A cumulative autoregressive model for choice behavior

The group choice behavior of human subjects is assumed to be, in part, oscillatory in nature. A true a priori predictive model based on the integrated autoregressive moving-average process proposed by G.E.P. Box is presented and compared with human subject data from a two-choice predictive situation with π = 0.60. The oscillatory patterns and predictions of the model are shown to be quite similar to those found in the subject data.     

A class of limit distributions for maximum cumulative sum

Let X₁, X₂, ... be a sequence of independent identically distributed random variables with zero mathematical expectation and finite variances. S_o=0 and S_n=∑ _i=1 ⁿ X_i. It is proved that is the limit distribution function of the normalized random variable a(k, n)} for some sequence of centering constants a (k,n).     

A cumulative hierarchy of sets for constructive set theory

The von Neumann hierarchy of sets is heavily used as a basic tool in classical set theory, being an underlying ingredient in many proofs and concepts. In constructive set theories like without the powerset axiom however, it loses much of its potency by ceasing to be a hierarchy of sets as its single stages become only classes. This article proposes an alternative cumulative hierarchy which does not have this drawback and provides examples of how it can be used to prove new theorems in .     

A branch-and-cut-and-price algorithm for the cumulative capacitated vehicle routing problem

In this paper we consider the Cumulative Capacitated Vehicle Routing Problem (CCVRP), which is a variation of the well-known Capacitated Vehicle Routing Problem (CVRP). In this problem, the traditional objective of minimizing total distance or time traveled by the vehicles is replaced by minimizing the sum of arrival times at the customers. We propose a branch-and-cut-and-price algorithm for obtaining optimal solutions to the problem. To the best of our knowledge, this is the first published exact algorithm for the CCVRP. We present computational results based on a set of standard CVRP benchmarks and investigate the effect of modifying the number of vehicles available.     

Optimal replacement model with age-dependent failure type based on a cumulative repair-cost limit policy

This paper presents a replacement model with age-dependent failure type based on a cumulative repair-cost limit policy, whose concept uses the information of all repair costs to decide whether the system is repaired or replaced. As failures occur, the system experiences one of the two types of failures: a type-I failure (minor), rectified by a minimal repair; or a type-II failure (catastrophic) that calls for a replacement. A critical type-I failure means a minor failure at which the accumulated repair cost exceeds the pre-determined limit for the first time. The system is replaced at the nth type-I failure, or at a critical type-I failure, or at first type-II failure, whichever occurs first. The optimal number of minimal repairs before replacement which minimizes the mean cost rate is derived and studied in terms of its existence and uniqueness. Several classical models in maintenance literature are special cases of our model.     

A Robust Algorithm for Blind Total Variation Restoration

Image restoration is a fundamental problem in image processing. Blind image restoration has a great value in its practical application. However, it is not an easy problem to solve due to its complexity and difficulty. In this paper, we combine our robust algorithm for known blur operator with an alternating minimization implicit iterative scheme to deal with blind deconvolution problem, recover the image and identify the point spread function（PSF）. The only assumption needed is satisfy the practical physical sense. Numerical experiments demonstrate that this minimization algorithm is efficient and robust over a wide range of PSF and have almost the same results compared with known PSF algorithm.     

A maxmin policy for bond management

A simple immunization problem is formulated as a maxmin optimal control problem and analytically solved by means of dynamic programming. The optimal control law, namely the immunization policy, turns out to be quite different from any duration-based immunization policy. Moreover, it is seemingly able to discriminate between favourable and unfavourable changes in the yield curve.     

A minting policy for commemorative coins

The official commemorative coins have exhibited an extraordinary increase in price during the last ten years. This has been accompanied by a commensurate increase in the sale of new issues. In 1973 alone, the Israeli Treasury generated a net profit of over 5 million dollars from the sale of commemorative coins. The Bank of Israel was interested in safeguarding the future profit generating potential of minting new coins and in learning how decisions relating to minting policy influence the long-range profits. Therefore, (1) the relationship between various coin characteristics and economic data, and the market price of old issues, as well as (2) the relationship between the profit from a new issue and the gains experienced from older issues and other coin characteristics, were determined using regression analysis. Based on the above, a dynamic model was constructed to show the relationship between the controllable variables (various minting policies) and the long-range present value of the net profit to be generated by them. Since the derivation of an optimal analytic solution seemed infeasible, several minting policies were simulated, and as a result a set of improved policies recommended.     

A time evolution model for total-variation based blind deconvolution

We propose a time evolution model for total-variation based blind deconvolution consisting of two evolution equations evolving the signal by means of a nonlinear scale space method and the kernel by using a diffusion equation starting from the zero signal and a delta function respectively. A preliminary numerical test consisting of blind deconvolution of a noiseless blurred image is presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A brain storm optimization approach for the cumulative capacitated vehicle routing problem

The cumulative capacitated vehicle routing problem (CCVRP) is a combinatorial optimization problem which aims to minimize the sum of arrival times at customers. This paper presents a brain storm optimization algorithm to solve the CCVRP. Based on the characteristics of the CCVRP, we design new convergent and divergent operations. The convergent operation picks up and perturbs the best-so-far solution. It decomposes the resulting solution into a set of independent partial solutions and then determines a set of subproblems which are smaller CCVRPs. Instead of directly generating solutions for the original problem, the divergent operation selects one of three operators to generate new solutions for subproblems and then assembles a solution to the original problem by using those new solutions to the subproblems. The proposed algorithm was tested on benchmark instances, some of which have more than 560 nodes. The results show that our algorithm is very effective in contrast to the existing algorithms. Most notably, the proposed algorithm can find new best solutions for 8 medium instances and 7 large instances within short time.     

A fixed-point algorithm for blind source separation with nonlinear autocorrelation

This paper addresses blind source separation (BSS) problem when source signals have the temporal structure with nonlinear autocorrelation. Using the temporal characteristics of sources, we develop an objective function based on the nonlinear autocorrelation of sources. Maximizing the objective function, we propose a fixed-point source separation algorithm. Furthermore, we give some mathematical properties of the algorithm. Computer simulations for sources with square temporal autocorrelation and the real-world applications in the analysis of the magnetoencephalographic recordings (MEG) illustrate the efficiency of the proposed approach. Thus, the presented BSS algorithm, which is based on the nonlinear measure of temporal autocorrelation, provides a novel statistical property to perform BSS.     

A dynamic policy for grouping maintenance activities

A maintenance activity carried out on a technical system often involves a system-dependent set-up cost that is the same for all maintenance activities carried out on that system. Grouping activities thus saves costs since execution of a group of activities requires only one set-up. Many maintenance models consider the grouping of maintenance activities on a long-term basis with an infinite horizon. This makes it very difficult to incorporate short-term circumstances such as opportunities or a varying use of components because these are either not known beforehand or make the problem intractable. In this paper we propose a rolling-horizon approach that takes a long-term tentative plan as a basis for a subsequent adaptation according to information that becomes available on the short term. This yields a dynamic grouping policy that assists the maintenance manager in his planning job. We present a fast approach that allows interactive planning by showing how shifts from the tentative planning work out. We illustrate our approach with examples.