<p>This thesis investigates the statistical properties of preliminary test estimators of linear models with normally distributed errors. Specifically, we derive exact expressions for the mean, variance and quadratic risk (i.e. the Mean Square Error) of estimators whose form are determined by the outcome of a statistical test. In the process, some new results on the moments of truncated linear or quadratic forms in normal vectors are established.</p><p>In the first paper (Paper I), we consider the estimation of the vector of regression coefficients under a model selection procedure where it is assumed that the analyst chooses between two nested linear models by some of the standard model selection criteria. This is shown to be equivalent to estimation under a preliminary test of some linear restrictions on the vector of regression coefficients. The main contribution of Paper I compared to earlier research is the generality of the form of the test statistic; we only assume it to be a quadratic form in the (translated) observation vector. Paper II paper deals with the estimation of the regression coefficients under a preliminary test for homoscedasticity of the error variances. In Paper III, we investigate the statistical properties of estimators, truncated at zero, of variance components in linear models with random effects. Paper IV establishes some new results on the moments of truncated linear and/or quadratic forms in normally distributed vectors. These results are used in Papers I-III. In Paper V we study some algebraic properties of matrices that occur in the comparison of two nested models. Specifically we derive an expression for the inertia (the number of positive, negative and zero eigenvalues) of this type of matrices.</p>

This thesis investigates the statistical properties of preliminary test estimators of linear models with normally distributed errors. Specifically, we derive exact expressions for the mean, variance and quadratic risk (i.e. the Mean Square Error) of estimators whose form are determined by the outcome of a statistical test. In the process, some new results on the moments of truncated linear or quadratic forms in normal vectors are established. In the first paper (Paper I), we consider the estimation of the vector of regression coefficients under a model selection procedure where it is assumed that the analyst chooses between two nested linear models by some of the standard model selection criteria. This is shown to be equivalent to estimation under a preliminary test of some linear restrictions on the vector of regression coefficients. The main contribution of Paper I compared to earlier research is the generality of the form of the test statistic; we only assume it to be a quadratic form in the (translated) observation vector. Paper II paper deals with the estimation of the regression coefficients under a preliminary test for homoscedasticity of the error variances. In Paper III, we investigate the statistical properties of estimators, truncated at zero, of variance components in linear models with random effects. Paper IV establishes some new results on the moments of truncated linear and/or quadratic forms in normally distributed vectors. These results are used in Papers I-III. In Paper V we study some algebraic properties of matrices that occur in the comparison of two nested models. Specifically we derive an expression for the inertia (the number of positive, negative and zero eigenvalues) of this type of matrices.

The purpose of this travel cost study is to determine how rider behaviors and site characteristics influence repeat visits for equestrian trail riding in Kentucky. Primary data was collected via a survey developed and administered to trail riders in person and online. The average surveyed trail rider tends to be female, about 46 years old, with some higher education, and an annual household income of $65,000. She makes 11 trips to a specified site per year, 8 of which are daytrips, usually in the fall, and traveling 132 miles round trip. From other information gathered, an index of trail characteristics was developed to identify positive attributes of trails. To account for overdispersion of the number of visits per year, a negative binomial distribution in the estimation was used. The primary variables significant to explaining repeat visits to a site include distance in miles, the index of characteristics, and gender. Given consumer surplus estimates of $800 per equestrian it is recommended that established trails maximize desired characteristics. For new trail development it is recommended that trail characteristics are maximized and that they are built closer to the urban areas of the state since most riders are coming from these areas.

