Mathematics Colloquium

WHEN:
Thursday, September 6, 2007 at 2:30 PM

WHERE:
Durham Science Center, Room 116

WHAT:

ABSTRACT:
We will consider some probabilistic and combinatorial problems of a branch of mathematics known as The Theory of Error-Correcting Codes. Codes built on the space of DNA n-sequences can be implemented in Biomolecular Computing and could have other important applications.  The minimum distance parameter of such code (consisting of codewords) is a measure of how dissimilar the codewords are. In other words, the distance is indirectly a measure of the likelihood of undetectable or uncorrectable errors occurring during hybridization, i.e., coalescing of two oppositely directed DNA strands into a DNA duplex which is based on hydrogen bonds between some pairs of nucleic acids. To identify distance, an abstract similarity function must be used to model the actual bonding energies of DNA strands.
In order to accomplish DNA computing, it is necessary to have DNA codes of large size and small energies of hybridization between the DNA sequences. The ultimate criterion for the value of a similarity for DNA codes is the degree to which it approximates actual bonding energies, which in turn determines the degree to which similarity approximates the likelihood of one codeword mistakenly binding to the reverse complement of another codeword. One can use the space of DNA sequences endowed with a measure of similarity. The similarity function between DNA sequences has an immediate application in determining the similarities between genes, expressed as DNA sequences, in any existing genome. A conventional similarity function for measuring codeword similarity is the well-known deletion similarity, i.e., the length of a longest common subsequence. In our recent work we suggested to use the length of a longest common block subsequence, which imposes an additional adjacency requirement, with the goal of modeling actual bonding energies. In this talk we will introduce the concept of a stem similarity function, which provides a more accurate estimation of the hybridization energy.  

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