This study is an empirical analysis of household expenditure behavior using the Linear and Quadratic Expenditure Systems. The expenditure systems are estimated using data collected in 1972 by the Departmento Administrativo Nacional de Estadisticas (DANE) of Bogota, Colombia. The Linear Expenditure System(LES) has been estimated frequently since the initial work of Stone(1954), while the Quadratic Expenditure System(QES) is a relatively new system first estimated by Howe(1974). The LES is derived from the maximization of a modified Cobb-Douglas utility function, and the QES is derived from an indirect utility function through the application of Roy's(1941) Identity. The LES is a special case of the QES, and by estimating the more general QES, the validity of the restrictive assumptions of the LES can be tested. In the cross-section, the most severe restriction is that the income-consumption functions must be linear. Using the more flexible QES, consumption is a nonlinear function of income, which means that the marginal budget shares may vary for households at different income levels. The empirical results of this study indicate that the marginal budget shares do vary across income levels, and that the income-consumption functions are, in fact, nonlinear. For the 5219 households in the DANE survey, hundreds of expenditure items have been aggregated into the seven categories of food, housing, clothing, medical care, education, durable goods, and miscellaneous goods and services. The expenditure systems are estimated for the entire sample, for the sample divided according to income, urban/rural status, number of household members, and the education level of the household head. The empirical results confirm the superiority of the QES in most cases as judged by likelihood ratio tests. These results reinforce the conclusions of Howe(1974) and Pollak and Wales(1978a, 1978b) that the QES provides a statistically significant improvement over the LES. The empirical results of this study are useful to development planners in Colombia in order to more accurately predict the ultimate effects of income redistribution. In addition, the results help to evaluate the possibility of a leading sector of growth in the Colombian economy. Finally, the empirical results are compared with those from the Colombian study of Howe(1974) to test the sensitivity of the parameters to the data base which is used.

This dissertation examines two separate issues concerning systems of demand equations. The first essay deals with the econometric implementation of demand systems and the second analyzes the demand for integer-ordered goods. In the first essay, we examine the consequences of adopting the random utility hypothesis as an approach for randomizing a system of demand equations. Random utility models are appealing since they allow the usual assumption of deterministic utility maximizing behavior by each consumer to co-exist with the apparent randomness across individuals which is exhibited by data. Our results show that the use of random utility models implies that the disturbances of the demand equations may not be homoscedastic but must be functions of prices and/or income. If the demand system is generated by random utility maximization, then empirical studies of demand which have assumed homoscedastic disturbances will suffer the usual inferential difficulties. A possible explanation for the prevalent finding of nonsymmetry, therefore, is provided by the fact that most previous demand studies have, in fact, assumed homoscedasticity. An appropriate structure for the disturbances is obtained for the specific case of the linear expenditure system. A system of demand equations for international travel is estimated and compared using both the typical homoscedastic disturbances and the alternative specification we derive. The second essay develops a model of consumer behavior when consumers are confronted with lumpy alternatives. Specifically, the case of a single discrete good which can be purchased only in integer quantities is modeled. The model uses a systems approach, incorporating demand for the discrete good with demand for continuous goods into a complete system of demand equations. After deriving a general form for the mixed integer/continuous model, a particular functional form for the model is derived by imposing linearity constraints on the demand equations. To obtain the stochastic specification, the framework of random utility maximization is adopted. Finally, the model is shown to be identified and an estimation procedure is developed using maximum likelihood methods.

