Pseudo-High-Order Symplectic Integrators

Symplectic N-body integrators are widely used to study problems in celestial mechanics. The most popular algorithms are of 2nd and 4th order, requiring 2 and 6 substeps per timestep, respectively. The number of substeps increases rapidly with order in timestep, rendering higher-order methods impractical. However, symplectic integrators are often applied to systems in which perturbations between bodies are a small factor of the force due to a dominant central mass. In this case, it is possible to create optimized symplectic algorithms that require fewer substeps per timestep. This is achieved by only considering error terms of order epsilon, and neglecting those of order epsilon^2, epsilon^3 etc. Here we devise symplectic algorithms with 4 and 6 substeps per step which effectively behave as 4th and 6th-order integrators when epsilon is small. These algorithms are more efficient than the usual 2nd and 4th-order methods when applied to planetary systems.Comment: 14 pages, 5 figures. Accepted for publication in the Astronomical Journa

Primary Prevention of Child Abuse: Is It Really Possible?

Despite the growing interest in child abuse and its prevention, to date no systematic research has been conducted to determine the usefulness of instruments used to identify and predict abuse or neglect. The present study is a review and analysis of predictive instruments of abuse or neglect with the goal of identifying the predictive efficiency of the instruments. Analysis reveals a variety of problems with predictive efficiency, particularly as predicting individual risk of abuse or neglect relates to primary prevention. Implications of the findings and suggestions for practice are discussed

Support after brain tumor means different things: Family caregivers\u27 experiences of support and relationship changes

Shorter hospital stays and greater emphasis on outpatient care means that family members have the primary responsibility for supporting a person with brain tumor to manage the physical, cognitive, behavioral, and emotional effects of the illness and its treatment. Given the integral role of family caregivers, it is essential to understand their experience of the impact of brain tumor and their own support needs. Accordingly, this qualitative study aimed to investigate family caregivers\u27 experiences of support and relationship changes in the context of brain tumor. In-depth interviews were conducted with 11 family caregivers (8 spouse/partner, 3 parents) of people with malignant or benign tumor. A thematic analysis of interview transcripts identified two major themes, namely, Meanings of Support and Relationship Impacts. The Meanings of Support theme was characterized by intertwined and distinct support needs, varied expectations of support and factors influencing support expectations. The Relationship Impacts theme depicted mixed experiences of strengthened, maintained, and strained relations with the person with brain tumor. Overall, the findings highlight that there is considerable variability in caregivers\u27 experiences and expectations of support and the impact of brain tumor on relationships. The implications of these findings for the provision of caregiver support are discussed

Spatial Graphs with Local Knots

It is shown that for any locally knotted edge of a 3-connected graph in $S^3$, there is a ball that contains all of the local knots of that edge and is unique up to an isotopy setwise fixing the graph. This result is applied to the study of topological symmetry groups of graphs embedded in $S^3$.Comment: 20 pages, 3 figures; in v. 2 the proof of Theorem 1 has been clarified, and other minor revisions have been mad