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Efficient Physical Embedding of Topologically Complex Information Processing Networks in Brains and Computer Circuits

Figure 4

Allometric and Rentian scaling of VLSI circuits and mammalian brains.

In computer circuits (A), the number of connections at the boundary of a chip scales in a Rentian power law with the number of processing elements; the Rent exponent is greater for high performance computers (shown in blue) than for simpler dynamic memory circuits (shown in red); see pp. 416–421 in [76] for data values plotted here. In the cerebral hemispheres of mammalian brains (B), there is an allometric scaling relationship between white matter volume (related to connectivity of elements) and gray matter volume (related to number of processing elements); see Table 1 in [26] for data values plotted here. The exponent of this volume scaling relationship over species, , is simply related to the Rent exponent of mammalian cerebral connectivity, . Lines fitted through the intercept of the data show the allometric scaling relationship predicted by the Rent exponent estimated for neuroimaging data on a single species (Homo sapiens), using MRI (cyan, ) and DSI (blue, ) (Table 1). Errors in the fits are smaller than the line width.

Figure 4