Many evolutionary game theory papers have obtained their results when the bounded rationality which creates change vanishes. In our first chapter we consider whether such results are actually a good reflection of a population whose bounded rationality is small yet persistent. Our model consists of a two type population with three stable equilibria. Firstly we find that results from the standard vanishing noise approach can be very different from those obtained when noise is small but constant. Secondly when the results differ the small and persistent noise approach selects an equilibrium with a co-existence of conventions. Our second chapter generalises the model of our first chapter to a population of many player types and several stable equilibria. Firstly we produce the characteristics of the long run equilibria under vanishing noise analysis. Secondly we find that the introduction of a small neutral group into a divided society can produce a welfare improving switch in the long run equilibrium towards social co-ordination. Our third chapter combines the model of the second chapter with the message of the first. We show numerically that the long run location of a heterogenous population with extremely low levels of bounded rationality can be completely different to the equilibria selected through vanishing noise analysis. We also show that such an event is not a rare occurrence and find that over a third of populations are misrepresented by stochastic stability. Our final chapter conducts a review of the literature on social threshold models. We give a thorough description of each paper and discuss the main assumptions that drive the key results.

In this thesis we investigate the quantum aspects of black holes near extremality. In particular we seek evidence that a near-extremal black hole has a microscopic description in terms of a two dimensional conformal field theory (CFT). We first demonstrate how the low temperature expansion of the first law of thermodynamics leads to an expression for the entropy of extremal black holes which can be recast as the Cardy formula for the entropy of a chiral two dimensional CFT, in agreement with the Extremal Black Hole/CFT correspondence. We apply Sen’s entropy function formalism to fortify this result by reproducing it in a gravitational setup. We extend our first law analysis to a class of near-Extremal Vanishing Horizon (near-EVH) black holes. These black holes have low entropy and temperature, and their geometries contain locally asymptotically AdS3 throats in the near horizon region. The low temperature expansion of the first law is compatible with the first law for a three dimensional BTZ black hole. As the BTZ black hole has an AdS/CFT description in terms of a non-chiral two dimensional CFT, our result can be viewed as thermodynamic evidence for the EVH/CFT correspondence, which states that gravity on the near horizon EVH geometry is described by a 2d CFT. A near-EVH black hole, or low energy excitation around an EVH black hole, is described by excitations of the dual 2d CFT. As case studies of our first law analysis and the EVH/CFT correspondence, we focus on two asymptotically AdS5× S5 classes of near-EVH black holes. The two cases have interesting individual properties and, by the AdS/CFT correspondence, dual descriptions as states in N = 4 super Yang-Mills theory . We can compare these (UV) pictures to the two dimensional descriptions that emerge from the near horizon, or low energy, dynamics. All EVH near horizon geometries have local AdS3 factors which become BTZ black holes when the configurations are excited from EVH to near-EVH. In the study of static black holes with three R-charges, we examine the non-BPS and near- BPS regimes separately. While the non-BPS near horizon limit is locally regular, in the near- BPS case the near horizon procedure requires focussing geometrically on a strip of the horizon, and the degrees of freedom of the dual CFT2 can be associated with stretched strings between giant gravitons in the transverse five-sphere. The near-EVH limit of non-BPS stationary charged black holes is obtained by taking the vanishing limit of one or both of the angular momenta. When one of the momenta is small, the AdS3 angle is a combination of azimuthal angles in the AdS5 and S5 regions of the geometry. Taking the vanishing limit of both of the angular momenta leads to a near horizon limit which contains a BTZ black hole that is non-trivially fibred by a three-sphere. For each of the case studies we use the AdS3/CFT2 dictionary to specify dual IR CFT2 descriptions of the black holes. We outline a map between the UV and IR near-EVH excitations and demonstrate how the first law reduces in the near-EVH limit to the first law of a BTZ black hole. As a consistency check we compare our results with those of the Kerr/CFT correspondence.

