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Models are important tools for understanding the hydrological processes that govern water transport in the landscape and for prediction at times and places where no observations are available. The degree of trust placed on models, however, should not exceed the quality of the data they are fed with. The overall aim of this thesis was to tune the modeling process to account for the uncertainty in the data, by identifying robust parameter values using methods from computational geometry. The methods were developed and tested on data from the Choluteca River basin in Honduras. Quality control of precipitation and discharge data resulted in a rejection of 22% percent of daily raingage data and the complete removal of one out of the seven discharge stations analyzed. The raingage network was not found sufficient to capture the spatial and temporal variability of precipitation in the Choluteca River basin. The temporal variability of discharge was evaluated through a Monte Carlo assessment of the rating-equation parameter values over a moving time window of stage-discharge measurements. Al hydrometric stations showed considerable temporal variability in the stage-discharge relationship, which was largest for low flows, albeit with no common trend. The problem with limited data quality was addressed by identifying robust model parameter values within the set of well-performing (behavioral) parameter-value vectors with computational-geometry methods. The hypothesis that geometrically deep parameter-value vectors within the behavioral set were hydrologically robust was tested, and verified, using two depth functions. Deep parameter-value vectors tended to perform better than shallow ones, were less sensitive to small changes in their values, and were better suited to temporal transfer. Depth functions rank multidimensional data. Methods to visualize the multivariate distribution of behavioral parameters based on the ranked values were developed. It was shown that, by projecting along a common dimension, the multivariate distribution of behavioral parameters for models of varying complexity could be compared using the proposed visualization tools. This has a potential to aid in the selection of an adequate model structure considering the uncertainty in the data. These methods allowed to quantify observational uncertainties. Geometric methods have only recently begun to be used in hydrology. It was shown that they can be used to identify robust parameter values, and some of their potential uses were highlighted. / Modeller är viktiga verktyg för att förstå de hydrologiska processer som bestämmer vattnets transport i landskapet och för prognoser för tider och platser där det saknas mätdata. Graden av tillit till modeller bör emellertid inte överstiga kvaliteten på de data som de matas med. Det övergripande syftet med denna avhandling var att anpassa modelleringsprocessen så att den tar hänsyn till osäkerheten i data och identifierar robusta parametervärden med hjälp av metoder från beräkningsgeometrin. Metoderna var utvecklade och testades på data från Cholutecaflodens avrinningsområde i Honduras. Kvalitetskontrollen i nederbörds- och vattenföringsdata resulterade i att 22 % av de dagliga nederbördsobservationerna måste kasseras liksom alla data från en av sju analyserade vattenföringsstationer. Observationsnätet för nederbörd befanns otillräckligt för att fånga upp den rumsliga och tidsmässiga variabiliteten i den övre delen av Cholutecaflodens avrinningsområde. Vattenföringens tidsvariation utvärderades med en Monte Carlo-skattning av värdet på parametrarna i avbördningskurvan i ett rörligt tidsfönster av vattenföringsmätningar. Alla vattenföringsstationer uppvisade stor tidsvariation i avbördningskurvan som var störst för låga flöden, dock inte med någon gemensam trend. Problemet med den måttliga datakvaliteten bedömdes med hjälp av robusta modellparametervärden som identifierades med hjälp av beräkningsgeometriska metoder. Hypotesen att djupa parametervärdesuppsättningar var robusta testades och verifierades genom två djupfunktioner. Geometriskt djupa parametervärdesuppsättningar verkade ge bättre hydrologiska resultat än ytliga, var mindre känsliga för små ändringar i parametervärden och var bättre lämpade för förflyttning i tiden. Metoder utvecklades för att visualisera multivariata fördelningar av välpresterande parametrar baserade på de rangordnade värdena. Genom att projicera längs en gemensam dimension, kunde multivariata fördelningar av välpresterande parametrar hos modeller med varierande komplexitet jämföras med hjälp av det föreslagna visualiseringsverktyget. Det har alltså potentialen att bistå vid valet av en adekvat modellstruktur som tar hänsyn till osäkerheten i data. Dessa metoder möjliggjorde kvantifiering av observationsosäkerheter. Geometriska metoder har helt nyligen börjat användas inom hydrologin. I studien demonstrerades att de kan användas för att identifiera robusta parametervärdesuppsättningar och några av metodernas potentiella användningsområden belystes.

