Abstract
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 in the form of a matrix, called a contact map. These maps are very similar to recurrence plots of dynamical systems. Consequently, the same methods can be used for reconstructing the underlying spatial structure, either the chromosome 3D spatial structure or the attractor in the phase space. These methods involve two steps: (1) de- riving a complete distance matrix of the structure using graph distances on a contact network associated with the contact map; (2) reconstructing the structure from this distance matrix, using well-established methods from distance geometry or multidimensional scaling. We here review the different options for implementing the first step, according to the binary, graded or weighted nature of the contact map. We illustrate on three benchmarks (Lorenz model, white noise and EEG data) a novel spectral criterion reflecting the spatial dimension relevant in the second step.