Signal prediction by anticipatory relaxation dynamics

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.

Anticipated synchronization in human EEG data: Unidirectional causality with negative phase lag

Understanding the functional connectivity of the brain has become a major goal of neuroscience. In many situations the relative phase difference, together with coherence patterns, has been employed to infer the direction of the information flow. However, it has been recently shown in local field potential data from monkeys the existence of a synchronized regime in which unidirectionally coupled areas can present both positive and negative phase differences. During the counterintuitive regime, called anticipated synchronization (AS), the phase difference does not reflect the causality. Here we investigate coherence and causality at the alpha frequency band (f∼10 Hz) between pairs of electroencephalogram (EEG) electrodes in humans during a GO/NO-GO task. We show that human EEG signals can exhibit anticipated synchronization, which is characterized by a unidirectional influence from an electrode A to an electrode B, but the electrode B leads the electrode A in time. To the best of our knowledge, this is the first verification of AS in EEG signals and in the human brain. The usual delayed synchronization (DS) regime is also present between many pairs. DS is characterized by a unidirectional influence from an electrode A to an electrode B and a positive phase difference between A and B which indicates that the electrode A leads the electrode B in time. Moreover we show that EEG signals exhibit diversity in the phase relations: the pairs of electrodes can present in-phase, antiphase, or out-of-phase synchronization with a similar distribution of positive and negative phase differences.

Anticipation and negative group delay in a retina

The mechanism of negative group delay (NGD) is used to understand the anticipatory capability of a retina. Experiments with retinas from bullfrogs are performed to compare with the predictions of the NGD model. In particular, whole field stochastic stimulations with various autocorrelation times are used to probe anticipatory responses from the retina. We find that the NGD model can reproduce essential features of experimental observations characterized by the cross correlations between the stimulation and the retinal responses. Experiments with dark light pulse stimulations further support the NGD mechanism, with the retina producing time-advanced pulse responses. However, no time-advanced pulse responses are produced by bright pulses. Counterintuitively, the NGD model shows that it is the delay in the system which gives rise to anticipation because of the negative feedback adaptation mechanism.

Phase bistability between anticipated and delayed synchronization in neuronal populations

Two dynamical systems unidirectionally coupled in a sender-receiver configuration can synchronize with a nonzero phase lag. In particular, the system can exhibit anticipated synchronization (AS), which is characterized by a negative phase lag, if the receiver also receives a delayed negative self-feedback. Recently, AS was shown to occur between cortical-like neuronal populations in which the self-feedback is mediated by inhibitory synapses. In this biologically plausible scenario, a transition from the usual delayed synchronization (with positive phase lag) to AS can be mediated by the inhibitory conductances in the receiver population. Here we show that depending on the relation between excitatory and inhibitory synaptic conductances the system can also exhibit phase bistability between anticipated and delayed synchronization. Furthermore, we show that the amount of noise at the receiver and the synaptic conductances can mediate the transition from stable phase locking to a bistable regime and eventually to a phase drift. We suggest that our spiking neuronal populations model could be potentially useful to study phase bistability in cortical regions related to bistable perception.

Exploring the Phase-Locking Mechanisms Yielding Delayed and Anticipated Synchronization in Neuronal Circuits

Synchronization is one of the brain mechanisms allowing the coordination of neuronal activity required in many cognitive tasks. Anticipated Synchronization (AS) is a specific type of out-of-phase synchronization that occurs when two systems are unidirectionally coupled and, consequently, the information is transmitted from the sender to the receiver, but the receiver leads the sender in time. It has been shown that the primate cortex could operate in a regime of AS as part of normal neurocognitive function. However it is still unclear what is the mechanism that gives rise to anticipated synchronization in neuronal motifs. Here, we investigate the synchronization properties of cortical motifs on multiple scales and show that the internal dynamics of the receiver, which is related to its free running frequency in the uncoupled situation, is the main ingredient for AS to occur. For biologically plausible parameters, including excitation/inhibition balance, we found that the phase difference between the sender and the receiver decreases when the free running frequency of the receiver increases. As a consequence, the system switches from the usual delayed synchronization (DS) regime to an AS regime. We show that at three different scales, neuronal microcircuits, spiking neuronal populations and neural mass models, both the inhibitory loop and the external current acting on the receiver mediate the DS-AS transition for the sender-receiver configuration by changing the free running frequency of the receiver. Therefore, we propose that a faster internal dynamics of the receiver system is the main mechanism underlying anticipated synchronization in brain circuits.

A delayed-feedback filter with negative group delay

A filter with delay-induced negative group delay is presented. The filter consists of multiple time-delayed feedback terms, which lead to a negative group delay for frequencies in the baseband. It can be used for the real-time prediction of band-limited signals. The filter is universal as it does not rely on a specific model of the signal. Specifically, as long as the signal to be predicted is band-limited with a known cutoff frequency, the filter predicts the signal in real time up to a prediction horizon that depends on the cutoff frequency. How signal prediction arises from the negative group delay of the filter is worked out in detail. Its properties, including stability, are derived analytically and demonstrated by numerical simulations. For chaotic systems, the filter is predictive during phases of high predictability.

The Leaky Integrator with Recurrent Inhibition as a Predictor

The leaky integrator, the basis for many neuronal models, possesses a negative group delay when a time-delayed recurrent inhibition is added to it. By means of this delay, the leaky integrator becomes a predictor for some frequency components of the input signal. The prediction properties are derived analytically, and an application to a local field potential is provided.