## 3 Results and Discussion
### Consistent Notations, Physical Dimensions and Units  
Consistent notations are required for two purposes: (i) within the manuscript (MS), they suggest that the concept was well thought-out, and the readers' interest has also been taken into account, and (ii) outside the MS, those notations are to be used, which are common in the given (sub)field of science. Common notations enhance the understanding and citation rate. Different notations for the same variable or quantity point to sloppy work and lead to rejection eventually. Furthermore, it reveals that the authorship was not set according to the Vancouver criteria [27] (see Appendix A).  
The SI standard physical dimensions are as follows (corresponding symbols are in brackets): time (T), length (L), mass (M), _etc._ The time is widely and unambiguously denoted by \"_i_\", or \"T\"; the authors of ref. [2] use \(x\), without any reason.  
\"Scalars are denoted by lower case letters \(x\), and vectors... as bold lower-case letters: \(\mathbf{x}=[x_{1},x_{2},\ldots x_{n}]\). Matrices are denoted by bold capital letters \(\mathbf{M}_{r}\),...\" [40].  
Contrary to the common notations the authors use capital letters with arrows on the top for vectors \(\stackrel{{\rightarrow}}{{(X)}}\) and indexed scalars for the same \(\mathbf{x}\) (time) variable, units are not given.  
Even worse, the match of \(\mathbf{x}\) would be \(\mathbf{y}\), but the authors of ref. [2] used either R or Es and T as estimated and target values in their Equations (6)-(13) and Equation (14), respectively. Moreover, Equations (14) and (23) should be identical according to the explanation, yet the left-hand sides of the equations are different (MSE and RMSE, respectively). A summa is missing from Equation (14) and an index (_i_) is missing from both.  
\begin{table}
\begin{tabular}{c l c c} \hline \hline
**Model Name** & \multicolumn{1}{c}{**Description**} & **RMSE** & **r-Square** \\ \hline Linear & R = \(663.71\times\times-543.225\) & \(3642.44\) & \(0713^{\circ}\) \\ \hline Logarithmic & R = \(-7997.93+5162.83\times\log(\mathbf{x})\) & \(9296.59\) & \(0.402\) \\ \hline Quadratic & R = \(2998.21-917.93\times\times+510.02\times\mathbf{x}^{2}\) & \(1272.1\) & \(0.965\) \\ \hline Cubic & R = \(-978.55+506.05\times\mathbf{B}2-61.95\times\mathbf{x}^{2}+242\times\mathbf{x}^{3}\) & \(324.33\) & \(0.997\) \\ \hline Compound & R = \(2.78\times 1.406^{\circ}\) & \(12\),\(585.79\) & \(0.904\) \\ \hline Power & R = \(0096\times\mathbf{x}^{3}\times\mathbf{x}^{0.6}\) & \(3450.96\) & \(0.984\) \\ \hline Exponential & R = \(2.786\times\mathrm{EXP}(0.341\times\mathbf{x})\) & \(12\),\(585.79^{\circ}\) & \(0.904\) \\ \hline Logistic & R = \(20731.084\) (\(1+\mathrm{EXP}(((4\times 3962.88)\times(23.88-\mathbf{x})/70731.08)+2)\)) & \(187.15\) & \(0.999\) \\ \hline \hline \end{tabular}
\end{table}
Table 12: Model description for Italy fitted by GWO.  
Figure 10: (Table 12 in ref. [2]): yellow markings show the different number of value precisions. Meaning of superscripts: A—2 value-, 3 decimal digits; B—3 value-, 2 decimal digits; C—3 value-, 3 decimal digits; D—4 value-, 2 decimal digits; E—5 value-, 2 decimal digits; F—6 value-, 2 decimal digits; G—7 value-, 2 decimal digits; H—7 value-, 3 decimal digits.  
Consistency within a document or a specific context is crucial. If you are writing or editing a document, it is advisable to pick one form and stick with it throughout the MS to maintain consistency.  
The correlation coefficient is a dimensionless quantity, hence its popularity: it is suitable for comparing quantities measured on different scales. In contrast, mean squared error and residual error have physical dimensions and, consequently, units. Ref. [2] never mentions physical dimension and [units], _e.g._, course of infection [number of infected persons], time [days].