## 1 Introduction
used the AF cycle length to show that patients with persistent AF had shorter cycle lengths and a higher degree of disorganized activity than patients with paroxysmal AF [22;23]; and [PERSON] et al. employed a spectral analysis to identify localized sites of high-frequency activity, reporting different distributions in paroxysmal versus permanent AF [24]. However, the aforesaid prior studies do not respond to the clinical demand for easy and intuitive interpretation methods for CFAEs [25]. In fact, clinicians demand the use of straightforward classification models which are readily understandable, fed with featureseasily applicable to CFAEs. Furthermore, previous methods do not provide any signal quality or stability assessment applied to the variables and recordings used to develop the introduced models to discriminate between AF types, so that the robustness of the approaches previously introduced can be compromised. In fact, the prior reported results miss the assessment of the intra-recording and intra-patient stability of the analyzed data, as well as the CFAE signal quality. By omitting the study of the stability and the signal quality evaluation, two main issues may arise: first, averaging among recording places and AF types without having previously checked the intra-recording and intra-patient stability may lead to an oversimplification of the processes taking place at different regions of the atria; second, the inclusion of artifacted or noisy segments unlinked to the AF mechanism, such as drifts or very distorted recordings, due to bad contacts of the recording electrode on the atrial walls, may lead to biased and unreliable results in the characterization of the atrial electrophysiological substrate. The present work has two principal objectives. On the one hand, to assess the stability of CFAEs with nonlinear indices, both intra-recording and intra-patient, and, on the other hand, to exploit nonlinear strategies and straightforward models to discriminate between the CFAEs of ParAF and PerAF from patients undergoing catheter ablation of the AF. In the first part of the manuscript, the intra-recording and intra-patient stability of CFAEs have been assessed with the nonlinear indices of determinism (DET) of a Recurrence Quantification Analysis (RQA) and sample entropy (SE). Furthermore, the presence of artifacted or noisy segments in CFAEs has been considered as well, evaluating the consequences of their discarding in the final outcome. The idea behind it is that a discarding process to remove poor quality segments may benefit the intra-recording and intra-patient stability assessment. Moreover, this approach may decrease the differences in the DET and SE between the intra-patient recording places, thus helping to quantify the atrial substrate with reliable and representative values. In the second part of the study, the exploitation of nonlinear strategies and the development of straightforward models to discriminate between ParAF and PerAF from the CFAEs of patients undergoing a CA of AF has been performed using, besides the nonlinear indices of DET and SE, the widely accepted indices of dominant frequency (DF) and the AF cycle length (AFCL). The indices extracted from CFAEs were processed and selected prior to being converted into features for coarse tree classification models. The assumption is that a thoughtful selection of reduced sets of indices, feeding straightforward classification models, would enable a more accurate discernment of ParAF versus PerAF CFAEs, thus providing a more understandable insight for atrial substrate evaluation and improved therapeutic decision for AF management.