Multicriterion linear programming problems : (Analytical survey)

An analytical survey of man-machine interactive procedures is presented. A decision maker's capabilities to carry out some information processing operations are discussed. A list of a decision maker's elementary operations used in different interactive procedures is given and their estimations from a psychological point of view are suggested. Three main criteria for estimation of man-machine procedures are proposed: reliability of information elicitation from decision maker, insignificant sensitivity to random decision maker's errors, and good speed of convergence to solution. Some procedures are evaluated in terms of these criteria.     

On Approximability of Boolean Formula Minimization

For a Boolean function given by a Boolean formula (or a binary circuit) S we discuss the problem of building a Boolean formula (binary circuit) of minimal size, which computes the function g equivalent to , or -equivalent to , i.e., . In this paper we prove that if P NP then this problem can not be approximated with a good approximation ratio by a polynomial time algorithm.     

中国师生对"对话交流、以学生为中心、学生自主"英语教学法的态度

Modern language teaching' especially English teaching as a foreign language, is now based on two fundamen tal approaches-traditional one with the teacher-dominated and the new emerging one with the learner-centered. This paper is a study of the survey of Chinese students regarding the attitudes of the two approaches on English learning. The conclusion of the research is positive on the new emerging approach of English learning by Chinese students.     

Battling balfour: ‘White Diplomacy’, the Russian Orthodox Church and the establishment of a Jewish State in Palestine1

ARCHITECTS OF YIDDISHISM AT THE BEGINNING OF THE TWENTIETH CENTURY. A STUDY IN JEWISH CULTURAL HISTORY, BY EMANUEL S. Goldsmith. Rutherford, Madison, Teaneck, Fairleigh Dickinson University Press and London, Associated University Presses, 1976. 309 pp. Illus. Bibl. Index. US $15.00, £7.50.     

Feature Selection for Consistent Biclustering via Fractional 0–1 Programming

Biclustering consists in simultaneous partitioning of the set of samples and the set of their attributes (features) into subsets (classes). Samples and features classified together are supposed to have a high relevance to each other which can be observed by intensity of their expressions. We define the notion of consistency for biclustering using interrelation between centroids of sample and feature classes. We prove that consistent biclustering implies separability of the classes by convex cones. While previous works on biclustering concentrated on unsupervised learning and did not consider employing a training set, whose classification is given, we propose a model for supervised biclustering, whose consistency is achieved by feature selection. The developed model involves solution of a fractional 0–1 programming problem. Preliminary computational results on microarray data mining problems are reported.This research work was partially supported by NSF, NIH and AirForce grants.     

On the central limit theorem along subsequences of sums of i.i.d. random variables

Let \(\mathbb{N } = \{1, 2, 3, \ldots \}\) . Let \(\{X, X_{n}; n \in \mathbb N \}\) be a sequence of i.i.d. random variables, and let \(S_{n} = \sum _{i=1}^{n}X_{i}, n \in \mathbb N \) . Then \( S_{n}/\sqrt{n} \Rightarrow N(0, \sigma ^{2})\) for some \(\sigma ^{2} < \infty \) whenever, for a subsequence \(\{n_{k}; k \in \mathbb N \}\) of \(\mathbb N \) , \( S_{n_{k}}/\sqrt{n_{k}} \Rightarrow N(0, \sigma ^{2})\) . Motivated by this result, we study the central limit theorem along subsequences of sums of i.i.d. random variables when \(\{\sqrt{n}; n \in \mathbb N \}\) is replaced by \(\{\sqrt{na_{n}};n \in \mathbb N \}\) with \(\lim _{n \rightarrow \infty } a_{n} = \infty \) . We show that, for given positive nondecreasing sequence \(\{a_{n}; n \in \mathbb N \}\) with \(\lim _{n \rightarrow \infty } a_{n} = \infty \) and \(\lim _{n \rightarrow \infty } a_{n+1}/a_{n} = 1\) and given nondecreasing function \(h(\cdot ): (0, \infty ) \rightarrow (0, \infty )\) with \(\lim _{x \rightarrow \infty } h(x) = \infty \) , there exists a sequence \(\{X, X_{n}; n \in \mathbb N \}\) of symmetric i.i.d. random variables such that \(\mathbb E h(|X|) = \infty \) and, for some subsequence \(\{n_{k}; k \in \mathbb N \}\) of \(\mathbb N \) , \( S_{n_{k}}/\sqrt{n_{k}a_{n_{k}}} \Rightarrow N(0, 1)\) . In particular, for given \(0 < p < 2\) and given nondecreasing function \(h(\cdot ): (0, \infty ) \rightarrow (0, \infty )\) with \(\lim _{x \rightarrow \infty } h(x) = \infty \) , there exists a sequence \(\{X, X_{n}; n \in \mathbb N \}\) of symmetric i.i.d. random variables such that \(\mathbb E h(|X|) = \infty \) and, for some subsequence \(\{n_{k}; k \in \mathbb N \}\) of \(\mathbb N \) , \( S_{n_{k}}/n_{k}^{1/p} \Rightarrow N(0, 1)\) .     

An integer programming framework for critical elements detection in graphs

This study presents an integer programming framework for minimizing the connectivity and cohesiveness properties of a given graph by removing nodes and edges subject to a joint budgetary constraint. The connectivity and cohesiveness metrics are assumed to be general functions of sizes of the remaining connected components and node degrees, respectively. We demonstrate that our approach encompasses, as special cases (possibly, under some mild conditions), several other models existing in the literature, including minimization of the total number of connected node pairs, minimization of the largest connected component size, and maximization of the number of connected components. We discuss computational complexity issues, derive linear mixed integer programming (MIP) formulations, and describe additional modeling enhancements aimed at improving the performance of MIP solvers. We also conduct extensive computational experiments with real-life and randomly generated network instances under various settings that reveal interesting insights and demonstrate advantages and limitations of the proposed framework.     

Finding checkerboard patterns via fractional 0–1 programming

Biclustering is a data mining technique used to simultaneously partition the set of samples and the set of their attributes (features) into subsets (clusters). Samples and features clustered together are supposed to have a high relevance to each other. In this paper we provide a new mathematical programming formulation for unsupervised biclustering. The proposed model involves the solution of a fractional 0–1 programming problem. A linear-mixed 0–1 reformulation as well as two heuristic-based approaches are developed. Encouraging computational results on clustering real DNA microarray data sets are presented. In addition, we also discuss theoretical computational complexity issues related to biclustering.     

Correction to: The impact of parental illness on children’s schooling and labour force participation: evidence from Vietnam

Review of Economics of the Household - The original version of this article unfortunately contained some errors in reference citations and in significance indicators in some of the tables. These...     

Modernization: the burden of the past

Embarking upon modernization, Russia will have to struggle with the debris of a degrading industrial society. The paper employs the concepts of ‘decay energy’ and ‘humanitarian catastrophe’, regarding these phenomena as inseparable from the transitional process. A detailed analysis of various types and forms of decay energy leads the author to the following conclusions: (1) minimization, elimination and/or conversion of disintegration forces and products of decay is an integral part of the modernization project for Russia; (2) this project ought to have an ideology, a leader, social forces supporting it, educational resources, and access to the media; (3) the environmental movement is one of the few collective actors poised to combat the decay forces, which possesses a well‐developed worldwide support network and has created a discourse that is comprehensible to the authorities as well as the business world and lay people; (4) for Russia with its numerous ‘frozen’ and ‘hot’ conflicts, this transition will be especially difficult and costly.