The Greek astronomer Ptolemy of Alexandria (second century) and the Indian mathematician Brahmagupta (sixth century) each have a significant theorem named after them. Both theorems have to do with cyclic quadrilaterals. Ptolemy's theorem states that: In a cyclic quadrilateral, the product of the diagonals is equal to the sum of the products of two…

The G coefficient is proven to be an inaccurate indicator of latent relations and, therefore, unacceptable as a measure of association when used in R-type factor analysis. The G coefficient is useful in measuring another type of relation, the simple agreement of scores for a pair of items. (Author/BS)

This paper establishes a loss function for the alpha factor analysis. Some analogies to the maximum likelihood factor analysis are discussed. (Author/BW)

When comparing k normal populations an investigator might want to know the probability that the population with the largest population mean will have the largest sample mean. This paper describes and illustrates methods of approximating this probability when the variances are unknown and possibly unequal. (Author/BW)

The canonical redundancy statistic, an estimate of the amount of shared variance between two sets of variables, exhibits an amount of bias similar to that of the first squared canonical correlation coefficient. Two formulae, Wherry and Olkin-Pratt, adequately correct the bias of the redundancy statistic. (Author/BW)

Bond criticized the base-free measure of change proposed by Tucker, Damarin, and Messick by pointing to an incorrect derivation which is here viewed instead as a correct derivation entailing an inadequately specified assumption. Bond's revision leads to negatively biased estimates, whereas the original approach leads to unbiased estimates.…

Estimates of sample size requirements for 2 X 2 tables, derived from three approximate formulae, were evaluated by comparison with exact calculations. Although different, the estimates derived from all three formulae were judged adequate for most practical purposes, with the most accurate results being obtained from Cohen's formula. (Author/JKS)

Discussion of bibliographies and sources focuses on the application of martingale theory to the generalized "success breeds success" principle, generalized in order to comprise other phenomena such as "failure breeds failure" and other production rhythms. Items are allowed to have multiple sources, and fractional assignment of…

Describes two similarity measures used in citation and co-citation analysis--the Jaccard index and Salton's cosine formula--and investigates the relationship between the two measures. It is shown that Salton's formula yields a numerical value that is twice Jaccard's index in most cases, and an explanation is offered. (13 references) (CLB)

Analyzes the computational complexity of optimal binary tree pruning for tree-structured vector quantization. Topics discussed include the combinatorial nature of the optimization problem; the complexity of optimal tree pruning; and finding a minimal size pruned tree. (11 references) (LRW)

Describes a string-searching algorithm for multiple patterns in a text string; explains the construction of a pattern-matching machine; presents a theoretical analysis and empirical evidence that supports the sublinearity of the algorithm; and compares this algorithm with the Boyer-Moore algorithm for a single pattern. (Contains 10 references.)…

Discusses the minimum average codeword length coding under the constraint that the codewords are monotonically nondecreasing in length. Bounds on the average length of an optimal monotonic code are derived, and sufficient conditions are given such that algorithms for optimal alphabetic codes can be used to find the optimal monotonic code. (six…

Studies the evolution of information production processes and their relation to the Lorenz dominance order as a theoretical framework for bibliometrics. The relation between the total number of sources, the total number of items, the average production, and the maximum production are examined. Geometric illustrations are provided. (Contains 14…

Discusses the measurement of the growth and obsolescence of literature and shows that growth and obsolescence can be studied by the same mathematical techniques. A combined growth-obsolescence theory is presented that can be measured with continuous rates, and three earlier papers are reconsidered and results are reproven. (Contains 18…

Investigates the modeling of changes in user interest in information filtering systems and develops a new technique for tracking user interest shifts based on a Bayesian approach. Presents an analytical study to establish the rate of convergence for a profile learning module with and without the user interest tracking component. (Author/LRW)