Fig 4 -

(A) Comparison between the storage capacity of Markovian binary synapses and binarized double well synapses defined in Eq (12). The parameters of the double well model are r1 = 0.1, r2 = 1, r3 = 0, θ = 0, f = 0.5, cN = 2000. The width of the potential C is chosen to maximize storage capacity. The transition probabilities of binary Markovian model are chosen to match probabilities of switching wells in the double well model. (B) Comparison between the SNRs of Markovian synapses and binarized double well synapses, as a function of time elapsed since the presentation of a given pattern. Green curve: SNR of the double well model with C = C* calculated using Eq (40). Red line: SNR of the Markov model with the same transition probability. Black line: Upper bound of SNR for two-state Markov models. Dashed line: critical SNR below which the memories are no longer retrievable [28]. The intersection between the SNR curve and this dashed line determines the storage capacity of the network. (C) Cartoon of the temporal evolution of the distribution of synapses that undergo potentiation at t = 0, i.e. those for which just before potentiation (top) and after (bottom). The highlighted region denotes the region around the maximum of the potential where synapses that reside in one of the wells can make a transition to the other well (r2 = 1). Just before potentiation (t = 0), the distribution is symmetric. The distribution is then shifted up by r2, before decaying towards the respective wells. As the distribution becomes asymmetric near 0 (within the range of 0 ± r2), the next presented uncorrelated patterns will cause more probability mass to shift towards the positive side than towards the negative side, as demonstrated in the bottom figure. (D) Distribution of connections that have been potentiated at time t = 0, at later times t = 2 and t = 3. Black dots indicate ±r2 = ±1, while red dots indicate the minima of the potential, ±C = ±2.7. As demonstrated in (C), an uncorrelated pattern leads to a larger probability of switching from the low well to the high well than the opposite transition, resulting in an increase in SNR from t = 2 to t = 3, as seen in (B). At longer times, the distribution eventually returns to a symmetric distribution, leading to a decrease in SNR.