Résumé
The physical proximity of genomic sites (to each other, within the 3D structure of a chromosome) can be experimentally measured in living cells and represented as a matrix, called a 'contact map'. Such contact maps have also been used to represent and analyse the 3D structure of proteins. They are closely related to recurrence plots of dynamical systems. In particular, the same reconstruction methods can be used. The main steps of the reconstruction of the underlying structures (chromosomes, proteins or attractors, respectively) are: (i) to compute a complete distance matrix using shortest-path distance on a weighted contact network derived from the contact map, (ii) to use a result of distance geometry based on the three dominant eigenvectors of the metric matrix derived from the distance matrix,(iii) or to approximate the 3D structure using multi-dimensional scaling techniques.This reconstruction algorithm can also be adapted as a tool to enhance under-sampled contact maps.In a different direction, analogies between the algebraic analysis (principal eigenvector of the correlation matrix) and motif analysis (topological domains seen as squares along the diagonal) of the respective contact matrices can be drawn.