TUCSON, Ariz. — The husband of Rep. Gabrielle Giffords says his wife’s condition has improved so much that she has been able to smile and give him a neck rub as he has kept a near-constant vigil at her hospital bedside.

The interactions with astronaut Mark Kelly are new signs of Giffords’ impressive progress in recovering from a gunshot wound to the head at a political event nine days ago. Giffords still cannot speak, because of a tube in her throat that is helping her breathe.