Managing a Farm in the Corn Borer Area

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Large deviation asymptotics for occupancy problems

In the standard formulation of the occupancy problem one considers the distribution of r balls in n cells, with each ball assigned independently to a given cell with probability 1/n. Although closed form expressions can be given for the distribution of various interesting quantities (such as the fraction of cells that contain a given number of balls), these expressions are often of limited practical use. Approximations provide an attractive alternative, and in the present paper we consider a large deviation approximation as r and n tend to infinity. In order to analyze the problem we first consider a dynamical model, where the balls are placed in the cells sequentially and ``time'' corresponds to the number of balls that have already been thrown. A complete large deviation analysis of this ``process level'' problem is carried out, and the rate function for the original problem is then obtained via the contraction principle. The variational problem that characterizes this rate function is analyzed, and a fairly complete and explicit solution is obtained. The minimizing trajectories and minimal cost are identified up to two constants, and the constants are characterized as the unique solution to an elementary fixed point problem. These results are then used to solve a number of interesting problems, including an overflow problem and the partial coupon collector's problem.Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/00911790400000013

Real Interest Rate, Credit Markets, and Economic Stabilization

The role of a real interest rate and a credit aggregate as intermediate monetary policy targets are investigated under the assumption of rational expectations. The analysis expands a standard aggregate model to include a credit market and a market determined interest rate on bank deposits. This allows the implications for output stabilization of real interest rate policy to be examined for a wider variety of shocks than normally considered in the literature, as well as allowing a credit aggregate policy to be studied.

'The big buzz': a qualitative study of how safe care is perceived, understood and improved in general practice

Background: Exploring frontline staff perceptions of patient safety is important, because they largely determine how improvement interventions are understood and implemented. However, research evidence in this area is very limited. This study therefore: explores participants’ understanding of patient safety as a concept; describes the factors thought to contribute to patient safety incidents (PSIs); and identifies existing improvement actions and potential opportunities for future interventions to help mitigate risks. Methods: A total of 34 semi-structured interviews were conducted with 11 general practitioners, 12 practice nurses and 11 practice managers in the West of Scotland. The data were thematically analysed. Results: Patient safety was considered an important and integral part of routine practice. Participants perceived a proportion of PSIs as being inevitable and therefore not preventable. However, there was consensus that most factors contributing to PSIs are amenable to improvement efforts and acknolwedgement that the potential exists for further enhancements in care procedures and systems. Most were aware of, or already using, a wide range of safety improvement tools for this purpose. While the vast majority was able to identify specific, safety-critical areas requiring further action, this was counter-balanced by the reality that additional resources were a decisive requirment. Conclusion: The perceptions of participants in this study are comparable with the international patient safety literature: frontline staff and clinicians are aware of and potentially able to address a wide range of safety threats. However, they require additional resources and support to do so

-Generic Computability, Turing Reducibility and Asymptotic Density

Generic computability has been studied in group theory and we now study it in the context of classical computability theory. A set A of natural numbers is generically computable if there is a partial computable function f whose domain has density 1 and which agrees with the characteristic function of A on its domain. A set A is coarsely computable if there is a computable set C such that the symmetric difference of A and C has density 0. We prove that there is a c.e. set which is generically computable but not coarsely computable and vice versa. We show that every nonzero Turing degree contains a set which is not coarsely computable. We prove that there is a c.e. set of density 1 which has no computable subset of density 1. As a corollary, there is a generically computable set A such that no generic algorithm for A has computable domain. We define a general notion of generic reducibility in the spirt of Turing reducibility and show that there is a natural order-preserving embedding of the Turing degrees into the generic degrees which is not surjective

FINANCIAL RISK IN COTTON PRODUCTION

Risk analysis continues to emphasize price and yield variability as the principal components of the decision-maker's risk environment. This research demonstrates the relative importance of financial risk for a representative cotton farm in Arizona. For highly leveraged operations, financial risk may account for 70 percent of the total risk faced by the producer. Implications for future risk analysis are discussed in light of these findings.Crop Production/Industries, Risk and Uncertainty,