Figure 13. Successful fits with SU start... | Rockefeller University Press

Figure 13.

Successful fits with SU start vectors. SU start vectors, containing 23 identical start parameters, were varied by the stochastic factor A = 102. 1,000 fits were performed for each SU start vector. SU start vectors of 10−6 to 101 were tested. (A) Histogram of successful fits for different SU start vectors. Among the successful fits for SU start vectors of 3 × 10−5 to 100, the differentiation with respect to a threshold refers to B. (B) Refined search for the fit minimum with SU start vectors of 3 × 10−5 to 100. The fits were sorted with respect to the MSE value, starting with the smallest. A normalized measure for the xth element in this sequence, C(MSEx), was computed with Eq. 16 (see Materials and methods). The diagram shows the plot of C(MSEx) as a function of the increasing MSNx number. The vast majority of fits consistently produced C(MSEx) values <10−10 or even <10−13. Setting a threshold to 10−10 (red line) allowed for the elimination of successful fits with higher MSE values. Other thresholds of ∼10−13 to ∼10−5 would also produce satisfying results. The tiny variability of C(MSEx) of 10−14 to 10−13 can be explained by the use of data points with different noise for different SU start vectors. (C) Plot of all determined parameters for SU start vectors varying from 3 × 10−5 to 100. The dimensions of Z1–Z4, Z5–Z10, Z11–Z14, and Z15 are μM−1, μM−2, μM−3, and μM−4, respectively. The other parameters are dimensionless. The true values are indicated. The accuracy of the determined parameters does not depend on a specific SU start vector.

Successful fits with SU start vectors. SU start vectors, containing 23 identical start parameters, were varied by the stochastic factor A = 10². 1,000 fits were performed for each SU start vector. SU start vectors of 10⁻⁶ to 10¹ were tested. (A) Histogram of successful fits for different SU start vectors. Among the successful fits for SU start vectors of 3 × 10⁻⁵ to 10⁰, the differentiation with respect to a threshold refers to B. (B) Refined search for the fit minimum with SU start vectors of 3 × 10⁻⁵ to 10⁰. The fits were sorted with respect to the MSE value, starting with the smallest. A normalized measure for the xth element in this sequence, C(MSE_x), was computed with Eq. 16 (see Materials and methods). The diagram shows the plot of C(MSE_x) as a function of the increasing MSN_x number. The vast majority of fits consistently produced C(MSE_x) values <10⁻¹⁰ or even <10⁻¹³. Setting a threshold to 10⁻¹⁰ (red line) allowed for the elimination of successful fits with higher MSE values. Other thresholds of ∼10⁻¹³ to ∼10⁻⁵ would also produce satisfying results. The tiny variability of C(MSE_x) of 10⁻¹⁴ to 10⁻¹³ can be explained by the use of data points with different noise for different SU start vectors. (C) Plot of all determined parameters for SU start vectors varying from 3 × 10⁻⁵ to 10⁰. The dimensions of Z₁–Z₄, Z₅–Z₁₀, Z₁₁–Z₁₄, and Z₁₅ are μM⁻¹, μM⁻², μM⁻³, and μM⁻⁴, respectively. The other parameters are dimensionless. The true values are indicated. The accuracy of the determined parameters does not depend on a specific SU start vector.