Maps of variability in cell lineage trees
Fig 5
Cyclic and tree-structured symmetries.
(a) A cyclic symmetry structure is one that remains invariant under a shift of all the variables (around the circle in the figure shown) that preserves their relative ordering. This cyclic symmetry defines the discrete Fourier transform. (b) A tree symmetry structure is one that remains invariant under permutations within groups and permutations of groups. This symmetry gives rise to ANOVA for nested pairs and also defines the Haar wavelet transform. It is applicable when it is just the leaf nodes that are of interest. (c) When all the nodes of a tree are of interest, the underlying symmetry is still that for the tree. The associated transformation is derived in this paper and discussed in the next section.