**5. Conclusions**

In this exploratory study we employed envelope analysis of demodulated waveforms for evoked and induced gamma oscillations in response to Kanizsa figures in a three-stimuli visual oddball task and compared outcomes in children and adolescents with ASD and in neurotypical peers. In ASD group, as compared to neurotypicals, significant differences in evoked and induced gamma oscillations were evident in larger gamma oscillations reflected in a higher area of gamma oscillation envelopes. Low frequency rTMS treatment in ASD resulted in a significant reduction of gamma responses to non-target stimuli and in improved accuracy of performance in the oddball task. Several rating scores of behavioral questionnaires also showed improvement post-TMS. Application of a novel metric for gamma oscillations based on envelope analysis using wavelet transformation allowed to suggest that gamma oscillations may provide a viable biomarker reflective of the excitatory/inhibitory balance of the cortex, a useful diagnostic index and a putative outcome measure of rTMS intervention in autism.

**Author Contributions:** All authors contributed substantially to the work reported in this paper. M.F.C., A.S.E.-B., M.S. and E.M.S. conceived and designed the experiment and data analysis strategy, participated in oddball test data collection, statistical analysis and interpretation of results. E.M.S. administered visual oddball test to patients and collected raw data. M.S. and M.G. participated in EEG data extraction, preprocessing and statistical analysis and also contributed in preparation of figures; E.L.C. and I.O. participated in reaction time and accuracy data processing and statistical analysis; A.S.E. assisted in preparation of methodological part related to EEG data handling, analysis and interpretation; M.F.C. participated in patient clinical records analysis and in interpretation of data and discussion, he also reviewed the manuscript and edited the final version. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Institutes of Health Eureka R01 Grant MH86784 to Manuel F. Casanova.

**Acknowledgments:** Funding for this study was provided by the NIH grant R01 MH086784 to Manuel F. Casanova.

**Conflicts of Interest:** The authors declare no conflict of interest.
