Radial-velocity measurements of Kepler-78. Top panel: radial velocities as a function of time, showing variations due to both stellar activity and the ultra-short-period planet Kepler-78b, but no significant long-term trends. The blue and red circles indicate the radial-velocity points gathered with the HARPS-N and HIRES spectrographs, respectively. Middle panel: zoom on the first 100 days, mainly showing the non-stationary stellar activity signal, which was modeled with Gaussian process regression and a quasi-periodic kernel (black solid line). Bottom panel: radial velocities phase-folded at the ephemeris of Kepler-78b (P = 0.35 d), after removing the Gaussian process model for the stellar activity variations.