Estimating a reduced rank regression model for non-normal variables

A method using third order moments for estimating the regression coefficients as well as the latent state scores of the reduced-rank regression model when the latent variable(s) are non-normally distributed is presented in this paper. It is shown that the factor analysis type indeterminacy of the regression coefficient matrices is eliminated. A real life example of the proposed method is presented. Differences of this solution with the reduced-rank regression eigen solution are discussed.     

Fluorescence spectra of different configurations of the diphenyl molecule in solid paraffin solutions

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 51, No. 2, pp. 212–217, August, 1989.     

Positive definite functions on the Heisenberg group

Work supported in part by the NSF     

A Recursive Algorithm for Order Cycle-time that Minimizes Logistics Cost

A firm's logistics cost, including shipping and inventory-carrying, is a substantial percentage of its sales. Nevertheless, typical inventory-control methods ignore or insufficiently represent the shipping cost. This paper describes a recursive algorithm that determines the reorder cycle-time that minimizes total logistics cost. It allows for a realistic accounting of shipping cost, which is modelled here as a function of shipping distance and weight. The algorithm uses a relaxation procedure to identify a suitable initial approximation to the optimal order cycle-time and then, through a series of recursive steps, moves to the optimal result. We demonstrate the algorithm with a single item, with a group of items that share a common order cycle, and with multi-items when item demands are random variables. Experience with this algorithm indicates that it converges to the optimal result in a very few steps.     

Error analysis: a tool for selecting travel demand models

In developing travel demand models it is generally assumed that the base-year data used in developing the parameters, as well as the forecasted data to be used as independent variables for the design year, are of acceptable quality. The purpose of this paper is to present the application of error propagation theory in assesing the predictive quality of one type of travel demand forecasting model (multinomial logit models) and to demonstrate how error considerations can be used as a tool for identifying the optimal model. The general conclusions of this study are that: (1) it is indeed possible to quantify errors in dependent variables in logit models as a consequence of errors in independent variables; and (2) error consideration can be used as a tool for identifying the optimal model from a set of candidate models. Further research is recommended to develop better insights into the phenomenon of error propagation so that the consideration of errors can be a factor in decisions on model selection.     

Schmidt analysis of pure-state entanglement

We examine the application of Schmidt mode analysis to pure-state entanglement. Several examples permitting exact analytic calculation of Schmidt eigenvalues and eigenfunctions are included, as well as evaluation of the associated degree of entanglement.     

Observation of the nonlinear effect in relativistic Thomson scattering of electron and laser beams

Thomson scattering of high-power laser and electron beams is a good test of electrodynamics in the high-field region. We demonstrated production of high-intensity X-rays in the head-on collision of a CO₂ laser and 60-MeV electron beams at Brookhaven National Laboratory, Accelerator Test Facility. The energy of an X-ray photon was limited at 6.5 keV in the linear (lowest order) Thomson scattering, but the nonlinear (higher order) process produces higher energy X-rays. We measured the angular distribution of the high-energy X-rays and confirmed that it agrees with theoretical predictions.