Currently, the most effective complete SAT solvers are based on the DPLL algorithm augmented by Clause Learning. These solvers can handle many real-world problems from application areas like verification, diagnosis, planning, and design. Clause Learning works by storing previously computed, intermediate results and then reusing them to prune the future search tree. Without Clause Learning, however, DPLL loses most of its effectiveness on real world problems. Recently there has been some work on obtaining a deeper understanding of the technique of Clause Learning. In this thesis, we contribute to the understanding of Clause Learning, and the Resolution proof system that underlies it, in a number of ways. We characterize Clause Learning as a new, intuitive Resolution refinement which we call CL. We then show that CL proofs can effectively p-simulate general Resolution. Furthermore, this result holds even for the more restrictive class of greedy, unit propagating CL proofs, which more accurately characterize Clause Learning as it is used in practice. This result is surprising and indicates that Clause Learning is significantly more powerful than was previously known. Since Clause Learning makes use of previously derived clauses, it motivates the study of Resolution space. We contribute to this area of study by proving that determining the variable space of a Resolution derivation is PSPACE-complete. The reduction also yields a surprising exponential size/space trade-off for Resolution in which an increase of just 3 units of variable space results in an exponential decrease in proofsize. This result runs counter to the intuitions of many in the SAT-solving community who have generally believed that proof-size should decrease smoothly as available space increases. In order to prove these Resolution results, we need to make use of some intuition regarding the relationship between Black-White Pebbling and Resolution. In fact, determining the complexity of Resolution variable space required us to first prove that Black-White Pebbling is PSPACE-complete. The complexity of the Black-White Pebbling Game has remained an open problem for 30 years and resisted numerous attempts to solve it. Its solution is the primary contribution of this thesis.

Currently, the most effective complete SAT solvers are based on the DPLL algorithm augmented by Clause Learning. These solvers can handle many real-world problems from application areas like verification, diagnosis, planning, and design. Clause Learning works by storing previously computed, intermediate results and then reusing them to prune the future search tree. Without Clause Learning, however, DPLL loses most of its effectiveness on real world problems. Recently there has been some work on obtaining a deeper understanding of the technique of Clause Learning. In this thesis, we contribute to the understanding of Clause Learning, and the Resolution proof system that underlies it, in a number of ways. We characterize Clause Learning as a new, intuitive Resolution refinement which we call CL. We then show that CL proofs can effectively p-simulate general Resolution. Furthermore, this result holds even for the more restrictive class of greedy, unit propagating CL proofs, which more accurately characterize Clause Learning as it is used in practice. This result is surprising and indicates that Clause Learning is significantly more powerful than was previously known. Since Clause Learning makes use of previously derived clauses, it motivates the study of Resolution space. We contribute to this area of study by proving that determining the variable space of a Resolution derivation is PSPACE-complete. The reduction also yields a surprising exponential size/space trade-off for Resolution in which an increase of just 3 units of variable space results in an exponential decrease in proofsize. This result runs counter to the intuitions of many in the SAT-solving community who have generally believed that proof-size should decrease smoothly as available space increases. In order to prove these Resolution results, we need to make use of some intuition regarding the relationship between Black-White Pebbling and Resolution. In fact, determining the complexity of Resolution variable space required us to first prove that Black-White Pebbling is PSPACE-complete. The complexity of the Black-White Pebbling Game has remained an open problem for 30 years and resisted numerous attempts to solve it. Its solution is the primary contribution of this thesis.

In this qualitative study, the interactive process of exploring and developing shared, familial meanings about biracial identity development was investigated from the perspectives of both parents and children in Black-White multiracial families. Specifically, this study examined how monoracial parents and their biracial children describe the influence parents have on the biracial children's identity development process from the biracial individuals' youth into adulthood. Monoracial parents and their children were also invited to share how they negotiated the uniqueness of a biracial identity in both the parents' and the children's social arenas. Data were obtained through in-person, semi-structured interviews with 10 monoracial mothers and 11 of their adult (ages 18 to 40) biracial children. The data were analyzed using phenomenological methodology. The analysis of participants' experiences of biracial identity development revealed four major themes: that family interactions and relationships contribute to the creation of identity for biracial individuals, that mothers intentionally worked to create an open family environment for their biracial children to grow up in, that parents and children affect and are affected by interactions with American culture and society throughout their development, and finally that growing up biracial is a unique experience within each of aforementioned contexts. While there were many shared experiences among the families, each family had its own exceptional story of strength and adjustment to the biracial identity development process. Across cases, the overarching theme was one of togetherness and resiliency for the mothers and their adult children. Data from this study has important implications for research and practice among a number of human service professionals. / Ph. D.

