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Let us translate the equilibrium (E_(x_, y_)) of system (4) to the origin by using the transformation (tilde{x}=x-x_) and (tilde{y}=y-y _).
Proof Performing a coordinate shift as follows: I ˜ = I − I ∗, R ˜ = R − R ∗, and letting F ˜ denote the transformed F, we translate the equilibrium point Q ( I ∗, R ∗ ) into Q ˜ ( 0, 0 ) and discuss the equilibrium point Q ˜ of the map F ˜.
Therefore, we illustrate in detail how to change coordinates in order to translate the equilibrium to zero.
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In order to translate the positive equilibrium to origin, we set and obtain (3.3).
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The Interaction-Identifier method follows recent efforts [ 12, 25, 26] to translate TF concentrations into the equilibrium probability of RNAP binding using thermodynamic models.
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