# Efficient Sleep-Wake Cycle Staging via Phase-Amplitude Coupling Pattern Classification
## 1 Introduction  
Historically considered merely a transient shutdown of brain activity, sleep is today better understood in not only its intricate generation mechanisms [1] but also in its crucial roles in supporting several different neural functions and homeostasis in general [2]. In fact, the alternation of states that characterize the sleep-wake cycle (SWC) in a circadian rhythmic pattern is the result of complex interactions of brain structures in multiple levels of organization, from cellular and molecular to widespread neural circuits [3]. By its turn, such a precise coordination of processes seems to be of uttermost importance to neuro-chemical cleansing [4], to the maturation and development of neural tissue in newborns and infants [5], and for memory consolidation in adults [6]. On the other side of the same coin, sleep may be disrupted in neurological scenarios [7] and the deterioration of sleep can induce neural dysfunction [8, 9]. Each stage of the SWC displays distinctive overt behavior and neural activity signatures, usually assessed by electromyography (EMG) and electroencephalography (EEG), respectively. In a simplistic way, the SWC can be divided into three major stages. First, wakefulness (WK) is characterized by high-power EMG with desynchronized low-amplitude EEG. By its turn, slow-wave sleep (SWS) features low EMG with synchronized high-amplitude low-frequency EEG patterns. Finally, rapid eye movement sleep (REM) displaysvirtually flat EMG and low-amplitude EEG tracings, intercalated with synchronization episodes in the theta frequency range. Importantly here, each of these different stages are inherently correlated with distinct neurobiological processes, such as the differential roles of SWS and REM in the consolidation of recently acquired memory traces [10; 11; 12]. For a proper assessment of the SWC and its relationship with brain function and dysfunction, it is thus of major importance to be able to characterize the rhythmic alternance of its stages [13; 14]. This is performed by detecting each of its stages in an objective and reproducible manner. Even though there are clear guidelines for their recognition by expert visual inspection of electrophysiological recordings [15], the process is very laborious, tedious, and prone to errors due to subjectivity, fatigue, and bias. For this reason, different automatic signal processing methods have been put forward by scholars in the field. One pioneering work proposed and tested a method based on the automatic clustering of points in a state map built from spectral content ratios, applied to the multi-channel local field potential (LFP) recording of animals [16]. More recently, the application of machine learning methods has become a major trend for sleep stage classification [17]. By also using the spectral content of mice LFP and EMG power assessed by the mean-covariance restricted Boltzmann machine approach, [PERSON] and collaborators were able to detect SWC stages, including NREM substages, while observing important differences across different genetic backgrounds [18]. [PERSON] and collaborators employed a support vector machine over a collection of signal features pre-screened from a set of 62 measurements extracted from time and frequency domains and of a non-linear nature [19]. Finally, convolutional neural networks have been applied to EMG and LFP signals, previously z-scored according to a novel proposal, in the work of [PERSON] et al., 2019 [20]. The authors observed good agreement between automatic and expert classification while also incorporating the algorithm into an open-source toolbox named Accusleep. Although representing valid contributions to automatic SWC staging, complex topologies of artificial neural networks (ANNs) yield no more than marginal improvements while requiring considerably higher computational resources and impairing neurobiological interpretability [21]. A more rational approach to this problem could be the usage of simpler machine learning models applied to more descriptive electrographic features.