Rates of black-white intermarriage in the United States have increased over the last sixty years, yet they remain at levels below other types of interracial/interethnic unions. Prior research has centered largely on individual-level factors associated with the formation of such unions, culminating in three not entirely consistent micro-level theories: status-caste exchange, status homogamy, and educational/economic success. Most of this literature does not consider contextual-level characteristics, which I argue should have an independent effect on the incidence of these unions. My dissertation explores these issues with microlevel and multilevel models using data from the 2006 American Community Survey. I examine both micro and macro level predictors of the odds of white women marrying black men, and black women marrying white men in the metropolitan areas of the U.S. in 2006. In my level one analyses, six logistic regression equations are estimated to test the efficacy of the abovementioned microlevel theories of interracial marriage for black and white women. Status-caste exchange theory is accorded no support from my investigation, and status homogamy theory receives inconsistent support for white women. The results clearly convey that educational/economic success theory is applicable for predicting intermarriage among white and black metropolitan women in the United States. Among white women, those with high occupational status and high annual income are more likely to be intermarried than those with low occupational status and lower income. Among black metropolitan women, those with high occupational status and high levels of education are more likely to be intermarried than those with low occupational status and low levels of education. In my multilevel analyses, four hierarchical generalized linear models are estimated to evaluate the likelihood of intermarriage for white and black women living in metropolitan areas in the United States. My results show that context matters in predicting and understanding intermarriage for both groups of women. Both the individual-level characteristics of the women, as well as the contextual-level characteristics of their metropolitan areas, were shown in my equations to impact their likelihood of being intermarried. Future research would benefit from the inclusion of social context in any consideration of intermarriage, particularly through the use of multilevel modeling, which until now, has not been utilized by researchers in this area.

The purpose of this qualitative study was to investigate the chronic daily concerns that eight self-identified Black-White interracial couples described as stressful and to identify the coping strategies that they utilized to reduce feelings of distress. Another goal of this study was to discover the actions that these eight couples took to maintain marital satisfaction. This investigation consisted of a total of 24 interviews, 16 individual and 8 couple interviews, based on the research questions guided by stress and coping theory. Couples identified three chronic stressors: Worrying About Children, Wanting to be Accepted, and Building a Successful Marriage; Nine coping strategies were identified: Distancing, Putting Family First, Problem-Solving, Accepting of Problems, Having Faith in God, Denial, Communicating With Spouse, Positive Reframing/Reflecting, and Escaping. Five maintenance behaviors were identified as well: Having Couple/Family Time, Communicating, Being Considerate, Getting Away Together, and Planning/Remembering Special Occasions. / Master of Science

No description available.

The Black-White biracial population is the largest and fastest growing subgroup of multiracial individuals in the United States. Despite substantial research literature on the positive relationship between Black racial identity and psychological wellbeing, Black-White biracial individuals are underrepresented in studies that provide evidence for this relationship. Root (1998) put forward an Ecological Metamodel of Biracial Identity, comprised of several factors related to contextual (e.g. class, regional history of race-relations, parental identity, extended family) and intra-psychic processes (e.g. social skills, coping skills). The ecological metamodel served as the theoretical framework for the current study. This study is a comprehensive investigation of the ecological system of one Black-White interracial family living in Virginia. Using an ethnographic research design, race-related messages delivered in environmental contexts (e.g. school, community, and home) and racial socialization messages received by Black-White biracial individuals were examined. The family recruited for this study consisted of four members: a White mother, a Black father, a 15 year-old male, and an 11 year-old female. Over the course of 6 months, the researcher conducted individual interviews with nuclear and extended family members; administered the White Racial Identity Attitudes Scale, the Multidimensional Inventory of Black Identity, the African Home Environment Inventory, and a genogram exercise; and engaged in participant observation and direct observation of the family in the home and at community events. Using an interpretive phenomenological analysis, themes were identified within and between data sources. Results revealed that parents communicate that race is not as important as other characteristics of an individual (e.g. honesty, work ethic). The majority White community environments frequently communicated stereotypes of Blacks and that the children are “different.” The children expressed differences in their racial identities, which is related to significant race-related events and perhaps gender effects. Because of the differing community and home race-related messages, the findings demonstrate the importance of understanding racial identity in multiple environmental contexts, which is particularly important for clinical applications for Black-White interracial families and Black-White biracial individuals in therapy. Future studies should explore possible reasons for gender differences in Black-White biracial identity and the interaction between socioeconomic status and race-related messages.

