Management of water resources is afflicted with uncertainties. Nowadays it is facing more and new uncertainties since pace and dimension of changes (e.g. climatic, demographic) are accelerating and are likely to increase even more in the future. Hence it is crucial to find pragmatic ways to deal with these uncertainties in water management. This thesis argues for an analytical yet pragmatic approach to enable decision-makers to deal with uncertainties in a more explicit and systematic way and allow for better informed decisions. The approach is based on the concept of framing and mental models, referring to different ways in which people make sense of the world and of uncertainties. It is analysed how uncertainties are framed and dealt with in water management practice and strategies are elaborated how dealing with uncertainties can be improved in water management practice. The research for this thesis has been closely linked to the EU research project NeWater (New Approaches to Adaptive Water Management under Uncertainty, www.newater.uos.de) (2005-2009). It draws on practical experiences of water managers at local and regional level in river basin management in three case studies, i.e. the German Wupper, the Dutch Kromme Rijn, both sub basins of the river Rhine, and the Doñana region located in the Guadalquivir Estuary in Spain. For the assessment of framing of uncertainty two different methods were developed and applied in the three river basins. Both aim at identifying parameters of importance in the process of framing uncertainty in order to understand how uncertainties get framed. The empirical research confirmed that indeed water managers are faced with a range of uncertainties and that so far no systematic approaches are applied for dealing with those in management practice. The results in the case studies suggest that there are no universal findings as to how actors frame uncertainties but rather that framings are dependent on the respective uncertainty situation, on roles (e.g. project leader, public administration, scientist etc.), and most often on personal traits. The case study findings moreover suggest that there are no universally valid parameters of influence in the framing of uncertainties. Neither could a clear superiority of one approach over the other be discerned. Nonetheless, the parameters of framing of uncertainty proved to be a supportive tool for preparing and structuring decision-making in the case studies and developing improvement options for dealing with uncertainty. Beyond the results of the development of approaches for the assessment of framing of uncertainty in water management practice, processes of communication and learning turned out to be of major importance. Making framings of uncertainties explicit by help of parameters of framing proved to be useful in the case studies for revealing different points of views on the uncertainties and with regard to the strategies to deal with them. This is a first step in enabling dialogue among opposed framers and an important precondition for reframing and learning which is crucial for the long-term performance in management of natural resources.

Nous étudions dans cette thèse divers aspects du transport optimal martingale en dimension plus grande que un, de la dualité à la structure locale, puis nous proposons finalement des méthodes d’approximation numérique.On prouve d’abord l’existence de composantes irréductibles intrinsèques aux transports martingales entre deux mesures données, ainsi que la canonicité de ces composantes. Nous avons ensuite prouvé un résultat de dualité pour le transport optimal martingale en dimension quelconque, la dualité point par point n’est plus vraie mais une forme de dualité quasi-sûre est démontrée. Cette dualité permet de démontrer la possibilité de décomposer le transport optimal quasi-sûre en une série de sous-problèmes de transports optimaux point par point sur chaque composante irréductible. On utilise enfin cette dualité pour démontrer un principe de monotonie martingale, analogue au célèbre principe de monotonie du transport optimal classique. Nous étudions ensuite la structure locale des transports optimaux, déduite de considérations différentielles. On obtient ainsi une caractérisation de cette structure en utilisant des outils de géométrie algébrique réelle. On en déduit la structure des transports optimaux martingales dans le cas des coûts puissances de la norme euclidienne, ce qui permet de résoudre une conjecture qui date de 2015. Finalement, nous avons comparé les méthodes numériques existantes et proposé une nouvelle méthode qui s’avère plus efficace et permet de traiter un problème intrinsèque de la contrainte martingale qu’est le défaut d’ordre convexe. On donne également des techniques pour gérer en pratique les problèmes numériques. / In this thesis, we study various aspects of martingale optimal transport in dimension greater than one, from duality to local structure, and finally we propose numerical approximation methods.We first prove the existence of irreducible intrinsic components to martingal transport between two given measurements, as well as the canonicity of these components. We have then proved a duality result for optimal martingale transport in any dimension, point by-point duality is no longer true but a form of quasi safe duality is demonstrated. This duality makes it possible to demonstrate the possibility of decomposing the quasi-safe optimal transport into a series of optimal transport subproblems point by point on each irreducible component. Finally, this duality is used to demonstrate a principle of martingale monotony, analogous to the famous monotonic principle of classical optimal transport. We then study the local structure of optimal transport, deduced from differential considerations. We thus obtain a characterization of this structure using tools of real algebraic geometry. We deduce the optimal martingal transport structure in the case of the power costs of the Euclidean norm, which makes it possible to solve a conjecture that dates from 2015. Finally, we compared the existingnumerical methods and proposed a new method which proves more efficient and allows to treat an intrinsic problem of the martingale constraint which is the defect of convex order. Techniques are also provided to manage digital problems in practice.

