Hypercube mapping

Input data mapping still corresponds to projection on a hypersphere however, ART uses vector direction to assess similarity rather than using a distance measure as shown in Fig. 15. This translates into the use of hypercone clusters in a unit hypercube. 

Virtual Topologies The practice of using an application topology on a machine with a different true topology (e.g., mapping a ring to a hypercube or mesh). 

In the remainder of this review we focus on the mathematical analysis of the piecewise linear equations largely based on earlier studies [34-48]. In Section IV we show that the logical structure can be mapped onto a hypercube in N dimensions, where each vertex of the hypercube represents the state of each of the N variables, and the dynamics and logical structure in the network are represented as directed edges on the hypercube. 

We then use the hypercube representation to carry out a nonlinear dynamical analysis of these networks. The key insight is that quantitative aspects of flows in phase space can be computed from linear fractional maps that represent the flows between boundaries on the hypercube. Analysis is possible because the composition of two linear fractional maps is a hnear fractional map. This analysis is useful for analyzing steady states, limit cycles, and chaotic dynamics in these networks. 

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