-I thought you'd enjoy this. Very clearly illustrated. Lower compression and larger expansion during times of low power demand.
It seems that the Atkinson cycle is counterproductive because it would require some energy to push the intake gases retrograde back into the intake, while the Budack cycle stops the inflow early before the gases enter the cylinder.
As he mentions at the end of the video, all this creative engineering didn't manage to offset the extra weight of the vehicle versus others in it's class, so it lags behind its direct competitors' gas mileage.