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We have electrochemically self-assembled regimented arrays of vertically standing nanowire metal-insulator-semiconductor diodes (MISD) embedded in an insulating matrix. Each diode is a 10-nm-diameter semiconductor (CdS) nanowire in contact with an underlying thin insulator ( ~20 nm thick), flanked by two metal electrodes. The density of these MISD devices exceeds 1011/cm2. The dc current-voltage characteristic of several devices in parallel displays an S-type nonlinearity, typical of an MISD. The negative differential resistance associated with the S-type nonlinearity can have a peak to valley ratio as large as 19:1 at room temperature. Individually, such devices can be used as thyristors, logic switches, and high-frequency oscillators. Collectively, they constitute a system of interacting nonlinear elements that could realize a nanoelectronic neuromorphic network model proposed more than a decade ago.