Decision Problems for Nash Equilibria in Stochastic Games

We analyse the computational complexity of finding Nash equilibria in stochastic multiplayer games with $\omega$-regular objectives. While the existence of an equilibrium whose payoff falls into a certain interval may be undecidable, we single out several decidable restrictions of the problem. First, restricting the search space to stationary, or pure stationary, equilibria results in problems that are typically contained in PSPACE and NP, respectively. Second, we show that the existence of an equilibrium with a binary payoff (i.e. an equilibrium where each player either wins or loses with probability 1) is decidable. We also establish that the existence of a Nash equilibrium with a certain binary payoff entails the existence of an equilibrium with the same payoff in pure, finite-state strategies.Comment: 22 pages, revised versio

Forest Biodiversity Assessment in Peruvian Andean Montane Cloud Forest

Cloud forests are unusual and fragile habitats, being one of the least studied and least understood ecosystems. The tropical Andean dominion is considered one of the most significant places in the world as rega rds biological diversity, with a very high level of endemism. The biodiversity was analysed in an isolated remnant area of a tropical montane cloud forest known as the ?Bosque de Neblina de Cuyas?, in the North of the Peruvian Andean range. Composition, structure and dead wood were measured or estimated. The values obtained were compared with other cloud forests. The study revealed a high level of forest biodiversity, although the level of biodiversity differs from one area to another: in the inner areas, where human pressure is almost inexistent, the biodiversity values increase. The high species richness and the low dominance among species bear testimony to this montane cloud forest as a real enclave of biodiversity

Dairy products and ovarian cancer: A pooled analysis of 12 cohort studies

Background: Dairy foods and their constituents (lactose and calcium) have been hypothesized to promote ovarian carcinogenesis. Although case-control studies have reported conflicting results for dairy foods and lactose, several cohort studies have shown positive associations between skim milk, lactose, and ovarian cancer. Methods: A pooled analysis of the primary data from 12 prospective cohort studies was conducted. The study population consisted of 553,217 women among whom 2,132 epithelial ovarian cases were identified. Study-specific relative risks and 95% confidence intervals were calculated by Cox proportional hazards models and then pooled by a random-effects model. Results: No statistically significant associations were observed between intakes of milk, cheese, yogurt, ice cream, and dietary and total calcium intake and risk of ovarian cancer. Higher lactose intakes comparing ≥30 versus <10 g/d were associated with a statistically significant higher risk of ovarian cancer, although the trend was not statistically significant (pooled multivariate relative risk, 1.19; 95% confidence interval, 1.01-1.40; P trend = 0.19). Associations for endometrioid, mucinous, and serous ovarian cancer were similar to the overall findings. Discussion: Overall, no associations were observed for intakes of specific dairy foods or calcium and ovarian cancer risk. A modest elevation in the risk of ovarian cancer was seen for lactose intake at the level that was equivalent to three or more servings of milk per day. Because a new dietary guideline recommends two to three servings of dairy products per day, the relation between dairy product consumption and ovarian cancer risk at these consumption levels deserves further examination. Copyright © 2006 American Association for Cancer Research

Fruits, vegetables, and colon cancer risk in a pooled analysis of 14 cohort studies

Background Fruit and vegetable intakes have been associated with a reduced risk of colon cancer; however, in more recent studies associations have been less consistent. Statistical power to examine associations by colon site has been limited in previous studies. Methods Fruit and vegetable intakes in relation to colon cancer risk were examined in the Pooling Project of Prospective Studies of Diet and Cancer. Relative risks (RRs) and 95% confidence intervals (CIs) were estimated separately in 14 studies using Cox proportional hazards model and then pooled using a random- effects model. Intakes of total fruits and vegetables, total fruits, and total vegetables were categorized according to quintiles and absolute cutpoints. Analyses were conducted for colon cancer overall and for proximal and distal colon cancer separately. All statistical tests were two-sided. Results Among 756 217 men and women followed for up to 6 to 20 years, depending on the study, 5838 were diagnosed with colon cancer. The pooled multivariable RRs (95% CIs) of colon cancer for the highest versus lowest quintiles of intake were 0.91 (0.82 to 1.01, Ptrend =.19) for total fruits and vegetables, 0.93 (0.85 to 1.02, Ptrend =.28) for total fruits, and 0.94 (0.86 to 1.02, P trend =.17) for total vegetables. Similar results were observed when intakes were categorized by identical absolute cut points across studies (pooled multivariable RR = 0.90, 95% CI = 0.77 to 1.05 for 800 or more versus <200 g/day of total fruits and vegetables, Ptrend =.06). The age-standardized incidence rates of colon cancer for these two intake categories were 54 and 61 per 100 000 person-years, respectively. When analyzed by colon site, the pooled multivari- able RRs (95% CIs) comparing total fruit and vegetable intakes of 800 or more versus less than 200 g/day were 0.74 (0.57 to 0.95, Ptrend =.02) for distal colon cancers and 1.02 (0.82 to 1.27, Ptrend =.57) for proximal colon cancers. Similar site-specific associations were observed for total fruits and total vegetables. Conclusion Fruit and vegetable intakes were not strongly associated with colon cancer risk overall but may be associated with a lower risk of distal colon cancer