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em Aberdeen University


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Acknowledgments This paper was developed within the scope of the IRTG 1740/TRP 2011/50151-0, funded by the DFG/FAPESP, and supported by the Government of the Russian Federation (Agreement No. 14.Z50.31.0033 with the Institute of Applied Physics RAS). The first author thanks Dr Roman Ovsyannikov for valuable discussions regarding estimation of the mistake probability.

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Acknowledgments This work is supported by National Science Foundation of China (Grant No. 61573064, 61074116 and 11547188), the Youth Scholars Program of Beijing Normal University (grant No. 2014NT38), and the Fundamental Research Funds for the Central Universities Beijing Nova Programme, China. XYY acknowledges the support from the National Natural Science Foundation of China (Grant No. 61304177) and the Fundamental Research Funds of BJTU (Grant No. 2015RC042).

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Acknowledgement One of us (AP) wishes to acknowledge S. Flach for enlightening discussions about the relationship between the DNLS equation and the rotor model.

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We wish to acknowledge A Pikovsky and M Zaks for useful discussions. This work has been financially supported by the EU project COSMOS (642563).