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In the parameter estimation below, we use (Delta t = 0.002~mbox{s}) and (Delta x=0.02) shown in the row indicated with a star.

Evaluating the ability of MiMAPT in multi-scale thermal analysis, a speed-up of 98× is reported compared to fine-grained method, while keeping false negatives at zero and the error of temperature estimation below 0.05 °C.

end{aligned} (8)The Kalman-updating formula is given by begin{aligned} widehat{r}_{k+1} = widehat{r}_{k+1|k} + M_{k+1}left( y_{k+1} - widehat{r}_{k+1|k}right), end{aligned} (9 where (M_{k+1}) is called the Kalman gain and determined in the state covariance estimation below.

The stiffness measurement phase followed the learning phase after a short 5 minute break (see stiffness estimation below).

Estimates of r (mean 2.9; SD.33) and K (mean 25.1; SD 7.2) were derived by fitting the Ricker map to the individual, untransformed subpopulation time series from the experimental controls (see Parameter estimation below).

Thus, we will report the results for the full sample with FIML estimation below.

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The time-course concentration dataset of all metabolites were measured using in vivo NMR [ 21, 22], and smoothened data used for the parameter estimations below were shown in Figure 8.

For our estimations below, we use γ ≈ 1.

In our estimations below, we account for differences in observable characteristics between treated and control states in two ways.

Therefore, only the results for cocaine were used in the estimations below.

All sample size estimations below are based on having 80% power to demonstrate a difference at the five percent level of significance using the models described above.

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