Computing DEA/AR efficiency and profit ratio measures with an illustrative bank application

This paper describes how the recent, published DEA/AR theory, in conjunction with software, provides measures of radial efficiency and profit ratios, This new DEA theory does not require use of the non-Archimedean principle, i.e., positive infinitesimals, and it allows for analysis of zero data entries. Further, this theory provides a comprehensive classification of the measures for both the efficient and inefficient decision-making units (DMUs). As programmed in the software, the efficiency principles are relative to the Charnes-Cooper-Rhodes ratio model and the Banker-Charnes-Cooper convex model, and the profitability principles are relative to the Thompson-Thrall profit ratio model. An illustrative application to 48 large U.S. banks illustrates some of the most fundamental computations, which are developed for a base option. Additional options may be exercised by the user to more fully utilize the theory. Additions to the software are being made to computer analytic centers and to make multiplier sensitivity analyses. Software utility updates and new DEA theory contributions continue to complement this computational capability.DEA is an advanced operations research method called Data Envelopment Analysis, and AR is an assurance region method used to bound the multipliers in the DEA model. Underlying data have been deposited with the editors.     

Existence and uniqueness of semimartingale reflecting Brownian motions in an orthant

Summary This work is concerned with the existence and uniqueness of a class of semimartingale reflecting Brownian motions which live in the non-negative orthant of ^d . Loosely speaking, such a process has a semimartingale decomposition such that in the interior of the orthant the process behaves like a Brownian motion with a constant drift and covariance matrix, and at each of the (d-1)-dimensional faces that form the boundary of the orthant, the bounded variation part of the process increases in a given direction (constant for any particular face) so as to confine the process to the orthant. For historical reasons, this pushing at the boundary is called instantaneous reflection. In 1988, Reiman and Williams proved that a necessary condition for the existence of such a semimartingale reflecting Brownian motion (SRBM) is that the reflection matrix formed by the directions of reflection be completely-L. In this work we prove that condition is sufficient for the existence of an SRBM and that the SRBM is unique in law. It follows from the uniqueness that an SRBM defines a strong Markov process. Our results have potential application to the study of diffusions arising as approximations tomulti-class queueing networks.Research supported in part by NSF Grants DMS 8657483, 8722351 and 9023335, and a grant from AT&T Bell Labs. In addition, R.J. Williams was supported in part during the period of this research by an Alfred P. Sloan Research Fellowship     

An automated procedure for the simultaneous determination of specific conductance and pH in natural water samples

An automated, continuous-flow system is utilized to determine specific conductance and pH simultaneously in natural waters. A direct electrometric procedure is used to determine values in the range pH 4–9. The specific conductance measurements are made with an electronically modified, commercially available conductivity meter interfaced to a separate module containing the readout control devices and printer. The system is designed to switch ranges automatically to accommodate optimum analysis of widely varying conductances ranging from a few μmhos cm^-1 to 15,000 μmho cm^-1. Thirty samples per hour can be analyzed. Comparison of manual and automated procedures for 40 samples showed that the average differences were 1.3% for specific conductance and 0.07 units for pH. The relative standard deviation for 25 replicate values for each of five samples was significantly less than 1% for the specific conductance determination; the standard deviation for the pH determination was ? 0.06 pH units.     

A structural and energetics analysis of the binding of a series of N-acetylneuraminic-acid-based inhibitors to influenza virus sialidase

Summary A molecular dynamics/energy-minimisation protocol has been used to analyse the structural and energetic effects of functional group substitution on the binding of a series of C4-modified 2-deoxy-2,3-didehydro-N-acetylneuraminic acid inhibitors to influenza virus sialidase. Based on the crystal structure of sialidase, a conformational searching protocol, incorporating multiple randomisation steps in a molecular dynamics simulation was used to generate a range of minimum-energy structures. The calculations were useful for predicting the number, location, and orientation of structural water molecules within protein-ligand complexes. Relative binding energies were calculated for the series of complexes using several empirical molecular modelling approaches. Energies were computed using molecular-mechanics-derived interactions as the sum of pairwise atomic nonbonded energies, and in a more rigorous manner including solvation effects as the change in total electrostatic energy of complexation, using a continuum-electrostatics (CE) approach. The CE approach exhibited the superior correlation with observed affinities. Both methods showed definite trends in observed and calculated binding affinities; in both cases inhibitors with a positively charged C4 substituent formed the tightest binding to the enzyme, as observed experimentally.This paper is based on a presentation given at the 14th Molecular Graphics and Modelling Society Conference, held in Cairns, Australia, August 27–September 1, 1995.Presently on a visiting postdoctoral fellowship in the Department of Biomolecular Structure, Glaxo Research & Development Ltd, Greenford, Middlesex UB6 OHE, U.K.     

A new approach to intermolecular forces in non-bonding regions

A new method to compute intermolecular energies in non-bonding regions is presented. It is based on the assumption that in such regions molecules can be reviewed as the sum of distorted, possibly overlapping, and electron exchanging atoms. The intermolecular energy change at a given distance is due to the sum of the atomic energy changes caused by these distortions. The energy change of any particular atom is computed in a Hartree—Fock model in which the effect of the other atom is represented by an effective potential. This potential in turn is computed from a calculation at a slightly larger intermolecular distance of the potential seen by an external electron in the field of the “other” atom. This potential computed in the RPA approximation and involves the distorted Hartree—Fock orbitals of the other atom (computed in a similar manner to the above) and the RPA response function of the other distorted atom.