Patterns and severity of menopausal symptoms among Jordanian women

We examined 359 women aged 45–65 years who visited Jordan University Hospital between February and November 2014. The menopausal symptoms were assessed using a validated Arabic version of the menopause rating scale. The mean age at menopause was 49.4 years. Women aged 50–55 years more frequently exhibited hot flushes and vaginal dryness. Although premenopausal women were 1.5 times more likely to experience irritability, perimenopausal women were more likely to experience hot flushes, physical and mental irritability, sexual problems, vaginal dryness, and joint and muscular discomfort. Hence, health care providers should focus on women at all stages of life.     

Domination in graphs with bounded propagation: algorithms,formulations and hardness results

We introduce a hierarchy of problems between the Dominating Set problem and the Power Dominating Set (PDS) problem called the ℓ-round power dominating set (ℓ-round PDS, for short) problem. For ℓ=1, this is the Dominating Set problem, and for ℓ≥n−1, this is the PDS problem; here n denotes the number of nodes in the input graph. In PDS the goal is to find a minimum size set of nodes S that power dominates all the nodes, where a node v is power dominated if (1) v is in S or it has a neighbor in S, or (2) v has a neighbor u such that u and all of its neighbors except v are power dominated. Note that rule (1) is the same as for the Dominating Set problem, and that rule (2) is a type of propagation rule that applies iteratively. The ℓ-round PDS problem has the same set of rules as PDS, except we apply rule (2) in “parallel” in at most ℓ−1 rounds. We prove that ℓ-round PDS cannot be approximated better than 2^log1-en2^{\log^{1-\epsilon}{n}} even for ℓ=4 in general graphs. We provide a dynamic programming algorithm to solve ℓ-round PDS optimally in polynomial time on graphs of bounded tree-width. We present a PTAS (polynomial time approximation scheme) for ℓ-round PDS on planar graphs for l = O(\fraclognloglogn)\ell=O(\frac{\log{n}}{\log{\log{n}}}) . Finally, we give integer programming formulations for ℓ-round PDS.