Fig. 6: Adaptation introduces history-dependence to SPA and SPI, a Bernoulli process.
a Quantization of SPA and SPI is evident within an individual experiment (same as Fig. 5) and its corresponding simulation (inset). The probability decreases exponentially with SPA and SPI quantized duration, reflecting a discrete Bernoulli process. b To find the precise history-dependence, one can imagine the efferent response to afferent UDS as a sequence of coin flips, as SPA and SPI are all-or-nothing binary events. State transitions in the afferent network destabilize the efferent network, which either persists in its current state, resulting in SPA or SPI (heads, probability p), or makes a corresponding transition (tails, prob. 1-p). The probability that a given efferent state lasts a single afferent UDS cycle is 1-p1 (the first mode in (a)), while the probability that it lasts between 1 and 2 cycles is p1(1-p2) (the second mode in a), where the subscript denotes the 1st/2nd transition. Unlike a memoryless process (i.e., p1 = p2) or brain state dependent process (i.e. p1 < p2), the model (inset) predicted that the probability of SPA or SPI should decrease when conditioned on SPA or SPI having occurred previously (i.e., p1 > p2, p < 10−16). This was confirmed in the in vivo data (main, p < 10−7) and reflects the underlying long-term memory of the adaptation in the efferent network. Wilcoxon signed ranked test was used to show significant differences.
