Abstract Not Provided. / Thesis / Master of Science (MSc)

A balanced double square in a string x consists of two squares starting in the same position and of comparable lengths. We present a unique fac- torization of the longer square into primitive components refereed to as the canonical factorization and analyze its properties. In particular, we examine the inversion factors and the right and left inversion subfactors. All three substrings are collectively referred to as rare factors as they occur only twice in a signi cant portion of the larger square. The inversion factors were es- sential for determining the classi cation of mutual con gurations of double squares and thus providing the best-to-date upper bound of 11n=6 for the number of distinct squares in a string of length n by Deza, Franek, and Thierry. The right and left inversion subfactors have the advantage of being half the length of the inversion factors, thus providing a stronger dis- crimination property for a possible third square. This part of the thesis was published by Bai, Franek, and Smyth. The canonical factorization and the right and left inversion subfactors are used to formulate and prove a signi cantly stronger version of the New Periodicity Lemma by Fan, Puglisi, Smyth, and Turpin, 2006, that basically restricts what kind of a third square can exists in a balanced double square. This part of the thesis was published by Bai, Franek, and Smyth. The canonical factorization and the inversion factors are applied to for- mulate and prove a stronger version of the Three Squares Lemma by Crochemore and Rytter. This part of the thesis was published by Bai, Deza, and Franek. / Thesis / Doctor of Philosophy (PhD)

abstract: It is common in the analysis of data to provide a goodness-of-fit test to assess the performance of a model. In the analysis of contingency tables, goodness-of-fit statistics are frequently employed when modeling social science, educational or psychological data where the interest is often directed at investigating the association among multi-categorical variables. Pearson's chi-squared statistic is well-known in goodness-of-fit testing, but it is sometimes considered to produce an omnibus test as it gives little guidance to the source of poor fit once the null hypothesis is rejected. However, its components can provide powerful directional tests. In this dissertation, orthogonal components are used to develop goodness-of-fit tests for models fit to the counts obtained from the cross-classification of multi-category dependent variables. Ordinal categories are assumed. Orthogonal components defined on marginals are obtained when analyzing multi-dimensional contingency tables through the use of the QR decomposition. A subset of these orthogonal components can be used to construct limited-information tests that allow one to identify the source of lack-of-fit and provide an increase in power compared to Pearson's test. These tests can address the adverse effects presented when data are sparse. The tests rely on the set of first- and second-order marginals jointly, the set of second-order marginals only, and the random forest method, a popular algorithm for modeling large complex data sets. The performance of these tests is compared to the likelihood ratio test as well as to tests based on orthogonal polynomial components. The derived goodness-of-fit tests are evaluated with studies for detecting two- and three-way associations that are not accounted for by a categorical variable factor model with a single latent variable. In addition the tests are used to investigate the case when the model misspecification involves parameter constraints for large and sparse contingency tables. The methodology proposed here is applied to data from the 38th round of the State Survey conducted by the Institute for Public Policy and Michigan State University Social Research (2005) . The results illustrate the use of the proposed techniques in the context of a sparse data set. / Dissertation/Thesis / Ph.D. Mathematics 2011

Urban space has transformed as a result of changing dynamics in 21th century. It has started to be considered as a consumer-focused by physical interventions. At this point, the concept of liveability has become significant since it approaches urban space in a holistic approach. This thesis discusses livability of urban square as it is one of the best places where liveability of urban space can be examined. In this study, Orhangazi Urban Square is chosen as a case study area. The aim of this study is to reveal &bdquo / what makes an urban square liveable

