A new study just published by the University of Scranton states that the walnut is full of the antioxident polyphenols. Dr. Johnny Buwden wrote an article about this on his blog that you might find interesting! http://jonnybowdenblog.com/and-the-winner-is-walnuts/ That being said, you don’t want to eat a lot of them because the fat content is high! 14g of walnuts = 9g fat!
Also, here is a video of a professor from California who is a vegan that did a study of diets across the board and is forced to find that low carb is the best. http://www.youtube.com/watch?v=eREuZEdMAVo