Tsoi, Hung Ming. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 88-90). / Abstracts in English and Chinese. / Preface --- p.7 / Chapter 1 --- Kahler Manifold --- p.10 / Chapter 1.1 --- Hermitian Manifold --- p.12 / Chapter 1.2 --- Kahler Manifold --- p.13 / Chapter 1.2.1 --- "Positive (l,l)-form" --- p.15 / Chapter 2 --- Vector Bundle --- p.16 / Chapter 2.1 --- Holomorphic Vector Bundle and Connection --- p.17 / Chapter 2.2 --- Hermitian Connection and Chern Connection --- p.18 / Chapter 2.2.1 --- Existence of Chern connection on a holomorphic vector bundle --- p.19 / Chapter 2.3 --- Curvature --- p.21 / Chapter 2.4 --- Positivity of Vector Bundles --- p.23 / Chapter 2.5 --- Chern Classes and Holomorphic Line Bundle --- p.24 / Chapter 2.5.1 --- Chern class in axiomatic approach --- p.25 / Chapter 2.5.2 --- Chern class in algebraic topology --- p.26 / Chapter 2.5.3 --- Chern class in terms of curvature --- p.27 / Chapter 2.5.4 --- In the case of hermitian line bundle --- p.28 / Chapter 3 --- Analytic Technique on Kahler Manifold --- p.30 / Chapter 3.1 --- Dolbeault Cohomology --- p.30 / Chapter 3.2 --- Commutator Relations on Kahler Manifold --- p.31 / Chapter 3.2.1 --- Commutator relation on a line bundle --- p.32 / Chapter 3.3 --- Hodge Theory --- p.33 / Chapter 3.4 --- Bochner Technique --- p.35 / Chapter 3.4.1 --- Bochner-Kodaira-Nakano identity --- p.36 / Chapter 4 --- Kodaira Vanishing Theorem and L2 estimate of d --- p.38 / Chapter 4.1 --- Kodaira Vanishing Theorem --- p.39 / Chapter 4.2 --- Extension of Kodaira Vanishing Theorem by L2 Method --- p.44 / Chapter 4.2.1 --- Plurisubharmonic functions and weakly pseudoconvex Kahler manifold --- p.47 / Chapter 5 --- Multiplier Ideal Sheaf --- p.55 / Chapter 5.1 --- Algebraic Properties of Multiplier Ideal Sheaf --- p.56 / Chapter 5.2 --- Some Calculations of Multiplier Ideal Sheaf --- p.59 / Chapter 6 --- Nadel Vanishing Theorem --- p.62 / Chapter 6.1 --- Nadel Vanishing Theorem by L2 Estimate of d --- p.62 / Chapter 6.2 --- The Original Setting of Nadel --- p.64 / Chapter 6.2.1 --- S-bounded and S-null sequence --- p.65 / Chapter 6.2.2 --- Multiplier ideal sheaf by Nadel --- p.67 / Chapter 6.3 --- Nadel Vanishing Theorem by Computation of Cech Cohomology --- p.69 / Chapter 6.3.1 --- L2 estimate of d --- p.69 / Chapter 6.3.2 --- Koszul cochain --- p.70 / Chapter 6.3.3 --- The cohomology vanishing theorem --- p.73 / Chapter 7 --- Kawamata-Viehweg Vanishing Theorem --- p.77 / Chapter 7.1 --- Numerically Effective Line Bundle --- p.77 / Chapter 7.2 --- Kawamata-Viehweg Vanishing Theorem --- p.85 / Bibliography --- p.88

Elections are the engine that drives democracy. The central question of this dissertation relates to the speed of that engine: How long does it take for elections to reflect changing preferences in the electorate? The findings presented in this dissertation suggest that electoral change is the result of a gradual process of natural selection in which the political environment, rather than district service activity, is the key variable. Comparing elections data across different types of district environment, I find evidence that the environment affects levels of competition and electoral outcomes. Utilizing an event history statistical model to examine various risk factors for electoral defeat, I find that the political environment of the district is the most important factor influencing the risk of defeat even when controlling for district service behaviors. Over time, the district environment operates as a self-correcting mechanism, purging political misfits and replacing them with representatives who better reflect the ideology of the district. Electoral change typically results more from evolution than revolution – it may not occur quickly, and it may not occur in every district, but it does occur when and where it is needed.

