Anticipation and negative group delay in a retina

Detection of Anticipatory Dynamics between a Pair of Zebrafish

Anticipatory dynamics (AD) is unusual in that responses from an information receiver can appear ahead of triggers from the source, and direction of information flow (DIF) is needed to establish causality. Although it is believed that anticipatory dynamics is important for animals' survival, natural examples are rare. Time series (trajectories) from a pair of interacting zebrafish are used to look for the existence of AD in natural systems. In order to obtain the DIF between the two trajectories, we have made use of a special experimental design to designate information source. However, we have also used common statistical tools such as Granger causality and transfer entropy to detect DIF. In our experiments, we found that a majority of the fish pairs do not show any anticipatory behaviors and only a few pairs displayed possible AD. Interestingly, for fish in this latter group, they do not display AD all the time. Our findings suggest that the formation of schooling of fish might not need the help of AD, and new tools are needed in the detection of causality in AD system.

Information synergy in the anticipatory dynamics of a retina

Anticipation is the phenomenon in which the response of a system is predictive of the stimulation. The encoding of stochastic light intensity (x) into spikes is investigated in an experiment with retinas from bullfrogs to understand the mechanism of anticipation of a retina. Partial information decomposition of the mutual information between the spike rates and the joint state {x,x[over ̇]} is found to be consistent with the encoding by the linear combination of x and x[over ̇] where x[over ̇] is the rate of change of x. This spike rate encoding form indicates that a retina is capable of anticipation based on the synergistic information generation between x and x[over ̇]. Our results suggest that illusions such as the anticipation studied here during retinal perception can originate from the recombination of information extracted in the retinal network.