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Table 4 p53 and mdm2 mRNA expression model: white noise with neglected kinetics

From: Least-squares methods for identifying biochemical regulatory networks from noisy measurements

Samplings per Experiment Algorithms ε M ε S ε F
   Mean STD Mean STD Mean STD
4 LS 1.34 0.34 1.01 0.14 0.04 0.01
  TLS 1.34 0.34 1.01 0.14 0.04 0.01
  CTLS 1.34 0.34 1.01 0.14 0.04 0.01
8 LS 0.95 0.27 0.50 0.02 0.03 0.01
  TLS 25.03 196.73 1.01 0.15 1.06 8.42
  CTLS 0.44 0.12 0.50 0.00 0.02 0.00
12 LS 0.61 0.08 0.50 0.00 0.02 0.00
  TLS 47.53 241.86 0.92 0.31 2.49 13.07
  CTLS 0.49 0.06 0.50 0.02 0.02 0.00
16 LS 0.44 0.06 0.50 0.00 0.02 0.00
  TLS 50.96 833.28 1.02 0.20 3.11 50.06
  CTLS 0.49 0.05 0.50 0.02 0.02 0.00
  1. The table shows the error comparisons in terms of the mean and the standard deviation (STD) for different number of data for each method based on 1000 Monte-Carlo Simulations. The measurements are taken every 2 hours and the states converge to steady states around the 16-th sample. ε M is the sum of two tems, i.e (1/N1) Σ |α i j | and (1/N2) Σ |β i j |, where α i j and β i j are the relative magnitude errors in the non-zero and zero elements of the true Jacobian, respectively, and N1 and N2 are the number of non-zero and zero elements in the true Jacobian, respectively. ε S is given by (1/n2) Σ |sign ( f ^ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacuWGMbGzgaqcaaaa@2E11@ i j ) - sign (f i j )|, i.e. the average sign differences, where f ^ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacuWGMbGzgaqcaaaa@2E11@ i j and f i j are the (i-th row, j-th column) elements of the estimated and the true Jacobian, respectively. ε F is the Frobenius norm of the difference between the estimated and the true Jacobian, i.e. || F ^ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacuWGgbGrgaqcaaaa@2DD1@ - F|| F .