Some Effects of the Human Genome Project on the Erdős Collaboration Graph

The Human Genome Project introduced large-scale collaborations involving dozens to hundreds of scientists into biology. It also created a pressing need to solve discrete mathematics problems involving tens of thousands of elements. In this paper, we use minimal path lengths in the Erdős Collaboration Graph between prominent individual researchers as a measure of the distance between disciplines, and we show that the Human Genome Project brought laboratory biology as a whole closer to mathematics. We also define a novel graph reduction method and a metric that emphasizes the robustness of collaborative connections between researchers; these can facilitate the analysis of both within- and between-community connectivity in collaboration graphs

Information analysis of DNA sequences

The problem of differentiating the informational content of coding (exons) and non-coding (introns) regions of a DNA sequence is one of the central problems of genomics. The introns are estimated to be nearly 95% of the DNA and since they do not seem to participate in the process of transcription of amino-acids, they have been termed “junk DNA.” Although it is believed that the non-coding regions in genomes have no role in cell growth and evolution, demonstration that these regions carry useful information would tend to falsify this belief. In this thesis, we consider entropy as a measure of information by modifying the entropy expression to take into account the varying length of these sequences. Exons are usually much shorter in length than introns; therefore the comparison of the entropy values needs to be normalized. A length correction strategy was employed using randomly generated nucleonic base strings built out of the alphabet of the same size as the exons under question. The distance between exons and introns is calculated based on their probability distributions. We found that Zipf’s distribution was not followed by the n-tuples in DNA sequences, and a newly modified power distribution derived from the Zipf’s distribution was found by trial and error that closely modeled the codon frequencies. Correlation and divergence tests were performed. Our analysis shows that introns carry nearly as much of information as exons, disproving the notion that they do not carry any information. The entropy findings of this thesis are likely to be of use in further study of other challenging works like the analysis of symmetry models of the genetic code