Made available in DSpace on 2014-06-11T19:25:32Z (GMT). No. of bitstreams: 0 Previous issue date: 2006-06-08Bitstream added on 2014-06-13T19:53:22Z : No. of bitstreams: 1 schinaider_sj_me_rcla.pdf: 576104 bytes, checksum: 41c3c4e7eec02c3dd98738011e8c7b76 (MD5) / Educação e aprendizado são assuntos de grande importância para a sociedade em vista do desenvolvimento tecnológico e do progresso social. No presente trabalho analisamos a distribuição estatística das notas dos candidatos ao vestibular (Exame de Admissão) da Academia da Força Aérea, situada em Pirassununga, Estado de São Paulo Brasil, onde se formam os Oficiais da Aeronáutica (Força Aérea Brasileira), entre os anos de 1999 a 2004, em busca de algumas características que indiquem o processo de aprendizagem em cada disciplina do vestibular. O exame de admissão consta de 4 disciplinas: Física, Matemática, Inglês e Português, todos com questões objetivas. Os candidatos melhor classificados são selecionados de acordo com o número de vagas determinado pelo Comando da Aeronáutica. Notou-se, claramente, que, nas disciplinas Física, Matemática e Inglês, as notas obedecem a uma distribuição do tipo Lei de Potência Gradualmente Truncada, como também foi observado anteriormente nas disciplinas, em conjunto, de Ciências Exatas e Biológicas. Na disciplina Português as notas obedecem a uma distribuição normal, resultado que se explica, considerando-se a dependência dos assuntos dados na área de Física, Matemática e Inglês (língua estrangeira) aos assuntos ministrados anteriormente, enquanto em Português, (língua materna) cada capítulo é relativamente independente. Também apresentamos sugestão para melhorar o ensino de ciências e matemáticas. / Science and Mathematic Education is a subject of great importance for the society in sight of recent technological and social program. In the present work, we study the statistical distribution of the marks obtained by the candidates in entrance examination of Air Force Academy, which prepare officers for Brazilian Air Force and is situated at Pirassununga São Paulo, in the period of 1999-2004. Our object is to find some characteristics of the process of learning in various disciplines. The admission examination consist of four disciplines; Physics, Mathematics, English and Portuguese. The candidates are selected in accordance with the merit list in the examination and number of seats available as determined by the Air Force Command. We showed that in the discipline of Physics, Mathematics and English, the distribution of marks obtained is in accordance with Gradually Truncated Power Law as also have been reported earlier in Exact and Biological Sciences in University entrance examination. In Portuguese the Distribution is Normal. We explained these results considering importance of the understanding of material given previously to understand a new chapter in area of Physics, Mathematics and English as our foreign language. In the case of Portuguese (Native Language), each chapter is relatively independent and thus not require knowledge of previous chapters. We also presented some suggestions to improve the science and Mathematics Education at High School level.

The main objective of this project is to develop a "black-box" multigrid preconditioner for the iterative solution of finite element discretisations of the convection-diffusion equation with dominant convection. This equation can be considered a stand alone scalar problem or as part of a more complex system of partial differential equations, such as the Navier-Stokes equations. The project will focus on the stand alone scalar problem. Multigrid is considered an optimal preconditioner for scalar elliptic problems. This strategy can also be used for convection-diffusion problems, however an appropriate robust smoother needs to be developed to achieve mesh-independent convergence. The focus of the thesis is on the development of such a smoother. In this context a novel smoother is developed referred to as truncated incomplete factorisation (tILU) smoother. In terms of computational complexity and memory requirements, the smoother is considerably less expensive than the standard ILU(0) smoother. At the same time, it exhibits the same robustness as ILU(0) with respect to the problem and discretisation parameters. The new smoother significantly outperforms the standard damped Jacobi smoother and is a competitor to the Gauss-Seidel smoother (and in a number of important cases tILU outperforms the Gauss-Seidel smoother). The new smoother depends on a single parameter (the truncation ratio). The project obtains a default value for this parameter and demonstrated the robust performance of the smoother on a broad range of problems. Therefore, the new smoothing method can be regarded as "black-box". Furthermore, the new smoother does not require any particular ordering of the nodes, which is a prerequisite for many robust smoothers developed for convection-dominated convection-diffusion problems. To test the effectiveness of the preconditioning methodology, we consider a number of model problems (in both 2D and 3D) including uniform and complex (recirculating) convection fields discretised by uniform, stretched and adaptively refined grids. The new multigrid preconditioner within block preconditioning of the Navier-Stokes equations was also tested. The numerical results gained during the investigation confirm that tILU is a scalable, robust smoother for both geometric and algebraic multigrid. Also, comprehensive tests show that the tILU smoother is a competitive method.