Cette thèse porte sur les questions d'évaluation et de couverture des options dans un modèle exponentiel-Lévy avec changements de régime. Un tel modèle est construit sur un processus additif markovien un peu comme le modèle de Black- Scholes est basé sur un mouvement Brownien. Du fait de l'existence de plusieurs sources d'aléa, nous sommes en présence d'un marché incomplet et ce fait rend inopérant les développements théoriques initiés par Black et Scholes et Merton dans le cadre d'un marché complet. Nous montrons dans cette thèse que l'utilisation de certains résultats de la théorie des processus additifs markoviens permet d'apporter des solutions aux problèmes d'évaluation et de couverture des options. Notamment, nous arrivons à caracté- riser la mesure martingale qui minimise l'entropie relative à la mesure de probabilit é historique ; aussi nous dérivons explicitement sous certaines conditions, le portefeuille optimal qui permet à un agent de minimiser localement le risque quadratique associé. Par ailleurs, dans une perspective plus pratique nous caract érisons le prix d'une option Européenne comme l'unique solution de viscosité d'un système d'équations intégro-di érentielles non-linéaires. Il s'agit là d'un premier pas pour la construction des schémas numériques pour approcher ledit prix. / This thesis focuses on the pricing and hedging problems of financial derivatives in a Markov-modulated exponential-Lévy model. Such model is built on a Markov additive process as much as the Black-Scholes model is based on Brownian motion. Since there exist many sources of randomness, we are dealing with an incomplete market and this makes inoperative techniques initiated by Black, Scholes and Merton in the context of a complete market. We show that, by using some results of the theory of Markov additive processes it is possible to provide solutions to the previous problems. In particular, we characterize the martingale measure which minimizes the relative entropy with respect to the physical probability measure. Also under some conditions, we derive explicitly the optimal portfolio which allows an agent to minimize the local quadratic risk associated. Furthermore, in a more practical perspective we characterize the price of a European type option as the unique viscosity solution of a system of nonlinear integro-di erential equations. This is a rst step towards the construction of e ective numerical schemes to approximate options price.

Performance engineers face the major challenge in modeling and simulation for the after-market power system due to system degradation and measurement errors. Currently, the majority in power generation industries utilizes the deterministic data matching method to calibrate the model and cascade system degradation, which causes significant calibration uncertainty and also the risk of providing performance guarantees. In this research work, a maximum-likelihood based simultaneous data reconciliation and model calibration (SDRMC) is used for power system modeling and simulation. By replacing the current deterministic data matching with SDRMC one can reduce the calibration uncertainty and mitigate the error propagation to the performance simulation. A modeling and simulation environment for a complex power system with certain degradation has been developed. In this environment multiple data sets are imported when carrying out simultaneous data reconciliation and model calibration. Calibration uncertainties are estimated through error analyses and populated to performance simulation by using principle of error propagation. System degradation is then quantified by performance comparison between the calibrated model and its expected new & clean status. To mitigate smearing effects caused by gross errors, gross error detection (GED) is carried out in two stages. The first stage is a screening stage, in which serious gross errors are eliminated in advance. The GED techniques used in the screening stage are based on multivariate data analysis (MDA), including multivariate data visualization and principle component analysis (PCA). Subtle gross errors are treated at the second stage, in which the serial bias compensation or robust M-estimator is engaged. To achieve a better efficiency in the combined scheme of the least squares based data reconciliation and the GED technique based on hypotheses testing, the Levenberg-Marquardt (LM) algorithm is utilized as the optimizer. To reduce the computation time and stabilize the problem solving for a complex power system such as a combined cycle power plant, meta-modeling using the response surface equation (RSE) and system/process decomposition are incorporated with the simultaneous scheme of SDRMC. The goal of this research work is to reduce the calibration uncertainties and, thus, the risks of providing performance guarantees arisen from uncertainties in performance simulation.