Cette thèse porte sur l'étude de deux modèles mathématiques pour une tâchevisuelle élémentaire: le regroupement perceptuel de points 2D. Le premier modèletraite la détection d'alignements de point perceptuellement relevant. Ledeuxième modèle étend ce cadre au cas plus général de la bonne continuation depoints. Dans les deux cas, les modèles proposés sont invariants au changementd'échelle, et non supervisés. Ils sont conçus pour être robustes au bruit,jusqu'au point où les structures à détecter deviennent mathématiquementimpossibles de distinguer du bruit. Les expériences presentées montrent unecohérence entre notre théorie de détéction et les processus de démasquage ayantlieu dans la perception humaine.Les modèles proposés sont basés dans la méthodologie a contrario, uneformalisation du principe de non accidentalité dans la théorie de laperception. Cette thèse fait deux contributions au méthodes a contrario. Une estl'introduction de seuils de détection adaptatifs qui sont conditionnels auxenvirons des structures évaluées. La deuxième contribution est une nouvellestratégie raffinée pour résoudre la redondance de plusieurs détectionssignificatives.Finalement, l'utilité du détecteur d'alignements de points comme outil générald'analyse de données est démontrée avec son application a une problème classiqueen vision par ordinateur: la détection de points de fuite. Le détecteurd'alignements de points proposé, utilisé avec des outils standards, produit desrésultats améliorant l'état de l'art.Visant à la recherche reproductible, toutes les méthodes sont soumis au journalIPOL, en incluant descriptions détaillées des algorithmes, du code sourcecommenté et démonstrations en ligne pour chaque méthode. / This thesis studies two mathematical models for an elementary visual task: theperceptual grouping of dot patterns. The first model handles the detection ofperceptually relevant arrangements of collinear dots. The second model extendsthis framework to the more general case of good continuation of dots. In bothcases, the proposed models are scale invariant and unsupervised. They aredesigned to be robust to noise, up to the point where the structures to detectbecome mathematically indistinguishable from noise. The experiments presentedshow a good match of our detection theory with the unmasking processes takingplace in human perception, supporting their perceptual plausibility.The proposed models are based on the a contrario framework, a formalization ofthe non-accidentalness principle in perception theory. This thesis makes twocontributions to the a contrario methodology. One is the introduction ofadaptive detection thresholds that are conditional to the structure's localsurroundings. The second is a new refined strategy for resolving the redundancyof multiple meaningful detections. Finally, the usefulness of the collinear point detector as a general patternanalysis tool is demonstrated by its application to a classic problem incomputer vision: the detection of vanishing points. The proposed dot alignmentdetector, used in conjunction with standard tools, produces improved resultsover the state-of-the-art methods in the literature.Aiming at reproducible research, all methods are submitted to the IPOL journal,including detailed descriptions of the algorithms, commented reference sourcecodes, and online demonstrations for each one.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20753号 / 理博第4329号 / 新制||理||1622(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)教授 森脇 淳, 教授 雪江 明彦, 教授 並河 良典 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

