Efficient Physical Embedding of Topologically Complex Information Processing Networks in Brains and Computer Circuits
Physical Rentian scaling in (A) a very large scale integrated circuit, (B) the nematode worm C. elegans, (C) the human cortical anatomical network estimated using conventional MRI in 259 normal volunteers and (D) the human cortical anatomical network estimated using diffusion spectrum imaging (DSI) from an independent sample of 5 normal volunteers, is shown by a power law scaling of the number of connections or edges () and number of processing elements () in a physical box; data points for each physical box are shown by black stars. The Rent exponents for each system were estimated by the gradients of the fitted red lines (see Table 1). Note: Data and linear shown in D are for a single subject. Insets Topological Rentian scaling in nervous and computational systems is shown by a power law scaling of the number of nodes () in a topological partition and the number of edges crossing the boundary of that partition (); data points for each topological partition are shown by black circles. The network topology of each system was iteratively partitioned in topological space. All networks contained a linear scaling regime (so-called Region I, filled black circles) and a regime at larger partition sizes where linear scaling broke down due to boundary effects (so-called Region II, empty black circles). The slope, , of the line through points within Region I was estimated using a weighted linear regression (red line); see Table 1. Note: Data and linear fits for all six DSI scans are shown in D.