Let p be a prime and q = pk. The polynomial gn,q isin Fp[x] defined by the functional equation Sigmaa isin Fq (x+a)n = gn,q(xq- x) gives rise to many permutation polynomials over finite fields. We are interested in triples (n,e;q) for which gn,q is a permutation polynomial of Fqe. In Chapters 2, 3, and 4 of this dissertation, we present many new families of permutation polynomials in the form of gn,q. The permutation behavior of gn,q is becoming increasingly more interesting and challenging. As we further explore the permutation behavior of gn,q, there is a clear indication that gn,q is a plenteous source of permutation polynomials. We also describe a piecewise construction of permutation polynomials over a finite field Fq which uses a subgroup of Fq*, a “selection” function, and several “case” functions. Chapter 5 of this dissertation is devoted to this piecewise construction which generalizes several recently discovered families of permutation polynomials.

The Normal Operations Safety Survey (NOSS) is an observational methodology to collect safety data during normal Air Traffic Control (ATC) operations. It aims to inform organizations about safety matters by using trained ATC staff to take a structured look at everyday operations. By monitoring normal operations through the use of direct over-the-shoulder observations, it is believed that safety deficiencies can be identified in a proactive manner prior to the occurrence of accidents or incidents. NOSS was developed as a collaborative effort between the International Civil Aviation Organization, ATC providers, controller representatives, government regulators, and academics to fill a gap in available ATC safety information. System designers consider three basic assumptions: the technology needed to achieve the system production goals, the training necessary for people to operate the technology, and the regulations that dictate system behavior. These assumptions represent the expected performance. When systems are deployed, however, particularly in realms as complex as ATC, they do not perform quite as designed. NOSS aims to capture the operational drift that invariably occurs upon system deployment. NOSS captures how the ATC system operates in reality, as opposed to how it was intended to operate. NOSS is premised on the Threat and Error Management (TEM) framework. TEM frames human performance in complex and dynamic settings from an operational perspective by simultaneously focusing on the environment and how operators respond to that environment. TEM posits that threats and errors are a part of everyday operations in ATC and must be managed in order to maintain safety margins. This dissertation describes NOSS and its contributions to ATC safety management systems. It addresses the validity and reliability of NOSS data and presents case studies from field trials conducted by a number of ATC providers. / text

The dissertation focuses on developing statistical models in environmental and life sciences. The Generalized Extreme Value distribution is used to model annual monthly maximum rainfall data from 44 locations in Florida. Time dependence of the rainfall data is incorporated into the model by assuming the location parameter to be a function of time, both linear and quadratic. Estimates and confidence intervals are obtained for return levels of return periods of 10, 20, 50, and 100 years. Locations are grouped into statistical profiles based on their similarities in return level graphs for all locations, and locations within each climatic zone. A family of extreme values distributions is applied to model simulated maximum drug concentration (Cmax) data of an anticoagulant drug. For small samples (n <̲ 100) data exhibited bimodality. The results of investigating a mixture of two extreme value distributions to model such bimodal data using two-parameter Gumbel, Pareto and Weibu ll concluded that a mixture of two Weibull distributions is the only suitable FTSel.For large samples , Cmax data are modeled using the Generalized Extreme Value, Gumbel, Weibull, and Pareto distributions. These results concluded that the Generalized Extreme Value distribution is the only suitable model. A system of random differential equations is used to investigate the drug concentration behavior in a three-compartment pharmacokinetic model which describes coumermycin's disposition. The rate constants used in the differential equations are assumed to have a trivariate distribution, and hence, simulated from the trivariate truncated normal probability distribution. Numerical solutions are developed under different combinations of the covariance structure and the nonrandom initial conditions. We study the dependence effect that such a pharmacokinetic system has among the three compartments as well as the effect of variance in identifying the concentration behavior in each compartment. We identify the time delays in each compartment. We extend these models to incorporate the identified time delays. We provide the graphical display of the time delay effects on the drug concentration behavior as well as the comparison of the deterministic behavior with and without the time delay, and effect of different sets of time delay on deterministic and stochastic behaviors.

