight of the vast range of applicability of this field of Mathematics has. It is hard to track back in the history of science to find the origins of this discipline. The works by Fibonacci, in the twelfth century, concerning the population growth rate of rabbits can be already considered to belong to the above mentioned field. Newton's legacy changed the prism through the humankind watched the universe and established the starting shot of several areas of knowledge including the study of difierential equations. Newton's second law relates the acceleration, the second derivative of the position of a body with the net force acting upon it. The formulation of the law of universal gravitation settled the many body problem, the fundamental question around the field of celestial mechanics has grown. Newton itself solved the two body problem, providing an analytical proof of Kepler's laws. In the subsequent years a number of authors, among of them Euler and Lagrange, exhausted Newton's powerful ideas but none of them was able to find a closed solution of the many body problem. By the end of the nineteenth century, Poincaré changed again the point of view: The French mathematician realized that the many body problem could not be solved in the sense his predecessors expected, however, many other fundamental questions could be addressed by studying the solutions of not quantitatively but by means of their geometrical and topological properties. The ideas that bloomed in Poincaré's mind are nowadays a source of inspiration for modern scientist facing problems located along all the spectrum of human knowledge. Poincaré understood that invariant structures organize the long term behaviour of the solutions of the system. Invariant objects are, therefore, the skeleton of the dynamics. These invariant structures and their linear normal behaviour are to be analyzed carefully and this shall lead to a good insight on global aspects of the phase space. For nonintegrable systems the task of studying invariant objects and their stability is, in general, a problem which is hard to be handled rigorously. Usually, the hypotheses needed to prove specific statements on the solutions of the systems reduce the applicability of the results. This is especially relevant in physical problems: Indeed, we cannot, for instance, choose the mass of Sun to be suficiently small. The advent of the computers changed the way to undertake studies of dynamical systems. The task of writing programs for solving, numerically, problems related to specific examples is, at the present time, as important as theoretical studies. This has two main consequences: On the first hand, more involved models can be chosen to study real problems and this allow us to understand better the relation between abstract concepts and physical phenomena. Secondly, even when facing fundamental questions on dynamics, the numerical studies give us data from which build our theoretical developments. Nowadays, a large number of commercial (or public) software packages helps scientist to study simple problems avoiding the tedious work to master numerical algorithms and programming languages. These programs are coded to work in the largest possible number of different situations, therefore, they do not have the eficiency that programs written specifically for a certain purpose have. Some of the computations presented in this dissertation cannot be performed by using commercial software or, at least, not in a reasonable amount of time. For this reason, a large part of the work presented here has to do with coding and debugging programs to perform numerical computations. These programs are written to be highly eficient and adapted to each problem. At the same time, the design is done so that specific blocks of the code can be used for other computations, that is, there exist a commitment between eficiency and reusability which is hard to achieve without having full control on the code. Under these guiding principles we undertake the study of applied dynamical systems according to the following stages: From a particular problem we get a simple model, then perform a number of numerical experiments that permits us to understand the invariant objects of the system, with that information, we can isolate the relevant phenomena and identify the key elements playing a role on it. Next, we try to find an even simpler model in which we can develop theoretical arguments and produce theorems that, with more effort, can be generalized or related to other problems which, in principle, seem to be difierent to the original one. Paraphrasing Carles Simó, from a physical problem we can take the lift to the abstract world, use theoretical arguments, come out with conclusions and, finally, lift down to the real world and apply these conclusions to specific problems (maybe not only the original one). This methodology has been developed in the last decades over the world when it turned out to outstand among the most powerful approaches to cope with problems in applied mathematics. The group of Dynamical Systems from Barcelona has been one of the bulwarks of this development from the late