Algorithmic and combinatorial studies inspired by problems of comparative genomics

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My research interests are in developing algorithmic approaches and combinatorial tools to solve theoretical problems inspired by biological problems arising in the field of comparative genomics. One of the basic aim of comparative genomics is to extract information from the comparison of genomes of different species. This information concerns the genomic sequence themselves, the order of appearance of genes in different genomes, the structure of small molecules (like RNA), etc. The general problem of extracting meaningful information from the resulting mass of biological information gives rise to many important theoretical problems on the fine combinatorics of words, permutations, trees or graphs. A first portion of my research program concerns the study and comparison of special trees and graphs representing non-coding RNA (ncRNA) structures. This study is of particular importance for biology because important cellular functions of ncRNA depend on their structural and combinatorial properties. Moreover, the fast expansion of complex databases of ncRNA structures (from barely 3 known families in 2002, to over 1,400 today) warrants the development of faster algorithms for the comparison and the analysis of such structures. A second portion concerns the study of permutations or signed permutations representing the order of appearance of genes in different genomes. Here, the problem consists in finding the median of a set of permutations under a distance d and is inspired by the gene order problem of comparative genomics, where the difference in order of appearance of genes in the genome of different species is used to evaluate the evolutionary distances between them. Finally, the expected theoretical results that will arise from the development of more efficient comparison algorithms in the field of bioinformatics is bound to help to solve similar problems in other field of computer science. We have already shown how our results may be applied in the context of software engineering where the maintenance of system requires the search of recurrent motifs in a program code.