Distribution of Synaptic Connection Strength Has a Heavy Tail

<div><p>(A) Estimated probability density function in log–log space, with both lognormal fit (<i>p</i>[<i>w</i>] = 0.426exp[−(ln[<i>w</i>] + 0.702)²/(2 × 0.9355)²]/<i>w</i>) and exponential fit (<i>p</i>[<i>w</i>] = 1.82exp[−1.683<i>w</i>]). Notice that the lognormal fit has a heavier tail than the exponential distribution. Error bars are standard deviations estimated by bootstrap method (not shown when narrower than the dot). The numbers on top on the dots are the actual counts (not shown when more than 50).</p> <p>(B) Estimated probability density distribution in semilog space, with the lognormal fit. The lognormal function shows up as a normal function in the semilog space.</p> <p>(C) Empirical cumulative density function for both the probability distribution of synaptic strengths and the synaptic contribution (normalized product of probability and connection strength). They are generated directly from the data rather than the fits. The vertical line illustrates the fact that 17% of the synaptic connections contribute to half of the total synaptic strengths.</p> <p>(D) Probability density function of synaptic connection strengths p(w) fitted by a lognormal function and the synaptic contribution defined as the product of the strength, w, and p(w). The total areas under both curves are normalized to 1.</p>