The concept of period length in the empirical application of cash-in-advance (CIA) models is introduced. CIA models posit that individuals and firms hold cash to purchase goods over a period. However, there has been no research into how long a period is. Existing empirical studies use quarterly or annual data in simulations or estimations of CIA models. This is inappropriate if individuals or firms conduct financial transactions at intervals which are more frequent than 3 months or 12 months. The period length which is empirically consistent with the theoretical restrictions imposed by a CIA model for 9 two-digit (SIC based) industries is determined to be one to six weeks, depending on the industry examined and money variable used. Unlike other empirical work using CIA models, the introduction of the concept of period length allows this model to display variability in the velocity of money. It is also found that the CIA binds between 1% to 13% of the time instead of nearly 100% as in other papers. The effectiveness of CIA in modeling the effect of money on firms and the demand for money by firms is demonstrated in two applications. Each application incorporates the period length concept described above. In the first application, it is found that money is not an omitted variable in the production function of a firm. This result is based upon the fact that the inclusion of money through the use of a CIA constraint into a model of production does not significantly affect the estimated partial elasticies of input substitution. This paper is the first empirical work reporting this result, and it casts some doubt on the results of several earlier papers which conclude that money does indeed belong as an argument in the production function. In the second application, the Euler equations of a firm subject to a CIA constraint are used to derive the firm' s money demand function. The CIA framework yields parameter restrictions for the money demand function which can be tested econometrically to evaluate the performance of the CIA model of money demand.

String theory is a rich and elegant framework which many believe furnishes a UV-complete unified theory of the fundamental interactions, including gravity. However, if true, it holds at energy scales out of the reach of any terrestrial particle accelerator. While we cannot observe the string regime directly, we live in a universe which has been evolving from the string scale since shortly after the Big Bang. It is possible that string theory underlies cosmological processes like inflation, and that cosmology could confirm or constrain stringy physics in the early universe. This makes the intersection of string theory with the early universe a potential window into otherwise inaccessible physics. The results of three papers at this intersection are presented in this thesis. First, we address a longstanding problem: the apparent incompatibility of the experimentally constrained axion decay constant with most string theoretic realisations of the axion. Using warped compactifications in heterotic string theory, we show that the axion decay constant can be lowered to acceptable values by the warp factor. Next, we move to the subject of cosmic strings: linelike topological defects formed during phase transitions in the early universe. It was realised recently that cosmic superstrings are produced in many models of brane inflation, and that cosmic superstrings are stable and can have tensions within the observational bounds. Although they are now known not to be the primary generators of primordial density perturbations leading to structure formation, the evolution of cosmic string networks could have important consequences for astrophysics and cosmology. In particular, there are quantitative differences between cosmic superstring networks and GUT cosmic string networks. We investigate the properties of cosmic superstring networks in warped backgrounds, where they are expected to be produced at the end of brane / Plusieurs croient voir en la théorie des cordes une riche et élégante façon d'obtenir une théorie UV complète et unifiée des interactions fondamentales, incluant la gravité. Même si elle s'avérait vrai, son application se restreindrait toutefois à des énergies hors d'atteinte des accélérateurs de particules terrestres. Malgré qu'on ne puisse observer le régime des cordes directement, l'univers dans lequel nous vivons a évolué à partir d'une échelle comparable à la taille d'une corde peu de temps après le Big Bang. Il est donc possible que la théorie des cordes soit à l'origine de processus cosmologiques comme l'inflation et que l'étude de ces derniers permette de confirmer ou de contraindre la physique des cordes alors que l'univers était jeune. Ainsi, à l'intersection de la théorie des cordes et du régime dans lequel se baignait l'univers naissant se trouve probablement une fenêtre pour la physique qui serait autrement inatteignable. Dans cette thèse, nous présentons les travaux de trois articles reliés à cette intersection. Premièrement, nous nous intéressons à un problème de longue date: l'apparente incompatibilité entre la valeur de la constante de désintégration de l'axion contrainte expérimentalement et celle prédite par la plupart des théories de cordes. En utilisant les compactifications déformées de la théorie hétérotique des cordes, nous montrons que la constante de désintégration de l'axion peut être diminuée à des valeurs acceptables grâce au facteur de déformation.Par la suite, nous nous tournons vers l'étude des cordes cosmiques: les défauts topologiques de type <<ligne>> se formant lors des transitions de phase dans l'univers naissant. Il fut découvert récemment que des supercordes cosmiques peuvent être produites par plusieurs modèles d'inflation de branes. Ces supercordes peuvent être stables et même avoir des valeu

