Hollywood actress Uma Thurman has reportedly ended her engagement to French-born financier Arki Busson, the father of her young daughter, Rosalind. Thurman, 43, and Busson, 51, began dating in 2007. They got engaged in 2008, then split up from 2009-11. Thurman accepted Busson's second marriage proposal in 2012, but they struggled to maintain their relationship because Thurman lives in New York and Busson is based in London. "Uma and Arki were due to attend a gala together on April 8, but Uma showed up without her engagement ring or her fiance," a source told The Daily Mail. "Arki was scheduled to attend and it seemed clear there was only one reason why he didn't show -- because he and Uma are no longer an item." "Uma lives in New York while Arki lives in London. He has been out and about without Uma since October when he went to a Halloween party alone," a second insider told the newspaper. "They have been at one or two events together, like Harvey Weinstein's pre-Bafta party in February, but on that occasion they looked miserable." Thurman has a son and daughter from her previous marriage to actor-writer Ethan Hawke. Busson has two sons from his relationship with supermodel Elle Macpherson.