I agree -- pilates has some great core exercises.
Better late than never, here's the frog breathing exercise. This exercise is probably familiar to practitioners of Chinese internal martial arts, and is similar to but predates glossopharyngeal breathing -- also called frog breathing -- which is taught to paralysis victims.
From seiza, inhale through your nose into your kidneys and lower diaphragm until your lungs are half full (or more as you get the hang of it). Starting at the top of your torso, contract your muscles to push the air deeper into your lungs. Keep your neck and head relaxed; you should feel no pressure in your head, and certainly not get red in the face. Continue pushing down with your chest, back, and abs. Visualize compressing the air into the size of a golf ball at your tan t'ien.
Then slowly exhale through your mouth while bowing forward, keeping your back slightly arched. Try to push all the air out of your lungs.
Inhale easily as you rise back up. Hold the breath a moment, then exhale. That's one rep.
(As always, consult a physician before doing any exercises, the Martial Edge folks and I disclaim any liability, etc.)