On K\"ahler conformal compactifications of U(n)U(n)-invariant ALE spaces

We prove that a certain class of ALE spaces always has a Kahler conformal compactification, and moreover provide explicit formulas for the conformal factor and the Kahler potential of said compactification. We then apply this to give a new and simple construction of the canonical Bochner-K\"ahler metric on certain weighted projective spaces, and also to explicitly construct a family Kahler edge-cone metrics on $\mathbb{CP}^2$, with singular set $\mathbb{CP}^1$, having cone angles $2\pi\beta$ for all $\beta>0$. We conclude by discussing how these results can be used to obtain certain well-known Einstein metrics.Comment: 14 page

Accuracy: The fundamental requirement for voting systems

There have been several attempts to develop a comprehensive account of the requirements for voting systems, particularly for public elections. Typically, these approaches identify a number of "high level" principals which are then refined either into more detailed statements or more formal constructs. Unfortunately, these approaches do not acknowledge the complexity and diversity of the contexts in which voting takes place. This paper takes a different approach by arguing that the only requirement for a voting system is that it is accurate. More detailed requirements can then be derived from this high level requirement for the particular context in which the system is implemented and deployed. A general, formal high level model for voting systems and their context is proposed. Several related definitions of accuracy for voting systems are then developed, illustrating how the term "accuracy" is in interpreted in different contexts. Finally, a context based requirement for voting system privacy is investigated as an example of deriving a subsidiary requirement from the high level requirement for accuracy

Selection, inheritance, and the evolution of parent-offspring interactions

Very few studies have examined parent-offspring interactions from a quantitative genetic perspective. We used a cross-fostering design and measured genetic correlations and components of social selection arising from two parental and two offspring behaviors in the burying beetle Nicrophorus vespilloides. Genetic correlations were assessed by examining behavior of relatives independent of common social influences. We found positive genetic correlations between all pairs of behaviors, including between parent and offspring behaviors. Patterns of selection were assessed by standardized performance and selection gradients. Parental provisioning had positive effects on offspring performance and fitness, while remaining near the larvae without feeding them had negative effects. Begging had positive effects on offspring performance and fitness, while increased competition among siblings had negative effects. Coadaptations between parenting and offspring behavior appear to be maintained by genetic correlations and functional trade-offs; parents that feed their offspring more also spend more time in the area where they can forage for themselves. Families with high levels of begging have high levels of sibling competition. Integrating information from genetics and selection thus provides a general explanation for why variation persists in seemingly beneficial traits expressed in parent-offspring interactions and illustrates why it is important to measure functionally related suites of behaviors