seventies to the present days. Following the guidelines presented in the previous section, we concern with several problems, mostly from the field of celestial mechanics but we also deal with a phenomenon coming from high energy physics. All these situations can be modeled by means of periodically time dependent Hamiltonian systems. To cope with those investigations, we develop software which can be used to perform computations in any periodically perturbed Hamiltonian system. We split the contents of this dissertation in two parts. The first one is devoted to general tolos to handle periodically time dependent Hamiltonians, even though we fill this first part with a number of illustrating examples, the goal is to keep the exposition in the abstract setting. Most of the contents of Part I deal with the development of software used to be applied in the second part. Some of the software has not been applied to the specific contents of Part II, this is left for future work. We also devote a whole chapter to some theoretical issues that, while are motivated by physical problems, they fall out of the category of periodic time dependent Hamiltonians. This splitting of contents has the intention of reecting, somehow, the basic methodological principles presented in the previous paragraph, keeping separated the abstract and the physical world but keeping in mind the lift
New results on modular forms and Fermattype equations by Eduardo Soto Ballesteros(
)
1 edition published in 2019 in English and held by 1 WorldCat member library worldwide
"Aquesta tesi té dos objectius. El primer és contribuir en la teoria de congruències entre formes modulars via representacions de Galois. El segon és resoldre nous problemes diofantins de tipus Fermat. En quant a representacions de Galois considerem, per una banda, congruències entre formes modulars amb signes diferents en un primer Steinberg comú i, per l'altra, la pujada de nivell en primers arbitraris sota la condició (AbsIrr). Aquest últim treball té aplicacions en la construcció de cadenes segures que permeten propagar propietats com la modularitat. En quant a problemes diofantins, utilitzem les representacions de Galois i el ja clàssic mètode Modular per mostrar noves famílies de l'anomenada conjectura de Fermat Asimptòtica amb Coeficients."  TDX
1 edition published in 2019 in English and held by 1 WorldCat member library worldwide
"Aquesta tesi té dos objectius. El primer és contribuir en la teoria de congruències entre formes modulars via representacions de Galois. El segon és resoldre nous problemes diofantins de tipus Fermat. En quant a representacions de Galois considerem, per una banda, congruències entre formes modulars amb signes diferents en un primer Steinberg comú i, per l'altra, la pujada de nivell en primers arbitraris sota la condició (AbsIrr). Aquest últim treball té aplicacions en la construcció de cadenes segures que permeten propagar propietats com la modularitat. En quant a problemes diofantins, utilitzem les representacions de Galois i el ja clàssic mètode Modular per mostrar noves famílies de l'anomenada conjectura de Fermat Asimptòtica amb Coeficients."  TDX
Improving Performance and Interpretability in Recognizing Facial Action Units with Deep Neural Networks by Cipiran Adrian Corneanu(
)
1 edition published in 2020 in English and held by 1 WorldCat member library worldwide
"Facial expressions are vital ways of communication between humans in social contexts. They are used as conversational markers and they convey information about affective and cognitive state. Many applications would benefit from the advance of automatic facial expression recognition (AFER). Robust AFER would improve humancomputer interaction, it would increase driving safety, would help medical personal to better take care of patients with impaired communication ability and could transform online education. In recent years significant advancement has been undertaken in AFER with the use of deep neural networks (DNN). Unfortunately this increase in performance came with increased opacity. The current status of DNNs as "blackbox" model hinders the advancement of the field. In this dissertation, we propose a new general framework for analysing deep neural networks based on the systematic study of their topology while they are learning patterns in the data. We use this framework to study a newly proposed DNN, specially built for Action Unit recognition which results in better understanding, control and increased performance. In summary, this dissertation has the following main contributions: a) Definition of comprehensive taxonomy of automatic computer vision approaches to automatic facial expression recognition followed by an extended review of historical and current trends in AFER. b) Proposal of a model that learns representation, patch and output structure of the face endtoend e) Introduction of a structure inference topology that replicates inference algorithm in probabilistic graphical models by using a recurrent neural network c) Extended ablation study and experimental analysis of the newly proposed architecture d) Analysis and improving performance of the previously proposed architecture for facial expression architecture using the new theoretical framework. e) Formulation of novel general framework for analysis of deep neural networks based on algebraic topology f) Analysis of fundamental topological differences between DNNs that learn and DNNs that memorize g) Demonstrating the use of newly proposed analytical framework on facial action unit recognition using DSIN."  TDX
