京都大学 / 0048 / 新制・課程博士 / 博士(医学) / 甲第20560号 / 医博第4245号 / 新制||医||1022(附属図書館) / 京都大学大学院医学研究科医学専攻 / (主査)教授 妹尾 浩, 教授 柳田 素子, 教授 西渕 光昭 / 学位規則第4条第1項該当 / Doctor of Medical Science / Kyoto University / DFAM

This thesis is about game theory, its general application to different games, and its different notions. We are going to focus on how different solutions can be found depending on how we view the game in question. We will particularly focus on games where the information is incomplete. In order to do so, we will use a game named ”The battle of sexes” as a guide throughout the entire thesis. We will adapt that game to the different kinds of games we will talk about. The importance with game theory and why it is an interesting field of study is that it gives a way to mathematically understand and analyse various situations in different other fields and real life areas. In this thesis we will not go deeper into the applications of game theory, but will mostly focus on the mathematical part of the field, and understanding how to find different desired outcomes for a given game. We will primarily lay out the fundamentals of game theory, in order for the reader to understand the basic notions of a game, a equilibria, and have the necessary knowledge to explore the field. Guillermo Owen’s book Game theory covers the field in a wider sense than this thesis, and is an interesting lecture to broaden ones knowledge on game theory.

This thesis is concerned with the solution of control and state constrained optimal control problems, which are governed by elliptic partial differential equations. Problems of this type are challenging since they suffer from the low regularity of the multiplier corresponding to the state constraint. Applying an augmented Lagrangian method we overcome these difficulties by working with multiplier approximations in $L^2(\Omega)$. For each problem class, we introduce the solution algorithm, carry out a thoroughly convergence analysis and illustrate our theoretical findings with numerical examples. The thesis is divided into two parts. The first part focuses on classical PDE constrained optimal control problems. We start by studying linear-quadratic objective functionals, which include the standard tracking type term and an additional regularization term as well as the case, where the regularization term is replaced by an $L^1(\Omega)$-norm term, which makes the problem ill-posed. We deepen our study of the augmented Lagrangian algorithm by examining the more complicated class of optimal control problems that are governed by a semilinear partial differential equation. The second part investigates the broader class of multi-player control problems. While the examination of jointly convex generalized Nash equilibrium problems (GNEP) is a simple extension of the linear elliptic optimal control case, the complexity is increased significantly for pure GNEPs. The existence of solutions of jointly convex GNEPs is well-studied. However, solution algorithms may suffer from non-uniqueness of solutions. Therefore, the last part of this thesis is devoted to the analysis of the uniqueness of normalized equilibria. / Die vorliegende Arbeit beschäftigt sich mit der Lösung von kontroll- und zustandsbeschränkten Optimalsteuerungsproblemen mit elliptischen partiellen Differentialgleichungen als Nebenbedingungen. Da die zur Zustandsbeschränkung zugehörigen Multiplikatoren nur eine niedrige Regularität aufweisen, sind Probleme dieses Typs besonders anspruchsvoll. Zur Lösung dieser Problemklasse wird ein augmentiertes Lagrange-Verfahren angewandt, das Annäherungen der Multiplikatoren in $L^2(\Omega)$ verwendet. Für jede Problemklasse erfolgt eine Präsentation des Lösungsalgorithmus, eine sorgfältige Konvergenzanalysis sowie eine Veranschaulichung der theoretischen Ergebnisse durch numerische Beispiele. Die Arbeit ist in zwei verschiedene Themenbereiche gegliedert. Der erste Teil widmet sich klassischen Optimalsteuerungsproblemen. Dabei wird zuerst der linear-quadratische und somit konvexe Fall untersucht. Hier setzt sich das Kostenfunktional aus einem Tracking-Type Term sowie einem $L^2(\Omega)$-Regularisierungsterm oder einem $L^1(\Omega)$-Term zusammen. Wir erweitern unsere Analysis auf nichtkonvexe Probleme. In diesem Fall erschwert die Nichtlinearität der zugrundeliegenden partiellen Differentialgleichung die Konvergenzanalysis des zugehörigen Optimalsteuerungsproblems maßgeblich. Der zweite Teil der Arbeit nutzt die Grundlagen, die im ersten Teil erarbeitet wurden und untersucht die allgemeiner gehaltene Problemklasse der Nash-Mehrspielerprobleme. Während die Untersuchung von konvexen verallgemeinerten Nash-Gleichsgewichtsproblemen (engl.: Generalized Nash Equilibrium Problem, kurz: GNEP) mit einer für alle Spieler identischen Restriktion eine einfache Erweiterung von linear elliptischen Optimalsteuerungsproblemen darstellt, erhöht sich der Schwierigkeitsgrad für Mehrspielerprobleme ohne gemeinsame Restriktion drastisch. Die Eindeutigkeit von normalisierten Nash-Gleichgewichten ist, im Gegensatz zu deren Existenz, nicht ausreichend erforscht, was insbesondere eine Schwierigkeit für Lösungsalgorithmen darstellt. Aus diesem Grund wird im letzten Teil dieser Arbeit die Eindeutigkeit von Lösungen gesondert betrachtet.

