A nonparametric estimator of mutual information is proposed and is shown to have asymptotic normality and efficiency, and a bias decaying exponentially in sample size. The asymptotic normality and the rapidly decaying bias together offer a viable inferential tool for assessing mutual information between two random elements on finite alphabets where the maximum likelihood estimator of mutual information greatly inflates the probability of type I error. The proposed estimator is illustrated by three examples in which the association between a pair of genes is assessed based on their expression levels. Several results of simulation study are also provided.

No abstract

The debate regarding to which similarity measure can be used in co-citation analysis lasted for many years. The mostly debated measure is Pearson's correlation coefficient r. It has been used as similarity measure in literature since the beginning of the technique in the 1980s. However, some researchers criticized using Pearson's r as a similarity measure because it does not fully satisfy the mathematical conditions of a good similarity metric and (or) because it doesn't meet some natural requirements a similarity measure should satisfy. Alternative similarity measures like cosine measure and chi square measure were also proposed and studied, which resulted in more controversies and debates about which similarity measure to use in co-citation analysis. In this article, we put forth the hypothesis that the researchers with high mutual information are closely related to each other and that the mutual information can be used as a similarity measure in author co-citation analysis. Given two researchers, the mutual information between them can be calculated based on their publications and their co-citation frequencies. A mutual information proximity matrix is then constructed. This proximity matrix meet the two requirements formulated by Ahlgren et al. (J Am Soc Inf Sci Technol 54(6):550-560, 2003). We conduct several experimental studies for the validation of our hypothesis and the results using mutual information are compared to the results using other similarity measures.

No abstract

The paper contains a generalization of the well-known 1D results on the absence of the a.c. spectrum ( in the spirit of the Simon–Spencer theorem) and localization to the wide class of “non-percolating” graphs, which include the Sierpiński lattice and quasi 1D trees. The main tools are cluster expansion of the resolvent and real analytic techniques (Kolmogorov’s lemma and similar estimates).