The two pathways are interconnected, as the LC inhibits the EWN. In eyes with ON, a relative afferent pupillary defect (RAPD), or Marcus-Gunn pupil, presents itself with pupillary asymmetry during the swinging flashlight test, in which the pupils constrict less when a flashlight is swung from the unaffected eye to the affected eye, secondary to a defect in the afferent pathway. Thus, the pupillary reflex is a useful indicator of both the afferent and autonomic nervous system function, reflecting both afferent, sympathetic, and parasympathetic activities. Sympathetic innervation determines the initial pupil diameter, whereas parasympathetic activity determines the amplitude and velocity of pupil contraction. Thus, pupillometry, i.e., the measurement of the pupil size and reactivity to light, is a cheap, easy to apply, and non-invasive technique to study many neurodegenerative diseases and even many characteristic brain states [6], such as concentration [7] and performance in doing complex tasks [8]. In our study, we focused on acute ON. It is not clear, however, which parameters of the pupil dynamics are useful to consider to assess the brain state, and there is no common agreement between researchers neither on a standard protocol to apply in terms of type and duration of the stimulus, nor on the characteristics that a pupillometric response should have to be considered as pathological [9; 10]. Indeed, pupil response is affected by significant inter- and intra-observer variability due to differences in ambient lighting, the intensity of the light stimulus, the method used to direct that stimulus, and the background characteristics of the examined subjects [10], such as eye disorders, age [11], smoking [12], drugs assumption, mental concentration [6], or even the emotional state [13]. This may be the main reason why a general consensus on the procedure is difficult and for neurodegenerative diseases, contrasting results exist [9]. Another debated point is the possibility that abnormalities in the pupillary response can be a premonitory sign that can help in an early diagnosis of the pathology [10; 14]; however, one first needs to identify the most important and stable features from pupillometric data before addressing this question and relating the response to the stage of the pathology. A first possible solution would be, as suggested for instance by [PERSON] [12] in 2021, to adjust the statistical analysis on all the possible confounders. The problem in doing this is that many possible confounders are known to date in the literature and just as many are probably still unknown. Thus, we would lose all the simplicity and convenience, both practical and economical, of pupillometric experiments. For instance, every pupillometric measurement should probably be preceded by a complete ophthalmologic visit, a full questionnaire on the past and present pathologies, a full list of the drugs assumed, and probably even psychological and cognitive tests. Finally, even if all these were possible, other possible confounders, such as the daytime of the experiment or the wakeful state of the subject are simply impossible to control. In our work we applied a different approach, we tried to exploit the maximum of the information contained in our pupillometric data, introducing some new parameters coming from methods used in physics (cinematic and random walk theory) or deeper signal processing (signal transformations, Hilbert transform, peaks detection) of the data, in order to increase the accuracy of the prediction of the pathology, without any additional test. From a methodological point of view, most of the recent works applying experimental conditions like ours on several neurologic diseases used simple descriptive statistical tests or analysis of variance or covariance [15; 16; 17; 18], which were based on standard computerized methods of feature extraction [19]. Some of them used generalized linear regression methods [20], sometimes considering random effects [12], to take into account the intra-subject variability.