N–Dimensional Orthogonal Tile Sizing Problem

AMS subject classification: 68Q22, 90C90

On Nilpotent Subsemigroups in some Matrix Semigroups

2000 Mathematics Subject Classification: 20M20, 20M10.

Supersymmetry and Ghosts in Quantum Mechanics

2000 Mathematics Subject Classification: 81Q60, 35Q40.

Density of Polynomials in the L^2 Space on the Real and the Imaginary Axes and in a Sobolev Space

2000 Mathematics Subject Classification: 41A10, 30E10, 41A65.

Oscillation Criteria of Second-Order Quasi-Linear Neutral Delay Difference Equations

2000 Mathematics Subject Classification: 39A10.

On strongly regular graphs with m2 = qm3 and m3 = qm2

2010 Mathematics Subject Classification: 05C50.

Environmental ethics for business sustainability

The paper derives operational principles from environmental ethics for business organizations in order to achieve sustainability. Business affects the natural environment at different levels. Individual biological creatures are affected by business via hunting, fishing, agriculture, animal testing, etc. Natural ecosystems are affected by business via mining, regulating rivers, building, polluting the air, water and land, etc. The Earth as a whole is affected by business via exterminating species, contributing to climate change, etc. Business has a natural, non-reciprocal responsibility toward natural beings affected by its functioning. At the level of individual biological creatures, awareness-based ethics is adequate for business. It implies that business should assure natural life conditions and painless existence for animals and other sentient beings. From this point of view a business activity system can be considered acceptable only if its aggregate impact on animal welfare is non-negative. At the level of natural ecosystems, ecosystem ethics is relevant for business. It implies that business should use natural ecosystems in a proper way, that is, not damaging the health of the ecosystem during use. From this point of view a business activity system can be considered acceptable only if its aggregate impact on ecosystem health is non-negative. At the level of the Earth as a whole, Gaian ethics applies to business. Its implication is that business should not contribute to the violation of the systemic patterns and global mechanisms of the Earth. From this point of view a business activity system can be considered acceptable only if its aggregate impact on the living planet is non-negative. Satisfying the above principles can assure business sustainability in an ethically meaningful way. In this case business performs its duty: not to harm nature or allow others to come to harm.

An evaluation of coping ability as a guide to the treatment of persons diagnosed with schizophrenia and substance abuse

This dissertation introduced substance abuse to the Dynamic Vulnerability Formulation (DVF) and the social competence model to determine if the relationship between schizophrenic symptomatology and coping ability in the DVF applied also to the dually diagnosed schizophrenic or if these variables needed to be modified. It compared the coping abilities of dually and singly diagnosed clients in day treatment and identified, examined, and assessed the relative influence of relevant mediating variables on two dimensions of coping ability of the dually diagnosed: coping skills and coping effort. These variables were: presence of negative and nonnegative symptoms, duration of mental illness, type of substance used, and age of first substance use.^ A priori effect sizes based on previous empirical research were used to interpret the results related to the comparison of demographic, socioeconomic, and treatment characteristics between the singly and dually diagnosed study samples. The data suggested that the singly diagnosed group had higher coping skills than the dually diagnosed group, particularly in the areas of housing stability, work affect, and total social adjustment. The dually diagnosed group had lower scores on one aspect of coping effort--agency or self-efficacy. The data supported the presence of an inverse relationship between symptom severity and coping skills, particularly for the dually diagnosed group. The data did not support the presence of an inverse relationship between symptom severity and coping effort, but did suggest a positive relationship between symptom severity and one measure of coping effort, agency, for the dually diagnosed group. Regression equations using each summary measure of coping skill--social adjustment and role functioning--yielded statistically significant F-ratios. Thirty-six percent of the variance in social adjustment and thirty-one percent of the variance in role functioning were explained by the relative influence of the relevant variables. Both negative and non-negative symptoms were the only significant predictors of social adjustment. The non-negative symptoms variable was the sole significant predictor of role functioning. The results of this study provided partial support for the use of the Dynamic Vulnerability Formulation (DVF) with the dually diagnosed. ^

The peopling of the Bahamas: A phylogeographical perspective

During the past 500 years, the Bahamas has been influenced by a wide array of settlers, including but not limited to, the Arawak Indians, Eleutherian Adventurers, British Loyalists, Creole slaves, liberated Africans as well as Chinese, Greek, Jewish, Lebanese, Jamaican and Haitian migrants. To date, however, only a few reports analyzing the genetic makeup and population dynamics of the Bahamas have been published, making this work pivotal in the endeavor to ascertain the genetic ancestry of these groups. As such, the current investigation was undertaken to genetically characterize six of the more densely populated islands throughout the Northwest (Grand Bahama and Abaco) and Central (Eleuthera, Exuma, Long Island and New Providence) Bahamas using different forensic marker systems. When autosomal STR markers are employed, the Bahamian collections were all found to receive differential contributions from the African, European, East Asian and Native American collections utilized in the analyses. Similar findings were also observed for two other Afro-Caribbean populations, Haiti and Jamaica, although the latter populace was found to share a greater proportion of its autosomal component with non-African sources than the former. On the contrary, analysis of the six Bahamian collections using high-resolution Y-chromosome markers identifies genetic signals emanating exclusively from Africans and Europeans, but this is likely the result of smaller sample sizes collected from each island and/or sex-biased gene flow from East Asian and Native American groups.