Cette thèse présente des travaux sur l’étude et la calibration de modèles d’équations aux dérivées partielles pour la croissance tumorale. La première partie porte sur l’analyse d’un modèle de croissance tumorale pour le cas de métastases au foie de tumeurs gastro-intestinales (GIST). Le modèle est un système d’équations aux dérivées partielles couplées et prend en compte plusieurs traitements dont un traitement anti-angiogénique. Le modèle permet de reproduire des données cliniques. La première partie de ce travail concerne la preuve d’existence/unicité de la solution du modèle. La seconde partie du travail porte sur l’étude du comportement asymptotique de la solution du modèle lorsqu’un paramètre du modèle, décrivant la capacité de la tumeur à évacuer la nécrose, converge vers 0. La seconde partie de la thèse concerne le développement d’un modèle de croissance pour des sphéroïdes tumoraux ainsi que sur la calibration de ce modèle à partir de données expérimentales in vitro. L’objectif est de développer un modèle permettant de reproduire quantitativement la distribution des cellules proliférantes à l’intérieur d’un sphéroïde en fonction de la concentration en nutriments. Le travail de modélisation et de calibration du modèle a été effectué à partir de données expérimentales permettant d’obtenir la répartition spatiale de cellules proliférantes dans un sphéroïde tumoral. / In this thesis, we present several works on the study and the calibration of partial differential equations models for tumor growth. The first part is devoted to the mathematical study of a model for tumor drug resistance in the case of gastro-intestinal tumor (GIST) metastases to the liver. The model we study consists in a coupled partial differential equations system and takes several treatments into account, such as a anti-angiogenic treatment. This model is able to reproduce clinical data. In a first part, we present the proof of the existence/uniqueness of the solution to this model. Then, in a second part, we study the asymptotic behavior of the solution when a parameter of this model, describing the capacity of the tumor to evacuate the necrosis, goes to 0. In the second part of this thesis, we present the development of model for tumor spheroids growth. We also present the model calibration thanks to in vitro experimental data. The main objective of this work is to reproduce quantitatively the proliferative cell distribution in a spheroid, as a function of the concentration of nutrients. The modeling and calibration of this model have been done thanks to experimental data consisting of proliferative cells distribution in a spheroid.

This thesis examines the impacts of possible climate change on selected buildings. For simulations in program BSim the author uses climatic data of SRES scenarios, specifically models B1, A1B and A2. It also includes a research on global warming, design and optimization of the measurement and control system at the production hall and a part of the energy audit for the office building.

Tato diplomová práce se zabývá posouzením tepelně-mechanické únavy výfukového potrubí. Nejprve byla provedena rešeršní studie, ve které je rozebrán fenomén tepelně-mechanické únavy. Byly prezentovány hlavní mechanismy poškození a přístupy k jejich modelování. Diskutována byla i specifická chování materiálu vystavenému tepelně-mechanickému zatěžování. Byl vypracován přehled vhodných modelů materiálu a modelů únavové životnosti společně s algoritmem predikce tepelně-mechanické únavy komponenty. Poté byl tento teoretický základ aplikován na praktický případ výfukového potrubí podléhajícího tepelně-mechanickému zatěžování. Dva tepelně závislé elasto-plastické modely materiálu byly nakalibrovány a validovány na základě experimentálních dat. Byl vytvořen diskretizovaný konečnoprvkový model sestavy výfukového potrubí. Model tepelných okrajových podmínek byl předepsán na základě výpočtů ustáleného sdruženého přestupu tepla. Slabě sdružená tepelně-deformační úloha byla vyřešena metodou konečných prvků pro oba modely materiálů. Bylo použito paradigma nesvázaného modelu únavy, které je vhodné pro nízkocyklovou únavu. Životnost byla tedy vyhodnocena jako součást post-procesoru. Použity byly dva modely únavové životnosti – energeticky založený model a deformačně založený model. Získané hodnoty životnosti byly porovnány vzhledem k použitým modelům materiálu a modelům únavové životnosti. Nakonec jsou diskutovány závěry této práce, oblasti dalšího výzkumu a navrženy možnosti na zlepšení použitých přístupů.

