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The toric locus of a reaction network is a smooth manifold
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We show that the toric locus of a reaction network is a smoothly embedded submanifold of the Euclidean space. More precisely, we prove that the toric locus of a reaction network is the image of an embedding and it is diffeomorphic to the product space between the affine invariant polyhedron of the network and its set of complex-balanced flux vectors. Moreover, we prove that within each affine invariant polyhedron, the complex-balanced equilibrium depends smoothly on the parameters (i.e., reaction rate constants). We also show that the complex-balanced equilibrium depends smoothly on the initial conditions.
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The Dimension of the Disguised Toric Locus of a Reaction Network
Claims an exact dimension formula for disguised toric loci, but the sign convention in the formula contradicts the paper's own map and fails on a simple star network.
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