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It has been suggested that CMOS technologies will hit scaling limits due to fundamental design issues at the regime of molecular electronics. In this project, the memristor device has been evaluated as a candidate for building high-density, high-performance computers at such a scale. Although memristors are already under active research and development as random access memory, in this project, we evaluate their potential for neuromorphic (brain-inspired) information processing in the context of reservoir computing. We quan- tify a memristor network's capability to analyze sets of time-dependent input data for pattern recognition applications. We pose the following key question: given a network of a certain design, which signals might it be particularly adept at recognizing? To answer that question, a rigorous mathematical approach has been developed and implemented as computer software. Our preliminary results indicate that the conceptual approach that has been developed can be used to answer this question, and suggest that memristor networks are capable of real-time pattern recognition.