1. A crosspoint architecture comprising: a plurality of electrodes; and a plurality of crossbar elements, each crossbar element disposed between a first and a second electrode in said plurality of electrodes, and each crossbar element comprising at least a symmetric or substantially symmetric resistive memory material used as a rectifier in series with a memory element, said symmetric or substantially symmetric resistive memory material used as said rectifier, in an ON state, supplying an ultrahigh current density that is greater than 10 6 A/cm 2 .