Sensory deficits represent a major global public health problem. According to the World Health Organization, vision impairment affects an estimated 300 million people worldwide, and hearing impairment affects an estimated 360 million people worldwide. Consistent clinical evaluations for all individuals with sensory deficits cannot be practically realized due to the rising costs of healthcare, capital and labor limitations, and inaccessibility to healthcare due to a multitude of factors including proximity. The high prevalence of visual and hearing deficits can be lessened through consistent, comprehensive, at-home testing which can allow a larger amount of the affected and at-risk populations to be screened for abnormal function earlier and prior to permanent loss, and provide a wealth of patient-specific data that can be used to understand the time-scale of diseases and monitor the effectiveness of clinical interventions in unprecedented detail. While health-oriented smartphone applications exhibit a strong presence on the app stores, these applications are seldom vetted by expert scientists, engineers, and clinicians, and there are considerable opportunities for methodological improvements. The present work discusses the creation, calibration, and proof-of-concept, preliminary validation of a suite of psychophysical tests implemented as smartphone applications that can be utilized to rapidly and objectively quantify several functional sensory behaviors including flicker sensitivity, contrast sensitivity, visual acuity, and hearing-in-noise. Rigorous steps were undertaken to perform the necessary calibrations (a feat not routinely achieved by the creators of existing medical smartphone applications), and ensure the technical validity of the varying stimuli presented. Preliminary tests in the clinic have documented the potential of these tests to objectively provide numerous quantifications of, but not limited to, individual visual and hearing function, and variation between normal and abnormal subjects and function. The foundation laid by this work allows novel psychophysical tests to rapidly be implemented, vetted, and added to this battery of publicly and universally accessible medical smartphone applications.

We introduce a hybrid approach in which images of an urban scene are automatically alignedwith a base geometry of the scene to determine model-relative external camera parameters. Thealgorithm takes as input a model of the scene and images with approximate external cameraparameters and aligns the images to the model by extracting the facades from the images andaligning the facades with the model by minimizing over a multivariate objective function. Theresulting image-pose pairs can be used to render photo-realistic views of the model via texturemapping.Several natural extensions to the base hybrid reconstruction technique are also introduced. Theseextensions, which include vanishing point based calibration refinement and video stream basedreconstruction, increase the accuracy of the base algorithm, reduce the amount of data that mustbe provided by the user as input to the algorithm, and provide a mechanism for automaticallycalibrating a large set of images for post processing steps such as automatic model enhancementand fly-through model visualization.Traditionally, photo-realistic urban reconstruction has been approached from purely image-basedor model-based approaches. Recently, research has been conducted on hybrid approaches, whichcombine the use of images and models. Such approaches typically require user assistance forcamera calibration. Our approach is an improvement over these methods because it does notrequire user assistance for camera calibration.

L'objet principal de cette thèse est de généraliser un certain nombre de résultats bien connus de la géométrie algébrique au cas k"{a}hlerien non nécessairement projectif. On généralise d'abord le théorème d'annulation de Nadel au cas k"{a}hlerien arbitraire. On obtient aussi un cas particulier du théorème d'annulation de Kawamata-Viehweg pour les variétés qui admettent une fibration vers un tore dont la fibre générique est projective. En utilisant ce résultat, on étudie le problème de déformation pour les variétés k"{a}hlériennes compactes sous une hypothèse portant sur les fibrés canoniques. On étudie enfin les variétés à fibré anticonique nef. On montre que si le fibré anticanonique est nef, alors le fibré tangent est à pentes semi-positif relative à la filtration de Harder-Narasimhan pour la polarization $omega_X ^{n-1}$. Comme application, on donne une preuve simple de la surjectivité de l'application d'Albanese, et on étudie aussi la trivialité locale de l'application d'Albanese. / The aim of this thesis is to generalize a certain number of results of algebraic geometry to K"{a}hler geometry. We first generalize the Nadel vanishing theorem to arbitrary compact K"{a}hler manifolds. We prove also a particular version of the Kawamata-Viehweg vanishing theorem for manifolds admitting a fibration to a torus such that the generic fiber is projective. Using this result, we study the theory of deformations of compact Kähler manifolds under certain assumptions on their canonical bundles. Finally, we study varieties with nef anticanonical bundles. We prove that the slopes of the Harder-Narasimhan filtration of the tangent bundles with respect to a polarization of the form $omega_X^{n-1}$ are semi-positive. As an application, we give a simple proof of the surjectivity of the Albanese map, and we investigate also the local triviality of the Albanese map.

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