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EURASIP Journal on Bioinformatics and Systems Biology

Table 1 Computational complexities for the phase computation schemes

From: Phase computations and phase models for discrete molecular oscillators

Scheme

Computational complexity

PhCompBF

O ( n per K N L + L K log 2 K )

PhCompLin

O N L log 2 d max 2 d to 1 d min

PhCompQuad

O N 2 L log 2 d max 2 d tol d min

  1. In order of increasing computational complexity, the schemes are PhCompLin (on linear isochron approximations), PhCompQuad (on quadratic isochron approximations), and PhCompBF (with no approximations). We denote by N the number of states in an oscillator, 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. We have nper as the number of periods that we simulate the RRE with the initial condition that is off the orbit, so that this solution of the RRE can be expected in practice to settle into periodicity, and the phase value associated with the stated initial condition can be computed (note that this is the essence of PhCompBF). The values dmax and dmin are respectively the maximum and minimum lengths of the interval in which a solution for phase is sought. The value dtol denotes a tolerance.
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