Neste trabalho é apresentado um estudo numérico sobre escoamentos incompressíveis, não isotérmicos, bi e tridimensionais nos regimes laminar e turbulento através da Simulação de Grandes Escalas e da utilização do Método de Elementos Finitos. Para tornar isso possível, é implementada a equação da energia e os termos de forças de campo (empuxo) em um algoritmo numérico desenvolvido em FORTRAN, já existente, que simula escoamentos incompressíveis, isotérmicos, tridimensionais, nos regimes laminar e turbulento. O código desenvolvido abrange escoamentos onde as formas básicas de troca térmica ocorrem por difusão e advecção. No que tange a natureza da convecção térmica é possível analisar escoamentos com convecção forçada, mista ou natural. O método numérico empregado é o de elementos finitos (FEM) e a discretização espacial das equações que governam o fenômeno (continuidade, conservação da quantidade de movimento e conservação da energia) é realizada através do método de Galerkin. Para a análise dos termos temporais nos escoamentos transientes aplica-se o esquema temporal explícito de Taylor-Galerkin. O elemento finito utilizado é o hexaedro isoparamétrico de oito nós. É empregado o método da pseudo-compressibilidade com o objetivo de manter os termos derivados da pressão na equação da continuidade, pois essa ausência gera uma dificuldade adicional na discretização das equações. Para a abordagem da turbulência é empregada a simulação de grandes escalas (LES) com modelagem sub-malha clássica de Smagorinsky para a viscosidade e a difusividade turbulenta. Visando a melhoria no tempo de processamento foi utilizada integração explícita das matrizes dos elementos e a técnica de processamento paralelo OpenMP. São apresentados resultados para escoamentos com vários números de Reynolds, Prandtl e de Grashoff dos campos de velocidade, pressão e temperatura para escoamentos em cavidade bidimensional, nos regimes laminar e turbulento, e para o degrau tri-dimensional no regime laminar. As simulações para escoamentos em cavidades nos regimes laminar e na região de transição são comparados com os resultados de outros autores, se mostrando bastante satisfatórios, tanto no regime transiente como no permanente. Além disso, a inserção das forças de campo no código melhorou os resultados obtidos com o mesmo. As outras simulações são apresentadas como novos casos e tiveram um comportamento qualitativamente satisfatório. / A numerical study about non-isothermal, bi and three-dimensional, incompressible, laminar and turbulent flows is done in this work using Large Eddy Simulation and Finite Element Method. To became this possible, is implemented the energy equation and buoyance forces (in the Navier-Stokes equations) in a numerical algorithm, developed in FORTRAN, already existent, that simulate isothermal, three-dimensional, incompressible, laminar and turbulent flows. The developed code includes flows where the basic forms of heat transfer are diffusion or advection. About the nature of thermal convection it is possible to analyze the forced, mixed or natural convection flows. The numerical method used is the finite element method (FEM) and the spatial discretization of governing equations of phenomena (mass, conservation of momentum and conservation of energy) is done through Galerkin method. To analyze the time-dependent terms in transient flows is employed a time-explicit Taylor-Galerkin scheme. The finite element used is the isoparametric hexahedral with eight nodes. It is used the pseudo-compressibility method to keep the pressure terms in continuity equation, because without these terms there are additional difficulties to obtain the discretizated equations. Regarding the turbulence approach, it is employed the large eddy simulation (LES) and for subgrid-scales is used the classical Smagorinsky model to turbulent viscosity and diffusivity. To minimize the processing time is used explicit integration of element matrix and the multiprocessing technical OpenMP. Results are presented to a wide range of Reynolds, Prandtl and Grashoff numbers for velocity, pressure and temperature fields to laminar and turbulent, bi-dimensional, lid-driven cavity flow and a laminar three-dimensional backward-facing step. Simulations of lid-driven cavity flows in laminar and transitional regimes is compared with others authors results, presenting good agreement, in both transient and permanent regimes. Besides that, the implementation of buoyance forces in the present code improved the results obtained by it. The others simulations are presented like new cases and had qualitatively good behavior.

