Group Sum Chromatic Number of Graphs

We investigate the \textit{group sum chromatic number} (\gchi(G)) of graphs, i.e. the smallest value $s$ such that taking any Abelian group \gr of order $s$, there exists a function f:E(G)\rightarrow \gr such that the sums of edge labels properly colour the vertices. It is known that \gchi(G)\in\{\chi(G),\chi(G)+1\} for any graph $G$ with no component of order less than $3$ and we characterize the graphs for which \gchi(G)=\chi(G).Comment: Accepted for publication in European Journal of Combinatorics, Elsevie

Group Irregularity Strength of Connected Graphs

We investigate the group irregularity strength ($s_g(G)$) of graphs, i.e. the smallest value of $s$ such that taking any Abelian group \gr of order $s$, there exists a function f:E(G)\rightarrow \gr such that the sums of edge labels at every vertex are distinct. We prove that for any connected graph $G$ of order at least 3, $s_g(G)=n$ if $n\neq 4k+2$ and $s_g(G)\leq n+1$ otherwise, except the case of some infinite family of stars

Automated Shack-Hartmann seeing measurements at the South Pole

The statistics and dynamics of the atmospheric seeing at the South Pole have been studied over a period of 101 days in winter. These measurements have been made with the first fully autonomous differential image motion monitor, the A-DIMM. The analysis shows an average seeing of 1.9″ with a standard deviation of 0.6″. The extensive set of data has allowed the study of the seeing time variations, showing that the seeing varies by a factor of two within a characteristic time of 2 hours

Physical activity and glioma: A case–control study with follow-up for survival

Purpose: High-grade disease accounts for ~ 70% of all glioma, and has a high mortality rate. Few modifiable exposures are known to be related to glioma risk or mortality. Methods: We examined associations between lifetime physical activity and physical activity at different ages (15–18 years, 19–29 years, 30–39 years, last 10 years) with the risk of glioma diagnosis, using data from a hospital-based family case–control study (495 cases; 371 controls). We followed up cases over a median of 25 months to examine whether physical activity was associated with all-cause mortality. Physical activity and potential confounders were assessed by self-administered questionnaire. We examined associations between physical activity (metabolic equivalent [MET]-h/wk) and glioma risk using unconditional logistic regression and with all-cause mortality in cases using Cox regression. Results: We noted a reduced risk of glioma for the highest ( ≥ 47 MET-h/wk) versus lowest ( \u3c 24 METh/wk) category of physical activity for lifetime activity (OR = 0.58, 95% CI: 0.38–0.89) and at 15–18 years (OR = 0.57, 95% CI: 0.39–0.83). We did not observe any association between physical activity and all-cause mortality (HR for lifetime physical activity = 0.91, 95% CI: 0.64–1.29). Conclusion: Our findings are consistent with previous research that suggested physical activity during adolescence might be protective against glioma. Engaging in physical activity during adolescence has many health benefits; this health behavior may also offer protection against glioma

Estrogen receptors ERα and ERβ in proliferation in the rodent mammary gland

Most evidence supports the view that ERα is responsible for estrogen (ovarian estradiol, E(2))-induced proliferation in the epithelial cells of the mammary gland, but despite this, proliferating epithelial cells do not express ERα. We have examined this apparent paradox by studying the role of ERα and ERβ in E(2)-induced proliferation in mammary glands (measured by BrdUrd incorporation into DNA) in mice with intact ERβ (WT mice) and those in which the ERβ gene has been inactivated (ERβ(-/-) mice). On treatment of ERβ(-/-) mice with E(2) or ovariectomized WT mice with E(2), tamoxifen, or a specific ERβ agonist (BAG), the number of BrdUrd-labeled cells in mammary glands increased from 3.4% in controls to 28-38% in the treated mice. This indicates that both ERα and ERβ can mediate E(2)-induced proliferation independently of each other. With specific antibodies, ERβ was found in both epithelial and stromal cells, whereas ERα was strictly epithelial. Within 4 h of a single dose of E(2), ERα was lost from the nuclei of epithelial cells. In WT mice, ERα reappeared by 24 h, but in ERβ(-/-) mice, return to the nucleus was delayed by 24 h. At 4 h after E(2), neither ERα nor progesterone receptor was detectable in BrdUrd-labeled nuclei but by 48 h after E(2), 29% of the BrdUrd-labeled cells expressed ERα, and 21-38% expressed progesterone receptor. During 3 weeks of continuous E(2) treatment, ERβ remained in the nucleus, but there was no detectable ERα. With tamoxifen treatment, ERα remained in the nucleus, but ERβ was lost. From these results, we conclude that ERα receives the proliferation signal from E(2), initiates DNA synthesis, and is then lost from cells. The subsequent steps in proliferation can proceed in the absence of either ERα or ERβ. ERβ facilitates the return of ERα to the nucleus and restores responsiveness to E(2). By down-regulating ERβ, tamoxifen may prolong refractoriness to E(2) in mammary epithelium