Fredholm Determinants, Differential Equations and Matrix Models

Orthogonal polynomial random matrix models of NxN hermitian matrices lead to Fredholm determinants of integral operators with kernel of the form (phi(x) psi(y) - psi(x) phi(y))/x-y. This paper is concerned with the Fredholm determinants of integral operators having kernel of this form and where the underlying set is a union of open intervals. The emphasis is on the determinants thought of as functions of the end-points of these intervals. We show that these Fredholm determinants with kernels of the general form described above are expressible in terms of solutions of systems of PDE's as long as phi and psi satisfy a certain type of differentiation formula. There is also an exponential variant of this analysis which includes the circular ensembles of NxN unitary matrices.Comment: 34 pages, LaTeX using RevTeX 3.0 macros; last version changes only the abstract and decreases length of typeset versio

Brain ischemia alters platelet ATP diphosphohydrolase and 5'-nucleotidase activities in naive and preconditioned rats

The effects of transient forebrain ischemia, reperfusion and ischemic preconditioning on rat blood platelet ATP diphosphohydrolase and 5'-nucleotidase activities were evaluated. Adult Wistar rats were submitted to 2 or 10 min of single ischemic episodes, or to 10 min of ischemia 1 day after a 2-min ischemic episode (ischemic preconditioning) by the four-vessel occlusion method. Rats submitted to single ischemic insults were reperfused for 60 min and for 1, 2, 5, 10 and 30 days after ischemia; preconditioned rats were reperfused for 60 min 1 and 2 days after the long ischemic episode. Brain ischemia (2 or 10 min) inhibited ATP and ADP hydrolysis by platelet ATP diphosphohydrolase. On the other hand, AMP hydrolysis by 5'-nucleotidase was increased after 2, but not 10, min of ischemia. Ischemic preconditioning followed by 10 min of ischemia caused activation of both enzymes. Variable periods of reperfusion distinctly affected each experimental group. Enzyme activities returned to control levels in the 2-min group. However, the decrease in ATP diphosphohydrolase activity was maintained up to 30 days of reperfusion after 10-min ischemia. 5'-Nucleotidase activity was decreased 60 min and 1 day following 10-min ischemia; interestingly, enzymatic activity was increased after 2 and 5 days of reperfusion, and returned to control levels after 10 days. Ischemic preconditioning cancelled the effects of 10-min ischemia on the enzymatic activities. These results indicate that brain ischemia and ischemic preconditioning induce peripheral effects on ecto-enzymes from rat platelets involved in nucleotide metabolism. Thus, ATP, ADP and AMP degradation and probably the generation of adenosine in the circulation may be altered, leading to regulation of microthrombus formation since ADP aggregates platelets and adenosine is an inhibitor of platelet aggregation

The importance of local forest benefits: Economic valuation of Non-Timber Forest Products in the Eastern Arc Mountains in Tanzania

Understanding the spatial distribution of the quantity and economic value of Non-Timber Forest Product (NTFP) collection gives insight into the benefits that local communities obtain from forests, and can inform decisions about the selection of forested areas that are eligible for conservation and enforcement of regulations. In this paper we estimate transferable household production functions of NTFP extraction in the Eastern Arc Mountains (EAM) in Tanzania, based on information from seven multi-site datasets related to the behaviour of over 2000 households. The study shows that the total benefit flow of charcoal, firewood, poles and thatch from the EAM to the local population has an estimated value of USD 42 million per year, and provides an important source of additional income for local communities, especially the poorest, who mainly depend on subsistence agriculture. The resulting map of economic values shows that benefits vary highly across space with population density, infrastructure and resource availability. We argue that if further restrictions on forest access to promote conservation are considered, this will require additional policies to prevent a consequent increase in poverty, and an enforced trade-off between conservation and energy supply to rural and urban households