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The toric locus of a reaction network is a smooth manifold

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arxiv 2309.15241 v1 pith:Q5QH4L65 submitted 2023-09-26 math.DS

classification math.DS
keywords networkreactioncomplex-balancedlocussmoothlytoricaffinedepends
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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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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The Dimension of the Disguised Toric Locus of a Reaction Network

    q-bio.MN 2024-12 reject novelty 6.0 of 10

    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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