Biomedical subjects

R Arratia

Publications and source records attributed to R Arratia.

3 recordsLinked to original sources

PubMed1991

Genomic mapping by anchoring random clones: a mathematical analysis.

A complete physical map of the DNA of an organism, consisting of overlapping clones spanning the genome, is an extremely useful tool for genomic analysis. Various methods for the construction of such physical maps are available. One approach is to assemble the physical map by "fingerprinting" a large number of random clones and inferring overlap between clones with sufficiently similar fingerprints. E.S. Lander and M.S. Waterman (1988, Genomics 2:231-239) have recently provided a mathematical analysis of such physical mapping schemes, useful for planning such a project. Another approach is to assemble the physical map by "anchoring" a large number of random clones--that is, by taking random short regions called anchors and identifying the clones containing each anchor. Here, we provide a mathematical analysis of such a physical mapping scheme.

Chromosome Mapping↗

PubMed1989

Tutorial on large deviations for the binomial distribution.

We present, in an easy to use form, the large deviation theory of the binomial distribution: how to approximate the probability of k or more successes in n independent trials, each with success probability p, when the specified fraction of successes, a identical to k/n, satisfies 0 less than p less than a less than 1.

Amino Acid Sequence↗

PubMed1987

Phase transitions in sequence matches and nucleic acid structure.

Analyses of phase transitions in biopolymers have previously been restricted to studies of average behavior along macromolecules. Extremal properties, such as longest helical region, can now be studied with a new family of probability distributions [Arratia, R., Gordon, L. & Waterman, M. S. (1986) Ann. Stat. 14, 971-993]. Not only is such extremal behavior analyzed with great precision, but new phase transitions are determined. One phase transition occurs when behavior of the free energy of the longest helical region abruptly changes from proportional to sequence length. The annealing of two single-stranded molecules and the melting of a double helix are both considered. These results, initially suggested by studies of optimal matching of random DNA sequences [Smith, T. F., Waterman, M. S. & Burks, C. (1985) Nucleic Acids Res. 13, 645-656], also have importance for significance tests in comparison of nucleic acid or protein sequences.

Base Sequence↗