On the complexity of path problems in properly colored directed graphs

We address the complexity class of several problems related to finding a path in a properly colored directed graph. A properly colored graph is defined as a graph G whose vertex set is partitioned into $\mathcal{X}(G)$ stable subsets, where $\mathcal{X}(G)$ denotes the chromatic number of G. We show that to find a simple path that meets all the colors in a properly colored directed graph is NP-complete, and so are the problems of finding a shortest and longest of such paths between two specific nodes.     

An optimal property of the “(r,k ) class estimators”

The purpose of this work is to display optimal conditions, in terms of the Mean Square Error criterion of the (r,k) class estimators. This will be done with respect to the ordinary ridge repression, principal components and ordinary least squares estimate.     

Risk alignment in health care quality and financing: optimizing value

How should health care best consolidate rational cost control while preserving and enhancing quality? That is, how can a system best optimize value? A limitation of many current health management modalities may be that the power to control health spending has been expropriated from physician providers, while they are still fully responsible for quality. Assigning responsibility without authority is a significant predicament. There are growing indications that well-organized, well-managed groups of high quality physicians may be able to directly manage both types of risk-quality and financial. The best way to optimize responsibility and authority, and to control financial and quality risks, is to place such responsibility and authority within the same entity.