When working with embedded systems, secure and fast applications are desired. To achieve this the applications needs to be analyzed and optimized so that they will not be deadlocked or communicate inefficiently. For this purpose an analysis program that can track communications, deadlocks and response times is needed. Operating System Embedded, OSE, is a wide spread real-time operating system that is used in embedded systems. OSE-applications are excellent candidates for analysis and there exists such a tool, VirtualTime, for that purpose. To analyze an OSE-application a model needs to be written that VirtualTime can analyze. This takes up time and effort as the models can require a lot of work to write. In this thesis we have investigated and implemented a prototype that translates OSE-application code into VirtualTime simulation model code. We used the transformation tool TXL to translate communication and timing behaviors. In the translation one needs to preserve the communication and timing behavior and throw away other unnecessary code in the OSE-application. This complicates the translation and sophisticated methods like backward slicing might be necessary. A proposed method in this thesis could help with the problem.

Dans cette thèse nous présentons dans un premier temps une nouvelle notion de différentiabilité généralisée pour les applications multivoques, faisant intervenir des applications positivement homogènes: la H-différentiabilité. Nous étudions la stabilité de cette notion en utilisant la convergence de Fischer, d'abord dédiée aux ensembles mais que nous avons adaptée aux applications multivoques. Nous nous intéressons ensuite à l'étude de la dépendance continue des ensembles de points fixes d'une application multivoque contractante par rapport aux données. Finalement nous analysons la convergence d'une méthode d'approximations successives de type forward-backward splitting, des zéros de la somme de deux opérateurs multivoques non monotones, jouissants notamment de propriétés de pseudo H-différentiabilité / In this thesis we present at first a new concept of generalized differentiation for setvalued mappings, involving positively homogeneous applications: the H-differentiability. We study the stability of this notion by using Fischer convergence,firstly dedicated to sets but which we have adapted to set-valued mappings. We establish the continuous dependence of fixed points sets of set-valued contraction and finally we study the convergence of a forward-backward splitting method for approximating the zeros of the sum of two non-monotone set-valued mappings, notably using properties of pseudo H-differentiability.

In order to prevent, detect and fix errors in software, various tools for programmers are available, while some of them are able to reason about the behaviour of the program. In the case of C# programming language, the main representatives are Microsoft FxCop, Code Contracts and Pex. Those tools can, indeed, help to build a highly reliable software. However, when a company wants to include them in the software development process, there is a significant overhead involved. Therefore, we created a "light- weight" assertion verification tool called AskTheCode that can help the user to focus on a particular problem at a time that needs to be solved. Because of its goal-driven approach, we decided to implement it using backward symbolic execution. Although it can currently handle only basic C# statements and data types, the evaluation against the existing tools shows that it has the potential to eventually provide significant added value to the user once developed further. Powered by TCPDF (www.tcpdf.org)

The broader research area investigated during this programme was conceived from a goal to contribute towards solving the challenge of food security in the 21st century through the reduction of crop loss and minimisation of fungicide use. This is aimed to be achieved through the introduction of an empirical approach to agricultural disease monitoring. In line with this, the SYIELD project, initiated by a consortium involving University of Manchester and Syngenta, among others, proposed a novel biosensor design that can electrochemically detect viable airborne pathogens by exploiting the biology of plant-pathogen interaction. This approach offers improvement on the inefficient and largely experimental methods currently used. Within this context, this PhD focused on the adoption of multidisciplinary methods to address three key objectives that are central to the success of the SYIELD project: local spore ingress near canopies, the evaluation of a suitable model that can describe spore transport, and multivariate analysis of the potential monitoring network built from these biosensors. The local transport of spores was first investigated by carrying out a field trial experiment at Rothamsted Research UK in order to investigate spore ingress in OSR canopies, generate reliable data for testing the prototype biosensor, and evaluate a trajectory model. During the experiment, spores were air-sampled and quantified using established manual detection methods. Results showed that the manual methods, such as colourimetric detection are more sensitive than the proposed biosensor, suggesting the proxy measurement mechanism used by the biosensor may not be reliable in live deployments where spores are likely to be contaminated by impurities and other inhibitors of oxalic acid production. Spores quantified using the more reliable quantitative Polymerase Chain Reaction proved informative and provided novel of data of high experimental value. The dispersal of this data was found to fit a power decay law, a finding that is consistent with experiments in other crops. In the second area investigated, a 3D backward Lagrangian Stochastic model was parameterised and evaluated with the field trial data. The bLS model, parameterised with Monin-Obukhov Similarity Theory (MOST) variables showed good agreement with experimental data and compared favourably in terms of performance statistics with a recent application of an LS model in a maize canopy. Results obtained from the model were found to be more accurate above the canopy than below it. This was attributed to a higher error during initialisation of release velocities below the canopy. Overall, the bLS model performed well and demonstrated suitability for adoption in estimating above-canopy spore concentration profiles which can further be used for designing efficient deployment strategies. The final area of focus was the monitoring of a potential biosensor network. A novel framework based on Multivariate Statistical Process Control concepts was proposed and applied to data from a pollution-monitoring network. The main limitation of traditional MSPC in spatial data applications was identified as a lack of spatial awareness by the PCA model when considering correlation breakdowns caused by an incoming erroneous observation. This resulted in misclassification of healthy measurements as erroneous. The proposed Kriging-augmented MSPC approach was able to incorporate this capability and significantly reduce the number of false alarms.

