A “maximum node clustering” problem

In this note we introduce a graph problem, called Maximum Node Clustering (MNC). We prove that the problem (which is easily shown to be strongly NP-complete) can be approximated in polynomial time within a ratio arbitrarily close to 2. For the special case where the graph is a tree, the problem is NP-complete in the ordinary sense; for this case we present a pseudopolynomial algorithm based on dynamic programming, and a related Fully Polynomial Time Approximation Scheme (FPTAS). Also, the tree case is shown to be exactly solvable in time, where n is the number of nodes.     

Lay and Expert Interpretations of Cancer Cluster Evidence

Conflict frequently occurs between community members and environmental/public health officials when an unusual number of cancer cases is reported. This conflict may result from different ways in which laypeople and experts interpret facts to judge whether there is an environmental cause of the cancer cases, but little is known about this issue. Volunteer laypeople (N= 551) and epidemiologists (N= 105) read a hypothetical scenario about cases of cancer on one neighborhood block. Participants judged whether each of the 23 facts about the situation made it “much more likely” to “much less likely” that something in town was causing the cancer cases (7‐point scale). The facts were designed to be “alarming,”“reassuring,” or “neutral” (i.e., according to epidemiological principles, should increase, decrease, or have no impact on the likelihood of an environmental cause). The laypeople were alarmed by most of the facts (mean response significantly greater than the scale midpoint), including all of the neutral facts and over half of the reassuring facts. The experts were more balanced: they were alarmed by none of the neutral or reassuring facts. Their responses showed significantly less alarm than the laypeople's responses (p < 0.0001 for all comparisons). This study reveals that laypeople are not reassured by information that substantially lowers the chance of an environmental cause for cancer cases. Lay responses differ significantly and systematically from experts who are far less alarmed by relevant facts. These findings may help explain the conflicts between the two groups in situations where concern about cases of cancer arises in a community.     

Parental Divorce and Offspring Depressive Symptoms: Dutch Developmental Trends During Early Adolescence

In this study, we investigated if the association between parental divorce and depressive symptoms changes during early adolescence and if developmental patterns are similar for boys and girls. Data were collected in a prospective population cohort of Dutch adolescents (N = 2,149), aged 10 – 15 years. Outcome variables were self‐reported and parent‐reported depressive symptoms. The effects of divorce were adjusted for parental depression. In both self‐reported and parent‐reported data, we found a three‐way interaction of gender, age, and parental divorce, indicating that with increasing age, parental divorce became more strongly associated with depressive symptoms among girls, but not boys. These results suggest that girls with divorced parents are at particularly high risk to develop depressive symptoms during adolescence.