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As an ESWAT member, Deunan is a specialist in weapons handling, explosive devices manipulations, hand-to-hand combat, and an excellent Landmate pilot. According the Appleseed Databook, she is trained to be ambidextrous. In the original manga, Briareos (her lover and partner) was a cyborg before Deunan arrived at Olympus, and she managed to lose an eye in Volume 4, due to a training accident. In the 2004 movie, it is shown that Briareos becomes a cyborg only after he leaves on a mission and is presumed (by Deunan) to be missing.
The following data is from the 2004 Movie adaptation.
The daughter of Carl and Dr. Gilliam Knute, Deunan, who is considered a highly skilled warrior, has spent almost her entire life fighting a war that has been, for the most part, over. It isn't until she is captured by an ES.W.A.T. (Especial Weapons And Tactics) team in the middle of a ruined city that she is finally evacuated from the Badlands. She also reunites with her former lover Briareos who is a part of the team sent to recover her. He is now a cyborg, having lost over 75% of his natural body to injuries. She also befriends a girl called Hitomi.
The day after she wis brought to the city of Olympus, Deunan learns that over half of the population of the city is composed of artificial humans called Bioroids. She also found out that her new friend, Hitomi, is one herself. Deunan soon becomes embroiled in the fight between a faction of humans and Olympus as some humans strive to wipe out the Biodriods completely. When she's sent on a mission to retrieve the Appleseed, she learns of her past and also of a greater conspiracy.
(Source: Wikipedia, edited)