En esta tesis doctoral se aborda el problema del control predictivo sujeto a restricciones definidas como la unión no convexa de varios poliedros. Los controladores propuestos son de utilidad, por un lado, para procesos que presentan de manera natural restricciones de dicha forma y, por otra parte, como una alternativa al control predictivo no lineal cuando períodos de muestreo bajos no permiten la aplicación de programación no lineal. En los primeros capítulos del trabajo se demuestra la existencia de una solución explícita a los problemas de optimización que aparecen al plantear este tipo de controladores predictivos. Dicha solución es afín a tramos definidos mediante desigualdades lineales y cuadráticas. Se introducen dos metodologías diferentes para la obtención de esta solución explícita: la metodología de intersección, división y unión y la de la envolvente convexa. La primera de estas metodologías se basa en formular subproblemas con las restricciones convexas cuya unión forma las restricciones originales y obtener la solución explícita del problema original a partir de las soluciones de dichos subproblemas. La segunda metodología planteada se basa en el cálculo de la envolvente convexa de los conjuntos de restricciones y la obtención de la solución explícita del problema convexo definido por estas nuevas restricciones. Se demuestra como parte de las regiones de la solución explícita del problema original coinciden con las del nuevo problema, y se propone un procedimiento para identificarlas y obtener el resto de regiones, completando la solución explícita buscada. Se estudian también algoritmos eficientes para la implementación en línea de leyes de control explícitas como las obtenidas. En particular, se propone un algoritmo basado en un árbol binario de una partición lineal y una comparación de índices de costes en las regiones en las que sea necesario. / Pérez Soler, E. (2011). CONTROL PREDICTIVO SUJETO A RESTRICCIONES POLIÉDRICAS NO CONVEXAS: SOLUCIÓN EXPLÍCITA Y ESTABILIDAD [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/9315 / Palancia

Afin d'étudier les limites d'existence de la chaîne isotopique des azotes, une expérience a été menée au RIBF-RIKEN en utilisant le spectromètre SAMURAI couplé au détecteur de neutrons NEBULA. Les systèmes étudiés - 23N*, 24N et 25N ont été produits via des réactions de knockout de quelques nucléons ou de fragmentation à partir de faisceau secondaires de haute énergie (~250 MeV/nucléon). La méthode utilisée pour caractériser ces systèmes est celle de la masse invariante qui nécessite la cinématique complète des réactions étudiées. Pour interpréter les résultats, une simulation de la totalité du dispositif expérimental a été utilisée. L'étalonnage des détecteurs et les techniques d'analyse ont été testés en sondant l'état fondamental connu du 16B. Dans le cas du 23N, une étude de spectroscopie gamma en vol a permis de confirmer qu'il ne possédait pas d'état excité lié. Nous avons pu le sonder à travers 3 voies de réactions distinctes : Le knockout d'un proton du 24O, la fragmentation à partir du 27Ne et la diffusion inélastique. Dans tous les cas, nous avons observé une résonance l=0 à environ 3,5 MeV d'énergie d'excitation. Cette résonance a été interprétée, en s'appuyant sur des calculs de modèle en couche, comme le premier état excité du 23N de spin parité Jpi=3/2-. Dans l'ensemble des voies une seconde résonance possédant une énergie d'excitation d'environ 5 MeV était nécessaire pour décrire les spectres en énergie-relative fragment-neutron mesurés.Le 24N a été observé pour la première fois lors de notre expérience comme une résonance autour de 1,3 MeV au dessus du seuil d'émission neutron. Nous avons pu sonder ce système via 4 réactions, le knockout de deux ou trois protons respectivement du 26F et du 27Ne et des réactions de fragmentation à partir du 27F et du 28Ne. L'ensemble de ces spectres peut être ajusté à l'aide d'une résonance l=2. Des considérations théoriques simples nous suggèrent que cette dernière correspond au doublet 2-,1- prédit comme l'état fondamental du 24N par le modèle en couche.Le 25N a également été observé pour la première fois lors de notre expérience. Malgré une statistique relativement limitée, les spectres des réactions de knockout de deux et trois protons du 27F et 28Ne, montrent une structure claire environ 1,7 MeV au dessus du seuil d'émission de deux neutrons qui peut être identifiée comme l'état fondamental 1/2- prédit par le modèle en couche. / To study the most neutron-rich nitrogen isotopes an experiment has been undertaken at the RIBF-RIKEN using the SAMURAI spectrometer and NEBULA neutron array. The nuclei of interest - 23N*, 24N and 25N - were produced via nucleon knockout and fragmentation reactions from high-energy (~250 MeV/nucleon) secondary beams. The technique of invariant-mass spectroscopy, which requires the measurement in complete kinematics of the beam-like reaction products, was employed to characterise these unbound systems. In the case of the 23N, in-flight gamma-ray spectroscopy was performed and it has been possible to confirm that it has no bound excited states. Three reaction channels - the knockout of a proton from 24O, the fragmentation of 27Ne and inelastic scattering – were employed to search for unbound excited states. In all these channels, an l=0 resonance was observed at around 3.5 MeV excitation energy. This resonance is interpreted, through comparison with shell model calculations, as the Jpi=3/2- first excited state of 23N. In all channels, another resonance with an excitation energy of close to 5 MeV was necessary to fully describe the fragment-neutron relative energy spectra. The nucleus 24N was observed here for the first time as resonance-like peak some 1.3 MeV above the one-neutron decay threshold. Four reaction channels were investigated: the knockout of two and three protons from 26F and 27Ne, respectively, and fragmentation of 27F and 28Ne. All the relative energy spectra were consistent with the population of an l=2 resonance. Simple considerations suggest that this is the 2-,1- ground-state doublet predicted by the shell model. The nucleus 25N was also observed here for the first time. Despite the relatively limited statistics, both two-proton and three-proton removal from 27F and 28Ne, exhibited a clear structure some 1.7 MeV above the two-neutron decay threshold which, based on simple considerations, may be identified with the expected 1/2- ground state.

Physical systems are usually not closed and insight about their internal structure is experimentally derived by scattering. This is efficiently described by resonance eigenfunctions of non-Hermitian quantum systems with a corresponding classical dynamics that allows for the escape of particles. For the phase-space distribution of resonance eigenfunctions in chaotic systems with partial and full escape we obtain a universal description of their semiclassical limit in terms of classical conditional invariant measures with the same decay rate. For partial escape, we introduce a family of conditionally invariant measures with arbitrary decay rates based on the hyperbolic dynamics and the natural measures of forward and backward dynamics. These measures explain the multifractal phase-space structure of resonance eigenfunctions and their dependence on the decay rate. Additionally, for the nontrivial limit of full escape we motivate the hypothesis that resonance eigenfunctions are described by conditionally invariant measures that are uniformly distributed on sets with the same temporal distance to the quantum resolved chaotic saddle. Overall we confirm quantum-to-classical correspondence for the phase-space densities, for their fractal dimensions, and by evaluating their Jensen–Shannon distance in a generic chaotic map with partial and full escape, respectively. / Typische physikalische Systeme sind nicht geschlossen, sodass ihre innere Struktur mit Hilfe von Streuexperimenten untersucht werden kann. Diese werden mit Hilfe einer nicht-Hermiteschen Quantendynamik und deren Resonanzeigenzuständen beschrieben. Die dabei zugrunde liegende klassische Dynamik berücksichtigt den Verlust von Teilchen. Für die semiklassische Phasenraumverteilung solcher Resonanzeigenzustände in chaotischen Systemen mit partieller und voller Öffnung entwickeln wir eine universelle Beschreibung mittels bedingt invarianter Maße gleicher Zerfallsrate. Für partiellen Zerfall stellen wir eine Familie bedingt invarianter Maße mit beliebiger Zerfallsrate vor, welche auf der hyperbolischen Dynamik und den natürlichen Maßen der vorwärts gerichteten und der invertierten Dynamik aufbauen. Diese Maße erklären die multifraktale Phasenraumstruktur der Resonanzzustände und deren Abhängigkeit von der Zerfallsrate. Darüber hinaus motivieren wir für den nicht trivialen Grenzfall voll geöffneter Systeme die Hypothese, dass Resonanzeigenzustände durch ein bedingt invariantes Maß beschrieben werden, welches gleichverteilt auf solchen Mengen ist, die den gleichen zeitlichen Abstand zum quantenunscharfen chaotischen Sattel haben. Insgesamt bestätigen wir die quantenklassische Korrespondenz für die Phasenraumdichten, deren fraktale Dimensionen und durch Auswertung ihres Jensen–Shannon Abstandes in einer generischen chaotischen Abbildung sowohl für partielle als auch für volle Öffnung.