1 edition published in 2020 in English and held by 1 WorldCat member library worldwide
"Facial expressions are vital ways of communication between humans in social contexts. They are used as conversational markers and they convey information about affective and cognitive state. Many applications would benefit from the advance of automatic facial expression recognition (AFER). Robust AFER would improve humancomputer interaction, it would increase driving safety, would help medical personal to better take care of patients with impaired communication ability and could transform online education. In recent years significant advancement has been undertaken in AFER with the use of deep neural networks (DNN). Unfortunately this increase in performance came with increased opacity. The current status of DNNs as "blackbox" model hinders the advancement of the field. In this dissertation, we propose a new general framework for analysing deep neural networks based on the systematic study of their topology while they are learning patterns in the data. We use this framework to study a newly proposed DNN, specially built for Action Unit recognition which results in better understanding, control and increased performance. In summary, this dissertation has the following main contributions: a) Definition of comprehensive taxonomy of automatic computer vision approaches to automatic facial expression recognition followed by an extended review of historical and current trends in AFER. b) Proposal of a model that learns representation, patch and output structure of the face endtoend e) Introduction of a structure inference topology that replicates inference algorithm in probabilistic graphical models by using a recurrent neural network c) Extended ablation study and experimental analysis of the newly proposed architecture d) Analysis and improving performance of the previously proposed architecture for facial expression architecture using the new theoretical framework. e) Formulation of novel general framework for analysis of deep neural networks based on algebraic topology f) Analysis of fundamental topological differences between DNNs that learn and DNNs that memorize g) Demonstrating the use of newly proposed analytical framework on facial action unit recognition using DSIN."  TDX
Function and operator theory on large Bergman spaces by
Hicham Arroussi(
)
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
The theory of Bergman spaces has been a central subject of study in complex analysis during the past decades. The book [7] by S. Bergman contains the first systematic treatment of the Hilbert space of square integrable analytic functions with respect to Lebesgue area measure on a domain. His approach was based on a reproducing kernel that became known as the Bergman kernel function. When attention was later directed to the spaces AP over the unit disk, it was natural to call them Bergman spaces. As counterparts of Hardy spaces, they presented analogous problems. However, although many problems in Hardy spaces were well understood by the 1970s, their counterparts for Bergman spaces were generally viewed as intractable, and only some isolated progress was done. The 1980s saw the emerging of operator theoretic studies related to Bergman spaces with important contributions by several authors. Their achievements on Bergman spaces with standard weights are presented in Zhu's book [77]. The main breakthroughs came in the 1990s, where in a flurry of important advances, problems previously considered intractable began to be solved. First came Hedenmalm's construction of canonical divisors [26], then Seip's description [59] of sampling and interpolating sequences on Bergman spaces, and later on, the study of Aleman, Richter and Sundberg [1] on the invariant subspaces of A2, among others. This attracted other workers to the field and inspired a period of intense research on Bergman spaces and related topics. Nowadays there are rich theories on Bergman spaces that can be found on the textbooks [27] and [22]. Meanwhile, also in the nineties, some isolated problems on Bergman spaces with exponential type weights began to be studied. These spaces are large in the sense that they contain all the Bergman spaces with standard weights, and their study presented new difficulties, as the techniques and ideas that led to success when working on the analogous problems for standard Bergman spaces, failed to work on that context. It is the main goal of this work to do a deep study of the function theoretic properties of such spaces, as well as of some operators acting on them. It turns out that large Bergman spaces are close in spirit to Fock spaces [79], and many times mixing classical techniques from both Bergman and Fock spaces in an appropriate way, can led to some success when studying large Bergman spaces