Un des défis majeurs en traitement radar consiste à identifier une cible cachée dans un environnement bruité. Pour ce faire, il est nécessaire de caractériser finement les propriétés statistiques du bruit, en particulier sa matrice de covariance. Sous l'hypothèse gaussienne, cette dernière est estimée par la matrice de covariance empirique (SCM) dont le comportement est parfaitement connu. Cependant, dans de nombreuses applications actuelles, tels les systèmes radar modernes à haute résolution par exemple, les données collectées sont de nature hétérogène, et ne peuvent être proprement décrites par un processus gaussien. Pour pallier ce problème, les distributions symétriques elliptiques complexes, caractérisant mieux ces phénomènes physiques complexes, ont été proposées. Dans ce cas, les performances de la SCM sont très médiocres et les M-estimateurs apparaissent comme une bonne alternative, principalement en raison de leur flexibilité par rapport au modèle statistique et de leur robustesse aux données aberrantes et/ou aux données manquantes. Cependant, le comportement de tels estimateurs reste encore mal compris. Dans ce contexte, les contributions de cette thèse sont multiples.D'abord, une approche originale pour analyser les propriétés statistiques des M-estimateurs est proposée, révélant que les propriétés statistiques des M-estimateurs peuvent être bien approximées par une distribution de Wishart. Grâce à ces résultats, nous analysons la décomposition de la matrice de covariance en éléments propres. Selon l'application, la matrice de covariance peut posséder une structure particulière impliquant valeurs propres multiples contenant les informations d'intérêt. Nous abordons ainsi divers scénarios rencontrés dans la pratique et proposons des procédures robustes basées sur des M-estimateurs. De plus, nous étudions le problème de la détection robuste du signal. Les propriétés statistiques de diverses statistiques de détection adaptative construites avec des M-estimateurs sont analysées. Enfin, la dernière partie de ces travaux est consacrée au traitement des images radar à synthèse d'ouverture polarimétriques (PolSAR). En imagerie PolSAR, un effet particulier appelé speckle dégrade considérablement la qualité de l'image. Dans cette thèse, nous montrons comment les nouvelles propriétés statistiques des M-estimateurs peuvent être exploitées afin de construire de nouvelles techniques pour la réduction du speckle. / One of the main challenges in radar processing is to identify a target hidden in a disturbance environment. To this end, the noise statistical properties, especially the ones of the disturbance covariance matrix, need to be determined. Under the Gaussian assumption, the latter is estimated by the sample covariance matrix (SCM) whose behavior is perfectly known. However, in many applications, such as, for instance, the modern high resolution radar systems, collected data exhibit a heterogeneous nature that cannot be adequately described by a Gaussian process. To overcome this problem, Complex Elliptically Symmetric distributions have been proposed since they can correctly model these data behavior. In this case, the SCM performs very poorly and M-estimators appear as a good alternative, mainly due to their flexibility to the statistical model and their robustness to outliers and/or missing data. However, the behavior of such estimators still remains unclear and not well understood. In this context, the contributions of this thesis are multiple.First, an original approach to analyze the statistical properties of M-estimators is proposed, revealing that the statistical properties of M-estimators can be approximately well-described by a Wishart distribution. Thanks to these results, we go further and analyze the eigendecomposition of the covariance matrix. Depending on the application, the covariance matrix can exhibit a particular structure involving multiple eigenvalues containing the information of interest. We thus address various scenarios met in practice and propose robust procedures based on M-estimators. Furthermore, we study the robust signal detection problem. The statistical properties of various adaptive detection statistics built with M-estimators are analyzed. Finally, the last part deals with polarimetric synthetic aperture radar (PolSAR) image processing. In PolSAR imaging, a particular effect called speckle significantly degrades the image quality. In this thesis, we demonstrate how the new statistical properties of M-estimators can be exploited in order to build new despeckling techniques.

