Meditation techniques are often used to influence stress-dependent diseases, such as anxiety, hypertensive disorders or coronary disease, tension headaches or dependencies. However, evidence of successful treatment by meditation in these diseases is weak. One reason may be the difficulty of objective monitoring during meditation and degree of mastery of meditation techniques by individual patients for individual patients.

Longitudinal studies demonstrate that meditation practice significantly changes early stimuli processing, which leads to improved dynamics and flexibility of brain functions related to attention. Improved dynamics and flexibility of brain functions are achieved by a more flexible allocation of attention resources that most likely modulate early processing based on independent stimuli. Three different human brain neuron networks control the functions of wakefulness, orientation and executive control. The right frontal and right parietal cortices and the thalamus are important for maintaining wakefulness. The superior parietal cortex, temporoparietal junction, frontal eye fields and superior colliculus control the orientation function. The anterior cingulate cortex, ventral lateral cortex, prefrontal cortex and basal ganglia are associated with the control of executive processes. If atten- tion is no longer focused on the meditation object, the “default mode” is activated, including the posterior cingu- late, medial prefrontal cortex, posterior lateral parietal temporal cortex and parahippocampal gyrus [1] . The co- operation between these brain areas may, to a certain degree, be estimated using the similarities of EEG signals detected by the electrodes placed over these areas. Thanks to its clinical use (see overview in Baer [2] and Di- donna [3] ), vipassana or insight meditation, especially its secularised version called mindfulness meditation, is an increasingly common subject of research. This study compares the EEG signal complexity measures in expe- rienced meditators (more than 1000 hours of meditation practice) before and during meditation. Under vipassana meditation, both types of attention regulation are used and are complementary to each other. Therefore, this type of meditation is also sometimes called samatha-vipassana. Concentration is necessary for the basic stabilisation of attention. However, in the later stages of meditation practice, a greater emphasis is placed on mindfulness.

Brain activity is spatially coherent, and its degree of freedom is low in the idle state. To activate the various parts of the brain, EEG activity spreads to a large number of neural networks, and the resulting signal can be appropriately modelled by a stochastic system producing linearly correlated noise with a high degree of freedom. Traditionally, EEG signals are considered linear stochastic processes, which have been used for decades as the gold standard in many clinical applications [4] . Some papers [5] show that the degrees of complexity of linearly correlated noise are very similar to measures complexity derived from purely chaotic systems. Measures of fractal dimensions are derived from fractals, which are formally (mathematically) defined. Many real-world phenomena have fractal properties. Therefore, it may be useful to describe them by the fractal dimension. The fractal dimension of the time series cannot be precisely calculated and must be estimated. Various degrees of the fractal dimension are sensitive to the numerical and experimental noise and also to the length of the time series. No physical object is a true fractal, because it cannot have self-similarity at all scales. Therefore, the fractal dimension rather expresses the suitability of describing the properties of fractal modelling. The complexity of the signal can be analyzed directly in the time domain, frequency domain or phase space [6] .

The Sevcik method of calculating the fractal dimension has the advantage of small amplitude sensitivity to noise, and the accuracy of estimating the fractal dimension is independent on the length of the evaluated signal [7] . Unlike fractal dimension analysis, using EEG entropy permutation doesn’t require stationarity and can be applied to non-stationary EEG signal without segmentation [8] . Measures derived from the theory of non-linear dynamical systems may produce unreliable results for linearly filtered noise [9] . Moreover, the EEG signal is only weakly non-linear [10] [11] . To distinguish the filtered noise from the non-linear signal, surrogate data testing is often used. Unfortunately, this method is reliable only for stationary signals [12] , but EEG signals are non-stationary.

Only one study to date has compared concentration and mindfulness within the same group of meditators from the performance spectrum perspective [13] . A similar study of permutation entropy and fractal dimension has not yet been performed. In general, fractal dimension and permutation entropy are considered important parameters and features of EEG signals and biosignals. Studies of EEG complexity during meditation are sporadic. When compared to rest, meditation was accompanied by a focused decrease of dimensional complexity estimates over the midline frontal and central regions [14] . The aim of the present study was to evaluate the non-linearity of EEG signals of two states (before meditation and during meditation). We expected that non-linear analysis would allow objective monitoring during meditation.

For both types of meditation, global permutation entropy decreased (Table 1). In contrast, the fractal dimension for both types of meditation increased. This increase was statistically significant only in calming meditation (Table 2).

Permutation entropy showed promise in differentiating between EEG recordings before and during both types of meditation (Table 1). Reduced permutation entropy during meditation indicates that the meditative state requires control to maintain the resource allocation of attention associated with inhibition of inappropriate stimuli. The reduction of permutation entropy may be due to more strongly linked oscillators or inactivation of previously active neural networks [21] . It is likely that this effect is influenced by the activities of the cingulate, which is included in the meditation process [22] . Can you imagine that a meditative experience accompanied by a reduc-

tion in permutation entropy turns “off” unnecessary neural network activity to maintain focus on internalised attention. According to the Hebb’s rule, a population of neurons forms a functional unit to process information, and at the same time, the number of activated neuronal populations can be regarded as an indicator of the com- plexity of neuronal computing operations in the brain [21] [23] , which is reflected in the value of the permutation entropy. Increasing the value of the fractal dimension cannot be explained by increasing the amplitude of the signal due to EEG synchronisation in meditation, because the Sevcik fractal dimension, unlike the Katz fractal dimension, is insensitive to the amplitude of the evaluated signal [7] . This result can be interpreted as an increase in self-similarity of EEG signals. This phenomenon may be related to increased self-organisation of the hierarchical structure oscillators in the brain during meditation.

Improved control of attentional control [24] was associated with a reduction in the complexity of the EEG, while various normal and pathological conditions associated with loss of attention [25] [26] and a divergent way of thinking [27] have been associated with increasing complexity mainly in the frontal areas. These findings are consistent with a significant increase in the fractal dimension of meditation of calm that requires focused attention, but during insight meditation, activating the network, most likely mirrorcells, produces significant changes from pre-meditation signals.

The weakness of the work performed is missing statistical testing compared to the surrogate data. This technique allows for a stationary signal to distinguish linearly filtered noise from non-linear time series. However, for non-stationary signals, this technique can only reflect the non-stationarity of the signal. This method could be used in testing the FD, which requires a stationary signal, and its estimates were used in the one-second segments that were considered as acceptably stationary [19] . The permutation entropy, however, does not require a stationary signal [8] , and the non-stationary segments of the EEG signal that were estimated by this method might cause the failure of that approach.

As this study verified the existence of statistically significant differences between certain features of EEG time series before meditation and during both types of meditation, further study should attempt to verify this difference on out-of-sample data sets. Following verification on multiple data sets, machine learning algorithms, such as artificial neural networks, decision trees and other classifiers, can utilize these features as attributes to detect calming and insight meditation.