Adaptation of a 3-factor model for the Pittsburgh Sleep Quality Index in Portuguese older adults

The present study examined the factor structure of the Pittsburgh Sleep Quality Index (PSQI) in a sample of older Portuguese adults using a cross-validation approach. Design is a cross-sectional. A convenience sample of 204 community-dwelling older adults (M=70.05, SD=7.15) were included. The global sleep quality (GSQ) score ranged from 0 to 18 with a mean of 5.98 (SD +/- 3.45). The distribution showed that gender and perception of oneself as healthy influences GSQ in this sample. Cronbach's alpha was 0.69, but increased to 0.70 if the "use of sleep medication" component was deleted. Exploratory factor analysis (EPA) demonstrated two factor model is better than one factor, and a model fit with good indices (chi-square=8.649, df=8, p=0.373). Confirmatory factor analysis (CFA) was performed on the single factor, two factor, and three factor models, with and without the "use of sleep medications" component. The best model was the 3-factor model without the "use of sleep medications" component (chi-square=1.214, df=6, GFI=0.997, AGFI=0.918, CFI=0.986, RMSEA=0.046). The adaptation of the model is similar to the original model, with the only change being the exclusion of the "use of medications to sleep" component. We suggest using that component as a complementary qualitative assessment of health.Foundation for Science and Technology - Portugal (CIEO - Research Centre for Spatial and Organizational Dynamics, University of Algarve, Portugal)Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior (CAPES) [BEX 1990/15-2]info:eu-repo/semantics/publishedVersio

On the number of pancake stacks requiring four flips to be sorted

Using existing classification results for the 7- and 8-cycles in the pancake graph, we determine the number of permutations that require 4 pancake flips (prefix reversals) to be sorted. A similar characterization of the 8-cycles in the burnt pancake graph, due to the authors, is used to derive a formula for the number of signed permutations requiring 4 (burnt) pancake flips to be sorted. We furthermore provide an analogous characterization of the 9-cycles in the burnt pancake graph. Finally we present numerical evidence that polynomial formulae exist giving the number of signed permutations that require $k$ flips to be sorted, with $5\leq k\leq9$.Comment: We have finalized for the paper for publication in DMTCS, updated a reference to its published version, moved the abstract to its proper location, and added a thank you to the referees. The paper has 27 pages, 6 figures, and 2 table

Cycles in the burnt pancake graphs

The pancake graph $P_n$ is the Cayley graph of the symmetric group $S_n$ on $n$ elements generated by prefix reversals. $P_n$ has been shown to have properties that makes it a useful network scheme for parallel processors. For example, it is $(n-1)$-regular, vertex-transitive, and one can embed cycles in it of length $\ell$ with $6\leq\ell\leq n!$. The burnt pancake graph $BP_n$, which is the Cayley graph of the group of signed permutations $B_n$ using prefix reversals as generators, has similar properties. Indeed, $BP_n$ is $n$-regular and vertex-transitive. In this paper, we show that $BP_n$ has every cycle of length $\ell$ with $8\leq\ell\leq 2^n n!$. The proof given is a constructive one that utilizes the recursive structure of $BP_n$. We also present a complete characterization of all the $8$-cycles in $BP_n$ for $n \geq 2$, which are the smallest cycles embeddable in $BP_n$, by presenting their canonical forms as products of the prefix reversal generators.Comment: Added a reference, clarified some definitions, fixed some typos. 42 pages, 9 figures, 20 pages of appendice