Figure 1

Input-output recurrence plot of synaptic transmission data. Stimulation parameters as in Fig. 3b, 3d, 3e. (a) Excerpt of a recurrence plot for neighborhood dimensions $ϵ=0.35\mathrm{mV}$, $\delta =290\mathrm{ms}$. Matrix elements $[i,j]$ are colored black when $\Theta (ϵ-\parallel {\mathbf{A}}_i-{\mathbf{A}}_j\parallel )\Theta (\delta -\parallel \mathbf{\Delta }{\mathbf{t}}_i-\mathbf{\Delta }{\mathbf{t}}_j\parallel )=1$. $m=n=2$. (b) Cumulative logarithmic histogram of diagonal lengths in a recurrence plot of a complete time series $\left(30\min \right)$. The correlation exponent of the joint input-output process is estimated from the slope of this plot (1.75).Reuse & Permissions

Figure 2

Input-output correlation entropy of the noise-driven logistic map [Eq. (7)]. Time series consisted of 5000 points, and results from 500 trials were averaged. Symbols denote various noise levels relative to the standard deviation of the unperturbed map ${\sigma }_{\xi }∕{\sigma }_{\mathrm{up}}$: $◇=0.5$, $◁=0.25$, $엯=0.01$, $m=n=6$. $x_0=0.7$, $a=4$ (a,b) and $a=3$ (c,d). (a) $\mu$ as a function of $ϵ$ for $\delta \to 0$, (b) $\mu$ as a function of $ϵ$ estimated solely from the output time series $(\delta \to \infty )$. (c) As for (a) but for $a=3$. (d) As for (b) but for $a=3$.Reuse & Permissions

Figure 3

Synaptic transmission at a cortical synapse. (a) Six consecutive postsynaptic responses (top) and ensemble mean response (bottom, 50 responses) to the presynaptic stimulation pattern indicated below. (b) Whole-cell recording in synaptically coupled pyramidal neurons of the rat cortex. (c) A segment of a continuous recording showing evoked and spontaneous EPSPs (upper traces) during naturalistic stimulation (APs in lower traces) with parameters $R_p=30\mathrm{Hz}$, ${\lambda }_b=0.2\mathrm{Hz}$, ${\tau }_b=200\mathrm{ms}$, average rate $1.2\mathrm{Hz}$ (see text). (d), (e) Corresponding distributions of interspike intervals (e) and postsynaptic EPSP amplitudes (e) for an experiment lasting $30\text{minutes}$.Reuse & Permissions

Figure 4

(Color online) Clustering of amplitudes of responses with reliable futures. (a) The history vector was defined only by the last interspike interval and last EPSP amplitude. Points are coded according to the dispersion value (see text) as indicated on the right using 50 nearest neighbors. Stimulus parameters were $R_{\text{peak}}=30\mathrm{Hz}$, ${\tau }_b=200\mathrm{ms}$ ${\lambda }_b=0.2\mathrm{Hz}$, which amount to an average rate of $1.2\mathrm{Hz}$. (b) Control for (a) using a random permutation of the amplitude time series.Reuse & Permissions

Figure 5

Convergence of $K_2$-entropy estimate $\mu$ for synaptic data. (a) A typical $\mu \left(ϵ\right)$ relationship at a very small $\delta =0.018\mathrm{ms}$. A clear convergence is seen as $ϵ\to 0$. Stimulation parameters as in Fig. 1. Total number of stimulation events in the time series was 2594. The mean of 50 randomly shuffled controls is shown as a dashed line. The standard deviation $\sigma$ of these controls was maximal for $ϵ\to 0$, $\sigma <0.18$. Gray 엯 denotes the mean of 50 surrogates with a large shift between the amplitude and interspike interval time series (see text). A shift $>10\text{minutes}$ was randomly chosen, $\sigma <0.43$ (b). $\mu \left(ϵ\right)$ before and after induction of spike-timing dependent plasticity (STDP). Gray line denotes the data before the induction of STDP, black solid line denotes after induction. The means of 50 randomly shuffled controls are shown as corresponding dashed lines, $\sigma <0.44$ before STDP and $\sigma <0.43$ after STDP. Stimulation parameters were $\overline{R}=30\mathrm{Hz}$, ${\lambda }_b=0.5\mathrm{Hz}$ ${\tau }_b=400\mathrm{ms}$, average rate $6\mathrm{Hz}$. The stimulation before and after STDP induction was identical, with 3000 stimulation events.Reuse & Permissions

Figure 6

(a) Analysis of a biophysically based model of synaptic transmission [24], driven by the same stimulus timing as used in Fig. 5a. The model parameters were $U_{se}=0.5$, ${\tau }_{\mathrm{rec}}=800\mathrm{ms}$, $N=5$, the mean quantal size $q=0.2\mathrm{mV}$ for all release sites, see Ref. 24 for details. Graphs are shown for three different levels of variability of the quantal content. (b) Same analysis as in (a) but with a logarithmic scale in $ϵ$ to demonstrate the divergence between the macroscopic mean-field model with additional extrinsic Gaussian noise (solid line) and the microscopic stochastic model (dotted line). The standard deviation of the Gaussian noise was estimated from average ensemble fluctuations of 1000 surrogates of the stochastic model [parameters as in (a)]. The model parameters for the deterministic model were chosen accordingly, $U_{se}=0.5$, $A_{se}=1$, ${\tau }_{\mathrm{rec}}=800\mathrm{ms}$.Reuse & Permissions