Richard A. Redner

An improved method for gas lift allocation optimization

A new method for finding the optimum gas injection rates for a group of continuous gas lift wells to maximize the total oil production rate is established. The new method uses a quasi-Newton nonlinear optimization technique which is incorporated with the gradient projection method. The method is capable of accommodating restrictions to the gas injection rates. The only requirement for fast convergence s that a reasonable estimate of the gas injection rates must be supplied as an initial point to the optimization method. A method of estimating the gas injection rates is developed for that purpose. A computer program is developed capable of implementing the new optimization method as well as generating the initial estimate of the gas injection rates. This program is then successfully tested on field data under both unlimited and limited gas supply. The new optimization technique demonstrates superior performance, faster convergence, and greater application.

A note on the use of nonlinear filtering in computer graphics

The application of nonlinear median and alpha-trimmed mean filters to computer graphics is discussed. The filters are simple to implement, do not require large amounts of CPU time to execute, and can be applied iteratively for better control over the filtering effects. A series of examples shows that the filters eliminate spike noise in a stochastic sampling application without smearing the final image.<<ETX>>

Estimating the parameters of mixture models with modal estimators

This paper extends some of the work presented in Redner and Walker [I9841 on the maximum likelihood estimate of parameters in a mixture model to a Bayesian modal estimate. The problem of determining the mode of the joint posterior distribution is discussed. Necessary conditions are given for a choice of parameters to be the mode and a numerical scheme based on the EM algorithm is presented. Some theoretical remarks on the resulting iterative scheme and simulation results are also given.

Nonparametric probability density estimation using normalized b–splines

We present a new nonparametric density estimate based on normalized tensor B–Splines. We show under the expected conditions that the non- parametric density estimate converges in mean square error and integrated mean square error. Results of simulations are also presented.

On the Limiting Distribution of Pair-Summable Potential Functions in Many-Particle Systems

For systems with finite phase space volume, the density of states can be viewed as a multiple of the probability density of the energy, when the phase space variables are independent uniformly distributed random variables. We show that the distribution of a random variable proportional to the sum of pairwise interactions of independent identically distributed random variables converges to a limiting distribution as the number of variables goes to infinity, when the interaction satisfies certain homogeneity requirements. The moments of this distribution are simple combinations of cyclic integrals of the potential function. The existence of this limit gives information about the structure function of some systems in statistical mechanics having pair-summable interactions, even in the absence of a thermodynamic limit. The result is applied to several examples, including systems of two-dimensional point vortices.

Smooth B-spline illumination maps for bidirectional ray tracing

In this paper we introduce B-spline illumination maps and their generalizations and extensions for use in realistic image generation algorithms. The B-spline lighting functions (i.e., illumination maps) are defined as weighted probability density functions. The lighting functions can be estimated from random data and may be used in bidirectional distributed ray tracing programs as well as radiosity oriented algorithms. The use of these lighting functions in a bidirectional ray tracing system that can handle dispersion as well as the focusing of light through lenses is presented.

Convergence rates for uniform B-spline density estimators on bounded and semi-infinite domains

Convergence rates for B-spline nonparametric density estimators on bounded and semi-infinite domains are discussed. We show how B-spline estimators can be adjusted to account for edge effects and then determine the mean integrated squared error for the adjusted estimator and its derivatives.

Function estimation using partitions of unity

We present a new nonparametric function estimate based on partitions of unity. These density estimates are applicable not only to subsets of R n but to arbitrary metric spaces. They can be used for estimating conditional expectations, and for constructing both nonparametric energy density and nonparametric probability density estimates. We show that under reasonable conditions that the nonparametric density estimates converge in mean square error and under slightly more restrictive conditions that they converge in integrated mean square error. A computer graphics application is presented.

Simple Procedures for Imposing Constraints for Nonlinear Least Squares Optimization

Nonlinear regression method (least squares, least absolute value, etc.) have gained acceptance as practical technology for analyzing well-test pressure data. Even for relatively simple problems, however, commonly used algorithms sometimes converge to nonfeasible parameter estimates (e.g., negative permeabilities) resulting in a failure of the method. The primary objective of this work is to present a new method for imaging the objective function across all boundaries imposed to satisfy physical constraints on the parameters. The algorithm is extremely simple and reliable. The method uses an equivalent unconstrained objective function to impose the physical constraints required in the original problem. Thus, it can be used with standard unconstrained least squares software without reprogramming and provides a viable alternative to penalty functions for imposing constraints when estimating well and reservoir parameters from pressure transient data. In this work, the authors also present two methods of implementing the penalty function approach for imposing parameter constraints in a general unconstrained least squares algorithm. Based on their experience, the new imaging method always converges to a feasible solution in less time than the penalty function methods.

Convergence rates for uniform b-spline density estimators part ii: multiple dimensions

B-Spline density estimators were discussed by Gehringer and Redner in 1992 [9] and later extended to function estimation using partitions of unity over metric spaces in Redner and Gehringer in 1994 [12] to solve problems in computer graphics. In Part I of this paper [11] we returned to the uniform B-Spline density estimators in one dimension. We proved that the B-Spline density estimator and all of its nontrivial derivatives converge in mean integrated squared errorand the asymptotic rate of convergence was determined. In Part II of this paper we establish equivalent results for the asymptotic rates of convergence of the multiple dimensional B-Splinedensity estimator as well as the rates of convergence of all of its partial derivatives.