Both authors apologized for their remarks.

The authors then retracted the paper "in its entirety" and apologized to anyone within or outside the scientific community who might have been led astray by the chicanery.

The author apologizes to her readers, but continuing serious health problems have made writing difficult for her.

If he has confused you, the author apologizes.

The authors deeply apologize to the authors of that paper and to the scientific community.

The author and publishers apologized in court, stating they had made a mistake.

The tweets were deleted, and the authors apologized.

I therefore ask that the author of these remarks and these actions apologise or withdraw her remarks.

A public apology defames the author of the article apologised for by suggesting that the author has written carelessly.

This is an apologia in which it's not entirely clear why the author is apologizing.