Oriented coloring: complexity and approximation

International audienceThis paper is devoted to an oriented coloring problem motivated by a task assignment model. A recent result established the NP-completeness of deciding whether a digraph is k-oriented colorable; we extend this result to the classes of bipartite digraphs and circuit-free digraphs. Finally, we investigate the approximation of this problem: both positive and negative results are devised

First month prednisone dose predicts prednisone burden during the following 11 months: An observational study from the RELES cohort

Aim: To study the influence of prednisone dose during the first month after systemic lupus erythematosus (SLE) diagnosis (prednisone-1) on glucocorticoid burden during the subsequent 11 months (prednisone-2–12). Methods: 223 patients from the Registro Español de Lupus Eritematoso Sistémico inception cohort were studied. The cumulative dose of prednisone-1 and prednisone-2–12 were calculated and recoded into a four-level categorical variable: no prednisone, low dose (up to 7.5 mg/day), medium dose (up to 30 mg/day) and high dose (over 30 mg/day). The association between the cumulative prednisone-1 and prednisone-2–12 doses was tested. We analysed whether the four-level prednisone-1 categorical variable was an independent predictor of an average dose >7.5 mg/day of prednisone-2–12. Adjusting variables included age, immunosuppressives, antimalarials, methyl-prednisolone pulses, lupus nephritis and baseline SLE Disease Activity Index (SLEDAI). Results: Within the first month, 113 patients (51%) did not receive any prednisone, 24 patients (11%) received average low doses, 46 patients (21%) received medium doses and 40 patients (18%) received high doses. There was a strong association between prednisone-1 and prednisone-2–12 dose categories (p7.5 mg/day, while patients receiving low-dose prednisone-1 were not (adjusted OR 1.4, 95% CI 0. 0.38 to 5.2). If the analysis was restricted to the 158 patients with a baseline SLEDAI of =6, the model did not change. Conclusion: The dose of prednisone during the first month after the diagnosis of SLE is an independent predictor of prednisone burden during the following 11 months

Effect of alirocumab on mortality after acute coronary syndromes. An analysis of the ODYSSEY OUTCOMES randomized clinical trial

Background: Previous trials of PCSK9 (proprotein convertase subtilisin-kexin type 9) inhibitors demonstrated reductions in major adverse cardiovascular events, but not death. We assessed the effects of alirocumab on death after index acute coronary syndrome. Methods: ODYSSEY OUTCOMES (Evaluation of Cardiovascular Outcomes After an Acute Coronary Syndrome During Treatment With Alirocumab) was a double-blind, randomized comparison of alirocumab or placebo in 18 924 patients who had an ACS 1 to 12 months previously and elevated atherogenic lipoproteins despite intensive statin therapy. Alirocumab dose was blindly titrated to target achieved low-density lipoprotein cholesterol (LDL-C) between 25 and 50 mg/dL. We examined the effects of treatment on all-cause death and its components, cardiovascular and noncardiovascular death, with log-rank testing. Joint semiparametric models tested associations between nonfatal cardiovascular events and cardiovascular or noncardiovascular death. Results: Median follow-up was 2.8 years. Death occurred in 334 (3.5%) and 392 (4.1%) patients, respectively, in the alirocumab and placebo groups (hazard ratio [HR], 0.85; 95% CI, 0.73 to 0.98; P=0.03, nominal P value). This resulted from nonsignificantly fewer cardiovascular (240 [2.5%] vs 271 [2.9%]; HR, 0.88; 95% CI, 0.74 to 1.05; P=0.15) and noncardiovascular (94 [1.0%] vs 121 [1.3%]; HR, 0.77; 95% CI, 0.59 to 1.01; P=0.06) deaths with alirocumab. In a prespecified analysis of 8242 patients eligible for ≥3 years follow-up, alirocumab reduced death (HR, 0.78; 95% CI, 0.65 to 0.94; P=0.01). Patients with nonfatal cardiovascular events were at increased risk for cardiovascular and noncardiovascular deaths (P<0.0001 for the associations). Alirocumab reduced total nonfatal cardiovascular events (P<0.001) and thereby may have attenuated the number of cardiovascular and noncardiovascular deaths. A post hoc analysis found that, compared to patients with lower LDL-C, patients with baseline LDL-C ≥100 mg/dL (2.59 mmol/L) had a greater absolute risk of death and a larger mortality benefit from alirocumab (HR, 0.71; 95% CI, 0.56 to 0.90; Pinteraction=0.007). In the alirocumab group, all-cause death declined wit h achieved LDL-C at 4 months of treatment, to a level of approximately 30 mg/dL (adjusted P=0.017 for linear trend). Conclusions: Alirocumab added to intensive statin therapy has the potential to reduce death after acute coronary syndrome, particularly if treatment is maintained for ≥3 years, if baseline LDL-C is ≥100 mg/dL, or if achieved LDL-C is low. Clinical Trial Registration: URL: https://www.clinicaltrials.gov. Unique identifier: NCT01663402

Acyclic Improper Colorings of Graphs

In this paper, we introduce the new notion of acyclic improper colorings of graphs. An improper coloring of a graph G is a mapping c from the set of vertices of G to a set of colors such that for every color i, the subgraph induced by the vertices with color i satisfies some property depending on i. Such an improper coloring is acyclic if for every two distinct colors i and j, the subgraph induced by all the edges linking a i-colored vertex and a j-colored vertex is acyclic. We prove that every outerplanar graph can be acyclically 2-colored in such a way that every monochromatic subgraph has degree at most five and that this result is best possible. For planar graphs, we prove some negative results and state some open problems. 1 Introduction Let G be a graph. We denote by V (G) the vertex set of G and by E(G) the edge set of G. A coloring of G is a mapping c from V (G) to a finite set of colors C. The mapping c is a k-coloring of G if the set C has k elements. A coloring c is pro..