Sulfur in Cometary Dust

The computer-intensive project consisted of the analysis and synthesis of existing data on composition of comet Halley dust particles. The main objective was to obtain a complete inventory of sulfur containing compounds in the comet Halley dust by building upon the existing classification of organic and inorganic compounds and applying a variety of statistical techniques for cluster and cross-correlational analyses. A student hired for this project wrote and tested the software to perform cluster analysis. The following tasks were carried out: (1) selecting the data from existing database for the proposed project; (2) finding access to a standard library of statistical routines for cluster analysis; (3) reformatting the data as necessary for input into the library routines; (4) performing cluster analysis and constructing hierarchical cluster trees using three methods to define the proximity of clusters; (5) presenting the output results in different formats to facilitate the interpretation of the obtained cluster trees; (6) selecting groups of data points common for all three trees as stable clusters. We have also considered the chemistry of sulfur in inorganic compounds

Dynamic and Structure of the Italian stock market based on returns and volume trading

In this paper we introduce a new method to describe dynamical patterns of multidimensional time. The method combines the tools of Symbolic Time Series Analysis with the nearest neighbor single linkage clustering algorithm. Data symbolization allows to obtain a metric distance between two different time series that is used to construct an ultrametric distance. The methodology is applied to examine the dynamics and structure of the Italian stock market considering both asset returns and volume trading to model the market. We derive a hierarchical organization, constructing minimal-spanning and hierarchical trees, both in normal and extreme situations of the market. From these trees we detect four clusters of firms according to their proximity. We show that the financial cluster is in a central position of the minimal spanning tree, both in normal and extreme situations, reflecting that financial companies represent more than 30% of the Italian market capitalization. We also show that the derived clusters corresponds with companies sharing common economic activities.

Solving non-uniqueness in agglomerative hierarchical clustering using multidendrograms

In agglomerative hierarchical clustering, pair-group methods suffer from a problem of non-uniqueness when two or more distances between different clusters coincide during the amalgamation process. The traditional approach for solving this drawback has been to take any arbitrary criterion in order to break ties between distances, which results in different hierarchical classifications depending on the criterion followed. In this article we propose a variable-group algorithm that consists in grouping more than two clusters at the same time when ties occur. We give a tree representation for the results of the algorithm, which we call a multidendrogram, as well as a generalization of the Lance and Williams' formula which enables the implementation of the algorithm in a recursive way.Comment: Free Software for Agglomerative Hierarchical Clustering using Multidendrograms available at http://deim.urv.cat/~sgomez/multidendrograms.ph