Storing cycles in Hopfield-type neural networks
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The storage of pattern sequences is one of the most important tasks in both biological and artificial intelligence systems. Clarifying the underlying mathematical principles for both the storage and retrieval of pattern sequences in neural networks is fundamental for understanding the generation of rhythmic movements in animal nervous systems, as well as for designing electrical circuits to produce and control rhythmic output. In this dissertation, we investigate algebraic structures of binary cyclic patterns (or for short cycles) and study relations between these structures and the topology and ...