1/f optimal information transportation

PRL 105, 040601 (2010):

In living neural networks, the connection between function and information transport is studied with experimental techniques of increasing efficiency [1] from which an attractive perspective is emerging; i.e., these complex networks live in a state of phase transition (collective, cooperative behavior), a critical condition that has the effect of optimizing information transmission [2]. From the studies of complex networks, it is evident that the statistical distributions for network properties are inverse power laws and that the power-law index is a measure of the degree of complexity. Intimate connections exist between neural organization and information theory, the empirical laws of perception [3], and the production of 1=f noise [4], with
the surprising property that 1=f signals are encoded and transmitted by sensory neurons with higher efficiency than white noise signals [5]. Although 1=f noise production is interpreted by psychologists as a manifestation of human cognition [6], and by neurophysiologists [7] as a sign of neural activity, a theory explaining why this form of noise is important for communication purposes does not exist yet. The well known stochastic resonance phenomenon [8] describes the transport of information through a random medium, obeying the prescriptions of Kubo linear response theory (LRT) [9], being consequently limited [10] to the stationary equilibrium condition. There are many complex networks that generate 1=f noise and violate this condition:
Two relevant examples are blinking quantum dots [11] and liquid crystals [12]. The non-Poisson nature of the renewal processes generated in these examples [13] is accompanied by ergodicity breakdown and nonstationary behavior [14].