Combining the economic literature on principal-agent relationships with examples of marketplace innovations allows analysis of the evolution of methods for paying physicians. Agency theory and the economic principles of performance-based compensation are applied in the context of imperfect information, risk aversion, multiple interrelated tasks, and team production efficiencies. Fee-for-service and capitation are flawed methods of motivating physicians to achieve specific goals. Payment innovations that blend elements of fee-for-service, capitation, and case rates can preserve the advantages and attenuate the disadvantages of each. These innovations include capitation with fee-for-service carve-outs, department budgets with individual fee-for-service or "contact" capitation, and case rates for defined episodes of illness. The context within which payment incentives are embedded, includes such non-price mechanisms as screening and monitoring and such organizational relationships as employment and ownership. The analysis has implications for health services research and public policy with respect to physician payment incentives.

This accessible research monograph investigates how 'finite-dimensional' sets can be embedded into finite-dimensional Euclidean spaces. The first part brings together a number of abstract embedding results, and provides a unified treatment of four definitions of dimension that arise in disparate fields: Lebesgue covering dimension (from classical 'dimension theory'), Hausdorff dimension (from geometric measure theory), upper box-counting dimension (from dynamical systems), and Assouad dimension (from the theory of metric spaces). These abstract embedding results are applied in the second part of the book to the finite-dimensional global attractors that arise in certain infinite-dimensional dynamical systems, deducing practical consequences from the existence of such attractors: a version of the Takens time-delay embedding theorem valid in spatially extended systems, and a result on parametrisation by point values. This book will appeal to all researchers with an interest in dimension theory, particularly those working in dynamical systems.

In this paper we establish a mathematical framework for a range of inverse problems for functions, given a finite set of noisy observations. The problems are hence underdetermined and are often ill-posed. We study these problems from the viewpoint of Bayesian statistics, with the resulting posterior probability measure being defined on a space of functions. We develop an abstract framework for such problems which facilitates application of an infinite-dimensional version of Bayes theorem, leads to a well-posedness result for the posterior measure (continuity in a suitable probability metric with respect to changes in data), and also leads to a theory for the existence of maximizing the posterior probability (MAP) estimators for such Bayesian inverse problems on function space. A central idea underlying these results is that continuity properties and bounds on the forward model guide the choice of the prior measure for the inverse problem, leading to the desired results on well-posedness and MAP estimators; the PDE analysis and probability theory required are thus clearly dileneated, allowing a straightforward derivation of results. We show that the abstract theory applies to some concrete applications of interest by studying problems arising from data assimilation in fluid mechanics. The objective is to make inference about the underlying velocity field, on the basis of either Eulerian or Lagrangian observations. We study problems without model error, in which case the inference is on the initial condition, and problems with model error in which case the inference is on the initial condition and on the driving noise process or, equivalently, on the entire time-dependent velocity field. In order to undertake a relatively uncluttered mathematical analysis we consider the two-dimensional Navier-Stokes equation on a torus. The case of Eulerian observationsdirect observations of the velocity field itself-is then a model for weather forecasting. The case of Lagrangian observations-observations of passive tracers advected by the flow-is then a model for data arising in oceanography. The methodology which we describe herein may be applied to many other inverse problems in which it is of interest to find, given observations, an infinitedimensional object, such as the initial condition for a PDE. A similar approach might be adopted, for example, to determine an appropriate mathematical

TitleThe impact of hospital market structure on patient volume, average length of stay, and the cost of care A variety of recent proposals rely heavily on market forces as a means of controlling hospital cost inflation. Sceptics argue, however, that increased competition might iead to cost-increasing acquisitions of specialized clinical services and other forms of non-price colupetition as means of attracting physicians and patients. Using data from hospitals in 1972 we analyzed the impact of market structure on average hospital costs, measured in terms of both cost per patient and cost per patient day. Under the retrospective reimbursement system in place at the time, hospitals in more competitive environments exhibited significantly higher costs of production than did those in less competitive environments.

The relationship between random attractors and global attractors for dynamical systems is studied. If a partial differential equation is perturbed by an −small random term and certain hypotheses are satisfied, the upper semicontinuity of the random attractors is obtained as goes to zero. The results are applied to the Navier-Stokes equations and a problem of reaction-diffusion type, both perturbed by an additive white noise.

This paper documents the growing linkages between primary care-centered medical groups and specialists and between physicians and hospitals under managed care. We evaluate the two alternative forms of organizational coordination: "vertical integration," based on unified ownership, and "virtual integration," based on contractual networks. Excess capacity and the need for investment capital are major short-term determinants of these vertical versus virtual integration decisions in health care. In the longer term, the principal determinants are economies of scale, risk-bearing ability, transaction costs, and the capacity for innovation in methods of managing care.

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