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The Domain of Combinatorics
Some Highlights of Developmental Biology
An Elementary Branching Process
24 other sections not shown
adhesive energy approximation asymptotic blastula bond bond percolation boundary branching process cell type chain clone cluster number coefficient combinatorial concentration configuration consider continuum defined denotes determined DEVELOPMENTAL BIOLOGY differentiation dimensional distribution ectoderm eigenvalues equation equivalent example expansion factorial moments finite Galton-Watson process gastrulation given graph Hence homogeneous hydra infinite clusters infinite lattice initial interaction Ising model linear matrix mean cluster mean number mesoderm molecule morphogen nearest neighbor nematoblasts number of cells number of clusters number of sites obtained occurs pair parameter partition function pattern percolation problem population possible probability QN(x ratio restriction result rooted Bethe lattice s-clusters sequence site percolation solution solve spacial spherical model spin square lattice stem cells structure subgraphs Suppose tanh tion tissue total number transformation transition va(x variable vertex wave weight