Mary Ann Flanigan Wagner

Using Univariate Bézier Distributions to Model Simulation Input Processes

We describe a graphical, interactive technique for modeling univariate simulation input processes by using a family of probability distributions based on Bezier curves. This family has an open-ended parameterization and is capable of accurately representing an unlimited variety of distributional shapes. Our input-modeling technique is implemented in a self-contained, Windows-based software system called PRIME (PRobabilistic Input Modeling Environment). Several examples illustrate the advantages of this technique over conventional methods for simulation input modeling.

Using univariate Be´zier distributions to model simulation input processes

We describe a graphical, interactive technique for modeling bivariate simulation input processes using a distribution family based on Bezier curves and surfaces. This family has an open-ended parameterization and is capable of accurately representing an unlimited variety of shapes for marginal distributions together with many common types of bivariate stochastic dependence. Our input-modeling technique is implemented in a Windows-based software system called PRIME-PRobabilistic Input Modeling Environment. Several examples illustrate the application of PRIME to subjective and data-driven estimation of bivariate distributions representing simulation inputs.

Graphical interactive simulation input modeling with bivariate Bézier distributions

A graphical interactive technique for modeling bivariate simulation inputs is based on a family of continuous univariate and bivariate probability distributions with bounded support that are described by Be´zier curves and surfaces, respectively. This family of distributions has a natural, extensible parameterization so that all parameters have a meaningful interpretation; and the complete family is capable of accurately representing an unlimited variety of shapes for marginal distributions together with many common types of bivariate stochastic dependence. This approach to simulation input modeling is implemented in a Windows-based software system called PRIME-PRobabilistic Input Modeling Environment. Several examples illustrate the application of PRIME to subjective and data-driven estimation of bivariate distributions representing simulation inputs.

Single crystal x-ray diffraction studies of Southern bean mosaic virus.

Crystals of the cowpea strain of Southern bean mosaic virus were shown to belong to space group R32 whose hexagonal cell dimensions were a = 923(1), c = 299(1) . The orientation and position of the three virus particles in the rhombohedral cell were determined by a consideration of intensity spikes, packing arrangements, and the relative size of different classes of Bragg reflections. The unusually open packing arrangement was subsequently confirmed by electron microscopy observation of thin-sectioned crystals. A maximum particle diameter was found to be 284 . The X-ray diffraction patterns extend to 3 resolution.

The packing of Southern Bean Mosaic Virus in various crystal cells

Two new crystal forms of Southern Bean Mosaic Virus (Cowpea strain) are reported. These have been grown from buffered solutions of very high virus concentration. The particles pack in hexagonal arrays with the icosahedral vertices in contact. The rhombohedral (Type II) form shows a succession of three layers arranged in pseudo-cubic close packing, while the orthorhombic (Type III) crystals are pseudo-hexagonally close packed. The Type II crystals are particularly suitable for high-resolution structural studies due to their unusually good X-ray diffraction characteristics and the presence of only one-sixth of the virus per asymmetric unit.

Recent developments in input modeling with Bézier distributions

New methods are presented for estimating univariate and bivariate Bezier distributions. A likelihood ratio test is used to estimate the number of control points for a univariate Bezier distribution fitted to sample data. To estimate the control points of a bivariate Bezier distribution with fixed marginals based on either sample data or subjective information about the joint dependency structure, a linear-programming approach is formulated. These methods are implemented in the Windows-based software system called PRIME-PRobabilistic Input Modeling Environment. Several examples illustrate the application of these estimation procedures.

Crystalline cowpea chlorotic mottle virus

A variety of crystal forms of cowpea chlorotic mottle virus were grown, one of which gave useful X-ray diffraction diagrams. The unit cell has cubic symmetry of space group F432. The diameter of the virus was found to be consistent with that determined from electron microscopy studies.