Comments on “aggregation of equivalence relations” by P. C. Fishburn and A. Rubinstein

The theorem of the paper Aggregation of Equivalence Relations, by Fishburn and Rubinstein, states a result already known. This theorem improves a result from Mirkin (1975) and appears as a corollary occurring in Leclerc (1984).

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Resume L'unique théorème de l'article Aggregation of Equivalence Relations de Fishburn et Rubinstein est déja connu. Il améliore, en fait, un résultat de Mirkin (1975) et apparait en tant que corollaire dans Leclerc (1984).

     

The median procedure for n-trees

Let (X,d) be a metric space The functionM:X ^k 2 ^x defined by is the minimum } is called themedian procedure and has been found useful in various applications involving the notion of consensus Here we present axioms that characterizeM whenX is a certain class of trees (hierarchical classifications), andd is the symmetric difference metricWe would like to thank the referees and Editor for helpful comments     

金融稳定目标与货币政策框架演进

＂杰克逊霍尔共识＂基于价格稳定与金融稳定的一致性,以通货膨胀目标制定货币政策框架强调价格稳定的重要性。然而低通货膨胀与资产价格大幅波动并存,使得人们不断反思价格稳定与金融稳定之间的权衡性,因而较晚成立的欧洲央行,以＂双支柱战略＂货币政策框架尝试关注金融稳定。而此次金融危机的教训表明,央行应该更加积极主动地关注金融稳定目标,因而构建基于宏观审慎的货币政策框架,以同时实现价格稳定和金融稳定是其未来演进的方向。     

代换定理的证明及其应用

本文给出了代换定理的优于文献[1]的证明方法,并把代换定理与其他定理结合,构造了一个判定DNF表达式永真性的算法,使代换定理得到实际应用。     

Direct multicriteria clustering algorithms

In a multicriteria clustering problem, optimization over more than one criterion is required. The problem can be treated in different ways: by reduction to a clustering problem with the single criterion obtained as a combination of the given criteria; by constrained clustering algorithms where a selected critetion is considered as the clustering criterion and all others determine the constraints; or by direct algorithms. In this paper two types of direct algorithms for solving multicriteria clustering problem are proposed: the modified relocation algorithm, and the modified agglomerative algorithm. Different elaborations of these two types of algorithms are discussed and compared. Finally, two applications of the proposed algorithms are presented. Elaborated version of the talks presented at the First Conference of the International Federation of Classification Societies, Aachen, 1987, at the International Conference on Social Science Methodology, Dubrovnik, 1988, and at the Second Conference of the International Federation of Classification Societies, Charlottesville, 1989. This work was supported in part by the Research Council of Slovenia.     

Allocating the weights in the linear opinion pool

A standard approach to the combination of probabilistic opinions involves taking a weighted linear average of the individuals distributions. This paper reviews some of the possible interpretations that have been proposed for these weights in the literature on expert use. Several paradigms for selecting weights are also considered. Special attention is devoted to the Bayesian mechanism used for updating expert weights in the face of new information. An asymptotic result is proved which highlights the importance of choosing the initial weights carefully.     

Distribution of some similarity coefficients for dyadic binary data in the case of associated attributes

Parameters are derived of distributions of three coefficients of similarity between pairs (dyads) of operational taxonomic units for multivariate binary data (presence/absence of attributes) under statistical independence. These are applied to test independence for dyadic data. Association among attributes within operational taxonomic units is allowed. It is also permissible for the two units in the dyad to be drawn from different populations having different presence probabilities of attributes. The variance of the distribution of the similarity coefficients under statistical independence is shown to be relatively large in many empirical situations. This result implies that the practical interpretation of these coefficients requires much care. An application using the Jaccard index is given for the assessment of consensus between psychotherapists and their clients.

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La distribution des coefficients de similarité pour les données binaires et les attributs associés

Résumé Les paramètres de la distribution de trois coefficients de similarité entre paires d'éléments taxinomiques opérationels de données multivariables binaires (présence/absence) ont été dérivés dans l'hypothèse d'indépendance statistique. Ces paramètres sont utilisés dans un test d'indépendance pour les données dyadiques. L'existence est autorisée, dans la population d'éléments, d'une association entre plusieurs attributs. Il est également permis que les deux éléments de la dyade soient tirés de deux populations différentes, ayant différentes probabilit és quant à la présence des attributs. Dans beaucoup de situations empiriques, la variance des coefficients de similarité peut être relativement élevée dans le cas d'indépendance statistique. Par conséquence, ces coefficients doivent être interprétés avec précaution. Un exemple est donné pour le coefficient de Jaccard, qui a été employé dans une recherche sur la concordance entre des psychothérapeutes et leurs clients.

     

可信激励算法对区块链移动节点共识优化研究

节点可移动的物联网应用区块链时将节点称为区块链移动节点,区块链移动节点存在通信连通时间较短、算力和存储能力不足等问题导致网络达成共识时安全性和吞吐量较低.提出一种可信激励算法对共识过程进行优化,首先区块链移动节点接收共识所需信息完成初始化;其次每个区块链移动节点生成判决块,判决块包含对验证消息的投票结果、自身的可信因子和判决块的生成时间,根据判决块中在相邻区块链移动节点组成的集群中选出中继节点,中继节点传播验证消息到下一个集群,并产生区块存储在边缘服务器,一个中继为一跳,当跳数大于网络阈值跳数时完成共识;最后根据激励机制对节点奖励或惩罚,并按激励情况更新节点的行为标识反馈到共识.仿真结果表明,与应用在同样网络情况的PoET和PoS算法相比,可信激励算法在保证了一定的吞吐量情况下,有效降低验证消息验证失败率提高了共识安全性,更适合节点可移动的物联网网络.     

The median procedure for n-trees as a maximum likelihood method

A few axioms are presented which allow the median procedure for n-trees to be given a maximum likelihood interpretation.Research supported by grant number N00014-89-J-1643 from the Office of Naval Research. The author would like to thank the referees for their helpful comments.     

Character and OTU stability in five taxonomic groups

The character and OTU stability of classifications based on UPGMA clustering and maximum parsimony (MP) trees were compared for 5 datasets (families of angiosperms, families of orthopteroid insects, species of the fish genusIctalurus, genera of the salamander family Salamandridae, and genera of the frog family Myobatrachidae). Stability was investigated by taking different sized random subsamples of OTUs or characters, computing UPGMA clusters and an MP tree, and then comparing the resulting trees with those based on the entire dataset. Agreement was measured by two consensus indices, that of Colless, computed from strict consensus trees, and Stinebrickner's 0.5-consensus index. Tests of character stability generally showed a monotone decrease in agreement with the standard as smaller sets of characters are considered. The relative success of the two methods depended upon the dataset. Tests of OTU stability showed a monotone decrease in agreement for UPGMA as smaller sets of OTUs are considered. But for MP, agreement decreased and then increased again on the same scale. The apparent superiority of UPGMA relative to MP with respect to OTU stability depended upon the dataset. Considerations other than stability, such as computer efficiency or accuracy, will also determine the method of choice for classifications.