The following is an excerpt from the 7 principles of Russian Breathing according to Vladimir Vasiliev with commentary by Systema SLC. For more information pick up Let Every Breath: the Secrets of the Russian Breath Masters.
6.Independence – Breath should be independent of action, that is, you should practice rising on both the inhale cycle and exhale cycle.
It is often said that particular actions are performed on the inhale while others are performed on the exhale. This is particularly true of some varieties of Tai Chi, which suggest contracting on the exhale and expanding on the inhale. You may even notice that it is easier to squat on an exhale and stand on an inhale; after all, the body expands with oxygen on an inhale. This works well, in fact, we often begin class by moving on the floor during exhales and pausing during inhales because the body is most relaxed during exhales. Almost in contradiction to the principle of Independence, we often practice exhaling during a strike or while taking a strike.
However, without true independence of breath the principles of Leading and Pendulum are also broken. If you must exhale everytime you are struck, then your breath is not leading; your opponent is. If, for example, you decide to squat during an inhale because your opponent’s energy is moving downward, then you might force an exhale before you complete an inhale cycle. In this case, instead of letting your breath move naturally from inhale to exhale, you are restricting it. Therefore, you should practice performing every action on the inhale as well as the exhale. You should learn to take and give strikes on the inhale as well as the exhale.