Beyond Scale-Free Small-World Networks: Cortical Columns for Quick Brains

We study to what extent cortical columns with their particular wiring boost neural computation. Upon a vast survey of columnar networks performing various real-world cognitive tasks, we detect no signs of enhancement. It is on a mesoscopic—intercolumnar—scale that the existence of columns, largely irrespective of their inner organization, enhances the speed of information transfer and minimizes the total wiring length required to bind distributed columnar computations towards spatiotemporally coherent results. We suggest that brain efficiency may be related to a doubly fractal connectivity law, resulting in networks with efficiency properties beyond those by scale-free networks.

Figure 1

Ferret striate cortex, adaptation from Ref. 6: Log-density of photostimulation—evoked excitatory (a) and inhibitory (b) synaptic inputs (concentric rings $50\mu \mathrm{m}$ apart, from 19 pooled layer $2/3$ neurons). (I): Inner-columnar, (II): Intercolumnar scale. Vertical lines: Extensions of aligned physiological columns. Tilted dashed lines: Proposed long distance decay.

Figure 2

(I) (a) EI model, (b) EI-control network (uniform synaptic weights $w$, $\lambda =2$). $p_{\mathrm{con}}$: probability of a synaptic connection among neurons of distance $d$ for $C$ values as in the text, $w$: synaptic strength of the connections. (II) (a) LEI-model, (b) LEI-control network. Input strengths to populations are color coded.

Figure 3

Recognition rate $R$ for (a) Arabic Digit, and (b) Auslan recognition. Each data point represents an average over at least 20 experiments following a normal-like distribution each [cf. Supplemental Material Sec. (1b) [10]]. Blue: leaky integrate and fire, red: Izhikevich neurons. Left column: memoryless (ml), right column: integration (int) readout. (I) $EI$ network, dependence on rewiring parameter $\lambda$ (control networks: dashed curves), and on ratio $I$ of input receiving neurons, at local connectivity (i.e., $\lambda =2$). Ocher: Izhikevich neurons with $\lambda =0$. (II) $LEI$ networks, dependence on rewiring probability $p$. $p=0$: layered, $p=1$: homogeneous control network.

Figure 4

Main connectivity classes compared ($p$: connection probabilities, $d$: distance, $M$: cutoff, see text).

Figure 5

Left: SIT as a function of cell connections $k$. From top: doubly fractal ($\theta =0.2$, $\alpha =0.5$, $\beta =2.0$), fractal ($\theta =1$, $\alpha =0.7$), random, n.-n. topology. Network sizes: $N=4096$, averages over 100 experiments. Right: Connections $k_{\min }$ required for synchronization, and associated TWL. $N=512$, 10 experiments.