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
The theory of Bergman spaces has been a central subject of study in complex analysis during the past decades. The book [7] by S. Bergman contains the first systematic treatment of the Hilbert space of square integrable analytic functions with respect to Lebesgue area measure on a domain. His approach was based on a reproducing kernel that became known as the Bergman kernel function. When attention was later directed to the spaces AP over the unit disk, it was natural to call them Bergman spaces. As counterparts of Hardy spaces, they presented analogous problems. However, although many problems in Hardy spaces were well understood by the 1970s, their counterparts for Bergman spaces were generally viewed as intractable, and only some isolated progress was done. The 1980s saw the emerging of operator theoretic studies related to Bergman spaces with important contributions by several authors. Their achievements on Bergman spaces with standard weights are presented in Zhu's book [77]. The main breakthroughs came in the 1990s, where in a flurry of important advances, problems previously considered intractable began to be solved. First came Hedenmalm's construction of canonical divisors [26], then Seip's description [59] of sampling and interpolating sequences on Bergman spaces, and later on, the study of Aleman, Richter and Sundberg [1] on the invariant subspaces of A2, among others. This attracted other workers to the field and inspired a period of intense research on Bergman spaces and related topics. Nowadays there are rich theories on Bergman spaces that can be found on the textbooks [27] and [22]. Meanwhile, also in the nineties, some isolated problems on Bergman spaces with exponential type weights began to be studied. These spaces are large in the sense that they contain all the Bergman spaces with standard weights, and their study presented new difficulties, as the techniques and ideas that led to success when working on the analogous problems for standard Bergman spaces, failed to work on that context. It is the main goal of this work to do a deep study of the function theoretic properties of such spaces, as well as of some operators acting on them. It turns out that large Bergman spaces are close in spirit to Fock spaces [79], and many times mixing classical techniques from both Bergman and Fock spaces in an appropriate way, can led to some success when studying large Bergman spaces
On the Dynamics Around the Collinear Points in the SunJupiter System by Gladston Duarte Ferreira(
)
1 edition published in 2020 in English and held by 1 WorldCat member library worldwide
"This work aims the study of the Rapid Transition Mechanism that explains some properties of orbits of some spatial objects, as for instance, comet 39P/Oterma, which will be the main object of this research.Considering Sun and Jupiter are the masses that more influence the considered object, this mechanism describes a transition which makes the object to change from an orbit which is outside the Jupiter's one from one inside of it or viceversa.This mechanism is observed, in particular, in the phase space of the considered models: the Restricted ThreeBody Problem, both Planar Circular and Planar Elliptic. In these models three bodies are considered, two of them, named primaries, have positive mass and their orbits evolve according to the solution of the TwoBody Problem, i.e., they are circles, ellipses, parabolas or hyperbolas, having as focus (or centre) the centre of mass of both masses. The third body (which movement is to be described) is considered to have zero mass, hence it does not influence the movement of the primaries but it is under their gravitational influence. We will present the cases on which the orbit of the primaries is a circle or an ellipse and that the orbit of the third body is confined to the same plane of movement of the primaries.Having chosen the models to study this type of transition, we proceed to the study of the skeletons of these systems, i.e., which invariant objects are the more important and responsible to describe Oterma's dynamics. This methodology is general in the study of the phase space of dynamical system: these objects are equilibrium points, periodic orbits, tori, manifolds, atractors, repulsors, among others, based on each problem. To compute the equilibrium points L1 and L2 in the circular model (which will be also used in the elliptic one) it is enough to numerically solve a polynomial equation of 5th degree, known as Euler's quintic. Afterwards, the periodic orbits around them are computed via two approaches: a semianalytical one (which also permit the compute a good initial approximation of their stable and unstable invariant manifolds) using Birkhoff Normal Forms at the equilibirum points and a numerical one. In the elliptic model, the tori around L1 and L2 are computed using numerical techniques, approximating a parameterization using Fourier series. In fact, it is considered the mapping as integrating a period