This thesis is concerned with a certain class of algorithms for the solution of constrained optimization problems and generalized Nash equilibrium problems in Hilbert spaces. This class of algorithms is inspired by the alternating direction method of multipliers (ADMM) and eliminates the constraints using an augmented Lagrangian approach. The alternating direction method consists of splitting the augmented Lagrangian subproblem into smaller and more easily manageable parts. Before the algorithms are discussed, a substantial amount of background material, including the theory of Banach and Hilbert spaces, fixed-point iterations as well as convex and monotone set-valued analysis, is presented. Thereafter, certain optimization problems and generalized Nash equilibrium problems are reformulated and analyzed using variational inequalities and set-valued mappings. The analysis of the algorithms developed in the course of this thesis is rooted in these reformulations as variational inequalities and set-valued mappings. The first algorithms discussed and analyzed are one weakly and one strongly convergent ADMM-type algorithm for convex, linearly constrained optimization. By equipping the associated Hilbert space with the correct weighted scalar product, the analysis of these two methods is accomplished using the proximal point method and the Halpern method. The rest of the thesis is concerned with the development and analysis of ADMM-type algorithms for generalized Nash equilibrium problems that jointly share a linear equality constraint. The first class of these algorithms is completely parallelizable and uses a forward-backward idea for the analysis, whereas the second class of algorithms can be interpreted as a direct extension of the classical ADMM-method to generalized Nash equilibrium problems. At the end of this thesis, the numerical behavior of the discussed algorithms is demonstrated on a collection of examples. / Die vorliegende Arbeit behandelt eine Klasse von Algorithmen zur Lösung restringierter Optimierungsprobleme und verallgemeinerter Nash-Gleichgewichtsprobleme in Hilberträumen. Diese Klasse von Algorithmen ist angelehnt an die Alternating Direction Method of Multipliers (ADMM) und eliminiert die Nebenbedingungen durch einen Augmented-Lagrangian-Ansatz. Im Rahmen dessen wird in der Alternating Direction Method of Multipliers das jeweilige Augmented-Lagrangian-Teilproblem in kleinere Teilprobleme aufgespaltet. Zur Vorbereitung wird eine Vielzahl grundlegender Resultate präsentiert. Dies beinhaltet entsprechende Ergebnisse aus der Literatur zu der Theorie von Banach- und Hilberträumen, Fixpunktmethoden sowie konvexer und monotoner mengenwertiger Analysis. Im Anschluss werden gewisse Optimierungsprobleme sowie verallgemeinerte Nash-Gleichgewichtsprobleme als Variationsungleichungen und Inklusionen mit mengenwertigen Operatoren formuliert und analysiert. Die Analysis der im Rahmen dieser Arbeit entwickelten Algorithmen bezieht sich auf diese Reformulierungen als Variationsungleichungen und Inklusionsprobleme. Zuerst werden ein schwach und ein stark konvergenter paralleler ADMM-Algorithmus zur Lösung von separablen Optimierungsaufgaben mit linearen Gleichheitsnebenbedingungen präsentiert und analysiert. Durch die Ausstattung des zugehörigen Hilbertraums mit dem richtigen gewichteten Skalarprodukt gelingt die Analyse dieser beiden Methoden mit Hilfe der Proximalpunktmethode und der Halpern-Methode. Der Rest der Arbeit beschäftigt sich mit Algorithmen für verallgemeinerte Nash-Gleichgewichtsprobleme, die gemeinsame lineare Gleichheitsnebenbedingungen besitzen. Die erste Klasse von Algorithmen ist vollständig parallelisierbar und es wird ein Forward-Backward-Ansatz für die Analyse genutzt. Die zweite Klasse von Algorithmen kann hingegen als direkte Erweiterung des klassischen ADMM-Verfahrens auf verallgemeinerte Nash-Gleichgewichtsprobleme aufgefasst werden. Abschließend wird das Konvergenzverhalten der entwickelten Algorithmen an einer Sammlung von Beispielen demonstriert.