O escopo desta dissertação é o desenvolvimento de uma metodologia para a detecção e diagnóstico de falhas em processos industriais baseado em modelos empíricos no subespaço das variáveis do processo com expansão não linear das bases. A detecção e o diagnóstico de falhas são fundamentais para aumentar a segurança, confiabilidade e lucratividade de processos industriais. Métodos qualitativos, quantitativos e baseados em dados históricos do processo têm sido estudados amplamente. Para demonstrar as vantagens da metodologia proposta, ela será comparada com duas metodologias consideradas padrão, uma baseada em Análise de Componentes Principais (PCA) e a outra baseada em Mínimos Quadrados Parciais (PLS). Dois estudos de casos são empregados nessa comparação. O primeiro consiste em um tanque de aquecimento com mistura e o segundo contempla o estudo de caso do processo da Tennessee Eastman. As vantagens da metodologia proposta consistem na redução da dimensionalidade dos dados a serem usados para um diagnóstico adequado, além de detectar efetivamente a anormalidade e identificar as variáveis mais relacionadas à falha, permitindo um melhor diagnóstico. Além disso, devido à expansão das bases dos modelos é possível trabalhar efetivamente com sistemas não lineares, através de funções polinomiais e exponenciais dentro do modelo. Adicionalmente o trabalho contém uma metodologia de validação dos resultados da metodologia proposta, que consiste na eliminação das variáveis do melhor modelo obtido pelos Modelos Empíricos, através do método Backward Elimination. A metodologia proposta forneceu bons resultados na área do diagnóstico de falhas: conseguiu-se uma grande diminuição da dimensionalidade nos sistemas estudados em até 93,55%, bem como uma correta detecção de anormalidades e permitiu a determinação das variáveis mais relacionadas às anormalidades do processo. As comparações feitas com as metodologias padrões permitiram demonstrar que a metodologia proposta tem resultados superiores, pois consegue detectar as anormalidades em um espaço dimensional reduzido, detectando comportamentos não lineares e diminuindo incertezas. / Fault detection and diagnosis are critical to increasing the safety, reliability, and profitability of industrial processes. Qualitative and quantitative methods and process historical data have been extensively studied. This article proposes a methodology for fault detection and diagnosis, based on historical data of processes and the creation of empirical models with the expansion of nonlinear bases (polynomial and exponential bases) and regularization techniques. To demonstrate the advantages of the proposed approach, it is compared with two standard methodologies: Principal Components Analysis (PCA) and the Partial Least Squares (PLS), performed in two case studies: a mixed heating tank and the Tennessee Eastman Process. The advantages of the proposed methodology are the reduction of the dimensionality of the data used, in addition to the effective detection of abnormalities, identifying the variables most related to the fault. Furthermore, the work contains a methodology to validate the diagnosis results consisting of variable elimination from the best empirical models with the Backward Elimination algorithm. The proposed methodology achieved a promising performance, since it can decrease the dimensionality of the studied systems up to 93.55%, reducing uncertainties, and capturing nonlinear behaviors.

