京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第21535号 / 理博第4442号 / 新制||理||1638(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)准教授 加藤 周, 教授 重川 一郎, 教授 並河 良典 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

Background: CEO duality has been a highly discussed topic for the last 20 years. The trend shows that more and more companies and countries move towards a separation of the roles of CEO and chairman of the board, but the empirical results show little evidence that this is beneficial for firm performance. The two main accepted theories explaining if CEO duality has a positive or negative effect on firm performance has been the agency theory and the stewardship theory Purpose: The purpose of this study is to explain CEO duality´s effect on firm performance based on the agency and stewardship theory by analyzing and comparing the U.S. as an agency country versus Sweden & Japan as a stewardship country. The study also aims to contribute with evidence if a stewardship country as Sweden instead would benefit from a CEO duality board structure.   Method: To be able to fulfill our purpose was a deductive approach used for this study. A quantitative empirical method is used and data for the various dependent, independent and control variables were collected in order to get the results needed to be able to give answers to the stated hypotheses. The data collection consists of data from a total of 200 firms. 100 firms were collected from the U.S. market in order to represent the agency theory where 50 had a CEO duality board structure and 50 without. Furthermore, data from 50 Swedish non-CEO duality companies and 50 Japanese firms with CEO duality were collected as the stewardship country. The data was obtained between the years 2016-2020. Conclusion: The result indicates that CEO duality on some performance variables have a negative impact on firm performance. Contrary to our first hypothesis, our results suggested evidence that CEO duality had a negative effect on firm performance in the stewardship country (Sweden & Japan). In line with our second hypothesis, our results also suggested that CEO duality also had a negative impact on firm performance in the agency country, USA. Although not all performance variables were significant, the thesis could not provide any support for the stewardship theory explaining CEO duality relationship on firm performance.

It is well known that the group completion of the classifying space of the free permutative category is Ω∞ S∞, i.e. stable homotopy of the 0-sphere. Quillen´s S-1S construction can be applied to the free permutative category, which has a pictorial description by pseudo-tangles, and this leads to another pictorial descripted category G which has the classifying space Ω∞ S∞. With help of this model G we can give generators for the homotopy groups of Ω∞ S∞ for i=0,1,2. As a further application, we compute the fundamental group of the free permutative category with duality and show that the association of a duality structure on the categorial level does not lead to a group completion on the level of classifying spaces.

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.

Ce travail s’inscrit dans le domaine de l’ordonnancement à base de programmation par contraintes. Dans ce cadre, la contrainte de ressource la plus fréquemment rencontrée est la cumulative, qui permet de modéliser des processus se déroulant de manière parallèle.Nous étudions dans cette thèse la contrainte cumulative en nous aidant d’outils rarement utilisés en programmation par contraintes (analyse polyédrale, dualité de la programmation linéaire, dualité de la géométrie projective) et proposons deux contributions pour le domaine.Le renforcement cumulatif est un moyen de générer des contraintes cumulatives redondantes plus serrées, de manière analogue à la génération de coupes en programmation linéaire entière. Il s'agit ici de l'un des premiers exemples de contrainte globale redondante.Le Raisonnement Énergétique est une propagation extrêmement puissante pour la contrainte cumulative, avec jusque-là une complexité élevée en O(n^{3}). Nous proposons un algorithme qui calcule cette propagation avec une complexité O(n^{2}log n), ce qui constitue une amélioration significative de cet algorithme connu depuis plus de 25 ans. / This work falls in the scope of constraint-based scheduling. In this framework, the most frequently encountered resource constraint is the cumulative, which enables the modeling of parallel processes.In this thesis, we study the cumulative constraint with the help of tools rarely used in constraint programming (polyhedral analysis, linear programming duality, projective geometry duality) and propose two contributions for the domain.Cumulative strengthening is a means of generating tighter redundant cumulative constraints, analogous to the generation of cuts in integer linear programming. This is one of the first examples of a redundant global constraint.Energy Reasoning is an extremely powerful propagation for cumulative constraint, with hitherto a high complexity of O(n^{3}). We propose an algorithm that computes this propagation with a O(n^{2}log n) complexity, which is a significant improvement of this algorithm known for more than 25 years.

The study of integral operators on spaces of analytic functions has been considered for the past few decades. However, most of the studies in this line are based on spaces of analytic functions of the unit disc. For the analytic spaces of the upper half-plane, the literature is still scanty. Most notable is the recent work of Siskakis and Arvanitidis concerning the classical Ces`aro operator on Hardy spaces of the upper half-plane. In this dissertation, we characterize all continuous one-parameter groups of automorphisms of the upper halfplane according to the nature and location of their fixed points into three distinct classes, namely, the scaling, the translation, and the rotation groups. We then introduce the associated groups of weighted composition operators on both Hardy and weighted Bergman spaces of the half-plane. Interestingly, it turns out that these groups of composition operators form three strongly continuous groups of isometries. A detailed analysis of each of these groups of isometries is carried out. Specifically, we determine the spectral properties of the generators of every group, and using both spectral and semigroup theory of Banach spaces, we obtain concrete representations of the resolvents as integral operators on both Hardy and Bergman spaces of the half-plane. For the scaling group, the resulting resolvent operators are exactly the Ces`aro-like operators. The spectral properties of the obtained integral operators is also determined. Finally, we detail the theory of both Szeg¨o and Bergman projections of the half-plane, and use it to determine the duality properties of these spaces. Consequently, we obtain the adjoints of the resolvent operators on the reflexive Hardy and Bergman spaces of the half-plane.