of Jupiter and an invariant curve can be computed. Due to the strong instability of the region around the equilibirum points, we consider a representation using more than 1 section in the independent variable and the 1periodintegration is done in smaller steps  this approach is called parallel shooting.Finally, we visualize Oterma in this context. Changes of variable are done in order to fit its real data in both model. This lets us read Oterma's positions and velocities from JPLHorizons system and represent them in synodical coordinates. Approximating the initial coordinates (projecting them in the primaries plane of movement) and integrating them in the planar elliptic model we obtain a good hint that this model is suitable to reproduce, at least partially, Oterma's dynamics. With this, we are able to visualize Oterma inside the phase space and how it interacts with the considered invariant objects. In particular, making sections in the true anomaly and in the x coordinate at the same time, it is possible to compute invariant tori around L1 and around L2 which invariant manifolds are closer to Oterma's orbit. In addition, still in these double sections we are able to visualize the heteroclinic connections between these tori near Oterma's orbit."  TDX
1 edition published in 2020 in English and held by 1 WorldCat member library worldwide
"This work aims the study of the Rapid Transition Mechanism that explains some properties of orbits of some spatial objects, as for instance, comet 39P/Oterma, which will be the main object of this research.Considering Sun and Jupiter are the masses that more influence the considered object, this mechanism describes a transition which makes the object to change from an orbit which is outside the Jupiter's one from one inside of it or viceversa.This mechanism is observed, in particular, in the phase space of the considered models: the Restricted ThreeBody Problem, both Planar Circular and Planar Elliptic. In these models three bodies are considered, two of them, named primaries, have positive mass and their orbits evolve according to the solution of the TwoBody Problem, i.e., they are circles, ellipses, parabolas or hyperbolas, having as focus (or centre) the centre of mass of both masses. The third body (which movement is to be described) is considered to have zero mass, hence it does not influence the movement of the primaries but it is under their gravitational influence. We will present the cases on which the orbit of the primaries is a circle or an ellipse and that the orbit of the third body is confined to the same plane of movement of the primaries.Having chosen the models to study this type of transition, we proceed to the study of the skeletons of these systems, i.e., which invariant objects are the more important and responsible to describe Oterma's dynamics. This methodology is general in the study of the phase space of dynamical system: these objects are equilibrium points, periodic orbits, tori, manifolds, atractors, repulsors, among others, based on each problem. To compute the equilibrium points L1 and L2 in the circular model (which will be also used in the elliptic one) it is enough to numerically solve a polynomial equation of 5th degree, known as Euler's quintic. Afterwards, the periodic orbits around them are computed via two approaches: a semianalytical one (which also permit the compute a good initial approximation of their stable and unstable invariant manifolds) using Birkhoff Normal Forms at the equilibirum points and a numerical one. In the elliptic model, the tori around L1 and L2 are computed using numerical techniques, approximating a parameterization using Fourier series. In fact, it is considered the mapping as integrating a period of Jupiter and an invariant curve can be computed. Due to the strong instability of the region around the equilibirum points, we consider a representation using more than 1 section in the independent variable and the 1periodintegration is done in smaller steps  this approach is called parallel shooting.Finally, we visualize Oterma in this context. Changes of variable are done in order to fit its real data in both model. This lets us read Oterma's positions and velocities from JPLHorizons system and represent them in synodical coordinates. Approximating the initial coordinates (projecting them in the primaries plane of movement) and integrating them in the planar elliptic model we obtain a good hint that this model is suitable to reproduce, at least partially, Oterma's dynamics. With this, we are able to visualize Oterma inside the phase space and how it interacts with the considered invariant objects. In particular, making sections in the true anomaly and in the x coordinate at the same time, it is possible to compute invariant tori around L1 and around L2 which invariant manifolds are closer to Oterma's orbit. In addition, still in these double sections we are able to visualize the heteroclinic connections between these tori near Oterma's orbit."  TDX
Effective methods for recurrence solutions in delay differential equations by Joan Gimeno i Alquézar(
)