This dissertation examines how the relationship between microbes and the human body has been reconfigured over the course of the twentieth century and into the first decades of the twenty-first century. It presents a counter-narrative to the ways in which we have tended to view microbe-human relations to make sense of the emergence of twenty-first century microbial selves by focusing on the normal microbiota. / History of Science

Η παρούσα μεταπτυχιακή διατριβή ανήκει στο επιστημονικό πεδίο της Στατιστικής Θεωρίας Αποφάσεων και αποσκοπεί στην κατασκευή βελτιωμένων διαστημάτων εμπιστοσύνης για την διασπορά ενός πληθυσμού που προέρχεται από κανονική κατανομή. Η μελέτη του προβλήματος της κατασκευής ενός διαστήματος εμπιστοσύνης για την διασπορά μιας κανονικής κατανομής, παρουσιάστηκε στην εργασία του Shorrock (1990). Ειδικότερα, ο Shorrock σε αυτή του τη μελέτη κατασκεύασε διαστήματα εμπιστοσύνης που εξαρτώνταν από την δειγματική διασπορά και από τον δειγματικό μέσο. Συγκεκριμένα, τα νέα αυτά διαστήματα έχουν το ίδιο μήκος με το κλασικό διάστημα εμπιστοσύνης για την διασπορά, αλλά έχουν ομοιόμορφα μεγαλύτερη πιθανότητα κάλυψης. Αρχικά, εξετάζουμε λεπτομερώς τα γνωστά διαστήματα εμπιστοσύνης και πιο συγκεκριμένα, το διάστημα εμπιστοσύνης ίσων ουρών, ελαχίστου μήκους, λόγου πιθανοφανειών και το αμερόληπτο διάστημα εμπιστοσύνης για να γίνουν οι απαραίτητες συγκρίσεις με τα διαστήματα που θα παραχθούν στη συνέχεια. Το πρώτo διάστημα κατασκευάζεται ακολουθώντας μία διαδικασία που είναι αντίστοιχη με την μεθοδολογία εύρεσης του εκτιμητή τύπου Stein, γι' αυτό και το διάστημα που προκύπτει, ονομάζεται διάστημα εμπιστοσύνης τύπου Stein. Η κατασκευή του επόμενου διαστήματος βασίζεται στην μεθοδολογία εύρεσης του εκτιμητή Brown (1968) γι' αυτό και ονομάζεται διάστημα εμπιστοσύνης τύπου Brown. Κατ' όπιν και σε αναλογία με την μεθοδολογία εύρεσης των εκτιμητών Brewster and Zidek (1964) γενικεύεται το προηγούμενο διάστημα κατασκευάζοντας το διάστημα εμπιστσύνης Brewster and Zidek, το οποίο αποδεικνύεται με τη σειρά του ότι, είναι ένα γενικευμένο διάστημα Bayes. Έτσι, κάνοντας τη σύγκριση ως προς την πιθανότητα κάλυψης μεταξύ των νέων αυτών διαστημάτων και του κλασικού διαστήματος εμπιστοσύνης αποδεικνύεται πως αυτή είναι ομοιόμορφα μεγλύτερη για τα νέα διαστήματα. / This master thesis belongs to Statistic Decision Theory field and its purpose is the construction of improved confidence intervals for a normal variance. These intervals were studied by Shorrock (1990). Especially, the usual confidence interval for the variance of a normal distribution, is a function of the sample variance alone. However, in his work Shorrock constructs intervals for variance that also depend on the sample mean. The new intervals have the same length as the shortest interval, depending only on the sample variance and have uniformly higher probability of coverage. Initially, we study well known confidence intervals such as, confidence interval with equal tails, confidence interval of minimum length and then we construct the improved ones. More specifically, we construct a confidence interval analogue of the point estimator in Stein (1964), a confidence interval analogue of the point estimator in Brown (1968) and a Brewster and Zidek (1974) confidence interval, which is also a generalized Bayes interval. Thus, we understand that the intervals above, are improved because they have uniformly greater coverage probability than the shortest one.

A set of mathematical models, known as radiobiological Dose-Response models, have been developed, to model the biological effects and complications that arise following irradiation. The overall objective is to be able to apply these in clinical practice with confidence, and ensure more successful treatments are given to patients. This investigation serves to assess these models and their predictive power of NTCP following irradiation of the lung. Clinical data, from patients treated for inoperable stage III non-small cell lung cancer is obtained and the consequent biological effect (severity of pneumonitis) observed as a result of this radiation treatment is assessed by the models. By gaining more knowledge about the 3D dose-distribution and the incidence of radiation pneumonitis through the evaluation of the models, the main treatment goal, which is to maximise TCP and minimise NTCP can be achieved. Post treatment data is obtained regarding the clinical outcome or clinical endpoint for each patient, considered to be Radiation Pneumonitis. The clinical endpoint is a specific biological effect that may or may not have occurred,after a certain period, following irradiation. The models are assessed on their ability to predict a NTCP value that corresponds to the resulting clinical endpoint following treatment. Furthermore a software tool for the calculation of NTCP’s by the models is developed, in an attempt to provide an important tool for optimization of radiotherapy treatment planning. With our findings from this study, our aim is to further strengthen, support and challenge already existing literature on dose-response modelling. / -