Invariant object recognition is maybe the most basic and fundamental property of our visual system. It is the basis of many other cognitive tasks, like motor actions and social interactions. Hence, the theoretical understanding and modeling of invariant object recognition is one of the central problems in computational neuroscience. Indeed, object recognition consists of two different tasks: classification and identification. The focus of this thesis is on object identification under the basic geometrical transformations shift, scaling, and rotation. The visual system can perform shift, size, and rotation invariant object identification. This thesis consists of two parts. In the first part, we present and investigate the VisNet model proposed by Rolls. The generalization problems of VisNet triggered our development of a new neural network model for invariant object identification. Starting point for an improved generalization behavior is the search for an operation that extracts images features that are invariant under shifts, rotations, and scalings. Extracting invariant features guarantees that an object seen once in a specific pose can be identified in any pose. We present and investigate our model in the second part of this thesis.

La chaîne invariante (Ii ; CD74) est une protéine membranaire de type II qui joue un rôle majeur dans la présentation antigénique. Dans le réticulum endoplasmique (RE), Ii favorise l’assemblage du CMH II et prévient la liaison indésirable de polypeptides. Grâce à son motif di-leucine, la chaîne invariante cible le CMH II dans les endosomes. Une fois dans ces compartiments acides, Ii est dégradé, permettant la liaison de peptides de forte affinité qui seront ensuite présentés aux cellules T CD4+. Chez les souris déficientes en Ii murin (mIi), le CMH II présente une conformation non compacte typique des molécules vides ou liées faiblement à un peptide. Le transport du CMH II est aberrant ce qui conduit à une réduction de son expression en surface ainsi qu’à un défaut de présentation antigénique. De plus, Ii diversifie le répertoire de peptides et assure la sélection thymique des cellules T CD4+. Enfin, il a un rôle dans la maturation des cellules B et les souris déficientes en Ii présentent des nombres réduits de cellules B matures folliculaires (FO). L’isoforme mineure humaine p35 (Iip35) n’existe pas chez la souris et possède une extension cytoplasmique de 16 acides aminés contenant un motif R-x-R de rétention dans le RE. La sortie du RE est conditionnelle à la liaison du CMH II qui permet de masquer le motif de rétention. Iip35 agit comme dominant et impose la rétention aux autres isoformes d’Ii. Cependant, le rôle physiologique du motif R-x-R et, plus globalement, celui d’Iip35, demeurent nébuleux. Pour mieux cerner la fonction d’Iip35, nous avons généré des souris transgéniques (Tg) exprimant l’isoforme humaine Iip35 et avons analysé la conformation et le trafic du CMH II, la sélection thymique et la maturation des cellules B ainsi que la présentation antigénique. Nos résultats ont démontré qu’Iip35 favorise l’assemblage du CMH II dans le RE. Il induit également une conformation compacte du CMH II et augmente l’expression du CMH II en surface. De plus, Iip35 cible le CMH II dans les endosomes où un peptide de forte affinité se lie dans la niche peptidique. Par ailleurs, Iip35 diversifie le répertoire de peptides et rétablit totalement la sélection des cellules T CD4+ ainsi que le niveau d’expression du TCR de ces dernières. Iip35 restaure également la présentation antigénique de l’ovalbumine dont la présentation requiert l’expression d’Ii. Par contre, Iip35 rétablit la présentation des superantigènes mais à un niveau moindre que celui des souris sauvages. Ensuite, Iip35 permet le rétablissement de la sélection des cellules iNKT démontrant qu’il assiste la présentation des lipides par les molécules CD1d. Enfin, les résultats ont démontré qu’Iip35 restaure le développement des cellules B matures folliculaires (FO) mais pas celui des cellules B de la zone marginale. Ceci suggère qu’Iip35 est capable d’induire le développement des cellules FO sans stimulation préalable par le MIF (macrophage migration inhibitory factor). Ainsi, l’ensemble de ces résultats démontre qu’Iip35 est fonctionnel et assure la majorité des fonctions d’Ii. Cependant, Iip35 ne remplace pas mIi endogène concernant la maturation des cellules B MZ suggérant qu’il pourrait avoir un rôle de régulateur. / The invariant chain (Ii; CD74) is a type II membrane protein which plays a key role in antigen presentation as well as acting as a receptor for the cytokine MIF (macrophage migration inhibitory factor). In the endoplasmic reticulum (ER), Ii assists the folding of MHC II and prevents the loading of nascent polypeptides