1 edition published in 2020 in English and held by 1 WorldCat member library worldwide
"This thesis deals with the jet transport for numerical integrators andthe effective invariant object computation of delay differentialequations.Firstly we study how automatic differentiation (AD) affects when theyare applied to numerical integrators of ordinary differentialequations (ODEs). We prove that the use of AD is exactly the same asconsidering the initial ODE and add new equations to the calculationof the variational flow up to a certain order.With this result we propose to detail the effective computation whenthese equations are affected by a delay. In particular, thecomputation of the stability of equilibrium points, the computation ofperiodic orbits as well as their stability and continuation. Similarlythe computation of quasiorbits periodic and its stability. For suchcomputations, we avoid the explicit generation of the Jacobian matrixand we only require the matrixvector evaluation.Finally, we cover the existence, uniqueness and numerical computationof the slowest direction of the stable manifold of a limit cycle of astatedependent delay equation differential. The results areformulated in a posteriori format, which leads to rigorous proofs ofnumerical experiments. Specifically our result is applicable when youhave a delayed perturbation and it depends on the state of an ODE inthe plane."  TDX
1 edition published in 2020 in English and held by 1 WorldCat member library worldwide
"This thesis deals with the jet transport for numerical integrators andthe effective invariant object computation of delay differentialequations.Firstly we study how automatic differentiation (AD) affects when theyare applied to numerical integrators of ordinary differentialequations (ODEs). We prove that the use of AD is exactly the same asconsidering the initial ODE and add new equations to the calculationof the variational flow up to a certain order.With this result we propose to detail the effective computation whenthese equations are affected by a delay. In particular, thecomputation of the stability of equilibrium points, the computation ofperiodic orbits as well as their stability and continuation. Similarlythe computation of quasiorbits periodic and its stability. For suchcomputations, we avoid the explicit generation of the Jacobian matrixand we only require the matrixvector evaluation.Finally, we cover the existence, uniqueness and numerical computationof the slowest direction of the stable manifold of a limit cycle of astatedependent delay equation differential. The results areformulated in a posteriori format, which leads to rigorous proofs ofnumerical experiments. Specifically our result is applicable when youhave a delayed perturbation and it depends on the state of an ODE inthe plane."  TDX
Restricted Weak Type Extrapolation of MultiVariable Operators and Related Topics by Eduard Roure Perdices(
)
1 edition published in 2020 in English and held by 1 WorldCat member library worldwide
"A remarkable result in Harmonic Analysis is the socalled Rubio de Francia's extrapolation theorem. Roughly speaking, it says that if one has an operator T that is bounded on Lp(v), for some p 1 and every weight v in Ap, then T is bounded in Lq(w), for every q > 1 and every weight w in Aq.Rubio de Francia's extrapolation theory is very useful in practice, but there is an issue: it does not allow to produce estimates for q = 1. The works of M. J. Carro, L. Grafakos, and J. Soria [9], and M. J. Carro and J. Soria [14] give a solution to this problem, allowing to extrapolate down to the endpoint q = 1.In this project, we started building upon these works to produce multi variable extensions of the extrapolation results that they presented. We have succeeded in this endeavor, and now we possess extrapolation schemes in the setting of weighted Lorentz spaces that are of great use when trying to bound multivariable operators for which no sparse domination is known, and also when working with Lorentz spaces outside the Banachrange. As a particular case, we have studied producttype operators, twovariable commutators, averaging operators, and bilinear multipliers.Sawyertype inequalities play a fundamental role in the proof of our multivariable extrapolation schemes and are essential to complete the charac terization of the weighted restricted weak type bounds for the pointwise product of HardyLittlewood maximal operators. In this work, we have ex tended the classical weak (1, 1) Sawyertype inequalities proved in [27] to the general restricted weak type case, even in the multivariable setting.In 2017, at the University of Alabama, we started a collaboration with David V. CruzUribe to produce restricted weak type bounds for fractional operators, CalderónZygmund operators, and commutators of these operators. We managed to obtain satisfactory results on this matter, even twoweight norm inequalities, applying a wide variety of techniques on sparse domination, function spaces, and weighted theory."  TDX
1 edition published in 2020 in English and held by 1 WorldCat member library worldwide