Text analytics of social media: Sentiment analysis, event detection and summarization

In the last decade, large numbers of social media services have emerged and been widely used in people's daily life as important information sharing and acquisition tools. With a substantial amount of user-contributed text data on social media, it becomes a necessity to develop methods and tools for text analysis for this emerging data, in order to better utilize it to deliver meaningful information to users. ^ Previous work on text analytics in last several decades is mainly focused on traditional types of text like emails, news and academic literatures, and several critical issues to text data on social media have not been well explored: 1) how to detect sentiment from text on social media; 2) how to make use of social media's real-time nature; 3) how to address information overload for flexible information needs. ^ In this dissertation, we focus on these three problems. First, to detect sentiment of text on social media, we propose a non-negative matrix tri-factorization (tri-NMF) based dual active supervision method to minimize human labeling efforts for the new type of data. Second, to make use of social media's real-time nature, we propose approaches to detect events from text streams on social media. Third, to address information overload for flexible information needs, we propose two summarization framework, dominating set based summarization framework and learning-to-rank based summarization framework. The dominating set based summarization framework can be applied for different types of summarization problems, while the learning-to-rank based summarization framework helps utilize the existing training data to guild the new summarization tasks. In addition, we integrate these techneques in an application study of event summarization for sports games as an example of how to better utilize social media data. ^

Text Analytics of Social Media: Sentiment Analysis, Event Detection and Summarization

In the last decade, large numbers of social media services have emerged and been widely used in people's daily life as important information sharing and acquisition tools. With a substantial amount of user-contributed text data on social media, it becomes a necessity to develop methods and tools for text analysis for this emerging data, in order to better utilize it to deliver meaningful information to users. Previous work on text analytics in last several decades is mainly focused on traditional types of text like emails, news and academic literatures, and several critical issues to text data on social media have not been well explored: 1) how to detect sentiment from text on social media; 2) how to make use of social media's real-time nature; 3) how to address information overload for flexible information needs. In this dissertation, we focus on these three problems. First, to detect sentiment of text on social media, we propose a non-negative matrix tri-factorization (tri-NMF) based dual active supervision method to minimize human labeling efforts for the new type of data. Second, to make use of social media's real-time nature, we propose approaches to detect events from text streams on social media. Third, to address information overload for flexible information needs, we propose two summarization framework, dominating set based summarization framework and learning-to-rank based summarization framework. The dominating set based summarization framework can be applied for different types of summarization problems, while the learning-to-rank based summarization framework helps utilize the existing training data to guild the new summarization tasks. In addition, we integrate these techneques in an application study of event summarization for sports games as an example of how to better utilize social media data.

Geometric inequalities for initial data with symmetries

We consider a class of initial data sets (Σ,h,K) for the Einstein constraint equations which we define to be generalized Brill (GB) data. This class of data is simply connected, U(1)²-invariant, maximal, and four-dimensional with two asymptotic ends. We study the properties of GB data and in particular the topology of Σ. The GB initial data sets have applications in geometric inequalities in general relativity. We construct a mass functional M for GB initial data sets and we show:(i) the mass of any GB data is greater than or equals M, (ii) it is a non-negative functional for a broad subclass of GB data, (iii) it evaluates to the ADM mass of reduced t − φi symmetric data set, (iv) its critical points are stationary U(1)²-invariant vacuum solutions to the Einstein equations. Then we use this mass functional and prove two geometric inequalities: (1) a positive mass theorem for subclass of GB initial data which includes Myers-Perry black holes, (2) a class of local mass-angular momenta inequalities for U(1)²-invariant black holes. Finally, we construct a one-parameter family of initial data sets which we show can be seen as small deformations of the extreme Myers- Perry black hole which preserve the horizon geometry and angular momenta but have strictly greater energy.

(Table 1) Sr, Nd and Os isotopic composition from marine sediments of the Bengal Fan

