Methods and apparatus for amplifying a signal are provided. In some embodiments, a computer-implemented method, computer program product, and data processing system produce a maximal-index-satisfiable query tree. The test sample includes a first component and a second component. When words are relocated or edited on the writing surface, the anchored annotations are also relocated and may even be reshaped according to the changes in the anchored words. When congestion occurs, selective transmission units perform discard initiation or termination on data having the flow identifier data indicating the layered audiovisual data retained, based on the control code data for performing the discard-initiating or -terminating operation of the packet data. A snap grid space may comprise a two-dimensional or three-dimensional virtual space within an augmented reality environment in which one or more virtual objects may be positioned.