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To update the front rear axis accompanied by the state transition, we propose the following: (2 where is the front rear axis and the suffix i represents the cells that change position by the lattice replacement.

where x i represents the number of times T cell clone i is represented in the total X from the lung primary, y i represents the number of times T cell clone i is represented in the total Y from the paired brain metastasis, and λ x and λ y represent Simpson's Diversity Index λ for each paired lesion45.

We model each term's SVM output as a random event ŷ i and treat it as a noisy observation of a latent binary event y i representing the true label (i.e. cell-type) of a given sample (Fig. 1b).

First column represent the cell seeded CF-Rolls.

The dashed lines represent the cell outline.

As defined in 'Results', the number of cells (n i ) in the ith module, is expressed in terms of the period (λ i ), the grid field width (l i ) and a 'coverage factor' d representing the cell density as n i = dλ i / l i.

Further, N i = N 1 i, N 2 i, …, N n c i i represents the set of neighboring cells of i-th UE.

The current source Iph represents the cell photocurrent.

The strength of differential expression between any pair of experiments was estimated by M i = log2 ratio) = X i - X a, where a represented one particular cell type and i represented each given cell type in the set.

The strength of differential expression between any pair of experiments was estimated by M i = log2 ratio) = X i- X a, where a represented one particular cell type and i represented each given cell type in the set: B (basal), L (luminal), S (stromal), E (endothelial), G3 (Gleason 3) or G4 (Gleason 4).

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