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Table 2 Computational complexities for the phase equations

From: Phase computations and phase models for discrete molecular oscillators

Equation

Complexity (best)

Complexity (worst)

PhEqnLL

O ( M L + N L )

O ( N M L )

PhEqnQL

O ( N 2 L + M L )

O ( N 2 L + N M L )

  1. We provide the best and worst case computational complexities for the phase equations, PhEqnLL (on linear isochron and linear orbital deviation approximations) and PhEqnQL (on quadratic isochron and linear orbital deviation approximations), according as the stoichiometric matrix S is sparse (few entries per row) or fully dense. Note that the computational load the equations entail are much less than those of the phase computation schemes. We denote by N the number of states in an oscillator, M the number of possible reactions that can occur, K the number of timepoints along a single period, and L the number of total timepoints along the interval where a phase computation method is run.