Fixing numbers for matroids

Motivated by work in graph theory, we define the fixing number for a matroid. We give upper and lower bounds for fixing numbers for a general matroid in terms of the size and maximum orbit size (under the action of the matroid automorphism group). We prove the fixing numbers for the cycle matroid and bicircular matroid associated with 3-connected graphs are identical. Many of these results have interpretations through permutation groups, and we make this connection explicit.Comment: This is a major revision of a previous versio

The Pittsburgh Regional Diversity Survey

The Pittsburgh Regional Diversity Survey asked southwestern Pennsylvania residents for their views on diversity in the workplace, region and their neighborhood. Of the 3,553 people who took the online survey, 78 percent are white, 13.2 percent are African American, 3.9 percent are Hispanic, 2.9 percent are Asian and 2.1 percent are of mixed race. Here are the key findings:Overall, 68 percent of all residents surveyed "strongly agree" there is value in a diverse workplace. But an opinion gap exists along racial lines: 80 percent of minorities strongly agree a diverse workplace has value compared with fewer than 64 percent of white workers.Fewer than 30 percent of workers describe their workplace as "very diverse." White workers are almost twice as likely as minorities to describe workplaces as "very diverse."Only half of workers overall describe their employer as being very committed to hiring minority workers. And only 42 percent see their employers as being very committed to advancing and promoting minority workers.Minorities are much less likely to hold their employer's commitment to diversity in high regard. For example, 55 percent of white workers feel their employer is very committed to hiring minorities while 34 percent of minority workers say the same about their employer.73 percent of white workers say their race isn't a factor in getting a promotion while only 51 percent of minorities agree. And 31 percent of minorities see their race and ethnicity as a disadvantage in such decisions; only 13 percent of whites feel the same way.More than 86 percent of workers overall are satisfied to some degree with their job. But while 52 percent of white workers are very satisfied with their job, only 34 percent of minority workers feel the same way about theirs

Potential Impacts of Climate Change on Water Resources in South Carolina and Across the United States

2008 S.C. Water Resources Conference - Addressing Water Challenges Facing the State and Regio

Upscaling key ecosystem functions across the conterminous United States by a water-centric ecosystem model

We developed a water-centric monthly scale simulation model (WaSSI-C) by integrating empirical water and carbon flux measurements from the FLUXNET network and an existing water supply and demand accounting model (WaSSI). The WaSSI-C model was evaluated with basin-scale evapotranspiration (ET), gross ecosystem productivity (GEP), and net ecosystem exchange (NEE) estimates by multiple independent methods across 2103 eight-digit Hydrologic Unit Code watersheds in the conterminous United States from 2001 to 2006. Our results indicate that WaSSI-C captured the spatial and temporal variability and the effects of large droughts on key ecosystem fluxes. Our modeled mean (±standard deviation in space) ET (556 ± 228 mm yr−1) compared well to Moderate Resolution Imaging Spectroradiometer (MODIS) based (527 ± 251 mm yr−1) and watershed water balance based ET (571 ± 242 mm yr−1). Our mean annual GEP estimates (1362 ± 688 g C m−2 yr−1) compared well (R2 = 0.83) to estimates (1194 ± 649 g C m−2 yr−1) by eddy flux-based EC-MOD model, but both methods led significantly higher (25–30%) values than the standard MODIS product (904 ± 467 g C m−2 yr−1). Among the 18 water resource regions, the southeast ranked the highest in terms of its water yield and carbon sequestration capacity. When all ecosystems were considered, the mean NEE (−353 ± 298 g C m−2 yr−1) predicted by this study was 60% higher than EC-MOD\u27s estimate (−220 ± 225 g C m−2 yr−1) in absolute magnitude, suggesting overall high uncertainty in quantifying NEE at a large scale. Our water-centric model offers a new tool for examining the trade-offs between regional water and carbon resources under a changing environment

Friends or Strangers? A Feasibility Study of an Innovative Focus Group Methodology

Focus groups are useful tools for examining perceptions, feelings, and suggestions about topics, products, or issues. Typically, focus groups are held in formal facilities with “strangers” or participants who do not know each other. Recent work suggests that “friendship groups” may provide an innovative alternative for collecting group-level qualitative data. This approach involves recruiting a single “source participant” who hosts a group in his/her home and recruits friends possessing the characteristics desired for the study. In order to examine the feasibility of friendship groups as a defensible research methodology, we conducted a series of four friendship groups as a feasibility study. Our analysis examined data from questionnaires about demographics, levels of acquaintanceship, and experience taking part in the group; transcripts; observational data; and the time and costs for recruiting. Using these data, we examined group dynamics, implementation issues, and recruitment time and costs. Based on these analyses, our study determined that friendship groups have the potential to be a viable and cost-effective method of qualitative inquiry

In Vivo Measurements of Tumor Metabolism and Growth after Administration of Enzastaurin Using Small Animal FDG Positron Emission Tomography

Background. The use of 2-[18F]fluoro-2-deoxy-D-glucose ([18F]FDG) may help to establish the antitumor activity of enzastaurin, a novel protein kinase C-beta II (PKC-βII) inhibitor, in mouse xenografts. Methods. The hematologic cell line RAJI and the solid tumor cell line U87MG were each implanted in NOD/SCID mice. Standard tumor growth measurements and [18F]FDG PET imaging were performed weekly for up to three weeks after tumor implantation and growth. Results. Concomitant with caliper measurements, [18F]FDG PET imaging was performed to monitor glucose metabolism. Heterogeneity of glucose uptake in various areas of the tumors was observed after vehicle or enzastaurin treatment. This heterogeneity may limit the use of [18F]FDG PET imaging to measure enzastaurin-associated changes in xenograft tumors. Conclusion. [18F]FDG PET imaging technique does not correlate with standard caliper assessments in xenografts to assess the antitumor activity of enzastaurin. Future studies are needed to determine the use of [18F]FDG PET imaging in preclinical models