[EN] A continuous and linear operator defined on a Banach space is hipercyclic if it supports a dense orbit, that is, if there exists a vector such that the set of all its iterations through the operator is dense in the space. The existence of dense orbits is closely related to the dynamic concept known as topological transitivity because, every continuous mapping defined on a complete metric space without isolated points is topologically transitive if and only if it admits points with dense orbit. Furthermore, if the operator supports a dense set of periodic points, then it is said to be chaotic in the sense of Devaney. The overall objective of this PhD thesis is to continue the study of chaotic dynamics of backward shift operators defined on sequence spaces. This PhD thesis has been structured into four chapters. The first two provide definitions, notations and basic techniques that will be used. The last two chapters present the new results we have obtained. More in detail: In the first chapter some preliminary definitions and results that will be useful in the development of later chapters are included. Notations to use are also set. In the first part of the chapter some basics of topological dynamics are presented. In the second part, the context of work is clearly stated. As already mentioned, the framework will be linear and infinite dimensional. Chapter 2 is devoted entirely to the study of the basic dynamics of the backward shift operator, specifically to the hypercyclicity and chaos of that operator defined on sequence spaces. The backward shift operator is undoubtedly the most widely used one when studying dynamic properties in this linear setting. Although this chapter does not contain new results, it seems appropriate to be included here, in an orderly manner, the results and basic proofs of the dynamic of shift operators, since it illustrates the techniques to be used in subsequent chapters. In Chapter 3, we study product recurrence properties for weighted backward shifts on sequence spaces. The backward shifts that have non-zero product recurrent points are characterized as Devaney chaotic shifts. We also give an example of weighted shift that admits points which are recurrent and distal, but not product recurrent, in contrast with the dynamics on compact sets. An example of a product recurrent point with unbounded orbit is also provided. We finish this chapter generalizing the above results to the more general setting of F-spaces or Fréchet spaces of sequences. In Chapter 4, we characterize chaos for operators of the form f(B), when defined on Banach sequence spaces, where f(z) = (a z+b)/(c z+d) is a Linear Fractional Transformation and B is the usual backward shift operator. The characterizations we obtained are 'computable' since they are expressed as conditions involving only the four complex numbers that define the transformation f. / [ES] Un operador lineal y continuo definido en un espacio de Banach es hipercíclico si admite un vector con órbita densa, es decir, si existe un vector de manera que el conjunto de todas sus iteraciones a través del operador es denso en el espacio. La existencia de órbitas densas está íntimamente relacionada con el concepto dinámico conocido como transitividad topológica ya que, toda aplicación continua definida en un espacio métrico completo sin puntos aislados es topológicamente transitiva, sí y solo si, admite puntos con órbita densa. Si además, el operador admite un conjunto denso de puntos periódicos, entonces se dice que es caótico en el sentido de Devaney. El objetivo general de esta tesis es continuar con el estudio de la dinámica caótica de los operadores desplazamiento a izquierda (operadores backward shift en inglés) definidos en espacios de sucesiones. Esta tesis doctoral se ha estructurado en cuatro capítulos. Los dos primeros proporcionan las definiciones, notaciones y técnicas básicas que se van a utilizar. Los dos últimos capítulos presentan los nuevos resultados que se han obtenido. Más detalladamente: En el primer capítulo se incluyen algunas definiciones y resultados, de carácter preliminar, que serán útiles en el desarrollo de la memoria. Se establecen también las notaciones a utilizar. En la primera parte del capítulo se recuerdan los conceptos básicos de dinámica topológica y, posteriormente, se describe el contexto de trabajo; que como ya se ha mencionado, será lineal e infinito dimensional. El Capítulo 2 está dedicado por completo al estudio de la dinámica básica del operador desplazamiento, en concreto, a la hiperciclicidad y el caos de dicho operador en espacios de sucesiones. El operador desplazamiento es sin duda el más utilizado a la hora de estudiar propiedades dinámicas. Aunque este capítulo no contiene resultados nuevos, parece procedente incluir aquí, de manera ordenada, los resultados y demostraciones básicas de la dinámica del operador desplazamiento, ya que ilustran las técnicas que se van a utilizar en capítulos posteriores. En el Capítulo 3 se estudian propiedades de recurrencia para operadores desplazamiento en espacios de sucesiones. Primero se prueba que el operador desplazamiento a izquierda es recurrente si y sólo si es hipercíclico, es decir, si es topológicamente transitivo. Se caracterizan también operadores desplazamiento que admiten puntos producto recurrentes no nulos como caóticos en el sentido de Devaney. Se