The codes are almost certainly related. P0410 indicates a malfunction of the Air Injection System. P0130 points to the O2 sensor before the catalytic converter (TWC). This O2 sensor is the one used to monitor the Air Injection function. When the air pump runs, it pumps fresh air into the exhaust stream. The O2 sensor percieves this as a lean condition and the voltage changes accordingly(it should drop to approx. 0V). As O2 sensors age they can lose the ability to reach their voltage limits. I'll bet the P0410 is being caused by the O2 sensor not performing to it's fullest. For what it's worth I've seen this dozens of times. Of course there's always the possibility that you have two separate issues, but the O2 sensor is the likely culprit. Let us know how it turns out.