On the NP-Hardness of Approximating Ordering Constraint Satisfaction Problems

We show improved NP-hardness of approximating Ordering Constraint Satisfaction Problems (OCSPs). For the two most well-studied OCSPs, Maximum Acyclic Subgraph and Maximum Betweenness, we prove inapproximability of $14/15+\epsilon$ and $1/2+\epsilon$. An OCSP is said to be approximation resistant if it is hard to approximate better than taking a uniformly random ordering. We prove that the Maximum Non-Betweenness Problem is approximation resistant and that there are width-$m$ approximation-resistant OCSPs accepting only a fraction $1 / (m/2)!$ of assignments. These results provide the first examples of approximation-resistant OCSPs subject only to P $\neq$ \NP

Effects of exposure to biomass burning on pulmonary inflammatory markers and pulmonary function in individuals with COPD

Introduction: Pulmonary rehabilitation (PR) has many benefits for individuals with COPD. However, it is not clear whether PR could prevent the hazards of air pollution exposure. This study aimed to analyze the effects of biomass burning exposure on pulmonary inflammatory markers and pulmonary function in individuals with COPD, participants and non-participants of PR. Methods: 35 subjects were divided into three groups: individuals with COPD who received PR (G1, n = 15), those who did not (G2, n = 10), and a control group composed of healthy individuals without COPD (CG, n = 10). Measurements of lung function and concentrations of IL-6, IL-10, and TNF-α in exhaled breath condensate samples were collected. The assessment and concentrations of particulate matter (PM10), nitrogen dioxide (NO2), ozone (O3), temperature (T), and relative air humidity (RAH) were recorded in biomass burning and non-burning periods. Results: There was a significant increase in the concentrations of air pollutants in the biomass burning period. In this period, an increase in IL-6 (G1p = 0.041, G2 p = .012), and a reduction in the FEV1/FVC ratio (G1p = 0.021, G2 p = .007) were observed in individuals with COPD. In G1, the increase in IL-6 concentrations correlated positively with O3 (r = 0.693; p = .006), and negatively with RAH (r = â0.773; p = .003) in the burning period. Conclusions: Individuals with COPD exposed to biomass burning demonstrated increased pulmonary inflammation and a reduction in the FEV1/FVC ratio, regardless of their engagement in PR. Keywords: COPD, Air pollution, Pulmonary inflammatory markers, Lung, Interleukins, Spirometr