Minmax subtree cover problem on cacti

AbstractLet G=(V,E) be a connected graph such that edges and vertices are weighted by nonnegative reals. Let p be a positive integer. The minmax subtree cover problem (MSC) asks to find a pair (X,T) of a partition X={X1,X2,…,Xp} of V and a set T of p subtrees T1,T2,…,Tp, each Ti containing Xi so as to minimize the maximum cost of the subtrees, where the cost of Ti is defined to be the sum of the weights of edges in Ti and the weights of vertices in Xi. In this paper, we propose an O(p2n) time (4-4/(p+1))-approximation algorithm for the MSC when G is a cactus

Amino acid and vitamin supplementation improved health conditions in elderly participants

The purpose of this study was to investigate the effects of supplementation with amino acids and vitamins on health conditions in unhealthy older people. One bedridden inpatient group (n = 10; mean age, 79.8 ± 8.5 y) and one outpatient group (n = 9; mean age, 72.9 ± 12.2 y) participated in this study. A mixture supplementation with amino acids containing arginine (500 mg/day), glutamine (600 mg/day), and leucine (1200 mg/day), and 11 kinds of vitamins was daily administrated for 8 weeks. In both groups, general blood biomarkers such as white blood cell count, natural killer cell activity, and C-reactive protein levels were measured. All measurements were taken before (baseline), at 4 weeks (mid-point), and after each trial (post-point). At mid-point, natural killer cell activity in the outpatient group increased significantly compared to baseline. At post-point, natural killer cell activity in the outpatient and inpatient groups increased significantly compared to baseline. The other blood biomarkers did not show any significant change throughout the trial. This pilot study suggested that a mixture of arginine, glutamine, leucine, and vitamins is useful to support innate immunity in unhealthy older people, even if their diseases, symptoms, and prescribed medicines are different