## 4 Results and Discussion
### Working Memory Data  
The ability to store and manipulate information for short periods of time, provided by WM, plays a key role in complex cognitive tasks such as comprehension, reasoning, planning and learning [29; 45]. WM consists of three distinct stages of information-processing: encoding, maintenance or retention, and retrieval [6], with the retention interval being considered as a defining component of WM, since it differentiates it from other memory types [27]. The most widely recognized model of WM [26] describes it as a several separate but interacting subsystems: a central component (central executive), two stimuli-dependent  
Figure 5: Results of the permutation tests carried out on the connectivity values estimated using CFD, \(\text{TE}_{\text{xx}}^{\theta\%}\) and \(\text{TE}_{\text{xx}}^{\theta\%}\), for the three noise conditions modeled (\(\text{SNR}=[6,3,1]\)), assuming interactions in the simulated data from the phase of \(\mathbf{\chi}_{\mathbf{q}}^{w}\) to the amplitude of \(\mathbf{\chi}_{\mathbf{q}}^{w}\). Statistically significant results are shown in white. storage subsystems (the phonological loop and the visuo-spatial sketchpad), and a system of limited capacity that allows for interaction between the other components (episodic buffer) [46]. Moreover, multiple studies have found that neural oscillatory activity in a wide range of frequencies is modulated during WM [47]. High-frequency activity, in the \(\beta\) and \(\gamma\) (>30 Hz) bands, seems to play a role in the encoding, retrieval, and maintenance of the stimulus; activity at lower frequencies, in the \(\theta\) and \(\alpha\) ranges, especially in frontal areas, is associated with the coordination and integration of different cognitive processes during the execution of WM tasks [48]. This has led to hypotheses about the cross-frequency coupling mechanisms underpinning WM, with oscillatory activity in the central executive component interacting with oscillations at other frequencies in the peripheral storage systems [12,49]. PAC interactions are thought to play a crucial role in WM [28], with bidirectional interactions linking the prefrontal cortex to parieto-occipital and medial temporal regions. [6,29]  
In this study, we test the proposed \(\mathrm{TE}_{\mathrm{zz}}^{\theta\theta^{*}}\) approach for the estimation of directed phase-amplitude interactions in the context of an important topic in the study of WM: how the characteristics of brain activity are modulated by changes in memory loads, as induced by WM tasks with different difficulty levels [48]. This topic is closely related to the concept of WM capacity, the amount of information that can be maintained and manipulated in WM [45]. WM capacity is, in turn, linked to important abilities, including non-verbal reasoning and control of attention, among others, and can be altered in people with psychiatric disorders [50]. We built a subject-dependent classification system based on features extracted through the proposed \(\mathrm{TE}_{\mathrm{xx}}^{\theta\theta^{*}}\) method from the EEG data recorded during the retention interval of a change-detection task: a task designed to test visuospatial working memory capacity. The goal of the classifier is to assign a particular cognitive load (number of elements in the memory array) to EEG data from a task trial characterized using our proposal. Figure 6 presents the classification accuracy for all subjects in the WM database as a function of the percentage of features used to train the classifier. The best results are obtained when 5% of the features are selected. These are those with the with the highest relevance values according to the CKA-based relevance vector \(\bar{\varrho}\), achieving an average classification accuracy of \(95.9\pm 3.1\%\) for the three classes corresponding to each cognitive load level in the change detection task. Figure 7 shows the highest accuracy obtained for each subject in the WM database, as well as the precision, recall, and F1 score values.