Full Implementation of Rank Dependent Prizes

A manager/mechanism designer must allocate a set of money prizes ($1, $2, .., $n) between n agents working in a team. The agents know the state i.e. who contributed most, second most, etc. The agents' prefer- ences over prizes are state independent. We incorporate the possibility that the manager knows the state with a tiny probability and present a simple mechanism that uniquely implement prizes that respects the true state.

Miscellaneous translations on oyster biology (contents page only - individual articles held as separate documents)

This is a translation of selected articles from the Japanese language publication Hiroshimaken Suisan Shikenjo Hokoku (Report of Hirshima Prefectural Fisheries Experimental Station), Hiroshima City, Japan, vol.22, no. 1, 1960, pages 1-76. Articles translated are: Haematological study of bacteria affected oysters, The distribution of oyster larvae and spatfalls in the Hiroshima City perimeter, On the investigation of the timing of spatfalls, On the prediction of oyster seeding at inner Hiroshima Bay, Oyster growth and its environment at the oyster farm in Hiroshima Bay

Back page of No. 44, 1986

Membership of CDF Council

Back page of No. 42, 1985

Charles Darwin Foundation for the Galapagos Islands.

Back page of No. 63, 2005

Instructions for Authors. Back cover with map.

Cluster analysis of heterogeneous rank data

Cluster analysis of ranking data, which occurs in consumer questionnaires, voting forms or other inquiries of preferences, attempts to identify typical groups of rank choices. Empirically measured rankings are often incomplete, i.e. different numbers of filled rank positions cause heterogeneity in the data. We propose a mixture approach for clustering of heterogeneous rank data. Rankings of different lengths can be described and compared by means of a single probabilistic model. A maximum entropy approach avoids hidden assumptions about missing rank positions. Parameter estimators and an efficient EM algorithm for unsupervised inference are derived for the ranking mixture model. Experiments on both synthetic data and real-world data demonstrate significantly improved parameter estimates on heterogeneous data when the incomplete rankings are included in the inference process.

Rank-preserving geometric means of positive semi-definite matrices

The generalization of the geometric mean of positive scalars to positive definite matrices has attracted considerable attention since the seminal work of Ando. The paper generalizes this framework of matrix means by proposing the definition of a rank-preserving mean for two or an arbitrary number of positive semi-definite matrices of fixed rank. The proposed mean is shown to be geometric in that it satisfies all the expected properties of a rank-preserving geometric mean. The work is motivated by operations on low-rank approximations of positive definite matrices in high-dimensional spaces.© 2012 Elsevier Inc. All rights reserved.