Rate of convergence for periodic homogenization of convex Hamilton-Jacobi equations in one dimension

Let $u^\varepsilon$ and $u$ be viscosity solutions of the oscillatory Hamilton-Jacobi equation and its corresponding effective equation. Given bounded, Lipschitz initial data, we present a simple proof to obtain the optimal rate of convergence $\mathcal{O}(\varepsilon)$ of $u^\varepsilon \rightarrow u$ as $\varepsilon \rightarrow 0^+$ for a large class of convex Hamiltonians $H(x,y,p)$ in one dimension. This class includes the Hamiltonians from classical mechanics with separable potential. The proof makes use of optimal control theory and a quantitative version of the ergodic theorem for periodic functions in dimension $n = 1$.Comment: 22 pages, typos corrected, references added, final accepted versio

State Prescription Drug Price Web Sites: How Useful to Consumers?

Compares ten sites and identifies key limitations due to data omissions, gaps between insured and uninsured consumers, and varied program implementation. Presents alternative policy options such as requiring price lists from pharmacies

Limited Options to Manage Specialty Drug Spending

Outlines rising trends in costs of and spending on specialty drugs; health plans' efforts to curb specialty drug spending, including patient cost sharing and utilization management; and efforts to integrate medical and pharmaceutical coverage

Striking Jump in Consumers Seeking Health Care Information

Examines shifts in how Americans seek health information from sources other than their doctors. Looks at growing Internet use and information-seeking for others, education as a factor, and the impact of information-seeking on perceptions of health issues

Word of Mouth and Physician Referrals Still Drive Health Care Provider Choice

Examines how consumers choose physicians, specialists, or medical facilities, including the use of physician referrals, word-of-mouth recommendations, health plan information, and the Internet. Explores implications for consumer-directed health care

Financial and Health Burdens of Chronic Conditions Grow

Points to rising rates of chronic conditions and obesity; growing numbers of patients with problems paying medical bills, even with insurance; and contributing factors such as declining private coverage and delays in accessing care. Outlines implications

Answer Sets for Logic Programs with Arbitrary Abstract Constraint Atoms

In this paper, we present two alternative approaches to defining answer sets for logic programs with arbitrary types of abstract constraint atoms (c-atoms). These approaches generalize the fixpoint-based and the level mapping based answer set semantics of normal logic programs to the case of logic programs with arbitrary types of c-atoms. The results are four different answer set definitions which are equivalent when applied to normal logic programs. The standard fixpoint-based semantics of logic programs is generalized in two directions, called answer set by reduct and answer set by complement. These definitions, which differ from each other in the treatment of negation-as-failure (naf) atoms, make use of an immediate consequence operator to perform answer set checking, whose definition relies on the notion of conditional satisfaction of c-atoms w.r.t. a pair of interpretations. The other two definitions, called strongly and weakly well-supported models, are generalizations of the notion of well-supported models of normal logic programs to the case of programs with c-atoms. As for the case of fixpoint-based semantics, the difference between these two definitions is rooted in the treatment of naf atoms. We prove that answer sets by reduct (resp. by complement) are equivalent to weakly (resp. strongly) well-supported models of a program, thus generalizing the theorem on the correspondence between stable models and well-supported models of a normal logic program to the class of programs with c-atoms. We show that the newly defined semantics coincide with previously introduced semantics for logic programs with monotone c-atoms, and they extend the original answer set semantics of normal logic programs. We also study some properties of answer sets of programs with c-atoms, and relate our definitions to several semantics for logic programs with aggregates presented in the literature

Key Findings From HSC's 2010 Site Visits: Health Care Markets Weather Economic Downturn, Brace for Health Reform

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Employer-Sponsored Health Insurance: Down, But Not Out

Presents findings from twelve metropolitan areas about employers' efforts to control employee healthcare costs in response to the recession and national healthcare reform by firm size. Projects employer trends through 2014, including greater cost sharing

Workplace Clinics: A Sign of Growing Employer Interest in Wellness

Examines the increasing employer demand for workplace clinics, clinic management models, types of services, challenges, regulations, and the clinics' potential impact, including their ability to raise productivity and help contain healthcare costs