Front selection in reaction-diffusion systems via diffusive normal forms

We show that propagation speeds in invasion processes modeled by reaction-diffusion systems are determined by marginal spectral stability conditions, as predicted by the marginal stability conjecture. This conjecture was recently settled in scalar equations; here we give a full proof for the multi-component case. The main new difficulty lies in precisely characterizing diffusive dynamics in the leading edge of invasion fronts. To overcome this, we introduce coordinate transformations which allow us to recognize a leading order diffusive equation relying only on an assumption of generic marginal pointwise stability. We are then able to use self-similar variables to give a detailed description of diffusive dynamics in the leading edge, which we match with a traveling invasion front in the wake. We then establish front selection by controlling these matching errors in a nonlinear iteration scheme, relying on sharp estimates on the linearization about the invasion front. Using appropriate rescalings and a functional analytic approach to regularize singular perturbations, we show that our assumptions hold in general reaction-diffusion systems when the nonlinearity undergoes a transcritical, saddle-node, or supercritical pitchfork bifurcation, demonstrating that our results capture universal aspects of the onset of instability in spatially extended systems. We discuss further applications to parametrically forced amplitude equations, competitive Lotka-Volterra systems, and a tumor growth model.Comment: 60 pages, 2 figure

Growth of cancer stem cell driven tumors: staged invasion, linear determinacy, and the tumor invasion paradox

We study growth of solid tumors in a partial differential equation model introduced by Hillen et al for the interaction between tumor cells (TCs) and cancer stem cells (CSCs). We find that invasion into the cancer-free state may be separated into two regimes, depending on the death rate of tumor cells. In the first, staged invasion regime, invasion into the cancer-free state is lead by tumor cells, which are then subsequently invaded at a slower speed by cancer stem cells. In the second, TC extinction regime, cancer stem cells directly invade the cancer-free state. Relying on recent results establishing front selection propagation under marginal stability assumptions, we use geometric singular perturbation theory to establish existence and selection properties of front solutions which describe both the primary and secondary invasion processes. With rigorous predictions for the invasion speeds, we are then able to heuristically predict how the total cancer mass as a function of time depends on the TC death rate, finding in some situations a tumor invasion paradox, in which increasing the TC death rate leads to an increase in the total cancer mass. Our methods give a general approach for verifying linear determinacy of spreading speeds of invasion fronts in systems with fast-slow structure

Approaches for assessing the presence and impact of thyroid hormone disrupting chemicals in delphinid cetaceans

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September 2006Cetacean blubber is a primary site for lipid storage, which the animal utilizes during periods of energetic stress. It is important to understand how the blubber responds to factors such as ontogeny, water temperature, reproductive status, and nutritional state because blubber is also the primary bioaccumulation site for persistent organic pollutants (POPs) such as polychlorinated biphenyls (PCBs). During periods of lipid mobilization such as lactation, PCBs from the blubber are mobilized into the circulatory system and may cause toxic effects. One particular toxic mechanism may include the induction of cytochrome P450 enzymes in the integument and liver, which could enhance the biotransformation of PCBs to hydroxylated metabolites (OH-PCBs). OH-PCBs may then interfere with thyroid hormone dependent neurodevelopment. The goals of these studies were to investigate the relationships between lipid dynamics and PCB effects and to devise a quantitative approach to assess neurodevelopment in delphinid cetaceans. Blubber morphology, cytochrome P450 1A1 (CYP1A1) expression in the skin-blubber biopsy, blubber and plasma PCBs, and plasma OH-PCBs were assessed in bottlenose dolphins (Tursiops truncatus). In addition, magnetic resonance (MR) images of the postmortem brain in situ were obtained from Atlantic white-sided dolphin (Lagenorhynchus acutus) specimens.These results showed that: 1) Factors such as ontogeny, water temperature, and reproductive status affected blubber morphology in bottlenose dolphins. In response to warmer water, the lipid content of the blubber decreased and this appeared to involve loss of lipids from adipocytes in the middle blubber layer. Similar to the effects of starvation on blubber morphology, lactation decreased adipocyte size predominantly in the deeper blubber, 2) CYP1A1 levels in the deep blubber were significantly related to the total plasma TEQ98 concentrations, adipocyte shrinkage, and plasma OH-PCB levels, 3) Through in situ MR imaging of stranded, Atlantic white-sided dolphin specimens, the size of brain structures that depend on thyroid hormones for maturation could be measured accurately. Future studies can use this technique, coupled with chemical analysis of brain regions, to determine if thyroid hormone disrupting chemicals in delphinid cetaceans are associated with changes in the size of brain structures.Funding for this research was provided by an Environmental Protection Agency STAR fellowship (U-91616101-2) awarded to Eric Montie, NOAA contract #WC1330- 02SE0257, NOAA contract #JHT04P1226, NOAA Fisheries Marine Mammal Health and Stranding Response Program, the Florida Protect Wild Dolphins License Plate Fund, the National Woman’s Farm and Garden Association Scholarship awarded to Eric Montie, Shields MRI and CT of Cape Cod, the Quebec Labrador Fund/Atlantic Center for the Environment, Woods Hole Oceanographic Institution Academic Programs Office, Office of Naval Research, and NOAA Fisheries Marine Mammal Health and Stranding Response Program

Quality of care in urology

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75376/1/j.1464-410X.2004.05064.x.pd

Where Are All The Gifted Black Girls? Giving High School Girls Voice Via Qualitative Research Approach And Black Feminist Theory

ABSTRACT WHERE ARE ALL THE GIFTED BLACK GIRLS? GIVING HIGH SCHOOL GIRLS VOICE VIA QUALITATIVE RESEARCH APPROACH AND BLACK FEMINIST THEORY by MARY L. MONTIE May 2013 Advisor: Dr. Karen L. Tonso Major: Educational Evaluation and Research Degree: Doctor of Philosophy Gifted programs in the United States under-represent African American (Black) children (Phi Delta Kappan, 1992). In 1993, African-American students were under-represented by 50% in gifted education, and 60% in 1998 (Grantham & Ford, 2003). Further, some speculate that gifted education programs are the most segregated educational programs in the nation (Ford, 1995). This proves especially true for Black gifted girl in urban educational arenas, where gifted Black girls are rarely recognized. The purpose of this research was to examine the circumstances surrounding how urban black girls--identified as showing academic promise--come either to be overlooked as qualified for gifted education or seem not to take up a sense of themselves as gifted, that is they see themselves as not fitting among those who are in gifted education. Three scholarly arenas frame this study: Feminist thought and theory, with an emphasis on Black feminist thought, notions of giftedness and gifted education, and policies and processes for identification of gifted Black girls. Eight gifted Black girls were individually interviewed twice, three teachers were individually interviewed, and three parents were interviewed in a focus group session. Four interview guides were constructed to focus on students\u27 perspectives of GS1 (pseudonym) and gifted education, parent strategies, and teachers\u27 roles in the identification of these gifted Black girls. Qualitative analysis strategies (Spradley1980) were utilized for data analysis. The curriculum of the gifted programming at GS1 (pseudonym) ultimately contributed greatly not only to how girls saw themselves as gifted, but also how they understood stereotypes about young Black women. The feminist curriculum and the feminist lens provided in the gifted programming at GS1 provided outlets for girls\u27 voices. Teachers interviewed not only understood the gifted Black girls\u27 culture, but also strengthened their relationships with the girls and with their parents by presenting and enforcing clear expectations for the gifted programming. Parents interviewed not only understood their gifted daughters\u27 uniqueness, but also the importance of their independence and security as young Black women