Racial inequality in educational and occupational attainment has been shown to be related to racial inequality in test scores and cognitive skills. Most research and policy attention has been given to the ability of schools to equalize test scores. I argue that a major reason why researchers have been unable to explain why schools have not closed the gap is because by the time children begin school it may be too late. Cognitive skills develop from infancy and as such, it should be unsurprising that by the time children are five years old the differences across groups are firmly established. Thus, this research attempts to uncover where the racial test-score gap begins by examining infants. I perform a series of analyses using ordinary least squares regression (OLS) and structural equation modeling (SEM) using the first wave of the Early Childhood Longitudinal Survey--Birth cohort (ECLS-B). I utilize the mother's race, rather than the child's race, in the analyses because looking at the mother's race makes the most logical sense since the mother's race is more likely than the child's to determine household income, marital status, mother's education, parenting styles, and so on. I demonstrate that there is little to no raw gap in cognitive skills between the infants of White and Black mothers in the United States. However, through SEM I find that when one controls for social, human, and financial capital, and for differences in health and type of childcare, the infants of African American mothers would actually do better than the infants of White mothers because of their precocious motor development. I find no support for genetics and childcare and only limited support for financial and human capital as mediators of the gap. However, there is support for family social capital and low birth weight as key mediators of the small Black-White test score gap in infancy.

This qualitative study examined how the racial identity of Black/White biracial college students shaped their college choice process, and the extent to which these students explored their racial identity at the University of Arizona. Sixteen self-identified Black/White biracial students were interviewed to learn what factors they considered during their college choice process. Additionally, these students were interviewed to understand how the context of this particular institution facilitated or hindered their racial identity exploration. This study found that Black/White biracial students approached their college choice process from a color-blind orientation which had unintended consequences on how these students explored and understood their racial identity in the context of a PWI. The predominantly White precollege contexts these students came from decentralized their racial identity early on; however, on campus Black/White biracial students were continuously confronted with messages that placed an emphasis on race. Implications for student services and for addressing the needs of Black/White biracial students are presented.

Using data from the 2006 Health and Retirement Study (HRS), this study examines what types of assets and levels of savings are held by Black near-retirees, while comparing how types of assets and levels of savings of Black near-retirees differ from those of White near-retirees. Through the use of multivariate analyses, this study further investigates the effects of being Black on the levels of savings, the likelihood of holding IRAs, and the likelihood of being financially prepared for retirement. The study sample includes 4,077 individuals between the ages of 51 and 64, and the subsamples consist of 680 Black and 3,397 White near-retirees. Descriptive findings suggest that Black near-retirees hold lower levels of financial assets (i.e., checking accounts, CDs, stocks, bonds, and other savings) and non-financial assets (i.e., business, real estate, vehicles, and residential home) compared to their White counterparts. The descriptive results further indicate that overall, the level of net worth, holding IRAs, and the investment assets-to-net worth ratio for Black near-retirees are lower than that for White near-retirees. The results from both the ordinary least squares (OLS) regression and the logistic regression analyses indicate that with all else being equal, being Black is a significant factor in predicting the levels of savings, the likelihood of holding retirement accounts, and the likelihood of being financially prepared for retirement among near-retirees aged 51-64. This study also explores how human capital factors and socioeconomic factors are associated with the levels of savings among Black Americans aged 51-64. The OLS results suggest that Blacks with higher education and longer job tenure, and who are married hold higher levels of net worth than other Blacks. The logit results indicate that Black near-retirees with a college education are more likely to hold IRAs; those with longer job tenure are more likely to hold IRAs; and those in the top income quartile are more likely to hold IRAs. The findings of the logit results also indicate that Black near-retirees with some college education, longer job tenure, and those in the higher income groups are more likely to be financially prepared for retirement.