It is an object of the invention to obtain a video encoder and a video decoder performing a highly accurate prediction of a picture, transformed by other than translation, within a short processing time in a small-scaled circuit. The apparatus includes a direct connection part for providing a direct connection in response to a connection request from the first network device, said request being a request to connect to a second network device in a second private network. A grouping section groups the specified receiver’s user together. As a result, the write gap does not protrude to mask the effects of the ion-beam etch used to form the taper. The control system also includes a test mode to test whether the detection system is working, to test whether various materials would be detected by the detection system, andor to test whether various materials would trigger the reaction system.