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Genetics, Vol 142, 267-284, Copyright © 1996
INVESTIGATIONS |
On the Consistency of a Physical Mapping Method to Reconstruct a Chromosome in Vitro
M. Xiong, H. J. Chen, R. A. Prade, Y. Wang, J. Griffith, W. E. Timberlake and J. Arnold
Department of Mathematics and Molecular Biology, University of Southern California, Los Angeles, California 90089
During recent years considerable effort has been invested in creating physical maps for a variety of organisms as part of the Human Genome Project and in creating various methods for physical mapping. The statistical consistency of a physical mapping method to reconstruct a chromosome, however, has not been investigated. In this paper, we first establish that a model of physical mapping by binary fingerprinting of DNA fragments is identifiable using the key assumption--for a large randomly generated recombinant DNA library, there exists a staircase of DNA fragments across the chromosomal region of interest. Then we briefly introduce epi-convergence theory of variational analysis and transform the physical mapping problem into a constrained stochastic optimization problem. By doing so, we prove epi-convergence of the physical mapping model and epi-convergence of the physical mapping method. Combining the identifiability of our physical mapping model and the epi-convergence of a physical mapping method, finally we establish strong consistency of a physical mapping method.
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