Pairs of Noncrossing Free Dyck Paths and Noncrossing Partitions

Using the bijection between partitions and vacillating tableaux, we establish a correspondence between pairs of noncrossing free Dyck paths of length $2n$ and noncrossing partitions of $[2n+1]$ with $n+1$ blocks. In terms of the number of up steps at odd positions, we find a characterization of Dyck paths constructed from pairs of noncrossing free Dyck paths by using the Labelle merging algorithm.Comment: 9 pages, 5 figures, revised version, to appear in Discrete Mathematic

The effects of indoor air pollution from solid fuel use on cognitive function among middle-aged and older population in China

Objectives Growing evidence has linked outdoor air pollution exposure with higher risk of cognitive impairments. However, the role of indoor air pollution in cognitive decline is not well elaborated. By using nationally representative longitudinal data, this study aimed to explore the effects of indoor air pollution from solid fuel use on cognitive function among middle-aged and older individuals in China. Methods Data were obtained from 2011-2015 waves of CHARLS (China Health and Retirement Longitudinal Study). Scores from the Telephone Interview of Cognitive Status and figure drawing/word recall tests were used to measure cognitive function in 39,482 individuals. Exposure to indoor air pollution was measured as use of solid fuel for cooking. Solid fuel was defined as coal, biomass charcoal, wood, and straw; clean fuel was defined as liquefied gas, natural gas, and electricity. Linear mixed effect models were applied to examine the effect of indoor air pollution from solid fuel use on cognitive function. Results Participants had an average global cognitive function of 9.67 (SD=4.13). Solid fuel users made up 49.71% of participants, but this proportion was much greater among those living in rural areas (64.22%). Compared with clean fuel users, solid fuel users had worse cognitive function. On average, solid fuel users had a 0.81 (95%CI: -0.89,-0.73) lower global cognition score, 0.63 (95%CI: -0.69,-0.57) lower mental health score, and 0.16 (95%CI: -0.22,-0.14) lower episodic memory score. These effects were stronger among participants who are female, aged 65 years old and above, have education level of primary school and below, or have cardiovascular diseases. Conclusions These results provide evidence for the role of indoor air pollution in neurobehavioral disorders in China. Promotion of practices like expanded use of clean fuel and improved stoves in households may be crucial to significantly reduce indoor air pollution and protect mental health