Die Fragestellung der Arbeit geht aus einem matriziellen Potenzmomentenproblem des folgenden Typs hervor: Für eine vorgegebene endliche Folge s0,...sm von q × q-Matrizen sind alle nicht-negativen Hermiteschen q × q-Maße σ auf Ω zu bestimmen, deren j-tes Moment für alle j=0,...,m-1 genau sj ist und deren m-tes Moment nichtnegativ hermitesch ist. Hier behandeln wir den Stieltjes-Fall Ω = [α, ∞) dieser Problemstellung. Die Lösungen dieses matriziellen Momentenproblems lassen sich in eindeutiger Weise mit gewissen holomorphen Matrixfunktionen, ihren sogenannten Stieltjes-Transformierten, identifizieren. Das Ziel der Betrachtungen dieser Arbeit ist, die Menge aller Werte zu charakterisieren, welche diese Stieltjes-Transformierten bei Auswertung in einem fixierten Punkt aus der oberen komplexen Halbebene annehmen können. Da sich jede Lösung eines Stieltjes-Momentenproblems so fortsetzen lässt, dass sie ein entsprechendes Hamburger-Momentenproblem löst, ist erwartbar, dass die Menge der Werte aller Stieltjes-Transformierten der Lösungen des Stieltjes-Momentenproblems in einem festen Punkt eine Teilmenge der Menge der Werte aller Stieltjes-Transformierten der Lösungen des Hamburger-Momentenproblems ist. An dieser Bemerkung anknüpfend besteht der Ansatz nun darin, das betrachtete Stieltjes-Momentenproblem auf zwei Momentenprobleme vom Hamburger-Typ zurückzuführen. Das erste der beiden ergibt sich auf natürliche Weise wie oben beschrieben. Das zweite ist einer Modifikation der vorgeschriebenen Datenfolge zuzuordnen, welche die linke Intervalgrenze des Integrationsgebiets [α, ∞) berücksichtigt. Die Menge der Werte, die von Stieltjes-Transformierten der Lösungen eines betrachteten Hamburger-Momentenproblems in einem festen Punkt angenommen werden können, stimmt mit einer Matrix-Kreisscheibe überein, deren Mittelpunkt, linker und rechter Halbradius explizit anhand der gegebenen Datenfolge ausgedrückt werden können. Ordnet man nun jedem der beiden Hamburger-Momentenprobleme, auf die das Stieltjes-Problem zurückgeführt wurde, die entsprechende Matrix-Kreisscheibe zu, so erhält man, dass die Menge, die zu charakterisieren unser Ziel ist, wie zu erwarten im Schnitt dieser beiden Matrix-Kreisscheiben liegt. Darüber hinaus zeigt sich, dass die Menge diesen Schnitt sogar ausfüllt. Der Beweis dieser Teilmengenbeziehung ist aufwendiger als die erste Richtung. Eine zentrale Rolle im Beweis nehmen gewisse Polynomsysteme mit Orthogonaleigenschaften ein. Bei der im Zentrum der Arbeit stehenden Untersuchung wurde ein Wert aus der oberen komplexen Halbebene fixiert, in welchem dann die Stieltjes-Transformierten der Lösungen eines Stieltjes-Problems ausgewertet wurden. Die analoge Fragestellung für die Wahl eines Punktes in (−∞, α) wurde zuvor mit unterschiedlichen Voraussetzungen in verschiedener Literatur behandelt. Der Fall, dass der Punkt in der unteren komplexen Halbebene liegen soll, lässt sich über ein Spiegelungsprinzip auf den Fall der oberen komplexen Halbebene zurückführen, womit dann alle Möglichkeiten, den Punkt zu fixieren, abgedeckt sind.:1. Introduction 2. Preliminaries and Notation 3. Special Classes of Matrix-Valued Functions 3.1. The Class Rq(Π+) of Matrix-Valued Herglotz-Nevanlinna Functions 3.2. Particular Subclasses of Rq(Π+) 3.3. Matrix-Valued Stieltjes Functions 4. Parameterization of Block Hankel Matrices and Related Sequences of Complex Matrices 4.1. The Sequence of H-parameters 4.2. The α-Stieltjes Parameterization 4.3. The α-Schur Transform 5. Some Considerations on Particular Matrix Polynomials 6. Special Rational Matrix-Valued Functions 7. Description of the Values of the Solutions of the Truncated Matricial Hamburger Moment Problem and Corresponding Matrix Balls 8. Pairs of Meromorphic Matrix-Valued Functions 8.1. Nevanlinna Pairs in Π+ 8.2. Nevanlinna Pairs in C \ R 8.3. Stieltjes Pairs in C \ [α, ∞) 9. A Special Quadruple of Matrix Polynomials 10. Further Identities for Matrix Polynomials 11. The [α, ∞)-Quadruple of Matrix Polynomials 12. Description of the Values of the Solutions of the Truncated Matricial Stieltjes Moment Problem and Corresponding Matrix Balls 12.1. First Discussion of the Corresponding Matrix Balls 12.2. Representation in the Case of an Odd Number of Prescribed Matricial Moments 12.2.1. Representation in the Case (sj )0j=0 of a Single Prescribed Matricial Moment 12.2.2. Explicit Connections 12.2.3. Representation as Intersection of two Matrix Balls 12.3. Representation in the Case of an Even Number of Prescribed Matricial Moments 13. Summary and Prospects A. Some Facts on Matrix Theory B. Some Facts on Orthogonal Projection Matrices C. Some Facts on the Integration Theory of Non-negative Hermitian Measures Nomenclature