This dissertation is focused on three lines of work. In the first part, we consider aspects of holography and gauge/gravity duality in lower and higher dimensions. In particular, we study the duality for exact solutions localized on the Randal-Sundrum 2-branes. We also test if some holographic principles in general relativity can be generalized to include higher derivative theories of gravity; namely Lovelock gravity. In the second part we consider the role of pseudo Nambu-Goldstone bosons (pNGBs) in inflationary cosmology. Specifically, we construct an inflationary model using string theory axions, and use these pNGBs to produce the observed coherent magnetic field in the Universe. The third part of the thesis is devoted to the study of the phenomenology of emergent phenomena. we investigated whether one could test if diffeomorphism invariance, the sacred symmetry of general relativity, is emergent. We also construct a new minimal vectorial Standard Model, and argue that the absence of mirror particles predicted by this model can give us a hint about the fundamental nature of space.

In this thesis we consider the application of Fenchel's duality theory and gradient-based methods for the training and hyperparameter optimization of Support Vector Machines. We show that the dualization of convex training problems is possible theoretically in a rather general formulation. For training problems following a special structure (for instance, standard training problems) we find that the resulting optimality conditions can be interpreted concretely. This approach immediately leads to the well-known notion of support vectors and a formulation of the Representer Theorem. The proposed theory is applied to several examples such that dual formulations of training problems and associated optimality conditions can be derived straightforwardly. Furthermore, we consider different formulations of the primal training problem which are equivalent under certain conditions. We also argue that the relation of the corresponding solutions to the solution of the dual training problem is not always intuitive. Based on the previous findings, we consider the application of customized optimization methods to the primal and dual training problems. A particular realization of Newton's method is derived which could be used to solve the primal training problem accurately. Moreover, we introduce a general convergence framework covering different types of decomposition methods for the solution of the dual training problem. In doing so, we are able to generalize well-known convergence results for the SMO method. Additionally, a discussion of the complexity of the SMO method and a motivation for a shrinking strategy reducing the computational effort is provided. In a last theoretical part, we consider the problem of hyperparameter optimization. We argue that this problem can be handled efficiently by means of gradient-based methods if the training problems are formulated appropriately. Finally, we evaluate the theoretical results concerning the training and hyperparameter optimization approaches practically by means of several example training problems.

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The goal of this thesis is two-fold. On the one hand, it pursues to provide a contribution to the conjugate duality by proposing a new duality concept, which can be understood as an umbrella for different meaningful perturbation methods. On the other hand, this thesis aims to investigate minimax location problems by means of the duality concept introduced in the first part of this work, followed by a numerical approach using epigraphical splitting methods. After summarizing some elements of the convex analysis as well as introducing important results needed later, we consider an optimization problem with geometric and cone constraints, whose objective function is a composition of n+1 functions. For this problem we propose a conjugate dual problem, where the functions involved in the objective function of the primal problem are decomposed. Furthermore, we formulate generalized interior point regularity conditions for strong duality and give necessary and sufficient optimality conditions. As applications of this approach we determine the formulae of the conjugate as well as the biconjugate of the objective function of the primal problem and analyze an optimization problem having as objective function the sum of reciprocals of concave functions. In the second part of this thesis we discuss in the sense of the introduced duality concept three classes of minimax location problems. The first one consists of nonlinear and linear single minimax location problems with geometric constraints, where the maximum of nonlinear or linear functions composed with gauges between pairs of a new and existing points will be minimized. The version of the nonlinear location problem is additionally considered with set-up costs. The second class of minimax location problems deals with multifacility location problems as suggested by Drezner (1991), where for each given point the sum of weighted distances to all facilities plus set-up costs is determined and the maximal value of these sums is to be minimized. As the last and third class the classical multifacility location problem with geometrical constraints is considered in a generalized form where the maximum of gauges between pairs of new facilities and the maximum of gauges between pairs of new and existing facilities will be minimized. To each of these location problems associated dual problems will be formulated as well as corresponding duality statements and necessary and sufficient optimality conditions. To illustrate the results of the duality approach and to give a more detailed characterization of the relations between the location problems and their corresponding duals, we consider examples in the Euclidean space. This thesis ends with a numerical approach for solving minimax location problems by epigraphical splitting methods. In this framework, we give formulae for the projections onto the epigraphs of several sums of powers of weighted norms as well as formulae for the projection onto the epigraphs of gauges. Numerical experiments document the usefulness of our approach for the discussed location problems.