Black Principals' Perceptions of How their Racial, Cultural, Personal, and Professional Identities Affect their Leadership

Thesis advisor: Elizabeth TwomeyThis dissertation addresses the negative way that blacks are viewed in mainstream society and how that image affects black educational leaders. Race has been historically used to subordinate blacks in the United States, and research suggests that a key factor in this subordination has been the systematic withdrawal of educational opportunities and access for blacks. This research posits that such racism and discrimination has affected the way blacks have formed their identities, specifically with regard to education. In this multiple-participant case study, black principals were interviewed to determine the ways in which they perceived their racial, cultural, personal, and professional identities to affect their leadership of schools. Findings stated that race heavily affected all areas of participants' identities. Race caused participants to feel more connected to minority students and communities, to advocate high expectations for minority students especially in addition to all other students, and to integrate diversity in the faculty to be representative of all students. Race also made it more difficult for participants to earn the trust and respect of faculty and parents and to discern whether people reacted negatively to their race or to other aspects of their leadership. Suggestions from this study included the inclusion of culture and race-specific coursework in educational leadership programs, increased promotion of diversity in recruitment for educators and educational leaders, and institutionalized support groups for principals of color. Methodological limitations, theoretical considerations, and implications for future research practice, and policy were also discussed.Thesis (PhD) — Boston College, 2009.Submitted to: Boston College. Lynch School of Education.Discipline: Educational Administration

Diversity Graphs

Bipartite graphs have long been used to study and model matching problems, and in this paper we introduce the bipartite graphs that explain a recent matching problem in computational biology. The problem is to match haplotypes to genotypes in a way that minimizes the number of haplotypes, a problem called the Pure Parsimony problem. The goal of this work is not to address the computational or biological issues but rather to explore the mathematical structure through a study of the underlying graph theory

Optimality regions and fluctuations for Bernoulli last passage models

We study the sequence alignment problem and its independent version,the discrete Hammersley process with an exploration penalty. We obtain rigorous upper bounds for the number of optimality regions in both models near the soft edge.At zero penalty the independent model becomes an exactly solvable model and we identify cases for which the law of the last passage time converges to a Tracy-Widom law

Positively hyperbolic varieties, tropicalization, and positroids

A variety of codimension c in complex affine space is positively hyperbolic if the imaginary part of any point in it does not lie in any positive linear subspace of dimension c. Positively hyperbolic hypersurfaces are defined by stable polynomials. We characterize these varieties using sign variations, and show that they are equivalently defined by being hyperbolic with respect to the positive part of the Grassmannian, in the sense of Shamovich and Vinnikov. Positively hyperbolic projective varieties have tropicalizations that are locally subfans of the type A hyperplane arrangement defined by x =x , in which the maximal cones satisfy a non-crossing condition. This gives new proofs of results of Choe–Oxley–Sokal–Wagner and Brändén on Newton polytopes and tropicalizations of stable polynomials. We settle the question of which tropical varieties can be obtained as tropicalizations of positively hyperbolic varieties in the case of tropical toric varieties, constant-coefficient tropical curves, and Bergman fans. Along the way, we give a new characterization of positroids in terms of a non-crossing condition on their Bergman fans. i

The Central Curve in Linear Programming

The central curve of a linear program is an algebraic curve specified by linear and quadratic constraints arising from complementary slackness. It is the union of the various central paths for minimizing or maximizing the cost function over any region in the associated hyperplane arrangement. We determine the degree, arithmetic genus and defining prime ideal of the central curve, thereby answering a question of Bayer and Lagarias. These invariants, along with the degree of the Gauss image of the curve, are expressed in terms of the matroid of the input matrix. Extending work of Dedieu, Malajovich and Shub, this yields an instance-specific bound on the total curvature of the central path, a quantity relevant for interior-point methods. The global geometry of central curves is studied in detail. © 2012 SFoCM