Everything in the universe has an opposite, and exists in complete harmony. Without one, we would not experience the other. It is this duality of experiences, perspectives and actions that I seek to study in this thesis. Dual natures are typically found in the unconventional life of Latin America, where barriers are not strictly defined and there is a constant mix of formality and informality. It is in this region, with its culture and history, that I plan to build a type of architecture that seeks to inspire the inhabitant to explore the possibility that one element can act in two opposing ways. Carnaval and Ash Wednesday will be the backdrops of the study, as I plan on designing both a market place and a church dedicated to these holidays. How can we perceive an element one way, but then completely different the next day? To answer this question I will develop both a church and a market in Panama City, Panama. / Master of Architecture

Cette thèse s'inscrit dans le cadre de la physique mathématique des interactions fondamentales. Elle porte sur l'étude des théories de champs qui décrivent les particules élémentaires. En particulier, les théories de champs de spin élevé (plus grand ou égal à 2) sont analysées. Mis à part pour le graviton, vecteur supposé des interactions gravitationnelles, il n'y a aucun indice que ces champs soient présents dans la nature. Cependant leur existence n'est pas impossible théoriquemement et ils interviennent dans la théorie des cordes, candidate pour une théorie quantique d'unification de toutes les forces fondamentales y compris la gravitation. En effet, les modes de vibration de la corde élémentaire sont décrits par des champs de spin élevé.   Dans ce travail, la dimension de l'espace-temps est laissée arbitraire, ce qui entraine la possibilité d'avoir plusieurs sortes (= représentations) de champs différentes ayant le même spin. Le premier aspect traité dans cette thèse concerne les dualités, symétries qui relient entre elles plusieurs théories. Il est montré que différentes représentations de champs de spin élevé sont duales au niveau de l'action. En particulier, en dimension quatre, la dualité échange la composante électrique et la composante magnétique d'un même champs. Cette propriété est ensuite utilisée pour introduire des sources magnétiques pour les champs de spin élevé. La construction généralise les travaux de Dirac sur le couplage au champ électromagnétique de monopoles magnétiques. Une condition de quantification est également dérivée pour des quantités conservées, qui généralise la condition de quantification de Dirac pour la charge électrique en présence de monopoles magnétiques. La deuxième partie de la thèse est consacrée aux interactions de champs de spin élevé. L'analyse est effectuée dans le formalisme de champs et d'antichamps dévelopé par Batalin et Vilkovsky. Elle repose sur la procédure de déformation de l'équation maîtresse mise au point par Henneaux et Barnich. Les champs étudiés sont les champs de spin deux exotiques (c-à-d différents du graviton) ainsi que les champs de spin trois complètement symétriques. Pour les premiers, il est prouvé que toutes les interactions doivent être abélienne. Il n'y a donc pas d'équivalent de la théorie d'Einstein pour ces champs. Dans le cas des champs de spin trois, plusieurs vertex cohérents au premier ordre sont obtenus. <br> In this thesis, we consider two aspects of higher-spin gauge field theories: dualities and interactions. The first aspect is related to the presence of dualities, i.e., 'hidden' symmetries among gauge field theories. Do two higher-spin theories corresponding to different irreducible representations of the Poincaré group have the same physical content. Duality relations were already known at the level of the equations of motion and Bianchi identities, here we prove (in some cases) that these dualities hold also at the level of the action. As a consequence, the dual theories are formally equivalent. For example, in five space-time dimensions the spin-two theory of Pauli and Fierz is dual to the theory of a mixed-symmetry spin-two field written by Curtright. In four space-time dimensions the duality exchanges the electric and magnetic degrees of freedom of the field. This property leads us to introduce external magnetic sources for higher-spin fields, thereby generalizing to arbitrary spin the work of Dirac on the coupling of magnetic monopoles to the electromagnetic field. Similarly to the quantization condition on the product of the electric and magnetic charges for electromagnetism, there is a quantization condition on the product of conserved ``electric' and ``magnetic' charges for higher spins. The second aspect of higher-spin gauge field theories that is analysed in this thesis is the problem of interactions. Self-interactions of exotic spin-two gauge fields are studied, as well as self-interactions of completely symmetric spin-three fields. This is done in the BRST field-antifield formalism developped by Batalin and Vilkovisky, using the technique of consistent deformations of the master equation proposed by Barnich and Henneaux.