"A remarkable result in Harmonic Analysis is the socalled Rubio de Francia's extrapolation theorem. Roughly speaking, it says that if one has an operator T that is bounded on Lp(v), for some p 1 and every weight v in Ap, then T is bounded in Lq(w), for every q > 1 and every weight w in Aq.Rubio de Francia's extrapolation theory is very useful in practice, but there is an issue: it does not allow to produce estimates for q = 1. The works of M. J. Carro, L. Grafakos, and J. Soria [9], and M. J. Carro and J. Soria [14] give a solution to this problem, allowing to extrapolate down to the endpoint q = 1.In this project, we started building upon these works to produce multi variable extensions of the extrapolation results that they presented. We have succeeded in this endeavor, and now we possess extrapolation schemes in the setting of weighted Lorentz spaces that are of great use when trying to bound multivariable operators for which no sparse domination is known, and also when working with Lorentz spaces outside the Banachrange. As a particular case, we have studied producttype operators, twovariable commutators, averaging operators, and bilinear multipliers.Sawyertype inequalities play a fundamental role in the proof of our multivariable extrapolation schemes and are essential to complete the charac terization of the weighted restricted weak type bounds for the pointwise product of HardyLittlewood maximal operators. In this work, we have ex tended the classical weak (1, 1) Sawyertype inequalities proved in [27] to the general restricted weak type case, even in the multivariable setting.In 2017, at the University of Alabama, we started a collaboration with David V. CruzUribe to produce restricted weak type bounds for fractional operators, CalderónZygmund operators, and commutators of these operators. We managed to obtain satisfactory results on this matter, even twoweight norm inequalities, applying a wide variety of techniques on sparse domination, function spaces, and weighted theory."  TDX
The Logic of Turing Progressions by Eduardo Hermo Reyes(
)
1 edition published in 2019 in English and held by 1 WorldCat member library worldwide
1 edition published in 2019 in English and held by 1 WorldCat member library worldwide
Contributions to stochastic analysis by Giulia Binotto(
)
1 edition published in 2018 in English and held by 1 WorldCat member library worldwide
The aim of this dissertation is to present some new results on stochastic analysis. It consists on three works that deal with two Gaussian processes: the Brownian motion and the fractional Brownian motion with Hurst parameter H less than 1/2. In the first work we construct a family of processes, from a single Poisson process and a sequence of independent random variables with common Bernoulli distribution, that converges in law to a complex Brownian motion. We find realizations of these processes that converge almost surely to the complex Brownian motion, uniformly on the unit time interval, and we derive the rate of convergence. In the second work, we establish the weak convergence, in the topology of the Skorohod space, of the symmetric Riemann sums for functionals of the fractional Brownian motion when the Hurst parameter takes a critical value that depends on the chosen measure. As a consequence, we derive a changeofvariable formula in distribution, where the correction term is a stochastic integral with respect to a Brownian motion that is independent of the fractional Brownian motion. The last work is devoted to prove that, when the delay goes to zero, the solution of delay differential equations driven by a Hölder continuous function of order in (1/3,1/2) converges with the supremum norm to the solution of the equation without delay
1 edition published in 2018 in English and held by 1 WorldCat member library worldwide
The aim of this dissertation is to present some new results on stochastic analysis. It consists on three works that deal with two Gaussian processes: the Brownian motion and the fractional Brownian motion with Hurst parameter H less than 1/2. In the first work we construct a family of processes, from a single Poisson process and a sequence of independent random variables with common Bernoulli distribution, that converges in law to a complex Brownian motion. We find realizations of these processes that converge almost surely to the complex Brownian motion, uniformly on the unit time interval, and we derive the rate of convergence. In the second work, we establish the weak convergence, in the topology of the Skorohod space, of the symmetric Riemann sums for functionals of the fractional Brownian motion when the Hurst parameter takes a critical value that depends on the chosen measure. As a consequence, we derive a changeofvariable formula in distribution, where the correction term is a stochastic integral with respect to a Brownian motion that is independent of the fractional Brownian motion. The last work is devoted to prove that, when the delay goes to zero, the solution of delay differential equations driven by a Hölder continuous function of order in (1/3,1/2) converges with the supremum norm to the solution of the equation without delay
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