## 4 Discussion  
Atypical functional connectivity features have been considerably investigated as a primary deficit in individuals with ASD. EEG is an appropriate tool because of its high temporal resolution for exploring the deficient dynamics and functional connectivity of neuronal networks in brain disorders. To our best knowledge, this study is the first attempt to employ the S estimator to process multichannel EEG signals for better understanding the changes of global synchronization in ASD. Results in this study showed that a significant increase of global synchronization in EEG with ASD can be observed. [PERSON] et al. showed that there was a correlation between alpha EEG coherence and the structural integrity of white matter in the studies for adult [36]. The increases in white matter in individuals with ASD tend to reduce in toddlerhood [37] or later childhood [38], thus finally resulting in predominantly hypo-connectivity between cortical areas in adults with ASD [38]. Results in this study were consistent with [PERSON] et al. [39]. [PERSON] et al. showed that the EEG coherence was statistically elevated during the memory tasks. Moreover, the increased theta coherence was correlated with the lower performance of the memories in ASD. Figure 3: Boxplots for all the 160 EEG epochs with ASD and control subjects using (**A**) Rényi entropy and (**B**) Shannon entropy. Each box gives the interquartile range containing 50% of values with a red line denoting the median. The whiskers present the overall range of the considered data. The study results in [40] suggested that, for adults with ASD, local hyper-connectivity in the frontal area appeared with long-range hypo-connectivity. The abnormal connectivity appeared in in ASD may be due to a primary imbalance between excitation/inhibition (E/I) ratio [41]. Therefore, the hyper-connectivity observed in ASD possibly results from their elevated E/I ratio. More and more evidence suggests that there are abnormalities in the synchronized oscillatory activity of neurons in ASD. [PERSON] et al. employed the cross-approximate entropy to investigate EEG signals synchronization of autism children [42]. They have demonstrated that there is more synchrony in pairs of sensors at alpha band in children with ASD. Some studies have attributed excessive short-range connectivity to increased density of cortical mini-columns [43] and increasing white matter in many regions of the cortex, including frontal, temporal and parietal [44]. In summary, the S estimator approach is employed to describe the changes in global synchronization of multichannel EEG signals of children with ASD in this study. We used an improved version of a cooperation index as S estimator, which is based on Renyi entropy, a generalization version of classic Shannon entropy, and an optimization step to quantitatively measure the global synchronization of multi-channel EEG both in children with ASD and healthy children. According to \(t\)-test results on Renyi entropy and Shannon entropy as described above, both Renyi entropy and Shannon entropy in children with ASD are higher than normal development children, and the index S\(\alpha\) could indeed handle multivariate EEG signals for overall integration function of the brain. In conclusion, our findings in this study described more global synchrony in children with ASD, which confirms that there are abnormalities in brain synchronization. In addition, the proposed method may offer insight into a more mechanistic understanding of autism, and may serve as a potential biomarker for diagnosis and treatment response of ASD. This research was founded in part by the National Key R&D Program (grant No. 2016 YFC1306203), National Science Foundation of China (grant Nos. 81571346, 81230023, and 61273063), Beijing Municipal Science & Technology Commission, and Beijing Municipal Commission of Education.