20,009 research outputs found

    Relaxing The Hamilton Jacobi Bellman Equation To Construct Inner And Outer Bounds On Reachable Sets

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    We consider the problem of overbounding and underbounding both the backward and forward reachable set for a given polynomial vector field, nonlinear in both state and input, with a given semialgebriac set of initial conditions and with inputs constrained pointwise to lie in a semialgebraic set. Specifically, we represent the forward reachable set using the value function which gives the optimal cost to go of an optimal control problems and if smooth satisfies the Hamilton-Jacobi- Bellman PDE. We then show that there exist polynomial upper and lower bounds to this value function and furthermore, these polynomial sub-value and super-value functions provide provable upper and lower bounds to the forward reachable set. Finally, by minimizing the distance between these sub-value and super-value functions in the L1-norm, we are able to construct inner and outer bounds for the reachable set and show numerically on several examples that for relatively small degree, the Hausdorff distance between these bounds is negligible

    Hidden-Markov Program Algebra with iteration

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    We use Hidden Markov Models to motivate a quantitative compositional semantics for noninterference-based security with iteration, including a refinement- or "implements" relation that compares two programs with respect to their information leakage; and we propose a program algebra for source-level reasoning about such programs, in particular as a means of establishing that an "implementation" program leaks no more than its "specification" program. This joins two themes: we extend our earlier work, having iteration but only qualitative, by making it quantitative; and we extend our earlier quantitative work by including iteration. We advocate stepwise refinement and source-level program algebra, both as conceptual reasoning tools and as targets for automated assistance. A selection of algebraic laws is given to support this view in the case of quantitative noninterference; and it is demonstrated on a simple iterated password-guessing attack

    Pennsylvania: Base Line Report - State Level Field Network Study of the Implementation of the Affordable Care Act

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    This report is part of a series of 21 state and regional studies examining the rollout of the ACA. The national network -- with 36 states and 61 researchers -- is led by the Rockefeller Institute of Government, the public policy research arm of the State University of New York, the Brookings Institution, and the Fels Institute of Government at the University of Pennsylvania.Although the ACA will no doubt have real financial consequences for insurers, hospitals, and health care providers, at this early stage in implementation, it is difficult to calculate precise gains and losses. For example, the Hospital Association of Pennsylvania supported the ACA, believing, in part, that reform was necessary to reduce current levels of uncompensated care and to reduce reliance on emergency care for patients who put off treatment for as long as possible to avoid out-of-pocket costs. The association agreed to significant cuts in Medicare and Medicaid to support the bill's passage. However, because cost savings from universal coverage have not yet been realized, hospitals reported cutting staff in April 2014 to offset the loss of Medicaid and Medicare funding. Safety net hospitals, which are required to serve all populations, seem especially affected, as many of their patients who fall into the Medicaid coverage gap are still showing up in emergency rooms without insurance