Mutual Information Rate and Bounds for It

The amount of information exchanged per unit of time between two nodes in a dynamical network or between two data sets is a powerful concept for analysing complex systems. This quantity, known as the mutual information rate (MIR), is calculated from the mutual information, which is rigorously defined only for random systems. Moreover, the definition of mutual information is based on probabilities of significant events. This work offers a simple alternative way to calculate the MIR in dynamical (deterministic) networks or between two time series (not fully deterministic), and to calculate its upper and lower bounds without having to calculate probabilities, but rather in terms of well known and well defined quantities in dynamical systems. As possible applications of our bounds, we study the relationship between synchronisation and the exchange of information in a system of two coupled maps and in experimental networks of coupled oscillators.

Effects of visual and auditory stimuli in a choice reaction time task

The effect produced by a warning stimulus(i) (WS) in reaction time (RT) tasks is commonly attributed to a facilitation of sensorimotor mechanisms by alertness. Recently, evidence was presented that this effect is also related to a proactive inhibition of motor control mechanisms. This inhibition would hinder responding to the WS instead of the target stimulus (TS). Some studies have shown that auditory WS produce a stronger facilitatory effect than visual WS. The present study investigated whether the former WS also produces a stronger inhibitory effect than the latter WS. In one session, the RTs to a visual target in two groups of volunteers were evaluated. In a second session, subjects reacted to the visual target both with (50% of the trials) and without (50% of the trials) a WS. During trials, when subjects received a WS, one group received a visual WS and the other group was presented with an auditory WS. In the first session, the mean RTs of the two groups did not differ significantly. In the second session, the mean RT of the two groups in the presence of the WS was shorter than in their absence. The mean RT in the absence of the auditory WS was significantly longer than the mean RT in the absence of the visual WS. Mean RTs did not differ significantly between the present conditions of the visual and auditory WS. The longer RTs of the auditory WS group as opposed to the visual WS group in the WS-absent trials suggest that auditory WS exert a stronger inhibitory influence on responsivity than visual WS.

Universal behavior of the Shannon mutual information of critical quantum chains

We consider the Shannon mutual information of subsystems of critical quantum chains in their ground states. Our results indicate a universal leading behavior for large subsystem sizes. Moreover, as happens with the entanglement entropy, its finite-size behavior yields the conformal anomaly c of the underlying conformal field theory governing the long-distance physics of the quantum chain. We study analytically a chain of coupled harmonic oscillators and numerically the Q-state Potts models (Q = 2, 3, and 4), the XXZ quantum chain, and the spin-1 Fateev-Zamolodchikov model. The Shannon mutual information is a quantity easily computed, and our results indicate that for relatively small lattice sizes, its finite-size behavior already detects the universality class of quantum critical behavior.