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We report the measurements of correlations between event-by-event fluctuations of amplitudes of anisotropic flow harmonics in nucleus-nucleus collisions, obtained for the first time using a new analysis method based on multiparticle cumulants in mixed harmonics. This novel method is robust against systematic biases originating from nonflow effects and by construction any dependence on symmetry planes is eliminated. We demonstrate that correlations of flow harmonics exhibit a better sensitivity to medium properties than the individual flow harmonics. Comparisons are made to predictions from Monte Carlo Glauber, viscous hydrodynamics, AMPT, and HIJING models. Together with the existing measurements of the individual flow harmonics the presented results provide further constraints on the initial conditions and the transport properties of the system produced in heavy-ion collisions.

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