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.     

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.     

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.     

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 \(\mathbb N \) , \( S_{n_{k}}/n_{k}^{1/p} \Rightarrow N(0, 1)\) .     

The Potential for Reducing Mortality in Russia

This article attempts to assess current national and regional reserves for reducing the mortality rate in Russia. It explores the potential to reduce the mortality rate in comparison to comparable international benchmarks in rates of growth and gains in life expectancy at birth, identifies a range of circumstances that have an adverse impact on the population’s health in post-Soviet Russia, and shows that the main reserve for reducing mortality remains the “lost health capital” that preceded the collapse of the Soviet Union and continued in the 1990s. Finally, it assesses the current regional potential for lowering the mortality rate, which is “hidden” in differences between regions leading in life expectancy (with the exception of extremes) and the country’s remaining territories. The conclusion presents data revealing the life expectancy of men and women.     

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.     

Sustainability and Risk: The Case of Russia

The majority of recent concepts of sustainable development assume that all societies will sooner or later reach the state of sustainable development, the question being how. For Russia, the question is another one: how can a society survive in the course of the long-term process of its devolution. At present, Russia and several other of the so-called transition societies are maintaining their sustainability at the expense of de-modernization, and the over-exploitation of natural and human resources, and there is a return to the values and structures of a traditional society. The paper attempts to adapt the concepts of the risk society developed by Ulrich Beck and Antony Giddens for a comprehension of Russian reality with a focus on the relationships between risk production, dissemination and sustainability.