According to the Puerto Rico Health Department as of January 2008, 258 cases of HIV, ages 10 -19 had been reported and 224 cases of AIDS, ages 13-19 (Puerto Rico Health Department, 2008). The purpose of this research was to describe the basic social processes of medication adherence in Puerto Rican youth who are HIV positive. Three research questions were proposed: 1) What are the basic social processes of medication adherence in Puerto Rican youth who are HIV- positive?; 2) What factors influence medication adherence (or nonadherence) among HIV- positive adolescents?; 3) What behaviors indicate that the HIV- positive adolescents adhere or do not adhere to their prescribed medications? The Autonomy Development of Adolescence by Steinberg provided the theoretical framework for this study. Grounded theory was used to study 13 Puerto Rican HIV-positive adolescents. Data collection included semi-structured, in-depth interviews, field notes, participant observation, and a demographic questionnaire. A substantive theory Striving to Live a Normal Life, with the core category of normal emerged from data analysis. Striving to Live a Normal Life explains how these Puerto Rican HIV-positive adolescents try to integrate their HIV status and treatment with their lives. These adolescents concentrate their lives on striving to live a normal life. A variety of ways is used to deal with HIV and has helped them visualize themselves as a normal adolescent with a normal life. Because they see themselves having a normal life, taking or not taking their medications for HIV is also seen as a normal part of their lives. This study suggests the beginning of understanding the concept and process of normalization in this population. These findings support the findings in a study done with HIV-positive adolescents from France in which the concept of normality was related to their lives. It also informs interventions to promote improved medication adherence among Puerto Rican youth who are HIV -positive.

The aim of this research was to establish what black adults' perceptions are of factors that contribute to healthy family functioning. Qualitative research was conducted. Random sampling was used to obtain eighteen black participants between the ages of 20 and 50. These participants responded in writing to the following open ended question: "What factors do you think contribute to healthy family functioning?" Semi-structured interviews were also conducted with the eight participants who presented with the richest data. Analysis of the data yielded 10 prevalent themes and eleven other themes. The 10 prevalent themes were: respect, love, communication, family time/spending time together, trust, understanding, discipline, availability for each other, boundaries and religion. The other eleven themes were: personal space, responsibility, hierarchy, family rules, conflict handling, morality, roles, maturity, intelligence, culture and forgiveness. The above mentioned 21 themes were grouped in seven broad categories, namely communication, conflict handling, affectionate involvement, family rules, boundaries, religion and other dimensions. All these themes were compared to existing research results. It appeared that themes of this study correspond with many dimensions of family functioning as indicated by family therapy models and existing research. Participants also indicated new dimensions not mentioned by the existing literature. Recommendations were made concerning future research. / Thesis (M.A. (Clinical Psychology))--North-West University, Potchefstroom Campus, 2005.

In this paper, we recover the amplitude of a seismic image by approximating the normal (demigrationmigration)operator. In this approximation, we make use of the property that curvelets remain invariant under the action of the normal operator. We propose a seismic amplitude recovery method that employs an eigenvalue like decomposition for the normal operator using curvelets as eigen-vectors. Subsequently, we propose an approximate non-linear singularity-preserving solution to the least-squares seismic imaging problem with sparseness in the curvelet domain and spatial continuity constraints. Our method is tested with a reverse-time ’wave-equation’ migration code simulating the acoustic wave equation on the SEG-AA salt model.

Lorenz curves are extensively used in economics to analyze income inequality metrics. In this thesis, we discuss confidence interval estimation methods for generalized Lorenz curve. We first obtain normal approximation (NA) and empirical likelihood (EL) based confidence intervals for generalized Lorenz curves. Then we perform simulation studies to compare coverage probabilities and lengths of the proposed EL-based confidence interval with the NA-based confidence interval for generalized Lorenz curve. Simulation results show that the EL-based confidence intervals have better coverage probabilities and shorter lengths than the NA-based intervals at 100p-th percentiles when p is greater than 0.50. Finally, two real examples on income are used to evaluate the applicability of these methods: the first example is the 2001 income data from the Panel Study of Income Dynamics (PSID) and the second example makes use of households’ median income for the USA by counties for the years 1999 and 2006