## 5 Conclusions
An accurate characterization of the PPG signal dynamic would allow functional modeling of hemodynamics and peripheral circulation, whatever the physiological peculiarities of each individual. We have indeed used a diffusive model of the PPG signal as a biometric marker, in which the hemodynamic specificity of each individual prevails with time and possible psychophysiological disturbances [57]. It is possible to build wearable devices that, in real-time, will not only authenticate an individual but also anticipate, through the dynamic parameterization of functional models, dynamic symptomatic perturbations of mild dysfunctions, such as stress, or even more severe ones, such as those related to cardiovascular diseases. The following are available at [[https://www.mdpi.com/article/10.3390/app11146508/s1](https://www.mdpi.com/article/10.3390/app11146508/s1)]([https://www.mdpi.com/article/10.3390/app11146508/s1](https://www.mdpi.com/article/10.3390/app11146508/s1)), all pictures in Figures 1 and 2: AllFigures1-2.zip. Conceptualization, J.d.P.-C. and A.P.G.-M.; methodology, J.d.P.-C.; software, J.d.P.-C.; validation, J.d.P.-C. and A.M.U. ; formal analysis, J.d.P.-C. and A.M.U. ; data curation, A.M.U. ; writing--original draft preparation, J.d.P.-C.; writing--review and editing, J.d.P.-C. and A.P.G.-M.; visualization, J.d.P.-C.; supervision, A.P.G.-M.; project administration, A.M.U. ; funding acquisition, A.P.G.-M. All authors have read and agreed to the published version of the manuscript. This research received no external funding. The data used in this study come from the FIS-PI12/00514 project in the Universidad Politecnica de Madrid. It was conducted according to the guidelines of the Declaration of Helsinki, and approved by the Institutional Review Board (or Ethics Committee) of Universidad Politecnica de Madrid (protocol code 2014-16-06 and date of approval 16 July 2014). The study includes 40 students from Universidad Politecnica de Madrid (UPM), between age 18 and 30. All signals captured from the middle finger of the left hand and sampled at a frequency of 250 Hz, say, sampling time \(\Delta t=4\) ms. The UPM Ethics Committee approved the study protocol. Participants gave their written informed consent. They were instructed to avoid using any psychotropic substance, alcohol, or tobacco, avoid physical exercise 24 h before each session, get up two hours before starting the sessions, and consume a light breakfast without coffee or tea. The authors would like to thank Life Supporting Technologies Group (LST-UPM) for taking part in project FIS-PI12/00514 from MINECO. Furthermore, the authors gratefully acknowledge the Universidad Politecnica de Madrid (www.upm.es, accessed on 19 March 2021) for providing computing resources on Magerit Supercomputer. Following the same line, the authors want to thank especially the support given by [PERSON], from the Universidad de Alcala (UAH) and the Spanish National Research Council (CSIC), providing a cluster of servers with which to execute some of the preliminary computational algorithmic tests of this work. The cluster consists of ten computing nodes, with a total of 64 cores, an Intel Xeon architecture, and 166 GB of memory. Finally, the authors would like to thank the referees for their useful comments. The authors declare no conflict of interest. Figure 17: The parameter \(K_{m}\) trend for the 40 subjects (PPG signals) that make up the pilot experiment [**computation time for all signals** on Magerit Supercomputer, a server cluster consisting of 68 Lenovo ThinkSystem SD530 nodes each with 2 \(\times\) 20-core Intel Xeon Gold 6230 processors at 2.10 GHz (1344 GFLOPS), 192 GB of RAM and 480 GB of local SSD: **117 h 14 min** and **30 s**]. At each iteration, the block size is increased by an additional 15,000 points until a total of 150,000 points is reached. The graph shows the averaged values of \(K_{m}\) in each block of increasing size (10 blocks in total) together with error bars indicating the standard deviation.