My thesis is about the dualistic connotation of the cage. The original intention of a cage is to create a boundary to enclose a target. However, a cage has a positive intent for protection. With this idea, I created kinetic sculpture and installation pieces referencing cages. While I understand the negative association of cages, I made them seductive through the careful consideration of lightness, fragility, and sheen. I have been exploring forms and material qualities to express the contradictory connotation of cages. Most of my work is made of wire because I have a great interest in the delicate nature of wirework. I use silver as my primary material for its impression of duality. Silver is desirable with its economic worth, but also it attracts our senses with its ability to be shiny and reflective. Conversely it could be manipulated to have a cold distant industrial look. In the end I wanted my audience to have unsettling desires.

Butoh and Surrealism share some common features, three of which are: duality, symbolism and the manipulation of time. This project is an examination of the intersection of these elements and the development of a movement practice using these three, shared focusing lenses of Butoh and Surrealism, culminating in a performance. The methodology of this study sought to generate movement through improvisation and studio exercises based upon a melded Butoh/Surrealist universe developed through applied research in the convergent elements of duality, symbolism and the manipulation of time. The elements that I distilled ultimately informed movement choices shaping a movement offering; a generated example of what could happen when this choreographic process is applied.

by Yung Siu-Pang. / Includes bibliographical references / Thesis (M.Ph.)--Chinese University of Hong Kong, 1985

by Lau Wai-tong. / Bibliography: leaves 45-47 / Thesis (M.Ph.)--Chinese University of Hong Kong, 1985

Holographic dualities are now an established tool in the study of universal properties of strongly coupled field theories. Yet, theories without translational symmetry are still poorly understood in this context. In this dissertation, we investigate three new approaches to this challenging problem. The first part of the dissertation concerns a class of phenomenological holographic models in which momentum relaxation can be achieved without breaking translational symmetry in the dual geometry. In particular, we focus on an example in which the dual geometry is similar to anti-de Sitter (AdS) Brans-Dicke theory. We study the thermodynamic and transport properties of the model and show that for strong momentum relaxation and low temperatures the model has insulator-like behaviour. In the second part, we go beyond the effective description and consider holographic theories which explicitly break translational symmetry. From the perspective of gravity, these theories translate to geometries that vary explicitly in the boundary space-like coordinates. We refer to these geometries as 'inhomogeneous' and investigate two approaches to study them. The first is motivated by the question: "what happens to a homogeneous geometry when coupled with a field varying randomly in space?". Starting from an AdS geometry at zero or finite temperature, we show that a spatially varying random Maxwell potential drives the dual field theory to a non-trivial infra-red fixed point characterised by an emerging scale invariance. Thermodynamic and transport properties of this disordered ground state are also discussed. The second is motivated by the complementary question: "how does a random geometry affect a probe field?". In the weak disorder limit, we show that disorder induces an additional power-law decay in the dual correlation functions. For certain choices of geometry profile, this contribution becomes dominant in the infra-red, indicating the breaking of perturbation theory and the possible existence of a phase transition induced by disorder. The third and last part of this dissertation switches from the gravity to the field theoretical side of the duality. We discuss the Sachdev-Ye-Kitaev (SYK) model, a disordered many-body model with distinctive black hole-like properties. We provide analytical and numerical evidence that these holographic properties are robust against a natural one-body deformation for a finite range of parameters. Outside this interval, this system undergoes a chaotic-integrable transition.