dan ejemplos de operadores desplazamiento ponderados que admiten puntos que son recurrentes y distales, pero no producto recurrentes, en contraste con la dinámica en conjuntos compactos. Se observa también que existen operadores con vectores que son producto recurrente pero que tienen órbita no acotada. Se finaliza el capítulo generalizando los resultados probados para operadores desplazamiento definidos en espacios de Banach de sucesiones a un contexto más general, en concreto a F-espacios o espacios de Fréchet de sucesiones. En el Capítulo 4 se caracteriza caos para operadores de la forma f(B), definidos en espacios de sucesiones de Banach, donde f(z)=(a z+b)/(c z+d) es una Transformación Fraccional Lineal y B es el operador desplazamiento a izquierda usual. Las caracterizaciones que se obtienen son 'computables' ya que se expresan como condiciones que involucran sólo los cuatro números complejos que definen la transformación f. / [CAT] Un operador lineal i continu definit en un espai de Banach és hipercíclic si admet un vector amb òrbita densa, és a dir, si existeix un vector de manera que el conjunt de totes les seues iteracions a través de l'operador és dens en l'espai. L'existència de òrbitas denses està íntimament relacionada amb el concepte dinàmic conegut com transitivitat topològica ja que, tota aplicació contínua definida en un espai mètric complet sense punts aïllats és topològicament transitiva, sí i solament si, admet punts amb òrbita densa. Si a més, l'operador admet un conjunt dens de punts periòdics, llavors es diu que és caòtic en el sentit de Devaney. L'objectiu general d'aquesta tesi és continuar amb l'estudi de la dinàmica caòtica dels operadors desplaçament a esquerra (operadors backward shift en anglès) definits en espais de successions. Aquesta memòria s'ha estructurat en quatre capítols. Els dos primers proporcionen les definicions, notacions i tècniques bàsiques que es van a utilitzar. Els dos últims capítols presenten els nous resultats que hem obtingut. Més detalladament: En el primer capítol s'inclouen algunes definicions i resultats, de caràcter preliminar, que seran útils en el desenvolupament de la memòria. S'estableixen també les notacions a utilitzar. En la primera part del capítol es recorden els conceptes bàsics de dinàmica topològica que anem a utilitzen i, posteriorment, es descriu el context de treball, que com ja hem esmentat, serà lineal i infinit dimensional. El Capítol 2 està dedicat per complet a l'estudi de la dinàmica bàsica de l'operador desplaçament, en concret a la hiperciclicitat i el caos d'aquest operador en espais de successions. L'operador desplaçament és sens dubte el més utilitzat a l'hora d'estudiar propietats dinàmiques. Encara que aquest capítol no conté resultats nous, sembla procedent incloure ací, de manera ordenada, els resultats i demostracions bàsiques de la dinàmica de l'operador desplaçament, ja que il·lustren les tècniques que es van a utilitzar en capítols posteriors. En el Capítol 3 s'estudien propietats de recurrència per a operadors desplaçament en espais de successions. Primer es prova que l'operador desplaçament a esquerra és recurrent si i només si és hipercíclic, és a dir, si és topològicament transitiu. Es caracteritzen també operadors desplaçament que admeten punts producte recurrents no nuls com a caòtics en el sentit de Devaney. Es donen exemples d'operadors desplaçament ponderats que admeten punts que són recurrents i distales, però no producte recurrents, en contrast amb la dinàmica en conjunts compactes. S'observa també que existeixen operadors amb vectors que són producte recurrent però que tenen òrbita no fitada. Es finalitza el capítol generalitzant els resultats provats per a operadors desplaçament definits en espais de Banach de successions a un context més general, en concret a F-espais o espais de Fréchet de successions. En el Capítol 4 es caracteritza caos per a operadors de la forma f(B), definits en espais de successions de Banach, on f(z)=(a z+b)/(c z+d) és una Transformació Fraccional Lineal i B és l'operador desplaçament a esquerra usual. Les caracteritzacions que s'obtenen són 'computables' ja que s'expressen com a condicions que involucren només els quatre nombres complexos que defineixen la transformació f. / Galán Céspedes, VJ. (2015). Dinámica y caos de operadores desplazamiento [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/58986 / TESIS

La bioinformática es la aplicación de las ciencias computacionales a la gestión y análisis de datos biológicos. A partir de 2005, con la aparición de los secuenciadores de ADN de nueva generación surge lo que se conoce como Next Generation Sequencing o NGS. Un único experimento biológico puesto en marcha en una máquina de secuenciación NGS puede producir fácilmente cientos de gigabytes o incluso terabytes de datos. Dependiendo de la técnica elegida este proceso puede realizarse en unas pocas horas o días. La disponibilidad de recursos locales asequibles, tales como los procesadores multinúcleo o las nuevas tarjetas gráfi cas preparadas para el cálculo de propósito general GPGPU (General Purpose Graphic Processing Unit ), constituye una gran oportunidad para hacer frente a estos problemas. En la actualidad, un tema abordado con frecuencia es el alineamiento de secuencias de ADN. En bioinformática, el alineamiento permite comparar dos o más secuencias de ADN, ARN, o