Thesis advisor: Shakeeb S.K. Khan / Thesis advisor: Zhijie Z.X. Xiao / Binary choice models can be easily estimated (using, e.g. maximum likelihood estimation) when the distribution of the latent error is known, as in Logit or Probit. In contrast, most estimators with unknown error distribution (e.g., maximum score, maximum rank correlation, or Klein-Spady) are computationally difficult or numerically unstable, making estimation impractical with more than a few regressors. The first chapter proposes an estimator that is convex at each iteration, and so is numerically well behaved even with many regressors and large sample sizes. The proposed estimator, which is root-n consistent and asymptotically normal, is based on batch gradient descent, while using a sieve to estimate the unknown error distribution function. Simulations show that the estimator has lower mean bias and root mean squared error than Klein-Spady estimator. It also requires less time to compute. The second chapter discusses the same estimator in high dimensional setting. The estimator is consistent with rate lower than root-n when the number of regressors grows slower than the number of observations and asymptotic normal when the square of the number of regressors grows slower than the number of observations. Both theory and simulation show that higher learning rate is needed with higher number of regressors. The third chapter provides an application of the proposed estimator to bankruptcy prediction. With more than 20 regressors, the proposed estimator performs better than logistic regression in terms of Area Under the Receiver Operating Characteristics using firm data one year or two years prior to bankruptcy, but worse than logistic regression using firm data three years prior to bankruptcy. / Thesis (PhD) — Boston College, 2022. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Economics.

Les choix des matériaux et de leurs procédés de mise en oeuvre connaissent et vont connaître des évolutions marquantes dans le monde de l’architecture. A l’époque actuelle, les évolutions sont largement induites par les techniques, mais aussi les représentations et les préceptes qui apparaissent avec l’émergence de la notion de développement durable dans notre société.Les outils d’aide à la conception existants à l’échelle des matériaux portent principalement sur les dimensions physiques (thermique, cycle de vie des matériaux, consommations, etc.). Nos travaux se questionnent sur l’intégration des dimensions techniques, écologiques et sensibles des matériaux dans un outil d’aide à la conception basé sur l’utilisation de la référence. L’activité référentielle est une approche propre aux phases initiales de projet. Ces phases correspondent aux premières propositions décisives, qui restent peu assistées par les outils numériques.Nos travaux visent à mettre en évidence les différentes caractéristiques des matériaux, mais surtout leurs interactions. Cette étude se distingue des approches classiques des matériaux, où généralement les différentes solutions constructives sont présentées matériau par matériau. En effet, nous nous basons sur une structuration de données et de connaissances interdisciplinaires (architecture, urbanisme, paysage, aspects esthétiques, aspects techniques, aspects cognitifs, approche de la perception, approche environnementale, etc.).Ces recherches tendent vers une première proposition d’un outil d’aide à la conception nommé DILEM’MAtériaux qui prend en compte les différentes dimensions des matériaux dans leur contribution à la genèse d’idées fondatrices, à la définition d’un ou des parti(s), ou concept(s) propres aux phases initiales de projet / The choice of materials and way of implementation is known and will be known as a significant growth in the world of architecture. Actually, changes are largely induced by technical dimension, but also representations and precepts that appear with the emergence of the concept of sustainable development in our society.Design support tools about materials scale focus on the physical dimensions (thermal, life cycle, refreshments, etc.). Our work is questioning the integration of technical, environmental and sensible dimensions in a design support tool based on reference. The referential activity is a specific approach in the initial phases of designing on a project. These phases correspond to crucial choice, which remain poorly assisted by digital tools.Our work aims to highlight the different characteristics of materials, but also their interactions. This study differs from conventional approaches of materials, which generally, constructive solutions are presented material by material. Indeed, we rely on a data structure and interdisciplinary knowledge (architecture, urbanism, landscape, aesthetic, technical, cognitive, perception approach, environmental approach, etc.).This research tends to be a first proposal for a design support tool named DILEM'MAtériaux that takes into account materials in their contribution to origin of founding ideas and definition of concept, in the initial phases of designing on a project.

This paper contains a discussion of topological dimension theory. Original proofs of theorems, as well as a presentation of theorems and proofs selected from Ryszard Engelking's Dimension Theory are contained within the body of this endeavor. Preliminary notation is introduced in Chapter I. Chapter II consists of the definition of and theorems relating to the small inductive dimension function Ind. Large inductive dimension is investigated in Chapter III. Chapter IV comprises the definition of covering dimension and theorems discussing the equivalence of the different dimension functions in certain topological settings. Arguments pertaining to the dimension o f Jn are also contained in Chapter IV.

