Saddlepoint approximation for moment generating functions of truncated random variables

We consider the problem of approximating the moment generating function (MGF) of a truncated random variable in terms of the MGF of the underlying (i.e., untruncated) random variable. The purpose of approximating the MGF is to enable the application of saddlepoint approximations to certain distributions determined by truncated random variables. Two important statistical applications are the following: the approximation of certain multivariate cumulative distribution functions; and the approximation of passage time distributions in ion channel models which incorporate time interval omission. We derive two types of representation for the MGF of a truncated random variable. One of these representations is obtained by exponential tilting. The second type of representation, which has two versions, is referred to as an exponential convolution representation. Each representation motivates a different approximation. It turns out that each of the three approximations is extremely accurate in those cases ``to which it is suited.'' Moreover, there is a simple rule of thumb for deciding which approximation to use in a given case, and if this rule is followed, then our numerical and theoretical results indicate that the resulting approximation will be extremely accurate.Comment: Published at http://dx.doi.org/10.1214/009053604000000689 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

The structural response of unsymmetrically laminated composite cylinders

The responses of an unsymmetrically laminated fiber-reinforced composite cylinder to an axial compressive load, a torsional load, and the temperature change associated with cooling from the processing temperature to the service temperature are investigated. These problems are considered axisymmetric and the response is studied in the context of linear elastic material behavior and geometrically linear kinematics. Four different laminates are studied: a general unsymmetric laminate; two unsymmetric but more conventional laminates; and a conventional quasi-isotropic symmetric laminate. The responses based on closed-form solutions for different boundary conditions are computed and studied in detail. Particular emphasis is directed at understanding the influence of elastic couplings in the laminates. The influence of coupling decreased from a large effect in the general unsymmetric laminate, to practically no effect in the quasi-isotropic laminate. For example, the torsional loading of the general unsymmetric laminate resulted in a radial displacement. The temperature change also caused a significant radial displacement to occur near the ends of the cylinder. On the other hand, the more conventional unsymmetric laminate and the quasi-isotropic cylinder did not deform radially when subjected to a torsional load. From the results obtained, it is clear the degree of elastic coupling can be controlled and indeed designed into a cylinder, the degree and character of the coupling being dictated by the application

Rotationally resolved collisional transfer rates in OH

Fluorescence lidar measurements of the hydroxyl radical require detailed information concerning collision induced processes in order to deduce the radical number density from a lidar return. The Goddard SFC OH lidar currently utilizes a broadband detector which precludes the necessity of fully understanding collisional redistribution of rotational energy within the excited state. Numerous advantages result however from the inclusion of a detector with a bandpass only slightly larger that the Doppler width of a rotational line. This however places more stringent requirements on the spectroscopy. Measurements were accordingly made of rotationally resolved quenching rates for collisions with O2, N2, and H2O. Rotational transfer rates were also measured for the same colliders. Quenching rates were measured using a Nd-YAG pumped Rh6G dye laser doubled into the UV. The OH lifetimes were measured as a function of pressure of quenching gas at total pressures of between 50 and 250 microns. Rotational transfer rates were measured by recording the emission spectrum on an intensified diode array and integrating over 10.000 laser shots

A minimization algorithm for non-concurrent PLA's

This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. As such, it is in the public domain, and under the provisions of Title 17, United States Code, Section 105, may not be copyrighted.International Journal of Electronics, Vol. 73, No. 6, Dec. 1992, pp. 1113-1119In the design of certain self-checking programmable logic arrays (PLAs), at most one line is activated in the AND plane, such as PLAs are termed non-concurrent. A heuristic algorithm for the minimization of non-concurrent PLAs is presented. It operates on two adjacent cubes, replacing them by one, two, and sometimes more than two cubes. The algorithm produces the best solutions known so far

A heat quench algorithm for the minimization of multiple-valued programmable logic arrays

This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. As such, it is in the public domain, and under the provisions of Title 17, United States Code, Section 105, may not be copyrighted.Computer and Electrical Engineering Journal, Vol. 22, No. 2, 1996, pp. 103-107, 1996imulated annealing has been used extensively to solve combinatorial problems. Although it does not guarantee optimum results, results are often optimum or near optimum. The primary disadvantage is slow speed. It has been suggested [1] that quenching (rapid cooling) yields results that are far from optimum. We challenge this perception by showing a context in which quenching yields good solutions with good computation speeds. In this paper, we present an algorithm in which quenching is combined with rapid heating. We have successfully applied this algorithm to the multiple-valued logic minimization problem. Our results suggest that this algorithm holds promise for problems where moves exist that leave the cost of the current solution unchanged. Key words: Multiple-valued logic, logic minimization, simulated annealing, heat quench, heuristic

A user's guide for V174, a program using a finite difference method to analyze transonic flow over oscillating wings

The design and usage of a pilot program using a finite difference method for calculating the pressure distributions over harmonically oscillating wings in transonic flow are discussed. The procedure used is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The steady velocity potential which must be obtained from some other program, is required for input. The unsteady differential equation is linear, complex in form with spatially varying coefficients. Because sinusoidal motion is assumed, time is not a variable. The numerical solution is obtained through a finite difference formulation and a line relaxation solution method

A MERLIN Observation of PSR B1951+32 and its associated Plerion

In an investigative 16 hour L band observation using the MERLIN radio interferometric array, we have resolved both the pulsar PSR B1951+32 and structure within the flat spectral radio continuum region, believed to be the synchrotron nebula associated with the interaction of the pulsar and its `host' supernova remnant CTB 80. The extended structure we see, significant at $\sim$ 4.5 $\sigma$, is of dimensions 2.5" $\times$ 0.75", and suggests a sharp bow shaped arc of shocked emission, which is correlated with similar structure observed in lower resolution radio maps and X-ray images. Using this MERLIN data as a new astrometric reference for other multiwavelength data we can place the pulsar at one edge of the HST reported optical synchrotron knot, ruling out previous suggested optical counterparts, and allowing an elementary analysis of the optical synchrotron emission which appears to trail the pulsar. The latter is possibly a consequence of pulsar wind replenishment, and we suggest that the knot is a result of magnetohydrodynamic (MHD) instabilities. These being so, it suggests a dynamical nature to the optical knot, which will require high resolution optical observations to confirm.Comment: 12 pages, 2 figures. Accepted for publication in ApJ