In this study I assess spatial and temporal patterns of sediment deposition in Pecausett Pond, located along the tidal extent of the Connecticut River, in order to assess the role of tides in the transport and storage of sediment and associated contaminants within floodplain tidal ponds. Findings reveal that tidal ponds have significantly higher rates of sedimentation compared to neighboring marshes due to the fact that these ponds have more accommodation space and receive uninterrupted tidal exchange with the main river. Tidal tie channels introduce a pulse of suspended sediment and contaminants from the main river into these ponds each flood tide, with sedimentation rates fast enough to allow settling before the subsequent ebb tide can transport these sediments back to the main river (i.e. tidal pumping). Some studies performed on the tidal floodplain of the Connecticut River show high deposition rates and have attributed periods of high accumulation to anomalously high river discharge events. However, this project shows that tides are more likely the major mechanism responsible for transporting and storing sediment and associated contaminants at backwater sites located along the tidal floodplain. Deposition rates in this 3-4 m deep pond exceed 2 cm/yr. These rates are far too high to maintain equilibrium morphology for much longer. However, ground penetrating radar surveys from the study site reveal truncated stratigraphy common to erosional unconformities, which suggest that mechanisms for sediment remobilization and removal may exist. Periods of episodic erosion therefore may be helping to maintain the morphology in this shallow environment, and allow for the high rates of short-term deposition. Further, a sudden increase in percent inorganic potentially associated with the opening or clearance of the tie-channel is observed at a sediment depth approximately between 1.9 to 2.2 m. A radiocarbon date obtained below this transition is consistent with a significant drop in sedimentation prior to this tie-channel development. High rates of sedimentation in Pecausett Pond are therefore likely relatively recent phenomena, transpiring over the last few centuries following early colonization.

In this thesis, newer Markov Chain Monte Carlo (MCMC) algorithms are implemented and compared in terms of their efficiency in the context of sampling from Gaussian processes under linear inequality constraints. Extending the framework of Gaussian process that uses Gibbs sampler, two MCMC algorithms, Exact Hamiltonian Monte Carlo (HMC) and Analytic Elliptical Slice Sampling (ESS), are used to sample values of truncated multivariate Gaussian distributions that are used for Gaussian process regression models with linear inequality constraints. In terms of generating samples from Gaussian processes under linear inequality constraints, the proposed methods generally produce samples that are less correlated than samples from the Gibbs sampler. Time-wise, Analytic ESS is proven to be a faster choice while Exact HMC produces the least correlated samples.

