Relating the small world coefficient to the entropy of 2D networks and applications in neuromorphic engineering

Abstract

The study of networks pervades science. The techniques of networks are recently being applied to biomedical disciplines, where the complexity of biomedical systems requires new schemes that can process elevated volumes of data with high efficiency. Artificial neural networks, on which much of artificial intelligence relies, are statistical models partially modeled on biological neural networks. They are capable of modeling and processing nonlinear relationships between inputs and outputs in parallel—in opposition to deterministic models and classical computation schemes, which perform tasks in linear sequences of calculations and may fail to keep up with the challenges of complex biological systems. For these biological or bio-inspired systems, the performance of the networks depends on their topological characteristics. Here, we generated a large number of configurations of points in a plane, in which the entropy s of the configurations was varied over large intervals. Then, we connected points using the Waxman model to obtain the corresponding networks. In correlating the entropy (s) to the small-world coefficient () of those networks, we found that SW varies hyperbolically with s as SW = 0.88 + 0.28/s, where s is expressed in millibits per node. Since the entropy of a distribution of points depends in turn on the density of those points in the plane, such a relationship suggests that the distribution of mass () in a complex system determines the topological characteristics () of that system. The small-world-ness of the system, in turn, determines its information efficiency. These findings may have implications in neuromorphic engineering, where chips modeled on biological brains may lead to machines that are able, as for some examples, to diagnose diseases, develop drugs and drug delivery systems faster, design personalized treatments targeted to patient’s needs.