In this thesis we consider a set of mobile users that employ cloud-based computation offloading. In computation offloading, user energy consumption can be decreased by uploading and executing jobs on a remote server, rather than processing the jobs locally. In order to execute jobs in the cloud however, the user uploads must occur over a base station channel which is shared by all of the uploading users. Since the job completion times are subject to hard deadline constraints, this restricts the feasible set of jobs that can be remotely processed, and may constrain the users ability to reduce energy usage. The system is modelled as a competitive game in which each user is interested in minimizing its own energy consumption. The game is subject to the real-time constraints imposed by the job execution deadlines, user specific channel bit rates, and the competition over the shared communication channel. The thesis shows that for a variety of parameters, a game where each user independently sets its offloading decisions always has a pure Nash equilibrium, and a Gauss-Seidel method for determining this equilibrium is introduced. Results are presented which illustrate that the system always converges to a Nash equilibrium using the Gauss-Seidel method. Data is also presented which show the number of Nash equilibria that are found, the number of iterations required, and the quality of the solutions. We find that the solutions perform well compared to a lower bound on total energy performance. / Thesis / Master of Applied Science (MASc)

The objective of this study was to investigate the diet-induced metabolic changes that affect the brain tissue of juvenile pigs with NAFLD. This study explored the liver- brain axis and metabolic markers in the frontal cortex (FC) affected by liver damage. 18 male (M) and 20 female (F) Iberian pigs were randomly allocated to 1 of 3 high-fructose high-fat liquid diets (lard, olive oil, and coconut oil) and fed for 10 consecutive weeks. “Healthy” Iberian pigs were fed a eucaloric diet to establish a physiological baseline. Protein precipitation extraction using ultra-performance liquid chromatography-tandem quadrupole mass spectrometry was performed for primary metabolic and bile acid assays on FC samples. Univariate data were analyzed by one-way ANOVA, which included diet as the fixed effect and both replicate and pen nested in the diet as random effects. A more pronounced separation was observed in the PLS-DA between the COC and LAR/OLI diets. LC, C14:0 SM, and kynurenine, all metabolites linked to brain health, showed elevated levels in COC-fed pigs and reduced levels in animals fed OLI. Each of the three diets demonstrated heightened ratios of secondary bile acids to primary bile acids, with OLI-fed pigs showing increased TDCA:CA and TLCA:CA ratios associated with neurodegeneration (MahmoudianDehkordi et al., 2019). In conclusion, results may suggest that LAR could represent a more favorable dietary intervention for promoting brain health in pediatric NAFLD but further research is required.

Indiana University-Purdue University Indianapolis (IUPUI) / Hepatic fibrosis is a cellular repair mechanism that is initiated upon prolonged damage to the liver, resulting in an accumulation of excess extracellular matrix. This eventually leads to the formation of scar tissue, which disrupts the hepatic architecture and causes liver dysfunction. Hepatic stellate cells (HSCs) play a major role in hepatic fibrosis. However, the molecular mechanisms remain incompletely understood. Yes-associated protein (YAP) and transcriptional coactivator with PDZ-binding motif (TAZ or WWTR1), key players of the Hippo pathway, have been implicated in the liver fibrosis, but the HSC-specific functions of YAP and TAZ are largely unclear. Here we have identified Sirtuin 6 (SIRT6), an NAD+ dependent deacetylase, as a key epigenetic regulator in the protection against hepatic fibrosis by suppressing the YAP/TAZ activity. SIRT6 has been previously implicated in the regulation of the canonical transforming growth factor β (TGFβ)-SMAD3 pathway. This study has revealed the significant contribution of the non-canonical pathways including the Hippo pathway to the development of hepatic fibrosis. HSC-specific Sirt6 deficient mice developed severe fibrosis when fed a high-fat-cholesterol-cholate diet compared to their wild-type counterparts. YAP became more active in the SIRT6-deficient HSCs. Expression of the YAP/TAZ downstream genes like CTGF, CYR61 and ANKRD1 were elevated in the SIRT6-deficient HSCs. Biochemical and mutagenic analyses have revealed that SIRT6 deacetylates YAP and TAZ at key lysine residues and reprograms the composition of the TEA domain transcription factor complex to suppress the YAP/TAZ function in the hepatic fibrogenesis.

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