Le cycle de division cellulaire et l'horloge circadienne sont deux processus fondamentaux de la régulation cellulaire qui génèrent une expression rythmique des gènes et des protéines. Dans les cellules mammifères, les mécanismes qui sous-tendent les interactions entre le cycle cellulaire et l'horloge restent très mal connus. Dans cette thèse, nous étudions ces deux oscillateurs biologiques, à la fois individuellement et en tant que système couplé, pour comprendre et reproduire leurs principales propriétés dynamiques, détecter les composants essentiels du cycle cellulaire et de l'horloge, et identifier les mécanismes de couplage. Chaque oscillateur biologique est modélisé par un système d'équations différentielles ordinaires non linéaires et ses paramètres sont calibrés par rapport à des données expérimentales: le modèle du cycle cellulaire se base sur les modifications post-traductionnelles du complexe Cdk1-CycB et mène à un oscillateur de relaxation dont la dynamique et la période sont contrôlés par les facteurs de croissance; le modèle de l'horloge circadienne reproduit l'oscillation antiphasique BMAL1/PER:CRY et l'adaptation de la durée des états d'activation et répression par rapport à deux signaux d’entrée hormonaux déphasés. Pour analyser les interactions entre les deux oscillateurs nous étudions la synchronisation des deux rythmes pour des régimes de couplage uni- ou bi-directionnels. Les simulations numériques reproduisent les ratios entre les périodes de l'horloge et du cycle cellulaire, tels que 1:1, 3:2 et 5:4. Notre étude suggère des mécanismes pour le ralentissement du cycle cellulaire avec des implications pour la conception de nouvelles chronothérapies. / The cell division cycle and the circadian clock are two fundamental processes of cellular control that generate cyclic patterns of gene activation and protein expression, which tend to be synchronous in healthy cells. In mammalian cells, the mechanisms that govern the interactions between cell cycle and clock are still not well identified. In this thesis we analyze these two biological oscillators, both separately and as a coupled system, to understand and reproduce their main dynamical properties, uncover essential cell cycle and clock components, and identify coupling mechanisms. Each biological oscillator is first modeled by a system of non-linear ordinary differential equations and its parameters calibrated against experimental data: the cell cycle model is based on post-translational modifications of the mitosis promoting factor and results in a relaxation oscillator whose dynamics and period are controlled by growth factor; the circadian clock model is transcription-based, recovers antiphasic BMAL1/PER:CRY oscillation and relates clock phases to metabolic states. This model shows how the relative duration of activating and repressing molecular clock states is adjusted in response to two out-of-phase hormonal inputs. Finally, we explore the interactions between the two oscillators by investigating the control of synchronization under uni- or bi-directional coupling schemes. Simulations of experimental protocols replicate the oscillators’ period-lock response and recover observed clock to cell cycle period ratios such as 1:1, 3:2 and 5:4. Our analysis suggests mechanisms for slowing down the cell cycle with implications for the design of new chronotherapies.

The goal of this thesis was the verification of the advanced time-dependent elasto-plastic material model for modeling diaphragm walls. Currently, this type of construction is solved usually with a combination of linear-elastic volume and plate elements. To express time-dependent behaviour, there are both, volume and plate, elements active in short-term conditions, then only volume elements in long-term conditions, while plate elements are deactivated. In this thesis, the Shotcrete material model, which can capture the time-dependent behaviour without combining two types of construction elements, is used. First, a theory of time-dependent behaviour is presented and a design of concrete structures by Eurocode 2 is discussed. Next, the Shotcrete material model is described, then used for modeling a biaxial test and calibration of compression and bending test. Following the gained knowledge, a real boundary value problem of deep excavation supported by diaphragm walls with the strut was solved. To calculate values of the internal forces and horizontal deformation in diaphragm walls, three types of material models are used.

Land and water resources degradation are the major problems on the Ethiopian highlands. Poor land use practices and improper management systems have played a significant role in causing high soil erosion rates, sediment transport and loss of agricultural nutrients. So far limited meas-ures have been taken to combat the problems. In this study a physically based watershed model, SWAT2005 was applied to the Northern Highlands of Ethiopia for modelling of the hydrology and sediment yield. The main objective of this study was to test the performance and feasibility of SWAT2005 model to examine the influence of topography, land use, soil and climatic condi-tion on streamflows, soil erosion and sediment yield. The model was calibrated and validated on four tributaries of Lake Tana as well as Anjeni watershed using SUFI-2, GLUE and ParaSol algo-rithms. SWAT and GIS based decision support system (MCE analysis) were also used to identify the most erosion prone areas in the Lake Tana Basin. Streamflows are more sensitive to the hy-drological response unites definition thresholds than subbasin discretization. Prediction of sedi-ment yield is highly sensitive to subbasin size and slope discretization. Baseflow is an important component of the total discharge within the study area that contributes more than the surface runoff. There is a good agreement between the measured and simulated flows and sediment yields with higher values of coefficients of determination and Nash Sutcliffe efficiency. The an-nual average measured sediment yield in Anjeni watershed was 24.6 tonnes/ha. The annual aver-age simulated sediment yield was 27.8 and 29.5 tonnes/ha for calibration and validation periods, respectively. The SWAT model indicated that 18.5 % of the Lake Tana Basin is erosion potential areas. Whereas the MCE result indicated that 25.5 % of the basin are erosion potential areas. The calibrated model can be used for further analysis of the effect of climate and land use change as well as other different management scenarios on streamflows and soil erosion. The result of the study could help different stakeholders to plan and implement appropriate soil and water conser-vation strategies. / QC 20101123