Abstract: A deformable optical lens with a lens membrane having an optically active portion that is configured to be shaped over an air-membrane interface according to a spherical cap and Zernike polynomials is provided. The spherical cap and the Zernike polynomials comprise a Zernike[4,0], (Noll[11]) polynomial and are sufficient to model the deformable optical lens to within approximately 2 micrometers.

Abstract: Methods and apparatus provide for a network device(s) employing tree tracer processing of a data packet(s) and/or a response(s) in order to discover and graphically represent all the paths within a hierarchical tree of network devices for multicast traffic flows. Specifically, a first network device receives a data packet. The data packet provides a multicast target MAC address. The first network device forwards the data packet to a plurality of network devices, where each of the plurality of the network devices belong to a multicast group identified according to the multicast target MAC address. Based on receipt of the data packet, the first network device generates and transmits a first response to a source of the data packet. The first response indicates a placement of the first network device with respect to a hierarchical tree of the plurality of network devices belonging to the multicast group.

Abstract: A network management and monitoring application employs diagnostic messages for confirming network path connectivity and identifying and locating connectivity faults. Diagnostic messages similar to conventional “ping” and “traceroute” messages traverse the network along a prescribed path for which diagnostic feedback is desired. The application receives and analyzes return messages sent from network entities along the path to ascertain connectivity issues on the path. The application receives layer 3 identifiers such as IP addresses, however performs diagnostic operations such as continuity checks based on layer 2 identifiers such as MAC (Media Access Control) identifiers because certain network entities operate on L2 identifiers and would otherwise evade a continuity check based on layer 3 identifiers.

Abstract: Methods and apparatus provide for a network device(s) employing tree tracer processing of a data packet(s) and/or a response(s) in order to discover and graphically represent all the paths within a hierarchical tree of network devices for multicast traffic flows. Specifically, a first network device receives a data packet. The data packet provides a multicast target MAC address. The first network device forwards the data packet to a plurality of network devices, where each of the plurality of the network devices belong to a multicast group identified according to the multicast target MAC address. Based on receipt of the data packet, the first network device generates and transmits a first response to a source of the data packet. The first response indicates a placement of the first network device with respect to a hierarchical tree of the plurality of network devices belonging to the multicast group.

Abstract: OAM may be implemented at an intermediate node on a PBT trunk in an Ethernet network by causing OAM frames to be addressed to the PBT trunk endpoint but causing the OAM frames to carry an indicia (Ether-type, OpCode, TLV value or combination of these and other fields) that the OAM frames are intended to be used for intermediate node OAM functions. The Ether-type, OpCode, and TLV values may be standardized values, or vendor specific values such as OpCode=51 or TLV=31 may be used. Addressing the OAM frames to the PBT trunk end point enables the OAM frames to follow the PBT trunk through the network. The OAM indicia signals to the intermediate nodes that the OAM frames are intended to be used to perform an intermediate node OAM function. The OAM frames may contain reverse trunk information to prevent the intermediate nodes from being required to store correlation between forward and reverse PBT trunks.