estructuras primarias proteicas, resaltando sus zonas de similitud. Dichas similitudes podrían indicar relaciones funcionales o evolutivas entre los genes o proteínas consultados. Además, la existencia de similitudes entre las secuencias de un individuo paciente y de otro individuo con una enfermedad genética detectada podría utilizarse de manera efectiva en el campo de la medicina diagnóstica. El problema en torno al que gira el desarrollo de la tesis doctoral consiste en la localización de fragmentos de secuencia cortos dentro del ADN. Esto se conoce bajo el sobrenombre de mapeo de secuencia o sequence mapping. Dicho mapeo debe permitir errores, pudiendo mapear secuencias incluso existiendo variabilidad genética o errores de lectura en el mapeo. Existen diversas técnicas para abordar el mapeo, pero desde la aparición de la NGS destaca la búsqueda por pre jos indexados y agrupados mediante la transformada de Burrows-Wheeler [28] (o BWT en lo sucesivo). Dicha transformada se empleó originalmente en técnicas de compresión de datos, como es el caso del algoritmo bzip2. Su utilización como herramienta para la indización y búsqueda posterior de información es más reciente [22]. La ventaja es que su complejidad computacional depende únicamente de la longitud de la secuencia a mapear. Por otra parte, una gran cantidad de técnicas de alineamiento se basan en algoritmos de programación dinámica, ya sea Smith-Watterman o modelos ocultos de Markov. Estos proporcionan mayor sensibilidad, permitiendo mayor cantidad de errores, pero su coste computacional es mayor y depende del tamaño de la secuencia multiplicado por el de la cadena de referencia. Muchas herramientas combinan una primera fase de búsqueda con la BWT de regiones candidatas al alineamiento y una segunda fase de alineamiento local en la que se mapean cadenas con Smith-Watterman o HMM. Cuando estamos mapeando permitiendo pocos errores, una segunda fase con un algoritmo de programación dinámica resulta demasiado costosa, por lo que una búsqueda inexacta basada en BWT puede resultar más e ficiente. La principal motivación de la tesis doctoral es la implementación de un algoritmo de búsqueda inexacta basado únicamente en la BWT, adaptándolo a las arquitecturas paralelas modernas, tanto en CPU como en GPGPU. El algoritmo constituirá un método nuevo de rami cación y poda adaptado a la información genómica. Durante el periodo de estancia se estudiarán los Modelos ocultos de Markov y se realizará una implementación sobre modelos de computación funcional GTA (Aggregate o Test o Generate), así como la paralelización en memoria compartida y distribuida de dicha plataforma de programación funcional. / Salavert Torres, J. (2014). Inexact Mapping of Short Biological Sequences in High Performance Computational Environments [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/43721 / TESIS

abstract: Cancer is a worldwide burden in every aspect: physically, emotionally, and financially. A need for innovation in cancer research has led to a vast interdisciplinary effort to search for the next breakthrough. Mathematical modeling allows for a unique look into the underlying cellular dynamics and allows for testing treatment strategies without the need for clinical trials. This dissertation explores several iterations of a dendritic cell (DC) therapy model and correspondingly investigates what each iteration teaches about response to treatment. In Chapter 2, motivated by the work of de Pillis et al. (2013), a mathematical model employing six ordinary differential (ODEs) and delay differential equations (DDEs) is formulated to understand the effectiveness of DC vaccines, accounting for cell trafficking with a blood and tumor compartment. A preliminary analysis is performed, with numerical simulations used to show the existence of oscillatory behavior. The model is then reduced to a system of four ODEs. Both models are validated using experimental data from melanoma-induced mice. Conditions under which the model admits rich dynamics observed in a clinical setting, such as periodic solutions and bistability, are established. Mathematical analysis proves the existence of a backward bifurcation and establishes thresholds for R0 that ensure tumor elimination or existence. A sensitivity analysis determines which parameters most significantly impact the reproduction number R0. Identifiability analysis reveals parameters of interest for estimation. Results are framed in terms of treatment implications, including effective combination and monotherapy strategies. In Chapter 3, a study of whether the observed complexity can be represented with a simplified model is conducted. The DC model of Chapter 2 is reduced to a non-dimensional system of two DDEs. Mathematical and numerical analysis explore the impact of immune response time on the stability and eradication of the tumor, including an analytical proof of conditions necessary for the existence of a Hopf bifurcation. In a limiting case, conditions for global stability of the tumor-free equilibrium are outlined. Lastly, Chapter 4 discusses future directions to explore. There still remain open questions to investigate and much work to be done, particularly involving uncertainty analysis. An outline of these steps is provided for future undertakings. / Dissertation/Thesis / Doctoral Dissertation Applied Mathematics 2020

博士（経営） / 85 p. / 一橋大学