Consider a group of n men and n women, each ranking the members of the opposite sex as a potential marriage partner. A matching (marriage) of men and women is called stable if there is no pair (man, woman) who are not matched but prefer each other to their partners in the matching. It is known that, for every instance of the rankings, there is at least one stable matching and that there are instances with exponentially many stable matchings. Assume that the instance is chosen uniformly at random among all $(n!)^{2n}$ possibilities. In this case the likely number of stable matchings is known to be $n^{1/2-o(1)}$, with high probability, and of order $n\ln n$, with probability $0.84$ at least. In this paper we show that the average number of fixed pairs (man, woman), i.e., pairs common to all stable matchings, is asymptotic to $\ln^2 n$. More generally, the average number of women (men) with k stable husbands (wives) is asymptotic to $(\ln ^{k+1} n)/(k-1)!$.

TRAMP is a software package for generating transposon maps that are used for DNA sequencing. The package provides a variety of automated tools that can always be overridden by the user. The central part of the package is its selection algorithm that finds the most robust map with the smallest number of inserts. TRAMP has been in daily use by the sequencing team at LBL since it was introduced in the Spring of 1994. It is applicable to any sequencing project utilizing the directed strategy.

An algorithm for estimating the difference between two tomographic images is proposed if the two data vectors are obtained in nonoverlapping time intervals. The algorithm takes advantage of statistical independence of the two vectors. The results are significantly different from the traditional approach in which the two images are reconstructed separately and then subtracted.

The work presented evaluates the statistical characteristics of regional bias and expected error in reconstructions of real positron emission tomography (PET) data of human brain fluoro-deoxiglucose (FDG) studies carried out by the maximum likelihood estimator (MLE) method with a robust stopping rule, and compares them with the results of filtered backprojection (FBP) reconstructions and with the method of sieves. The task of evaluating radioisotope uptake in regions-of-interest (ROIs) is investigated. An assessment of bias and variance in uptake measurements is carried out with simulated data. Then, by using three different transition matrices with different degrees of accuracy and a components of variance model for statistical analysis, it is shown that the characteristics obtained from real human FDG brain data are consistent with the results of the simulation studies.

Dynamic hashing with deferred splitting is a file organization scheme which increases storage utilization, as compared to standard dynamic hashing. In this scheme, splitting of a bucket is deferred if the bucket is full but its brother can accommodate new records. The performance of the scheme is analyzed. In a typical case the expected storage utilization increases from 69 to 76 percent.