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Table 1 The four-gene network example: white noise

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
3 LS 94.36 36.54 0.95 0.20 368.06 123.08
  TLS 94.36 36.54 0.95 0.20 368.06 123.08
  CTLS 94.36 36.54 0.95 0.20 368.06 123.08
6 LS 16.35 5.11 0.59 0.14 71.10 17.84
  TLS 196.04 2239.78 0.74 0.20 1778.75 24252.19
  CTLS 14.96 5.63 0.63 0.16 64.29 21.34
9 LS 7.87 2.42 0.46 0.09 35.73 9.03
  TLS 11.96 9.68 0.54 0.13 67.47 118.27
  CTLS 6.61 2.74 0.47 0.10 31.57 12.05
12 LS 5.19 1.64 0.40 0.06 24.98 6.47
  TLS 6.20 2.34 0.45 0.09 32.42 15.33
  CTLS 3.79 1.48 0.40 0.06 19.59 6.74
21 LS 3.74 1.06 0.38 0.02 18.12 4.39
  TLS 3.71 1.36 0.40 0.05 20.40 8.51
  CTLS 2.20 0.68 0.38 0.02 11.29 2.93
30 LS 3.70 0.87 0.41 0.06 17.21 3.62
  TLS 3.45 1.20 0.44 0.07 18.75 7.30
  CTLS 2.31 0.56 0.49 0.03 10.10 1.96
60 LS 3.75 0.66 0.50 0.01 17.05 2.59
  TLS 3.59 1.05 0.52 0.05 16.25 4.74
  CTLS 2.51 0.52 0.50 0.01 10.76 1.45
  1. The table shows the error comparisons in terms of the mean and the standard deviation (STD) for different numbers of data points for each method based on 1000 Monte-Carlo Simulations. ε M is the sum of two terms, i.e (l/N1) Σ |α ij | and (l/N2) Σ |β ij | where α ij and β ij 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@ ij ) - sign (f ij )|, i.e. the average sign differences, where f ^ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacuWGMbGzgaqcaaaa@2E11@ ij and f ij 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 .