Shift invariant preduals of ℓ₁(ℤ)

The Banach space ℓ<sub>1</sub>(ℤ) admits many non-isomorphic preduals, for example, C(K) for any compact countable space K, along with many more exotic Banach spaces. In this paper, we impose an extra condition: the predual must make the bilateral shift on ℓ<sub>1</sub>(ℤ) weak<sup>*</sup>-continuous. This is equivalent to making the natural convolution multiplication on ℓ<sub>1</sub>(ℤ) separately weak*-continuous and so turning ℓ<sub>1</sub>(ℤ) into a dual Banach algebra. We call such preduals <i>shift-invariant</i>. It is known that the only shift-invariant predual arising from the standard duality between C<sub>0</sub>(K) (for countable locally compact K) and ℓ<sub>1</sub>(ℤ) is c<sub>0</sub>(ℤ). We provide an explicit construction of an uncountable family of distinct preduals which do make the bilateral shift weak<sup>*</sup>-continuous. Using Szlenk index arguments, we show that merely as Banach spaces, these are all isomorphic to c<sub>0</sub>. We then build some theory to study such preduals, showing that they arise from certain semigroup compactifications of ℤ. This allows us to produce a large number of other examples, including non-isometric preduals, and preduals which are not Banach space isomorphic to c<sub>0</sub>

Geographic constraints on social network groups

Social groups are fundamental building blocks of human societies. While our social interactions have always been constrained by geography, it has been impossible, due to practical difficulties, to evaluate the nature of this restriction on social group structure. We construct a social network of individuals whose most frequent geographical locations are also known. We also classify the individuals into groups according to a community detection algorithm. We study the variation of geographical span for social groups of varying sizes, and explore the relationship between topological positions and geographic positions of their members. We find that small social groups are geographically very tight, but become much more clumped when the group size exceeds about 30 members. Also, we find no correlation between the topological positions and geographic positions of individuals within network communities. These results suggest that spreading processes face distinct structural and spatial constraints.Comment: 10 pages, 5 figure

UK experience of liver transplantation for erythropoietic protoporphyria

Erythropoietic protoporphyria (EPP) is characterised by excess production of free protoporphyrin from the bone marrow, most commonly due to deficiency of the enzyme ferrochelatase. Excess protoporphyrin gives rise to the cutaneous photosensitivity characteristic of the disease, and in a minority of patients leads to end-stage liver disease necessitating liver transplantation (LT). There is limited information regarding the timing, impact and long-term outcome of LT in such patients, thus we aimed to identify the indications and outcomes of all transplants performed for EPP in the UK using data from the UK Transplant Registry. Between 1987 and 2009, five patients underwent LT for EPP liver disease. Median follow-up was 60 months, and there were two deaths at 44 and 95 months from causes unrelated to liver disease. The remaining recipients are alive at 22.4 years, 61 months and 55 months after transplant. A high rate of postoperative biliary stricturing requiring multiple biliary interventions was observed. Recurrent EPP-liver disease occurred in 4/5 (80%) of patients but graft failure has not been observed. Given the role of biliary obstruction in inducing EPP-mediated liver damage, we suggest that consideration should be given for construction of a Roux loop at the time of transplant. Thus we demonstrate that although EPP liver transplant recipients have a good long-term survival, comparable to patients undergoing LT for other indications, biliary complications and disease recurrence are almost universal, and bone marrow transplantation should be considered where possible

Extensive Genetic Diversity and Substructuring Among Zebrafish Strains Revealed through Copy Number Variant Analysis

Copy number variants (CNVs) represent a substantial source of genomic variation in vertebrates and have been associated with numerous human diseases. Despite this, the extent of CNVs in the zebrafish, an important model for human disease, remains unknown. Using 80 zebrafish genomes, representing three commonly used laboratory strains and one native population, we constructed a genome-wide, high-resolution CNV map for the zebrafish comprising 6,080 CNV elements and encompassing 14.6% of the zebrafish reference genome. This amount of copy number variation is four times that previously observed in other vertebrates, including humans. Moreover, 69% of the CNV elements exhibited strain specificity, with the highest number observed for Tubingen. This variation likely arose, in part, from Tubingen's large founding size and composite population origin. Additional population genetic studies also provided important insight into the origins and substructure of these commonly used laboratory strains. This extensive variation among and within zebrafish strains may have functional effects that impact phenotype and, if not properly addressed, such extensive levels of germ-line variation and population substructure in this commonly used model organism can potentially confound studies intended for translation to human diseases.Stem Cell and Regenerative Biolog

Private Sector Union Density and the Wage Premium: Past, Present, and Future

The rise and decline of private sector unionization were among the more important features of the U.S. labor market during the twentieth century. Following a dramatic spurt in unionization after passage of the depression-era National Labor Relations Act (NLRA) of 1935, union density peaked in the mid-1950s, and then began a continuous decline. At the end of the century, the percentage of private wage and salary workers who were union members was less than 10 percent, not greatly different from union density prior to the NLRA

Computed CD4 percentage as a low-cost method for determining pediatric antiretroviral treatment eligibility

<p>Abstract</p> <p>Background</p> <p>The performance of the WHO recommendations for pediatric antiretroviral treatment (ART) in resource poor settings is insufficiently documented in routine care.</p> <p>Methods</p> <p>We compared clinical and immunological criteria in 366 children aged 0 to 12 years in Kinshasa and evaluated a simple computation to estimate CD4 percent, based on CD4 count, total white blood cell count and percentage lymphocytes. Kappa (κ) statistic was used to evaluate eligibility criteria and linear regression to determine trends of CD4 percent, count and total lymphocyte count (TLC).</p> <p>Results</p> <p>Agreement between clinical and immunological eligibility criteria was poor (κ = 0.26). One third of children clinically eligible for ART were ineligible using immunological criteria; one third of children immunologically eligible were ineligible using clinical criteria. Among children presenting in WHO stage I or II, 54 (32%) were eligible according to immunological criteria. Agreement with CD4 percent was poor for TLC (κ = 0.04), fair for total CD4 count (κ = 0.39) and substantial for CD4 percent computational estimate (κ = 0.71). Among 5 to 12 years old children, total CD4 count was higher in younger age groups (-32 cells/mm³per year older), CD4 percent was similar across age groups.</p> <p>Conclusion</p> <p>Age-specific thresholds for CD4 percent optimally determine pediatric ART eligibility. The use of CD4 percent computational estimate may increase ART access in settings with limited access to CD4 percent assays.</p