Selection methods for subgame perfect Nash equilibrium in a continuous setting

This thesis is focused on the issue of selection of Subgame Perfect Nash Equilibrium (SPNE) in the class of one-leader N-follower two-stage games where the players have a continuum of actions. We are mainly interested in selection methods satisfying the following significant features in the theory of equilibrium selection for such a class of games: obtaining an equilibrium selection by means of a constructive (in the sense of algorithmic) and motivated procedure, overcoming the difficulties due to the possible non-single-valuedness of the followers' best reply correspondence, providing motivations that would induce players to choose the actions leading to the designed selection, and revealing the leader to know the followers' best reply correspondence. Firstly, we analyze the case where the followers' best reply correspondence is assumed to be single-valued: in this case we show that finding SPNEs is equivalent to find the Stackelberg solutions of the Stackelberg problem associated to the game. Moreover, as regards to the related arising issue of the sufficient conditions ensuring the uniqueness of the followers' best reaction, we prove an existence and uniqueness result for Nash equilibria in two-player normal-form games where the action sets are Hilbert spaces and which allows the two compositions of the best reply functions to be not a contraction mapping. Furthermore, by applying such a result to the class of weighted potential games, we show the (lack of) connections between the Nash equilibria and the maximizers of the potential function. Then, in the case where the followers' best reply correspondence is not assumed to be single-valued, we examine preliminarily the SPNE selections deriving by exploiting the solutions of broadly studied problems in Optimization Theory (like the strong Stackelberg, the weak Stackelberg and the intermediate Stackelberg problems associated to the game). Since such selection methods, although behaviourally motivated, do not fit all the desirable features mentioned before, we focus on designing constructive methods to select an SPNE based on the Tikhonov regularization and on the proximal point methods (linked to the Moreau-Yosida regularization). After illustrated these two tools both in the optimization framework and in the applications to the selection of Nash equilibria in normal-form games, we present a constructive selection method for SPNEs based on the Tikhonov regularization in one-leader N-follower two-stage games (with N=1 and N>1), and a constructive selection method for SPNEs based on a learning approach which has a behavioural interpretation linked to the costs that players face when they deviate from their current actions (relying on the proximal point methods) in one-leader one-follower two-stage games

Development of imaging-based response predictors for personalized radiotherapy in head and neck cancer

Tumor response to chemoradiotherapy is heterogeneous in patients with head and neck cancer. At the same time, head and neck radiotherapy can lead to significant toxicity in treated patients. Personalization of treatment could improve response to treatment while minimizing side effects. The largest bottleneck to employ personalization approaches are the lack of methods for response and toxicity prediction. In this thesis we therefore provide improved approaches for response prediction. In part one, we present improved MRI techniques to measure response before and early during treatment. In part two we present dose response models for osteoradionecrosis of the mandible incorporating key spatial information and the equivalent uniform dose as a generalizable dose variable across different fractionation schemes. The presented MRI techniques and dose response models can now be validated in larger groups of patients, after which they could contribute to personalized treatment planning and decision making processes

Development of imaging-based response predictors for personalized radiotherapy in head and neck cancer

Tumor response to chemoradiotherapy is heterogeneous in patients with head and neck cancer. At the same time, head and neck radiotherapy can lead to significant toxicity in treated patients. Personalization of treatment could improve response to treatment while minimizing side effects. The largest bottleneck to employ personalization approaches are the lack of methods for response and toxicity prediction. In this thesis we therefore provide improved approaches for response prediction. In part one, we present improved MRI techniques to measure response before and early during treatment. In part two we present dose response models for osteoradionecrosis of the mandible incorporating key spatial information and the equivalent uniform dose as a generalizable dose variable across different fractionation schemes. The presented MRI techniques and dose response models can now be validated in larger groups of patients, after which they could contribute to personalized treatment planning and decision making processes

The medical applications of hyperpolarized Xe and nonproton magnetic resonance imaging

Hyperpolarized 129Xe (HP 129Xe) magnetic resonance imaging (MRI) is a relatively young field which is experiencing significant advancements each year. Conventional proton MRI is widely used in clinical practice as an anatomical medical imaging due to its superb soft tissue contrast. HP 129Xe MRI, on the other hand, may provide valuable information about internal organs functions and structure. HP 129Xe MRI has been recently clinically approved for lung imaging in the United Kingdom and the United States. It allows quantitative assessment of the lung function in addition to structural imaging. HP 129Xe has unique properties of anaesthetic, and may transfer to the blood stream and be further carried to the highly perfused organs. This gives the opportunity to assess brain perfusion with HP 129Xe and perform molecular imaging. However, the further progression of the HP 129Xe utilization for brain perfusion quantification and molecular imaging implementation is limited by the absence of certain crucial milestones. This thesis focused on providing important stepping stones for the further development of HP 129Xe molecular imaging and brain imaging. The effect of glycation on the spectroscopic characteristics of HP 129Xe was studied in whole sheep blood with magnetic resonance spectroscopy. An additional peak of HP 129Xe bound to glycated hemoglobin was observed. This finding should be implemented in the spectroscopic HP 129Xe studies in patients with diabetes. [...

