ON THE GRUNDY BONDAGE NUMBERS OF GRAPHS

For a graph $G=(V,E)$, a sequence $S=(v_1,\ldots,v_k)$ of distinct vertices of $G$ it is called a \emph{dominating sequence} if $N_G[v_i]\setminus \bigcup_{j=1}^{i-1}N[v_j]\neq\varnothing$. The maximum length of dominating sequences is denoted by $\gamma_{gr}(G)$. We define the Grundy bondage numbers $b_{gr}(G)$ of a graph $G$ to be the cardinality of a smallest set $E$ of edges for which $\gamma_{gr}(G-E)>\gamma_{gr}(G).$ In this paper the exact values of $b_{gr}(G)$ are determined for several classes of graphs

p-Wave holographic superconductors with Weyl corrections

We study the (3+1) dimensional p-wave holographic superconductors with Weyl corrections both numerically and analytically. We describe numerically the behavior of critical temperature $T_{c}$ with respect to charge density $\rho$ in a limited range of Weyl coupling parameter $\gamma$ and we find in general the condensation becomes harder with the increase of parameter $\gamma$. In strong coupling limit of Yang-Mills theory, we show that the minimum value of $T_{c}$ obtained from analytical approach is in good agreement with the numerical results, and finally show how we got remarkably a similar result in the critical exponent 1/2 of the chemical potential $\mu$ and the order parameter$$ with the numerical curves of superconductors.Comment: 7 pages, 1 figure, 1 table. One refrence added, presentations improve

Adjuvant Radiotherapy for Groin Node Metastases Following Surgery for Vulvar Cancer: A Systematic Review

Background: Lymph node metastasis in vulvar cancer is a critical prognostic factor associated with higher recurrence and decreased survival. A survival benefit is reported with adjuvant radiotherapy but with potential significant morbidity. We aim to clarify whether there is high-quality evidence to support the use of adjuvant radiotherapy in this setting. Objectives: The aim of the study was to assess the effectiveness and safety of adjuvant radiotherapy to locoregional metastatic nodal areas. Search Methods: We conducted a comprehensive and systematic literature search of MEDLINE, Embase, Cochrane Central Register of Controlled Trials, Google Scholar, ClinicalTrials.gov, and the National Cancer Institute. We considered only randomized controlled trials (RCTs). Main Results: We identified 1,760 records and finally retrieved only one eligible RCT (114 participants with positive inguinofemoral lymph nodes). All women had undergone radical vulvectomy and bilateral inguinal lymphadenectomy and had been randomized to adjuvant radiotherapy or to intraoperative ipsilateral pelvic lymphadenectomy without adjuvant radiotherapy. At 6 years, the overall survival (OS) was 51% versus 41% in favor of radiotherapy (HR 0.61; 95% CI 0.30–1.3) without significance and with very low certainty of evidence. At 6 year, the cumulative incidence of cancer-related deaths was 29% versus 51% in favor of adjuvant radiotherapy (HR 0.49; 95% CI 0.28–0.87). Recurrence-free survival at 6 years was 59% after adjuvant radiotherapy versus 48% after pelvic lymphadenectomy (HR 0.39; 95% CI 0.17–0.88). Three (5.3%) versus 13 (24.1%) groin recurrences were noted, respectively, in the adjuvant radiotherapy and pelvic lymphadenectomy groups. There was no significant difference in acute toxicities for pelvic lymphadenectomy compared to radiotherapy. In women with positive pelvic lymph nodes (20%), the OS at 6 year was 36% compared with 13% in favor of adjuvant radiotherapy. Late cutaneous toxicity rate appeared to be greater after radiotherapy (19% vs. 15%) but with less chronic lymphedema (16% vs. 22%). Conclusion: There is only very low-quality evidence on administering adjuvant radiotherapy for inguinal lymph node metastases. Although the identified study was a multicenter RCT, there was a reasonable imprecision and inconsistency because of small study numbers, wide confidence intervals in the data, and early trial closure, resulting in downgrading of the evidence

Modeled Microgravity Disrupts Collagen I/Integrin Signaling During Osteoblastic Differentiation of Human Mesenchymal Stem Cells

Spaceflight leads to reduced bone mineral density in weight bearing bones that is primarily attributed to a reduction in bone formation. We have previously demonstrated severely reduced osteoblastogenesis of human mesenchymal stem cells (hMSC) following seven days culture in modeled microgravity. One potential mechanism for reduced osteoblastic differentiation is disruption of type I collagen-integrin interactions and reduced integrin signaling. Integrins are heterodimeric transmembrane receptors that bind extracellular matrix proteins and produce signals essential for proper cellular function, survival, and differentiation. Therefore, we investigated the effects of modeled microgravity on integrin expression and function in hMSC. We demonstrate that seven days of culture in modeled microgravity leads to reduced expression of the extracellular matrix protein, type I collagen (Col I). Conversely, modeled microgravity consistently increases Col I-specific alpha2 and beta1 integrin protein expression. Despite this increase in integrin sub-unit expression, autophosphorylation of adhesion-dependent kinases, focal adhesion kinase (FAK) and proline-rich tyrosine kinase 2 (PYK2), is significantly reduced. Activation of Akt is unaffected by the reduction in FAK activation. However, reduced downstream signaling via the Ras-MAPK pathway is evidenced by a reduction in Ras and ERK activation. Taken together, our findings indicate that modeled microgravity decreases integrin/MAPK signaling, which likely contributes to the observed reduction in osteoblastogenesis

Is vitamin D status a determining factor for metabolic syndrome? A case-control study

This study was undertaken to assess vitamin D status in nonmenopausal women with metabolic syndrome (MeS) and to evaluate its possible role in inflammation and other components of MeS. A case-control study was conducted during late fall and winter 2009–10. A total of 375 women with waist circumference (WC) ≥88 cm were examined to find 100 who met MeS criteria according to the National Cholesterol Education Program (NCEP)/Adult Treatment Panel (ATP) III criteria (NCEP/ATP III). Of those without MeS, 100 age- and residence area-matched women were selected as a control group. Anthropometric and laboratory evaluations were performed. Waist-to-hip ratio (WHR), body mass index (BMI), homeostatic model of insulin resistance (HOMA-IR) and body fat mass (FM) were also evaluated. Women with MeS had significantly higher BMI, waist circumference (WC) and FM but lower serum osteocalcin than controls. There was no significant difference in serum 25 hydroxyvitamin D (25[OH]D), intact parathyroid hormone (iPTH) or vitamin D status between the two groups. Serum highly sensitive C-reactive protein (hsCRP) concentration was significantly higher in the MeS group, compared to the controls (3.4 ± 3.3 vs 2.0 ± 1.9 mg/L, P < 0.001). The difference remained significant even after controlling for BMI (P = 0.011), WC (P = 0.014) and FM (P = 0.005). When comparison was made only in those subjects with insulin resistance (HOMA-IR > 2.4), hsCRP was still higher in the MeS group (n = 79) than in the control group (n = 61) (P < 0.001). When data were categorized according to vitamin D status, in the MeS group significantly higher plasma glucose concentrations were observed in subjects with vitamin D deficiency compared to those with insufficiency or sufficiency (104.0 ± 11.7, 83.0 ± 11.3 and 83.2 ± 9.9 mg/dL, respectively, P < 0.001). Interestingly, their WC or WHR did not show any significant difference. In stepwise regression analysis, 25(OH)D was the main predictor of both hsCRP and plasma glucose. Vitamin D status may, at least in part, be a determining factor of systemic inflammation and the related metabolic derangements of MeS