in the peptide-binding groove. Di-leucine-like motifs contained in the Ii cytoplasmic tail target the MHC II-Ii complexes in the endocytic pathway. Once in low pH-endosomes, Ii is degraded allowing the binding of a high affinity peptide which is then presented on cell surface to CD4+ T cells. In Ii deficient mice, MHC II displays a “floppy” conformation typical of empty molecules or is loosely bound with peptides. The transport is aberrant leading to decreased surface expression of MHC II and defective antigenic presentation. Also, the lack of Ii restricts the peptide repertoire and impairs thymic selection of CD4+ T cells. Moreover, Ii regulates B cells maturation and Ii deficient mice display reduced numbers of mature follicular B cells (FO). The human minor p35 isoform (Iip35) does not exist in mice and displays a 16 amino acids N-terminal cytoplasmic extension containing a di-arginine (R-x-R) motif causing ER retention and acting as dominant in heterotrimeric complexes with Iip33. Upon binding to MHC II, the retention motif is masked, which allows the complexes to egress from the ER. The physiological role of the R-x-R motif is poorly understood. To shed light on Iip35 function, we generated transgenic mice expressing Iip35 and analyzed the conformation and traffic of MHC II, the thymic selection and the development of B cells as well as the antigenic presentation. Our results showed that Iip35 generates an MHC II in the right conformation and increases MHC II surface expression. Also, Iip35 targets MHC II into endosomes where high affinity peptides bind to the groove. We also showed that Iip35 diversifies the peptide repertoire and fully restores thymic selection of CD4+ T cells as well as the TCR levels on these cells. Then, Iip35 ensures presentation of the Ii-dependent antigen ovalbumin but does not totally rescue the presentation of superantigens. Interestingly, thymic selection of the iNKT cells is fully restored showing that Iip35 assists with lipids presentation by CD1d. Finally, Iip35 allows B cells to develope into FO B cells but does not support marginal zone (MZ) B cells maturation. This result suggests that MIF stimulation is not a prerequisite for FO B cells development. Altogether, these results showed that Iip35 is functional and has most of the CD74 functions. However, it cannot replace the endogenous Ii regarding the MZ B cells maturation suggesting that Iip35 could have regulatory functions by modulating the development of some cells.

As cadeias estocásticas de memória ilimitada são uma generalização natural das cadeias de Markov, no caso em que as probabilidades de transição podem depender de todo o passado da cadeia. Estas cadeias, introduzidas, independentemente, por Onicescu e Mihoc em 1935 e Doeblin e Fortet em 1937, vêm recebendo uma atenção crescente na literatura probabilística, não só por serem uma classe mais rica que a classe das cadeias de Markov, como por suas capacidades práticas de modelagem de dados científicos em diversas áreas, indo da biologia à linguística. Neste trabalho, as utilizamos para modelar a interação entre sequências de disparos neuronais. Nosso objetivo principal é desenvolver novos resultados matemáticos acerca das cadeias de memória ilimitada. Inicialmente, estudamos as condições que garantem a existência e a unicidade de cadeias estacionárias compatíveis com uma família de probabilidades de transição descontínua. Em seguida, tratamos do entendimento da fenomenologia dos trens de disparos neuronais e usamos da informação dirigida para modelar a informação que flui de uma sequência de disparos a outra. Nesta ocasião, fixamos limites da concentração para estimação da informação dirigida. / Stochastic chains with unbounded memory are a natural generalization of Markov chains, in the sense that the transition probabilities may depend on the whole past. These process, introduced independently by Onicescu and Mihoc in 1935 and Doeblin and Fortet in 1937, have been receiving increasing attention in the probabilistic literature, because they form a class richer than the Markov chains and have practical capabilities modelling of scientific data in several areas, from biology to linguistics. In this work, we use them to model interactions between spike trains. Our main goal is to develop new mathematical results about stochastic chains with unbounded memory. First, we study conditions that guarantee the existence and uniqueness of stationary chains compatible with a discontinuous family of transition probabilities. Then, we address the understanding of the phenomenology of spike trains and we propose to use directed information to quantify the information flow from one neuron to another. In this occasion, we fix concentration bounds for directed information estimation.

