Genomics, Pattern Avoidance, and Statistical Mechanics

Motivation

This event will bring together computational and mathematical biologists who are active in the field of genomics, computer scientists and mathematicians studying pattern avoidance, and mathematicians and physicists whose area of research is statistical mechanics.

There are many tantalising connections between these three fields. Examples include the following.

In the simplest form the problem of gene rearrangements corresponds to sorting by reversals. The permutations that are hardest to sort in this way are known as increasing oscillations, and are fundamental to the study of permutation classes.

The partially asymmetric simple exclusion process (PASEP) is a generalization of a one-dimensional gas model, exhibiting boundary-driven phase transitions and spontaneous symmetry-breaking. Properties of the PASEP are directly connected to counting occurrences of the vincular pattern 2-13 in permutations and to the combinatorics of permutation tableaux.

Evolution in viral populations can be modelled by theories of quasi-species. These theories have captured the attention of the statistical mechanics community since it was shown that they could be represented by a type of two-dimensional Ising model, the macroscopic distribution of the population corresponding to surface magnetization.

However, despite the existence of these links, there is little interaction between the different communities. The goals of this seminar are to

• build bridges between the three areas by bringing together experts from each field,
• identify themes and models that are common across the three areas,
• detail avenues of possible future research and define project ideas for cooperation between the communities.

In addition to presentations of recent research results, the Dagstuhl Seminar will include expository talks explaining the specific interests and questions of each community to the other two. The programme will also contain lectures surveying the interfaces between each pair of communities. In addition, there will be sessions on questions that are common to two or more of the fields. Opportunities will be provided for the discussion of open problems and other topics of shared interest.