Sr, Nd, and Os isotopic data are presented for sediments from diverse locations in the Bay of Bengal. These data allow the samples to be divided into three groups, related to their sedimentary contexts. The first group, mainly composed of sediments from the shelf off Bangladesh and the currently active fan, has Sr and Nd characteristics consistent with a dominantly Himalayan source. Their 187Os/188Os ratios (~1.2-1.5) show that the average detrital material delivered by the Ganga-Brahmaputra (G-B) river system is not unusually radiogenic. A large difference in 187Os/188Os ratio exists between these Bengal Fan sediments and Ganga bedloads (187Os/188Os ~2.5, Pierson-Wickmann et al. (2000, doi:10.1016/S0012-821X(00)00003-0)). This difference mainly reflects addition of a less radiogenic Brahmaputra component, though mineralogical sorting and loss of radiogenic Os during transport may also play some role. The second sample group contains sediments from elsewhere in the Bay, particularly those located on the continental slope. They display Os isotopic compositions (0.99-1.11) similar to that of present seawater and higher Os and Re concentrations. These characteristics suggest the presence of a large hydrogenous contribution, consistent with the lower sedimentation rate of these samples. Sr and Nd ratios indicate that a significant fraction of these sediments is derived from erosion of non-Himalayan sources, such as the Indo-Burman range. These observations could be explained by the deflection of sediments from the G-B river system by westward currents in the head of the Bay. The third group contains only one sample, but shows that in addition to a Himalayan source, sediment discharge from Sri Lanka may influence the detrital component in the distal part of the fan. The similarity between the isotopic compositions of the group I R/V Sonne samples and those of Ocean Drilling Program Leg 116 (France-Lanord et al., 1993; Reisberg et al., 1997, doi:10.1016/S0012-821X(00)00003-0) suggests that the material eroding in the Himalayas has been roughly constant since the Miocene. The high Os isotopic ratios of leachates of both Sonne group I and Miocene Leg 116 sediments imply that much of the leachable highly radiogenic Os component was conserved during transport through the estuary or interaction with seawater. In constrast, samples with lower, but still relatively high, sedimentation rates (Sonne groups II and III and Pliocene Leg 116) seem to have significantly adsorbed or exchanged Os and Re with seawater. This suggests that in some cases the Os isotopic ratios of leachates of detrital sediments can be used to constrain the ancient marine Os record, or conversely, to date unfossiliferous sediments.

Optimización de la factorización de matrices no negativas en Bioinformática

En los últimos años se ha incrementado el interés de la comunidad científica en la Factorización de matrices no negativas (Non-negative Matrix Factorization, NMF). Este método permite transformar un conjunto de datos de grandes dimensiones en una pequeña colección de elementos que poseen semántica propia en el contexto del análisis. En el caso de Bioinformática, NMF suele emplearse como base de algunos métodos de agrupamiento de datos, que emplean un modelo estadístico para determinar el número de clases más favorable. Este modelo requiere de una gran cantidad de ejecuciones de NMF con distintos parámetros de entrada, lo que representa una enorme carga de trabajo a nivel computacional. La mayoría de las implementaciones de NMF han ido quedando obsoletas ante el constante crecimiento de los datos que la comunidad científica busca analizar, bien sea porque los tiempos de cómputo llegan a alargarse hasta convertirse en inviables, o porque el tamaño de esos datos desborda los recursos del sistema. Por ello, esta tesis doctoral se centra en la optimización y paralelización de la factorización NMF, pero no solo a nivel teórico, sino con el objetivo de proporcionarle a la comunidad científica una nueva herramienta para el análisis de datos de origen biológico. NMF expone un alto grado de paralelismo a nivel de datos, de granularidad variable; mientras que los métodos de agrupamiento mencionados anteriormente presentan un paralelismo a nivel de cómputo, ya que las diversas instancias de NMF que se ejecutan son independientes. Por tanto, desde un punto de vista global, se plantea un modelo de optimización por capas donde se emplean diferentes tecnologías de alto rendimiento...

Methods for Imputing Missing Values and Synthesizing Confidential Values for Continuous and Magnitude Data

Abstract

Continuous variable is one of the major data types collected by the survey organizations. It can be incomplete such that the data collectors need to fill in the missingness. Or, it can contain sensitive information which needs protection from re-identification. One of the approaches to protect continuous microdata is to sum them up according to different cells of features. In this thesis, I represents novel methods of multiple imputation (MI) that can be applied to impute missing values and synthesize confidential values for continuous and magnitude data.

The first method is for limiting the disclosure risk of the continuous microdata whose marginal sums are fixed. The motivation for developing such a method comes from the magnitude tables of non-negative integer values in economic surveys. I present approaches based on a mixture of Poisson distributions to describe the multivariate distribution so that the marginals of the synthetic data are guaranteed to sum to the original totals. At the same time, I present methods for assessing disclosure risks in releasing such synthetic magnitude microdata. The illustration on a survey of manufacturing establishments shows that the disclosure risks are low while the information loss is acceptable.

The second method is for releasing synthetic continuous micro data by a nonstandard MI method. Traditionally, MI fits a model on the confidential values and then generates multiple synthetic datasets from this model. Its disclosure risk tends to be high, especially when the original data contain extreme values. I present a nonstandard MI approach conditioned on the protective intervals. Its basic idea is to estimate the model parameters from these intervals rather than the confidential values. The encouraging results of simple simulation studies suggest the potential of this new approach in limiting the posterior disclosure risk.

The third method is for imputing missing values in continuous and categorical variables. It is extended from a hierarchically coupled mixture model with local dependence. However, the new method separates the variables into non-focused (e.g., almost-fully-observed) and focused (e.g., missing-a-lot) ones. The sub-model structure of focused variables is more complex than that of non-focused ones. At the same time, their cluster indicators are linked together by tensor factorization and the focused continuous variables depend locally on non-focused values. The model properties suggest that moving the strongly associated non-focused variables to the side of focused ones can help to improve estimation accuracy, which is examined by several simulation studies. And this method is applied to data from the American Community Survey.