Spontaneous brain activity as a source of ideal $1/f$ noise

We study the electroencephalogram (EEG) of 30 closed-eye awake subjects with a technique of analysis recently proposed to detect punctual events signaling rapid transitions between different metastable states. After single-EEG-channel event detection, we study global properties of events simultaneously occurring among two or more electrodes termed coincidences. We convert the coincidences into a diffusion process with three distinct rules that can yield the same $\mu$ only in the case where the coincidences are driven by a renewal process. We establish that the time interval between two consecutive renewal events driving the coincidences has a waiting-time distribution with inverse power-law index $\mu \approx 2$ corresponding to ideal $1/f$ noise. We argue that this discovery, shared by all subjects of our study, supports the conviction that $1/f$ noise is an optimal communication channel for complex networks as in art or language and may therefore be the channel through which the brain influences complex processes and is influenced by them.

Figure 1

$S\left(t\right)$ for rule no. 3 (SJ), for subject 6 with different choices of $N_t$ and $\Delta t_c$.

Figure 2

Diffusion entropy $S\left(t\right)$ for rules no. 1 (AJ) and no. 3 (SJ) for subjects 7 and 22.

Figure 3

(a) Scatter plot of ${\delta }_{AJ}$ vs ${\delta }_{SJ}$. (b) Scatter plot of ${\mu }_{AJ}$ vs subject label.

Figure 4

(a) $t_n$ vs $n$ for subject 2. (b) ${\tau }_n$ vs $n$, same subject.

Figure 5

$\sigma \left(t\right)$ for rule no. 3 (SJ), for subject 2 with different choices of $N_T$ and $\Delta t_c$.

Figure 6

DFA using the three rules for subjects 2, 13, 23, and 27. Sampling time (2 ms).

Figure 7

Scatter plots: (a) $H_{SJ}$ vs $H_{AJ}$; (b) $H_{SJ}$ vs $H_{SV}$; (c) $H_{AJ}$ vs $H_{SV}$.