## 2 Materials and Methods
### PLR Features Extraction
Equation (1)), rescaling the s(t) with respect to the baseline, often occurring immediately after the switch off of the light:  
\[min\,\,\{D\}=min\,\{/\,\}_{t}\,\,\text{where }t\in[3s,\,5s] \tag{3}\]  
Another meaningful measure of the pupillary response is given by the maximum absolute velocity (\(max[v_{c}]\)) with which the minimum value of the pupil diameter is achieved, i.e., the velocity of the rescaled PLR signal estimated in the transition time between the initial scotopic phase and the scotopic one [12; 29; 30] (ref. Figure 1e). \[max\,\,\{v_{contraction}\}=\frac{1}{D_{0}}max\bigg{\{}\bigg{|}\frac{ds(t)}{dt} \bigg{|}\bigg{\}}_{t}\quad\text{where }t\in\Big{[}t_{photopic},\,\,t_{min\{PLR\}}\Big{]} \tag{4}\]  
Moving to the second scotopic phase, we obtained the portion of the PLR signal related to the return to the rest state of the pupil diameter. In this phase, two informative features for the characterization of the PLR signal are given by the latency time (\(T_{s}\)) between the real starting point of the scotopic phase (fixed to 3.5/4 \(s\)) and minimum diameter \(min\{s(t)\}\), and the maximum velocity to achieve the re-dilation of the pupil (\(max\{v_{d}\}\)) [12; 29; 30] (ref. Figure 1f,g). \[T_{s}=[3.5s,\,\,4s]-t_{min\{s(t)\}} \tag{5}\]  
\[max\,\,\{v_{dilution}\}=max\,\,\bigg{\{}\frac{ds(t)}{dt}\bigg{\}}_{t}\quad\text {where }t\in\Big{[}t_{min\{s(t)\}},\,\,t_{N}\Big{]},\,\,N\,\,\text{\it end \,\,point} \tag{6}\]  
This second scotopic phase represents the most informative section of the PLR signal and the longest one in terms of time points. The returning phase to the rest conditions \(\rho(x)\) could be modeled by an exponential recovery, providing information about the characteristic relaxation time of the process. This exponential relaxation is typical of many living processes involving ion channels in cells, such as when an electric signal is transmitted to the pupil [31; 32]. In our work, we tested several fitting functions for the best representation of the process, among which the Michaelis-Menten function, which is used to model several biological processes and the exponential obtained the best results in terms of root-mean-square error. Starting from this hypothesis we computed as PLR feature the characteristic time (\(\lambda_{t}\)) of the exponential recovery obtained by fitting the range of points between the \(t_{min\{s(t)\}}\) and the endpoint of the acquisition (ref. Figure 1h). \[\rho(x)=-c_{0}e^{-\lambda_{t}x}+c_{1} \tag{7}\]  
where \(c_{0}\) and \(c_{1}\) are the parameters of the exponential equations. A deeper analysis of the scotopic phase showed the presence of oscillatory behavior in the recovery section of the signals. This effect can be monitored by applying classical signal processing algorithms to that portion of the signal. We applied a strong smoothing algorithm to the scotopic section, evaluating the ratio between the raw signal and the smoothed one. In this way, we could emphasize the oscillatory behavior, obtaining a signal centered in 1, on which we applied a peak detection algorithm (ref. Figure 1i). We monitored the number of peaks (\(N_{peals}\)) identified on the processed signal as a feature for our study, i.e.,  
\[N_{peals}=\#\,of\,\,peals\,\left\{ \begin{array}{c}\Lambda(s(t))\\ s(t)\end{array} \right\}_{scotopic}\,\,\,\,\,\,\text{where $\Lambda$ smoothing algorithm} \tag{8}\]  
For a better description of this oscillatory behavior, we also added as features the peaks rate variability expressed in terms of the average value (\(\mu_{prr}\)) of the time distances among peaks (\(p_{i}\)) and corresponding standard deviation (\(\sigma_{prr}\)) (ref. Figure 1j), i.e.,  
\[\mu_{prr}(p)=\frac{1}{N_{peals}}\Big{(}\sum_{i=2}^{N_{peals}}p_{i}-p_{i-1} \Big{)} \tag{9}\]  
\[\sigma_{prr}(p)=\sqrt{\mu_{prr}(p^{2})-\mu_{prr}(p)^{2}} \tag{10}\]  
where \(p_{i}\) ranges in [1, \(N_{peals}\)]. Further analysis of the smoothed signal obtained on the whole PLR signal highlighted the presence of further important features.