This thesis discusses structural and ferroelectric properties of two well-known classes of materials, perovskite oxides and Hydrogen bonded ferroelectrics, using first-principles calculations. Certain aspects of first principles calculations are central to the problems presented in this thesis. Such as the ability to calculate polarization based on the modern theory of polarization and calculation of ferroelectric property under finite electric displacement field. Therefore, these fundamental theoretical approaches are discussed following an opening section on the basic methodology of density-functional theory. In addition to the discussion on theoretical methods, a brief review of different phenomena and techniques crucial to alter/enhance ferroelectric properties at the interfaces of perovskite materials has been presented along with examples. The first problem presented in this thesis proposes and validates an alternative quantitative measure of ferroelectric(FE) and antiferrodistortive(AFD) instabilities by means of calculating inverse capacitance and layer inverse capacitance of layered perovskites. The presented methodological approach is applied to BaTiO$_{3}$/CaTiO$_{3}$ and PbTiO$_{3}$/SrTiO$_{3}$ superlattices and it precisely estimates FE and AFD instabilities. Here we also present an approach to accurately predict the ferroelectric instabilities in large period superlattices from the statistical coefficients obtained from short period superlattices. In the second problem, we study ferroelectricity in an organic crystal(croconic acid) for which ferroelectric polarization is close to that of bulk BaTiO$_{3}$. We employ new meta-GGA functional named SCAN and revisit all structural and ferroelectric properties. Calculated X-ray absorption spectra(XAS) qualitatively and quantitatively agrees well with experimental O K-edge spectra. By discussing the origin of each XAS peak and their characteristic we demonstrate with a systematic approach the connection between ferroelectricity and XAS in croconic acid. Best to our knowledge such relation has not been realized in past. This study could prove XAS as a new way to measure ferroelectric instability in hydrogen-bonded organic ferroelectrics. / Physics

All-trans retinoic acid (atRA) mediated growth inhibition results in the arrest of the cell cycle during the G1 phase in CAOV3 cells but not SKOV3 ovarian carcinoma cells. The G1 checkpoint is regulated by a multitude of molecules such as the retinoblastoma family of proteins, cyclins, cyclin dependent kinases (CDKs) and cyclin dependent kinase inhibitors (CDKis). CAOV3 cells, which are atRA sensitive, have been shown to express p16INK4a (p16), a cyclin dependent kinase inhibitor regulating the G1 checkpoint. However, atRA resistant SKOV3 cells do not express p16. In these studies, we investigated the role of p16 in mediating atRA induced growth arrest. Our results show that overexpression of p16 in SKOV3 cells leads to growth inhibition following atRA treatment. However, the inhibition is short-term due to the loss of p16 expression. Nevertheless, these results show that p16 plays a role in atRA mediated growth inhibition in ovarian carcinoma cells and that modulation of p16 expression can determine the growth response to atRA. Additionally, we also examined the effect of atRA treatment on the expression of homeobox genes in the CAOV3 cells and SKOV3 cells model system. Homeobox genes comprise a family of transcription factors which function during embryonic development to control pattern formation, differentiation and proliferation. Besides their dominant role during embryogenesis, they are also expressed in adults. In human tumors, an association between the deregulation of the expression of homeobox genes and oncogenic transformation has been reported. It is known that some homeobox genes are atRA targets due to the presence of retinoic acid response element (RARE) either in their promoter region or in their 3' region. In these studies we examined the expression of 13 homeobox genes in CAOV3 cells and SKOV3 cells following ethanol or atRA treatment. The 13 homeobox genes were analyzed because previous studies done by our laboratory observed differences in expression of these homeobox genes when comparing atRA sensitive oral squamous carcinoma cells (SCC) to atRA resistant oral squamous cell carcinoma cells. Of the 13 homeobox genes analyzed in the ovarian carcinoma cell model system, we found HOXA1 and HOXB4 to be upregulated by atRA in CAOV3 cells but not in SKOV3 cells. We also found that the induction of HOXA1 and HOXB4 mRNA expression in CAOV3 cells occurred as a respond to atRA treatment and is not due to a generalized response because of overall growth reduction. Interestingly, HOXA1 has two alternatively spliced forms. The mRNA expression of the truncated form of HOXA1 is highly induced by atRA when compared to its full length form. HOXB1, which is HOXA1 target gene, was not upregulated following atRA treatment. These results suggest that: 1) expression of p16 plays a role in mediating atRA growth inhibition; 2) HOXA1 and HOXB4 also play a role in mediating growth suppression by atRA; and 3) the truncated form of HOXA1 is induced by atRA treatment and may play a role in mediating growth inhibition by atRA, perhaps by acting in a dominant negative fashion. / Microbiology and Immunology