Sequence Optimization in Pseudo-Continuous Arterial Spin Labeling

Dissertação de Mestrado em Engenharia Biomédica apresentada à Faculdade de Ciências e Tecnologia da Universidade de Coimbra.Arterial Spin Labeling (ASL) é uma técnica de Ressonância Magnética que fornece medidas quantitativas de fluxo sanguíneo cerebral (FSC) regional, de forma não invasiva, utilizando a água presente no sangue arterial como um marcador endógeno. Anormalidades ou perturbações no processo de perfusão podem ter efeitos marcantes, especialmente no cérebro, que é um órgão muito perfundido. De facto, várias condições patológicas (nomeadamente acidentes vasculares cerebrais agudos, tumores cerebrais, doenças neurodegenerativas e epilepsia) estão associadas a valores anormais de FSC. Portanto, ASL tem um valor fundamental no diagnóstico e acompanhamento do tratamento de doenças do cérebro. Pseudo-continuous ASL (pCASL) é o método de implementação recomendado para estudos ASL, uma vez que combina as vantagens de métodos anteriores, uma elevada relação sinal-ruído (S/N) e eficiência de inversão. O objetivo deste trabalho consiste na otimização e implementação de uma sequência pCASL desenvolvida in-house. Foram realizados quatro estudos para avaliar o desempenho dos parâmetros da sequência para medir perfusão na matéria cinzenta e o impacto na qualidade da imagem usando dois head coils diferentes: i) determinação da largura de banda e flip angle ótimos dos pulsos de inversão, ii) implementação de supressão do sinal do tecido estático completa e incompleta, iii) comparação de balanced/ unbalanced pCASL e sequências de aquisição nomeadamente Echo Planar Imging (EPI) e True Fast Imaging with Steady-state free Precession (TrueFISP) e iv) comparação da qualidade das imagens de perfusão obtidas com dois head coils diferentes. As imagens de perfusão foram adquiridas através de medições experimentais em voluntários saudáveis, para cada estudo. A análise dos dados foi realizada com o software MATLAB, usando scripts programados in-house e SPM8, e o impacto dos diferentes parâmetros no S/N e no FSC resultantes foi avaliado. Considerando os parâmetros testados, a análise dos resultados sugere o uso de pulsos de inversão Gauss, flip angle igual a 24º ou 28º e supressão completa do sinal estático, a fim de maximizar o S/N das imagens resultantes. Os resultados estão de acordo com publicações anteriores sobre a influência da supressão do sinal do tecido estático e flip angle no S/N. A maior contribuição deste trabalho consistiu no desenvolvimento de uma sequência de confiança adequada para futuras investigações experimentais de perfusão XII cerebral. No futuro seria interessante testar a capacidade da sequência para detetar alterações de perfusão em estudos funcionais. Palavras-Chave: Ressonância Magnética; Arterial Spin Labeling; Pseudo-Continuous Arterial Spin Labeling; Otimização Experimental; Sequênci

Proceedings Of The International Workshop On Numerical Modeling For Underground Mine Excavation Design

Numerical models play a significant role in the design of safe underground mining excavations and support systems. Advances in the capabilities of numerical modeling software, together with ever increasing computational speeds, have made it possible to investigate the very nature of the large-scale rock mass and its response to mining excavations. The improved understanding of the rock response obtained from modeling enhances our designs, resulting in greater stability and safety of the mining excavations. To help advance the state of the art in this field, the National Institute for Occupational Safety and Health organized the International Workshop on Numerical Modeling for Underground Mine Excavation Design. The workshop was held in Asheville, NC, on June 28, 2009, in association with the 43rd U.S. Rock Mechanics Symposium. The proceedings include 10 papers from leading rock mechanics and numerical modeling experts in the United States, Canada, Australia, and Germany. The papers address a wide range of issues, including various numerical modeling approaches, rock mass modeling, and applications in coal and metal mines

Proceedings of the International Workshop on Numerical Modeling for Underground Mine Excavation Design

"Numerical models play a significant role in the design of safe underground mining excavations and support systems. Advances in the capabilities of numerical modeling software, together with ever increasing computational speeds, have made it possible to investigate the very nature of the large-scale rock mass and its response to mining excavations. The improved understanding of the rock response obtained from modeling enhances our designs, resulting in greater stability and safety of the mining excavations. To help advance the state of the art in this field, the National Institute for Occupational Safety and Health organized the International Workshop on Numerical Modeling for Underground Mine Excavation Design. The workshop was held in Asheville, NC, on June 28, 2009, in association with the 43rd U.S. Rock Mechanics Symposium. The proceedings include 10 papers from leading rock mechanics and numerical modeling experts in the United States, Canada, Australia, and Germany. The papers address a wide range of issues, including various numerical modeling approaches, rock mass modeling, and applications in coal and metal mines." - NIOSHTIC-2An efficient approach to numerical simulation of coal mine-related -- geotechnical issues / D. P. Adhikary and H. Guo -- A review of recent experience in modeling of caving / M. Board and M. E. Pierce -- Characterization of natural fragmentation using a discrete fracture network approach and implications for current rock mass classification systems / D. Elmo, S. Rogers, and D. Kennard -- Three-dimensional modeling of large arrays of pillars for coal mine design / G.S. Esterhuizen, and C. Mark -- Numerical model evaluation of floor-bearing capacity in coal mines / M. M. Gadde -- It is better to be approximately right than precisely wrong: why simple models work in mining geomechanics / R. E. Hammah and J. H. Curran -- An overview of calibrating and using the LaModel program for coal mine design / K. A. Heasley -- Deep coal longwall panel design for strong strata: the influence of software choice on results / M. K. Larson and J. K. Whyatt -- Practical application of numerical modeling for the study of sudden floor heave failure mechanisms / H. Maleki, C. Stewart, R. Stone, and J. Abshire -- Advanced numerical solutions for strata control in mining / A. Studeny and C. Scioredited by Gabriel S. Esterhuizen, Christopher Mark, Ted M. Klemetti, and Robert J. Tuchman."June 2009."Includes bibliographical references