Les gaz d'atomes utlra-froids sont adaptés pour simuler des phénomènes observés en physique de la matière condensée, de part le haut degré d'ajustabilité de l'ensemble des paramètres avec une précision exceptionnelle.En particulier, la réalisation de pièges hautement anisotropes permet de confiner ces gaz en basse dimension, où le rôle des fluctuations quantiques est accru.Je m'attache en particulier au modèle de gaz de Bose unidimensionel dont les atomes interagissent localement, connu sous le nom de modèle de Lieb et Liniger. Les outils théoriques que j'emploie sont l'Ansatz de Bethe, la théorie conforme des champs, le formalisme des liquides de Tomonaga-Luttinger, ainsi qu'une équivalence exacte entre bosons et fermions.Ces méthodes exactes ou d'approximation me donnent accès, avec une précision remarquable, à la thermodynamique de l'état fondamental, au spectre d'excitations et aux fonctions de corrélation, depuis les corrélations locales à k corps jusqu'à la distribution en impulsion, ainsi qu'au facteur de structure dynamique. Ces observables fournissent des informations concernant les propriétés de cohérence et de superfluidité du gaz. Plus particulièrement, en me servant de la théorie de la réponse linéaire, j'étudie la force de traînée exercée par un faisceau laser gaussien remué dans le gaz.Enfin, je considère la situation où, en relâchant un degré de contrainte dû au piège, une structure à plusieurs modes apparaît et conduit à une augmentation progressive de la dimension effective du système. Tout du long, j'étudie l'effet d'un piège harmonique dans la dimension principale à travers le formalisme de l'Approximation de Densité Locale. / Ultracold atom gases are a versatile platform to simulate condensed matter physics phenomena, as virtually any parameter is experimentally tunable with a high accuracy.In particular, highly anisotropic traps allow the realization of low-dimensional systems, where the role of quantum fluctuations is enhanced. I investigate the paradigmatic model of a one-dimensional Bose gas with contact interactions, a.k.a the Lieb-Liniger model, using powerful analytical tools such as Bethe Ansatz, Conformal Field Theory and the Tomonaga-Luttinger liquid formalism, as well as the Bose-Fermi mapping.These exact and approximate methods allow me to investigate with high accuracy its Ground-State energy and thermodynamics, excitation spectra and correlation functions, from the k-body local correlations to the momentum distribution and the dynamical structure factor. These quantities yield useful informations on the coherence and superfluidity of a gas. In particular, I study the drag force exerted by a gaussian laser beam stirred into the gas in linear response theory.Then, releasing a transverse trapping, I study the appearance of a multimode structure and the dimensional crossover. All along, the effect of a harmonic trap in the longitudinal direction is studied within the Local Density Approximation.

Recently, Dawson and Feinstein showed that a Banach algebra integral extension B of a commutative Banach algebra A of topological stable rank one is again of topological stable rank one. In this thesis, we provide a partial converse to this statement: If an Arens-Hoffman extension A® of a commutative C*-algebra A has topological stable rank one then A has topological stable rank one.

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by Fiona Chan Siu Ling. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves [114-118]). / Chapter Chapter One --- "Fantasy, Postmodernism and Space" --- p.1 / Chapter Chapter Two --- Fantasy and Hyperspace --- p.27 / Chapter Chapter Three --- Fantasy and Cyberspace --- p.54 / Chapter Chapter Four --- The Constituting and the Constituted in the Postmodern --- p.81 / Works Cited --- p.114

Complex dynamics is the study of iteration of functions which map the complex plane onto itself. In general, their dynamics are quite complicated and hard to explain but for some simple classes of functions many interesting results can be proved. For example, one often studies the class of rational functions (i.e. quotients of polynomials) or, even more specifically, polynomials. Each such function f partitions the extended complex plane C into two regions, one where iteration of the function is chaotic and one where it is not. The nonchaotic region, called the Fatou Set, is the set of all points z such that, under iteration by f, the point z and all its neighbors do approximately the same thing. The remainder of the complex plane is called the Julia set and consists of those points which do not behave like all closely neighboring points. The Julia set of a polynomial typically has a complicated, self similar structure. Many questions can be asked about this structure. The one that we seek to investigate is the notion of the dimension of the Julia set. While the dimension of a line segment, disc, or cube is familiar, there are sets for which no integer dimension seems reasonable. The notion of Hausdorff dimension gives a reasonable way of assigning appropriate non-integer dimensions to such sets. Our goal is to investigate the behavior of the Hausdorff dimension of the Julia sets of a certain simple class of polynomials, namely fd,c(z) = zd + c. In particular, we seek to determine for what values of c and d the Hausdorff dimension of the Julia set varies continuously with c. Roughly speaking, given a fixed integer d > 1 and some complex c, do nearby values of c have Julia sets with Hausdorff dimension relatively close to each other? We find that for most values of c, the Hausdorff dimension of the Julia set does indeed vary continuously with c. However, we shall also construct an infinite set of discontinuities for each d. Our results are summarized in Theorem 10, Chapter 2. In Chapter 1 we state and briefly explain the terminology and definitions we use for the remainder of the paper. In Chapter 2 we will state the main theorems we prove later and deduce from them the desired continuity properties. In Chapters 3 we prove the major results of this paper.