The Psychology of Competence and Informed Consent: Understanding Decision-Making with Regard to Clinical Research

This Article examines the importance of patient autonomy and competence in medical decision making and how questions of competence affect informed consent. The author explores three hypothetical cases which outline the parameters of \u27competence\u27 by illustrating the methodologies used in making [determinations of competence], distinguishing between ethical and legal issues in the assessment of competence, and reviewing the procedures for surrogate decision making when competence is deemed impaired. The cases present questions on when to respect patient autonomy and when it may be appropriate to allow a surrogate to take over decision making

Physics Beyond the Standard Model

In these three lectures I review the need to go beyond the Standard Glashow- Weinberg-Salam Model and discuss some of the approaches that are explored in this direction.Comment: 5 pages, contribution to the CERN-Latin-American School of High-Energy Physics, Ibarra, Ecuador, 4 - 17 March 2015

The growth rate over trees of any family of set defined by a monadic second order formula is semi-computable

Monadic second order logic can be used to express many classical notions of sets of vertices of a graph as for instance: dominating sets, induced matchings, perfect codes, independent sets or irredundant sets. Bounds on the number of sets of any such family of sets are interesting from a combinatorial point of view and have algorithmic applications. Many such bounds on different families of sets over different classes of graphs are already provided in the literature. In particular, Rote recently showed that the number of minimal dominating sets in trees of order $n$ is at most $95^{\frac{n}{13}}$ and that this bound is asymptotically sharp up to a multiplicative constant. We build on his work to show that what he did for minimal dominating sets can be done for any family of sets definable by a monadic second order formula. We first show that, for any monadic second order formula over graphs that characterizes a given kind of subset of its vertices, the maximal number of such sets in a tree can be expressed as the \textit{growth rate of a bilinear system}. This mostly relies on well known links between monadic second order logic over trees and tree automata and basic tree automata manipulations. Then we show that this "growth rate" of a bilinear system can be approximated from above.We then use our implementation of this result to provide bounds on the number of independent dominating sets, total perfect dominating sets, induced matchings, maximal induced matchings, minimal perfect dominating sets, perfect codes and maximal irredundant sets on trees. We also solve a question from D. Y. Kang et al. regarding $r$-matchings and improve a bound from G\'orska and Skupie\'n on the number of maximal matchings on trees. Remark that this approach is easily generalizable to graphs of bounded tree width or clique width (or any similar class of graphs where tree automata are meaningful)