The subject of the thesis belongs to the theory of graphs. In 1966, C. St. J.A. Nash-Williams conjectured that the square of a block is hamiltonian. This conjecture quickly gained a wide popularity and, at the end of 1970, it was established by H. Fleischner. His proof of the existence of a hamiltonian cycle in the square of a block does not explicitly provide an algorithm for finding the cycle. The thesis will describe such an algorithm, with a running time O(n('2)) on every input with n vertices. For the most part, our algorithm follows closely the original lines of Fleischner's proof. The main difference occurs at the part where Fleischner proves the existence of a certain spanning subgraph in every connected bridgeless graph: we replace Fleischner's argument by a radically different one. This is the main original result of our thesis.

We consider free quantum field theory in de Sitter space, focusing on the casesof scalar, spin-1/2, and symmetric & anti-symmetric tensor fields of arbitrary spin. The field equations in global coordinates reduce to a one-dimensional Schrödinger problem in the timelike coordinate. These reduced equations possess a noteworthy structure: their potentials are of an algebraically special type which correspond to multi-soliton solutions of the Korteweg-de Vries equation. In an odd number of space-time dimensions these potentials are transparent – their reflection coefficients vanish identically. This has the remarkable consequence that odd-dimensional de Sitter space is transparent to the excitations of free, massive fields. Thus a quantum state with no particles in the distant past will evolve into a state with no particles in the distant future. This feature has been previously noted for scalar excitations, but the corresponding higher-spin behaviour is new. For completeness, we also review reflectionless scattering in one-dimensional quantum mechanics. / La théorie quantique des champs libres en espace de Sitter est considérée, avec une concentration sur les champs scalaires, les champs de spin-1/2, et les champs tensoriels symétriques & antisymétriques. Les équations en coordonnées globales sont réduites à un problème de type Schrödinger dans la coordonnée temporelle. Ces équations réduites possèdent une structure remarquable. Leurs potentiels correspondent à des solutions de l'équation Korteweg-de Vries décrivant plusieurs solitons cöincidents. Dans un nombre impair de dimensions spatio-temporelles, ces potentiels sont transparents – leurs coefficients de réflexion sont identiquement zéro. Ceci implique la conséquence remarquable que l'espace de Sitter en nombre impair de dimensions est transparent aux excitations des champs libres et massifs. Un état quantique sans particules dans le passé infini deviendra alors un état sans particules dans le futur infini. Cette caractéristique a déjà été perçue pour les excitations scalaires, mais non pour les excitations avec autre spin. Le sujet de diffusion transparente dans la mécanique quantique est également passé en revue.

We show that all fundamental barriers to simulations of various supersymmetric field theories in 3 and 4 dimensions with a lattice regulator can be removed with known and established methods and provide detailed procedures to accomplish this end for N=1 Super-Yang-Mills theory in 3 dimensions and N=4 Super-Yang-Mills theory in 4 dimensions. We also describe generalizations to various other 3 and 4D theories with varying levels of detail where appropriate and analyze a novel new approach to lattice supersymmetry: discretization of a particular topological twist of Super-Yang-Mills in 2 and 4 dimensions. / Nous montrons que les obstacles fondamentaux des simulations de différents domaines théoretiqe de champs supersymétriques de 3 et 4 dimensions avec Régularisation sur réseau peuvent être surmonté avec méthodes établies, et nous fournissons des procèdures dètaillées pour le théorie N=1 Super-Yang-Mills en 3 dimensions et N=4 Super-Yang-Mills en 4 dimensions. Nous décrivons, avec diffèrents niveaux de détail, les généralisations à divers autres thèories de 3 et 4D, et nous analysons un approche de réseau supersymétrie: discrétisation d'une torsion topologique de Super-Yang-Mills dans 2 et 4 dimensions.

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