Master of Landscape Architecture / Department of Landscape Architecture/Regional and Community Planning / Mary Catherine E. Kingery-Page / Over the past centuries, modernization and industrialization has resulted in increasingly disconnected communities. With the advent and increased availability of the personal vehicle, the desire for larger homes on larger lots, and a steady increase in population, cities are all-too-often relinquishing their open and community-oriented spaces to concrete and mortar. Gone are the medieval days in which cities and towns were centered on large community spaces - places where residents could gather, work, shop, and play together. Therefore, this Master’s Project and Report proposes the reintroduction of the town square – the quintessentially European notion of a central city space – as a means to unify modern American cities. To support this proposal, existing research regarding the various characteristics and qualities of squares is compiled. The resulting information, including work by Carolyn Francis and Claire Cooper Marcus, Cliff Moughtin, Leon Krier, and Camillo Sitte, is then critiqued and synthesized in order to establish function, form and spatial organization typologies of squares. These typologies address not only the use and formal attributes of individual squares, but also where squares should be located and how they can link to one another in order to form larger networks. Together, the research and types substantiate the square as both a refuge from the city and a place for community members to connect. In order to test the community connectivity of public squares, the research and typologies are applied to Super Neighborhood 22 in Houston, Texas. Houston established Super Neighborhoods as a means to link neighboring communities. In many cases, though, disconnections occur between the various natural and social systems found within the combined neighborhoods. Therefore, this Master’s Project and Report proposes a network of public squares as a means to unite the contrasting land uses, residents, and natural systems found within Super Neighborhood 22’s eleven smaller communities.

No description available.

This work is concerned with an evolution inclusion of a form, in a triple of spaces \V -> H -> V*", where U is a continuous non-decreasing process, M is a locally square-integrable martingale and the operators A (multi-valued) and B satisfy some monotonicity condition, a coercivity condition and a condition on growth in u. An existence and uniqueness theorem is proved for the solutions, using semi-implicit time-discretization schemes. Examples include evolution equations and inclusions driven by square integrable Levy martingales.

In this paper, an improved method [1] for the chemical synthesis of 2SeU-RNA was reported using a streamlined strategy employs 2'-O-Thiomopholine-4-carbothioate protecting group. And single step deprotection of the resulting oligoribonucleotide product using 1,2-diamines/toluene under anhydrous conditions would retain the Selenium atom introduced on the 2-possiton of the modified Uracil. The process is doable with most standard heterobase protection and deprotection, it greatly simplifies the synthesis of 2SeU-RNAs and can be applied to other Selenium modified RNAs synthesis. It makes the synthesis of RNA become as simple and efficient as the chemical synthesis of DNA. Furthermore, the design and synthesis of self-assembling 2SeU-RNA square are reported which enable further structure studies and application of unique 2SeU-RNAs.

This dissertation consists of two essays on predictability of asset prices. "Benchmarking problems and long horizon abnormal returns" and, "Low R-square in the cross section of expected returns". Long run abnormal returns following Initial Public Offerings (IPOs), Seasoned Equity Offers (SEO) and other firm level events are well documented in the finance literature. These findings are difficult to reconcile in an efficient markets world. I examine the seriousness of potential benchmarking errors on the measurement of abnormal returns. I find that the simpler, more parsimonious models perform better in practice and finds that excess performance is not predictable regardless of the APM. Thus, the long run underperformance following SEOs found in the literature is consistent with market efficiency because excess performance itself is not predictable. In the other essay, "Low R-square in the cross section of expected returns", I examine the “low R-square” phenomenon observed in the literature. CAPM predicts exact linear relationship between return and betas (SML). This means that estimated time series betas for firms should be related with firms' future returns. However, the estimated betas have almost no relationship with future returns. The cross-sectional R2 are surprising low (3% average) while time series R2 are higher (around 30 % average). He develops a simple asset pricing model that explains this phenomenon. Even in a perfect world where there are no errors in the benchmark measurement or estimation of the price of market risk the difference in R-squares can be quite large due to the difference in variance between the "market" and average returns. I document that market variance exceeds the variance of average returns, with few exceptions, for the last 74 years.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Bibliography: leaves 91-93. / by Mark Joseph Durst. / Ph.D.