Desenvolvemos as ideias centrais da Homologia Simplicial e provamos a invariância topológica dos grupos de homologia para espaços homeomorfos. Discutimos também a invariância topológica da característica de Euler-Poincaré mostrando a sua relação com os grupos de homologia através dos números de Betti. Adicionalmente apresentamos conceitos da Álgebra Abstrata, especificamente da teoria de Grupos, importantes para o entendimento formal da álgebra homológica. Ao final, propomos atividades didáticas com objetivo de trazer as ideias de triangulação e invariância topológica ao contexto da sala de aula. / We develop central ideas of Simplicial Homology and prove the topological invariance of homology groups for homeomorphic spaces. We also discuss topological invariance of Euler- Poincaré characteristic showing its relation with the homology groups through Betti numbers. In addition, we present concepts of abstract algebra, specifically of group theory, which are important to formal understanding of homological algebra. In the end, we propose didactic activities in order to bring the ideas of triangulation and topological invariance to context of math classes on basic education.

Nesta dissertação são investigados os sistemas diferenciais com integral primeira do tipo Morse-Bott definidos em superfícies compactas e orientáveis. A cada sistema, nas condições acima descritas, associa-se um grafo de modo que a correspondência entre os grafos e as classes de equivalência topologica orbital dos campos investigados seja bijetiva. Portanto, apresenta-se um invariante completo, chamado aqui de grafo de Bott, para essa classe de sistemas. Essa abordagem surgiu como uma iniciativa de generalizar o estudo realizado para sistemas Hamiltonianos com um grau de liberdade com integral primeira do tipo Morse definidos em superfícies 2-dimensionais compactas, onde os conceitos de átomos e fluxos gradiente foram aplicados por A.V. Bolsinov em [4] / In this dissertation are studied differential systems with a Morse-Bott first integral defined on compact orientable surfaces. For each system, under the conditions described above, is associated a graph so that the correspondence between graphs and the orbital topological equivalence classes of the systems are bijective. Therefore, we present a complete invariant, called here Bott graph for this class of systems. This approach has emerged as an initiative to generalize the study to systems Hamiltonian with one degree of freedom having a Morse first integral in 2-dimensional compact surfaces, where the concepts of atoms and gradient flows were applied by A.V. Bolsinov in [4]

Diversas abordagens vêm sendo empregadas para a descrição de texturas, entre elas a teoria dos conjuntos fuzzy e lógica fuzzy. O Local Fuzzy Pattern (LFP) é um descritor de texturas diferente dos demais métodos baseados em sistemas fuzzy, por não utilizar regras linguísticas e sim números fuzzy que são usados na codificação de um padrão local de escala de cinza. Resultados anteriores indicaram o LFP como um descritor eficaz para a classificação de texturas a partir de amostras rotacionadas ou não. Este trabalho propõe uma análise mais abrangente sobre sua viabilidade para aplicação em cada um desses problemas, além de propor uma modificação a este descritor, adaptando-o para a captura de padrões em multiresolução, o Sampled LFP. A avaliação da performance do LFP e do Sampled LFP para o problema de classificação de texturas foi feita através da aplicação de uma série de testes envolvendo amostras de imagens rotacionadas ou não das bases de imagens Outex, álbum de Brodatz e VisTex, onde a sensibilidade obtida por esses descritores foi comparada com um descritor de referência, a variante do Local Binary Pattern (LBP) melhor indicada para o teste em execução. Os resultados apontaram o LFP como um descritor não indicado para aplicações que trabalhem exclusivamente com amostras não rotacionadas, visto que o LBP mostrou maior eficácia para este tipo de problema. Já para a análise de amostras rotacionadas, o Sampled LFP se mostrou o melhor descritor entre os comparados. Todavia, foi verificado que o Sampled LFP somente supera o LBP para resoluções de análise maiores ou iguais a 32x32 pixels e que o primeiro