A note on the Cops & Robber game on graphs embedded in non-orientable surfaces

The Cops and Robber game is played on undirected finite graphs. A number of cops and one robber are positioned on vertices and take turns in sliding along edges. The cops win if they can catch the robber. The minimum number of cops needed to win on a graph is called its cop number. It is known that the cop number of a graph embedded on a surface $X$ of genus $g$ is at most $3g/2 + 3$, if $X$ is orientable (Schroeder 2004), and at most $2g+1$, otherwise (Nowakowski & Schroeder 1997). We improve the bounds for non-orientable surfaces by reduction to the orientable case using covering spaces. As corollaries, using Schroeder's results, we obtain the following: the maximum cop number of graphs embeddable in the projective plane is 3; the cop number of graphs embeddable in the Klein Bottle is at most 4, and an upper bound is $3g/2 + 3/2$ for all other $g$.Comment: 5 pages, 1 figur

Clinical Practice Guidelines for Childbearing Female Candidates for Bariatric Surgery, Pregnancy, and Post-partum Management After Bariatric Surgery

Emerging evidence suggests that bariatric surgery improves pregnancy outcomes of women with obesity by reducing the rates of gestational diabetes, pregnancy-induced hypertension, and macrosomia. However, it is associated with an increased risk of a small-for-gestational-age fetus and prematurity. Based on the work of a multidisciplinary task force, we propose clinical practice recommendations for pregnancy management following bariatric surgery. They are derived from a comprehensive review of the literature, existing guidelines, and expert opinion covering the preferred type of surgery for women of childbearing age, timing between surgery and pregnancy, contraception, systematic nutritional support and management of nutritional deficiencies, screening and management of gestational diabetes, weight gain during pregnancy, gastric banding management, surgical emergencies, obstetrical management, and specific care in the postpartum period and for newborns

LRP1 Receptor Controls Adipogenesis and Is Up-Regulated In Human and Mouse Obese Adipose Tissue

The cell surface low-density lipoprotein receptor-related protein 1, LRP1, plays a major role in lipid metabolism. The question that remains open concerns the function of LRP1 in adipogenesis. Here, we show that LRP1 is highly expressed in murine preadipocytes as well as in primary culture of human adipocytes. Moreover, LRP1 remains abundantly synthesised during mouse and human adipocyte differentiation. We demonstrate that LRP1 silencing in 3T3F442A murine preadipocytes significantly inhibits the expression of PPARγ, HSL and aP2 adipocyte differentiation markers after adipogenesis induction, and leads to lipid-depleted cells. We further show that the absence of lipids in LRP1-silenced preadipocytes is not caused by lipolysis induction. In addition, we provide the first evidences that LRP1 is significantly up-regulated in obese C57BI6/J mouse adipocytes and obese human adipose tissues. Interestingly, silencing of LRP1 in fully-differentiated adipocytes also reduces cellular lipid level and is associated with an increase of basal lipolysis. However, the ability of mature adipocytes to induce lipolysis is independent of LRP1 expression. Altogether, our findings highlight the dual role of LRP1 in the control of adipogenesis and lipid homeostasis, and suggest that LRP1 may be an important therapeutic target in obesity

Effect of eplerenone on extracellular cardiac matrix biomarkers in patients with acute ST-elevation myocardial infarction without heart failure: insights from the randomized double-blind REMINDER Study

Objective: Aldosterone stimulates cardiac collagen synthesis. Circulating biomarkers of collagen turnover provide a useful tool for the assessment of cardiac remodeling in patients with an acute myocardial infarction (MI).  Methods: The REMINDER trial assessed the effect of eplerenone in patients with an acute ST-elevation Myocardial Infarction (STEMI) without known heart failure (HF), when initiated within 24 h of symptom onset. The primary outcome was almost totally (>90%) driven by natriuretic peptide (NP) thresholds after 1-month post-MI (it also included a composite of cardiovascular death or re-hospitalization or new onset HF or sustained ventricular tachycardia or fibrillation or LVEF ≤40% after 1-month post-MI). This secondary analysis aims to assess the extracellular matrix marker (ECMM) levels with regards to: (1) patients` characteristics; (2) determinants; (3) and eplerenone effect.  Results: Serum levels of ECMM were measured in 526 (52%) of the 1012 patients enrolled in the REMINDER trial. Patients with procollagen type III N-terminal propeptide (PIIINP) above the median were older and had worse renal function (p < 0.05). Worse renal function was associated with increased levels of PIIINP (standardized β ≈ 0.20, p < 0.05). Eplerenone reduced PIIINP when the levels of this biomarker were above the median of 3.9 ng/mL (0.13 ± 1.48 vs. -0.37 ± 1.56 ng/mL, p = 0.008). Higher levels of PIIINP were independently associated with higher proportion of NP above the prespecified thresholds (HR = 1.95, 95% CI 1.16-3.29, p = 0.012).  Conclusions: Eplerenone effectively reduces PIIINP levels when baseline values were above the median. Eplerenone may limit ECMM formation in post-MI without HF