Indiana University-Purdue University Indianapolis (IUPUI) / Nanocomposite ceramics have been widely studied in order to tailor desired properties at high temperatures. Methodologies for development of material design are still under effect. While finite element modeling (FEM) provides significant insight on material behavior, few design researchers have addressed the design paradox that accompanies this rapid design space expansion. A surrogate optimization model management framework has been proposed to make this design process tractable. In the surrogate optimization material design tool, the analysis cost is reduced by performing simulations on the surrogate model instead of high fidelity finite element model. The methodology is incorporated to and the optimal number of silicon carbide (SiC) particles, in a silicon-nitride(Si3N4) composite with maximum fracture energy [2]. Along with a deterministic optimization algorithm, model uncertainties have also been considered with the use of robust design optimization (RDO) method ensuring a design of minimum sensitivity to changes in the parameters. These methodologies applied to nanocomposites design have a significant impact on cost and design cycle time reduced.

In this thesis, I explore everyday militarisation in UN peace operations by studying how Sweden's s 'peace nation' narrative is possibly militarised by participating in the robust peacekeeping operation in Mali. The aim is to increase understanding around how militarisation occurs in modern peace operations, domains that are meant to be peaceful but are becoming increasingly war-like. The Swedish narrative is generated through interviews with Swedish peacekeepers that have previously been deployed to Mali and through readings of the Swedish Armed Forces blog Malibloggen. The material is analysed through a narrative analysis inspired by Mieke Bal (2009). I find that the Swedish narrative is partly militarised during participation in the mission, as it can be argued that Sweden arranged its sense of belonging around military values and chose military modes of conflict resolution over civilian to some extent. The soldiers were also cognitively preparing for war and military measures were partially normalised. This result illustrates that when countries that regard themselves as 'peace nations' take part in militarised UN PSOs, their narrative can become militarised to some extent as they arrange their sense of belonging around values of war and military force. This, in turn, has implications for the spread of militarisation across the globe, potentially leading to a lower threshold of war.

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The control and optimization of chemical plants is a major area of research as it has the potential to improve both economic output and plant safety. It is often prudent to separate control and optimization tasks of varying complexities and time scales, creating a hierarchical control structure. Within this structure, it is beneficial for one control layer to be able to account for the effects of other layers. A clear example of this, and the basis of this work, is closed-loop dynamic real-time optimization (CL-DRTO), in which an economic optimization method considers both the plant behavior and the effects of an underlying model predictive controller (MPC). This technique can be expanded on to allow its use and methods to be employed in a greater diversity of applications, particularly unstable and uncertain plant environments. First, this work seeks to improve on existing robust MPC techniques, which incorporate plant uncertainty via direct multi-scenario modelling, by also including future MPC behavior through the use of the CL modelling technique of CL-DRTO. This allows the CL robust MPC to account for how future MPC executions will be affected by uncertain plant behavior. Second, Lyapunov MPC (LMPC) is a generally nonconvex technique which focuses on effective control of plants which exhibit open-loop unstable behavior. A new convex LMPC formulation is presented here which can be readily embedded into a CL-DRTO scheme. Next, uncertainty handling is incorporated directly into a CL-DRTO via a robust multi-scenario method to allow for the economic optimization to take uncertain plant behavior into account while also modelling MPC behavior under plant uncertainty. Finally, the robust CL-DRTO method is computationally expensive, so a decomposition method which separates the robust CL-DRTO into its respective scenario subproblems is developed to improve computation time, especially for large optimization problems. / Thesis / Doctor of Philosophy (PhD) / It is common for control and optimization of chemical plants to be performed in a multi-layered hierarchy. The ability to predict the behavior of other layers or the future behavior of the same layer can improve overall plant performance. This thesis presents optimization and control frameworks which use this concept to more effectively control and economically optimize chemical plants which are subject to uncertain behavior or instability. The strategy is shown, in a series of simulated case studies, to effectively control chemical plants with uncertain behavior, control and optimize unstable plant systems, and economically optimize uncertain chemical plants. One of the drawbacks of these strategies is the relatively large computation time required to solve the optimization problems. Therefore, for uncertain systems, the problem is separated into smaller pieces which are then coordinated towards a single solution. This results in reduced computation time.