Linear programming based decomposition approach in evaluating priorities from pairwise comparisons and error analysis

One of the most difficult issues in many real-life decisionmaking problems is how to estimate the pertinent data. An approach which uses pairwise comparisons was proposed by Saaty and is widely accepted as an effective way of determining these data. Suppose that two matrices with pairwise comparisons are available. Furthermore, suppose that there is an overlapping of the elements compared in these two matrices. The problem examined in this paper is how to combine the comparisons of the two matrices in order to derive the priorities of the elements considered in both matrices. A simple approach and a linear programming approach are formulated and analyzed in solving this problem. Computational results suggest that the LP approach, under certain conditions, is an effective way for dealing with this problem. The proposed approach is of critical importance because it can also result in a reduction of the total required number of comparisons.The author would like to thank Professors Stuart H. Mann, Pennsylvania State University, and Panos M. Pardalos, University of Florida, for their support and valuable comments during the early stages of this research.     

Refined quicksort asymptotics

The complexity of the Quicksort algorithm is usually measured by the number of key comparisons used during its execution. When operating on a list of n data, permuted uniformly at random, the appropriately normalized complexity Y_n is known to converge almost surely to a non‐degenerate random limit Y. This assumes a natural embedding of all Y_n on one probability space, e.g., via random binary search trees. In this note a central limit theorem for the error term in the latter almost sure convergence is shown: where denotes a standard normal random variable. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46, 346–361, 2015     

A New Diagonal Quasi-Newton Updating Method With Scaled Forward Finite Differences Directional Derivative for Unconstrained Optimization

A new diagonal quasi-Newton updating algorithm for unconstrained optimization is presented. The elements of the diagonal matrix approximating the Hessian are determined as scaled forward finite differences directional derivatives of the components of the gradient. Under mild classical assumptions, the convergence of the algorithm is proved to be linear. Numerical experiments with 80 unconstrained optimization test problems, of different structures and complexities, as well as five applications from MINPACK-2 collection, prove that the suggested algorithm is more efficient and more robust than the quasi-Newton diagonal algorithm retaining only the diagonal elements of the BFGS update, than the weak quasi-Newton diagonal algorithm, than the quasi-Cauchy diagonal algorithm, than the diagonal approximation of the Hessian by the least-change secant updating strategy and minimizing the trace of the matrix, than the Cauchy with Oren and Luenberger scaling algorithm in its complementary form (i.e. the Barzilai-Borwein algorithm), than the steepest descent algorithm, and than the classical BFGS algorithm. However, our algorithm is inferior to the limited memory BFGS algorithm (L-BFGS).     

Reliability of proficiency test results for metals and phthalates in plastics

In a recent article it was concluded that the Horwitz curve could not be used for evaluation of results from analysis of plastics. This conclusion was based on 15 different proficiency tests of which 11 were organized by the Institute for Interlaboratory Studies. The authors suggest that part of the poor interlaboratory reproducibility can be explained by the inhomogeneity of consumer plastic products. Also, the lack of standard methods has been mentioned as problematic. The value of the iis data sets used by the authors is discussed in this paper. More recent data are also investigated to determine whether the situation with regard to analysis of plastics is as bad as suggested by Ritter and Meyer.     

Further application of hybrid solution to another form of Boussinesq equations and comparisons

Recently, a new hybrid scheme is introduced for the solution of the Boussinesq equations. In this study, the hybrid scheme is used to solve another form of the Boussinesq equations. The hybrid solution is composed of finite‐volume and finite difference method. The finite‐volume method is applied to conservative part of the governing equations, whereas the higher order Boussinesq terms are discretized using the finite‐difference scheme. Fourth‐order accuracy is provided in both time and space. The solution is then applied to several test cases, which are taken from the previous studies. The results of this study are compared with experimental and theoretical results as well as those of the previous ones. The comparisons indicate that the Boussinesq equations solved here and in the previous study produce quite similar results. Copyright © 2006 John Wiley & Sons, Ltd.     

Chlorophyll-a determination: results of an interlaboratory comparison

A chlorophyll-a interlaboratory comparison was carried out to compare three different analytical chlorophyll-a determination methods: a German standard DIN 38412-16, a method of the HELCOM-Combine-Manual and the different “in-house” methods of participating laboratories. Eleven laboratories took part. They had to determinate the chlorophyll-a and phaeopigment content in two seawater samples taken from the Baltic Sea. Furthermore, for the assessment three different statistical evaluation methods were applied: the German standard DIN 38402-42, the Q-method combined with an estimator according to Huber and the Cofino-method. All analytical methods were appropriate to determine the chlorophyll-a content. The relative standard deviations of reproducibility for chlorophyll-a varied between 12 and 31%. None of the analytical methods was appropriate to determine the phaeopigment content quantitatively. The relative standard deviations of reproducibility for phaeopigments ranged between 87 and 158%. The applied statistical evaluation methods resulted in different assessments. The Q-method combined with an estimator according to Huber proved to be the best qualified method.Presented at the Eurachem PT Workshop September 2005, Portorož, Slovenia     

Computational comparison of value iteration algorithms for discounted Markov decision processes

This paper describes a computational comparison of value iteration algorithms for discounted Markov decision processes.     

FLOODING ON THE EEL RIVER: SYSTEM THEORETIC TIME SERIES,TRANSFER FUNCTION TIME SERIES,AND STRUCTURAL MODEL FORECASTS

Three models are developed to forecast precipitation, stream flow, and suspended sediment load for the Middle Fork Eel River basin near Dos Rios, California. The models are a structural model, a transfer function time series model, and a multivariate time series model based on the ideas of linear systems theory. Monthly observations from 1961 through 1970 were used to specify and estimate the models, and their performance was evaluated using 36 observations from 1971 through 1973. The comparisons show that all of the models are able to simulate the general trend of the data fairly well but that the two time series models capture the detail better. The system theoretic time series model fares the best, providing consistently better forecasts of all three series. We conclude that this model would be valuable for use in planning water supply systems in the Eel River basin.     

Queues with service times and interarrival times depending linearly and randomly upon waiting times

We consider a modification of the standardG/G/1 queue with unlimited waiting space and the first-in first-out discipline in which the service times and interarrival times depend linearly and randomly on the waiting times. In this model the waiting times satisfy a modified version of the classical Lindley recursion. We determine when the waiting-time distributions converge to a proper limit and we develop approximations for this steady-state limit, primarily by applying previous results of Vervaat [21] and Brandt [4] for the unrestricted recursionY _n+1=C _n Y _n +X _n . Particularly appealing for applications is a normal approximation for the stationary waiting time distribution in the case when the queue only rarely becomes empty. We also consider the problem of scheduling successive interarrival times at arrival epochs, with the objective of achieving nearly maximal throughput with nearly bounded waiting times, while making the interarrival time sequence relatively smooth. We identify policies depending linearly and deterministically upon the work in the system which meet these objectives reasonably well; with these policies the waiting times are approximately contained in a specified interval a specified fraction of time.