Penta-Extensions of Hereditary Classes of Graphs

Penta is the configuration shown in figure 1(a), where continuous lines represent edges and dotted lines represent non-edges. The vertex u in figure 1(a) is called the center of Penta. A graph G is called a pentagraph if every induced subgraph H of G has a vertex v which is not a center of induced Penta in H. The class of pentagraphs is a common generalization of chordal [triangulated] graphs and Mahadev graphs. We construct a polynomial-time algorithm that either find a maximum stable set of G or concludes that G is not a pentagraph. We propose a method for extending α-polynomial hereditary classes based on induced Pentas.     

The occurrence of happy and traumatic events in the life of common people

Until recent times, psychology and the social sciences have paid only limited attention to the positive aspects of human life. The present article aims to review psychological and epidemiological studies about the occurrence of happy and traumatic events in the life of common people, critically discussing their findings and suggesting new research directions. Overall, it has emerged that most people report having experienced at least one traumatic event in their lives; on the other hand, moderate happy experiences may occur with a daily frequency. Unfortunately, the studies conducted thus far suffer from methodological limitations as they did not consider extremely happy events and collected data about happy and traumatic events separately. The author emphasizes the necessity to jointly investigate the prevalence of both happy and traumatic events. Hopefully, this will permit to achieve more reliable indicators of quality of life, thus contributing to increase researchers’ understanding of what makes human existence joyful and sorrowful.     

Endothelial progenitor cell therapy for atherosclerosis: the philosopher's stone for an aging population?

Much of the increased risk for atherosclerosis progression with age may be a result of age-related declines in the capacity of precursor cells to repair damage in the arterial endothelium. To estimate the impact of progenitor cell therapy for atherosclerosis on cardiovascular disease (CVD) mortality, life expectancy, and survival, as compared with the lifetime control of conventional risk factors, we modeled the health effects of bone marrow-derived endothelial progenitor cell therapy using data from the 1950 to 1996 follow-up of the Framingham Heart Study. To model cardiovascular disease mortality, we assumed that progenitor cell therapy was applied at age 30, with the effect assumed to be a 10-year delay in atherosclerosis progression. Age projections were constructed analytically using the stochastic process model for risk factor dynamics and mortality and microsimulation techniques. We considered three types of interventions: (i) keeping risk factors within selected limits to model current clinical recommendations; (ii) an age shift of 10 years to model the effects of progenitor cell therapy; and (iii) elimination of a competing risk (such as cancer). Our study suggests that progenitor cell therapy might increase life expectancy in the population as much as the complete elimination of cancer (in females, an additional 3.67 versus 3.37 years; in males, an additional 5.94 versus 2.86 years, respectively).     

Rényi Statistics in Directed Families of Exponential Experiments*

Rényi statistics are considered in a directed family of general exponential models. These statistics are defined as Rényi distances between estimated and hypothetical model. An asymptotically quadratic approximation to the Rényi statistics is established, leading to similar asymptotic distribution results as established in the literature for the likelihood ratio statistics. Some arguments in favour of the Rényi statistics are discussed, and a numerical comparison of the Rényi goodness-of-fit tests with the likelihood ratio test is presented.     

Rényi statistics for testing composite hypotheses in general exponential models

We introduce a family of Rényi statistics of orders r?∈?R for testing composite hypotheses in general exponential models, as alternatives to the previously considered generalized likelihood ratio (GLR) statistic and generalized Wald statistic. If appropriately normalized exponential models converge in a specific sense when the sample size (observation window) tends to infinity, and if the hypothesis is regular, then these statistics are shown to be χ²-distributed under the hypothesis. The corresponding Rényi tests are shown to be consistent. The exact sizes and powers of asymptotically α-size Rényi, GLR and generalized Wald tests are evaluated for a concrete hypothesis about a bivariate Lévy process and moderate observation windows. In this concrete situation the exact sizes of the Rényi test of the order r?=?2 practically coincide with those of the GLR and generalized Wald tests but the exact powers of the Rényi test are on average somewhat better.