In part I of this dissertation, certain rich geometric properties hidden behind quadratic 0-1 programming are investigated. Especially, we derive new lower bounding methods and variable fixation techniques for quadratic 0-1 optimization problems by investigating geometric features of the ellipse contour of a (perturbed) convex quadratic function. These findings further lead to some new optimality conditions for quadratic 0-1 programming. Integrating these novel solution schemes into a proposed solution algorithm of a branch-and-bound type, we obtain promising preliminary computational results. / In part II of this dissertation, we present new results of the duality gap between the binary quadratic optimization problem and its Lagrangian dual. We first derive a necessary and sufficient condition for the zero duality gap and discuss its relationship with the polynomial solvability of the problem. We then characterize the zeroness of duality gap by the distance, delta, between the binary set and certain affine space C. Finally, we discuss a computational procedure of the distance delta. These results provide new insights into the duality gap and polynomial solvability of binary quadratic optimization problems. / The unconstraint quadratic binary problem (UBQP), as a classical combinatorial problem, finds wide applications in broad field and human activities including engineering, science, finance, etc. The NP-hardness of the combinatorial problems makes a great challenge to solve the ( UBQP). The main purpose of this research is to develop high performance solution method for solving (UBQP) via the geometric properties of the objective ellipse contour and the optimal solution. This research makes several contributions to advance the state-of-the-art of geometric approach of (UBQP). These contributions include both theoretical and numerical aspects as stated below. / Liu, Chunli. / Adviser: Duan Li. / Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3764. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 140-153). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

In this thesis we study the theory and algorithms for separated continuous linear programming (SCLP) and its extensions. / Throughout this thesis, some numerical examples are used to illustrate the algorithms that we propose. In particular, we solve a special LQ control problem with sign constraints on the state and the control variables as an instance of SCCP, yielding a new solution method for such kind of LQ control problems. / We first investigate the relationships among SCLP, the dual of SCLP and the corresponding discretized versions of them. By using the symmetric primal and dual structure and an even partition of the time interval [0, T], we show that the strong duality holds between SCLP and its dual problem under some mild assumption. This is actually an alternative proof for the strong duality theorem. The other constructive proof is due to Weiss [50]. Our new proof is more direct and can be easily extended to prove the same strong duality results for the extensions of SCLP. Based on these results, we propose an approximation algorithm which solves SCLP with any prescribed precision requirement. Our algorithm is in fact a polynomial-time approximation (PTA) scheme. The trade-off between the quality of the solution and the computational effort is explicit. / We then study the extensions of SCLP; that is, separated continuous conic programming (SCCP) and its generalized version (GSCCP). It turns out that our results on SCLP can be readily extended to SCCP and GSCCP. To our knowledge, SCCP and GSCCP are new models with novel applications. / Wang Xiaoqing. / "June 2005." / Advisers: Shuzhong Zhang; David Da-Wei Yao. / Source: Dissertation Abstracts International, Volume: 67-01, Section: B, page: 0520. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (p. 122-127). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

Lau, Fu Man. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 94-97). / Abstract also in Chinese. / Abstract --- p.i / Acknowledgements --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Notations and Preliminaries --- p.4 / Chapter 2.1 --- Introduction --- p.4 / Chapter 2.2 --- Basic notations --- p.4 / Chapter 2.3 --- On the properties of subdifferentials --- p.8 / Chapter 2.4 --- On the properties of normal cones --- p.9 / Chapter 2.5 --- Some computation rules for conjugate functions --- p.13 / Chapter 2.6 --- On the properties of epigraphs --- p.15 / Chapter 2.7 --- Set-valued analysis --- p.19 / Chapter 2.8 --- Weakly* sum of sets in dual spaces --- p.21 / Chapter 3 --- Sum of Epigraph Constraint Qualification (SECQ) --- p.31 / Chapter 3.1 --- Introduction --- p.31 / Chapter 3.2 --- Definition of the SECQ and its basic properties --- p.33 / Chapter 3.3 --- Relationship between the SECQ and other constraint qualifications --- p.39 / Chapter 3.3.1 --- The SECQ and the strong CHIP --- p.39 / Chapter 3.3.2 --- The SECQ and the linear regularity --- p.46 / Chapter 3.4 --- Interior-point conditions for the SECQ --- p.58 / Chapter 3.4.1 --- I is finite --- p.59 / Chapter 3.4.2 --- I is infinite --- p.61 / Chapter 4 --- Duality theory of semi-infinite optimization via weakly* sum of epigraph of conjugate functions --- p.70 / Chapter 4.1 --- Introduction --- p.70 / Chapter 4.2 --- Fenchel duality in semi-infinite convex optimization --- p.73 / Chapter 4.3 --- Sufficient conditions for Fenchel duality in semi-infinite convex optimization --- p.79 / Chapter 4.3.1 --- Continuous real-valued functions --- p.80 / Chapter 4.3.2 --- Nonnegative-valued functions --- p.84 / Bibliography --- p.94