The branch identifier I b (c j, t ) is used to define the relationship between a nucleus and its containing branch: c j, t ε B i ⇔ I b (c j, t ) = B i. Completing this formalization, we set ĉ to be the collection of all nuclei c.,., edges E, branches B, and development times o, s, ĉ = { c.,., E, B, o(e[ p/c]), s t}.
We will consider nuclei with k=2 s edges, where s is the rank of the matrix A. The reason for considering k=2 s will become clear in the Section ' The polynomial and circuits'.
Aberrant nuclei refer to nuclei with abnormal morphology, such as fragmented nuclei or nuclei with irregular shapes.
The results indicate that nucleation of singly faceted grain face nuclei and incoherent grain corner and grain edge nuclei are highly likely.
This eliminates nuclei that were bisected close to one edge, and minimizes out of focus NanoOrange signals from over (or under) lying cytoplasm.
There nuclei were located away from the blastoderm edge, as revealed by phalloidin co-staining (supplementary material Fig. S7D,D′,E,E′) and in section (supplementary material Fig. S7F).
The simulations show that the shapes of nuclei change from the equilibrium shape, which is edge-rounded square through diamond shape at small supersaturation to square shape.
The 2 s-nuclei corresponding to the term (17) must contain these edges.
Both tubulin- and actin-component cytoskeletal networks can be formalized using proximity graphs if edges are modeled as the cytoskeletal network linking the nuclei, nodes.