descritor é mais sensível ao número de amostras usadas em seu treinamento do que o segundo, sendo, portanto, um descritor indicado para o problema de classificação de amostras rotacionadas, onde seja possível trabalhar com imagens a partir de 32x32 pixels e que o número de amostras utilizadas para treinamento seja maximizado. / Several approaches have been employed for describing textures, including the fuzzy sets theory and fuzzy logic. The Local Fuzzy Pattern is a texture descriptor different from other methods based on fuzzy systems, which use linguistic rules to codify a texture. Instead, fuzzy numbers are applied in order to encode a local grayscale pattern. Previous results indicated the LFP as an effective descriptor employed to characterize statically oriented and rotated textures samples. This paper proposes a more comprehensive analysis of its feasibility for use in each of these problems, besides proposing a modification to this descriptor, adapting it to capture patterns in multiresolution, the Sampled LFP. The LFP and Sampled LFP performance evaluation when applied to the problem of texture classification was conducted by applying a series of tests involving images samples, rotated or not, from image databases such as Outex, the Brodatz album and Vistex, where the sensitivity obtained by these descriptors were compared with a reference descriptor, the variant Local Binary Pattern (LBP) best suited to running the test. The results indicated the LFP as a descriptor not suitable for applications who work exclusively with non-rotated samples, since the LBP showed greater efficacy for this problem kind. As for rotated samples analysis, the Sampled LFP proved the best descriptor among those compared. However, it was determined that the Sampled LFP only overcomes the LBP when the analysis resolutions are greater or equal to 32x32 pixels, besides that, the first descriptor is more sensitive to the number of training samples than the latter, therefore, this descriptor is indicated for the problem of rotated samples classification, where it is possible to work with resolution from 32x32 pixels while maximizing the number of samples used for training.

Resumo Neste trabalho apresentamos, em detalhes, a construção de uma teoria quântica dos campos topológica (TQCT). Podemos definir uma TQCT como um funtor simétrico monoidal da categoria dos cobordismos para a categoria dos espaços vetoriais. Em duas dimensões podemos encontrar uma descrição completa da categoria dos cobordismos e classificar todas as TQCT\'s. Em três dimensões é possível estender alguns invariantes para 3-variedades e construir uma TQCT 3D. Nossa construção é baseada no invariante para 3-variedades de Kuperberg, o qual envolve diagramas de Heegaard e álgebras de Hopf. Começamos com a apresentação do invariante de Kuperberg definido para toda variedade 3D compacta, orientável e sem bordo. Para cada álgebra de Hopf de dimensão finita constrói-se um invariante. Por fim, apresentamos a TQCT associada com o invariante de Kuperberg. Isto é feito usando-se o fato de que o invariante de Kuperberg é definido como uma soma de pesos locais tal qual uma função de partição. A TQCT decorre dos operadores advindos de variedades com bordo. / Abstract In this work we present in detail a construction of a topological quantum field theory (TQFT). We can define a TQFT as a symmetric monoidal functor from cobordism categories to category of vector spaces. In two dimension, we can give a complete description of cobordism categories and classify all TQFT\'s. In three dimension it is possible to extend some specific 3-manifold invariants and to construct a TQFT 3D. Our construction is based on the Kuperberg 3-manifold invariant which involves Heegaard diagrams and Hopf algebras. We start with the presentation of the Kuperberg invariant defined for every orientable compact 3-manifold without boundary. For each finite-dimensional Hopf algebra we can construct a invariant. Finally we presente the TQFT associated with the Kuperberg invariant. This is made using the fact that the Kuperberg invariant is defined like a sum of local weights in the same way as a partition function. The TQFT is constructed from the operators given by manifolds with boundary.