Correction. Brownian models of open processing networks: canonical representation of workload

Due to a printing error the above mentioned article [Annals of Applied Probability 10 (2000) 75--103, doi:10.1214/aoap/1019737665] had numerous equations appearing incorrectly in the print version of this paper. The entire article follows as it should have appeared. IMS apologizes to the author and the readers for this error. A recent paper by Harrison and Van Mieghem explained in general mathematical terms how one forms an ``equivalent workload formulation'' of a Brownian network model. Denoting by $Z(t)$ the state vector of the original Brownian network, one has a lower dimensional state descriptor $W(t)=MZ(t)$ in the equivalent workload formulation, where $M$ can be chosen as any basis matrix for a particular linear space. This paper considers Brownian models for a very general class of open processing networks, and in that context develops a more extensive interpretation of the equivalent workload formulation, thus extending earlier work by Laws on alternate routing problems. A linear program called the static planning problem is introduced to articulate the notion of ``heavy traffic'' for a general open network, and the dual of that linear program is used to define a canonical choice of the basis matrix $M$. To be specific, rows of the canonical $M$ are alternative basic optimal solutions of the dual linear program. If the network data satisfy a natural monotonicity condition, the canonical matrix $M$ is shown to be nonnegative, and another natural condition is identified which ensures that $M$ admits a factorization related to the notion of resource pooling.Comment: Published at http://dx.doi.org/10.1214/105051606000000583 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Electromagnetic atmosphere-plasma coupling: the global atmospheric electric circuit

A description is given of the global atmospheric electric circuit operating between the Earth’s surface and the ionosphere. Attention is drawn to the huge range of horizontal and vertical spatial scales, ranging from 10−9 m to 1012 m, concerned with the many important processes at work. A similarly enormous range of time scales is involved from 10−6 s to 109 s, in the physical effects and different phenomena that need to be considered. The current flowing in the global circuit is generated by disturbed weather such as thunderstorms and electrified rain/shower clouds, mostly occurring over the Earth’s land surface. The profile of electrical conductivity up through the atmosphere, determined mainly by galactic cosmic ray ionization, is a crucial parameter of the circuit. Model simulation results on the variation of the ionospheric potential, ∼250 kV positive with respect to the Earth’s potential, following lightning discharges and sprites are summarized. Experimental results comparing global circuit variations with the neutron rate recorded at Climax, Colorado, are then discussed. Within the return (load) part of the circuit in the fair weather regions remote from the generators, charge layers exist on the upper and lower edges of extensive layer clouds; new experimental evidence for these charge layers is also reviewed. Finally, some directions for future research in the subject are suggested

The MFA Paradox: More Protection and More Trade?

The textile industry's political power stemmed from its importance in southern states plus the power of the Southern delegation in the U.S. Congress in the 1960s. The strongest resistance to the industry's pressure for protection came from the foreign policy interests of the Executive branch. A constellation of influences explains why negotiated, or voluntary export restraints (VERs), sanctioned by international agreements (the Multi-Fiber Arrangement) was the form protection took. First, the Japanese industry, at the time the world's leading textile exporter, already in the 1930s had exhibited a willingness to accept negotiated agreements to trade disputes. Second, the U.S. Executive, having been a leader in establishing the GATT system to control the sort of unilateral restrictive actions that contributed to the 1930s depression, was reluctant to take unilateral action. Third, the arrangement was acceptable to the U.S. industry because, through their particular power over agricultural legislation, the Southern delegation won passage, as amendments to agriculture bills, of legislation to enforce these 'voluntary' restraints at the U.S. border. But because enforcement remained with the Executive branch, it tended to follow the letter of the agreements, hence exports could continue to expand by shifting to new product varieties and to new supplier countries.

Testing for Long Memory and Nonlinear Time Series: A Demand for Money Study

This paper draws attention to the limitations of the standard unit root/cointegration approach to economic and financial modelling, and to some of the alternatives based on the idea of fractional integration, long memory models, and the random field regression approach to nonlinearity. Following brief explanations of fractional integration and random field regression, and the methods of applying them, selected techniques are applied to a demand for money dataset. Comparisons of the results from this illustrative case study are presented, and conclusions are drawn that should aid practitioners in applied time-series econometrics.