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The mechanism of negative group delay (NGD) is used to understand the anticipatory capability of a retina. Experiments with retinas from bull frogs are performed to compare with the predictions of the NGD model. In particulars, whole field stochastic stimulation with various time correlations 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. The prediction horizon of a retina is found to depend on the correlation time of the stimulation as predicted by the NGD model. Experiments with dark and bright Gaussian light pulses further support the NGD mechanism; but only for the dark pulses indicating that the NGD effect of a retina might originate from its OFF response. Our finding suggests that sensory systems capable of using negative feedback for adaptation can give rise to anticipation as a consequence of the delay in the system.
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Lane formation in bidirectional pedestrian streams is based on a stimulus-response mechanism and strategies of navigation in a fast-changing environment. Although microscopic models that only guarantee volume exclusion can qualitatively reproduce this phenomenon, they are not sufficient for a quantitative description. To quantitatively describe this phenomenon, a minimal anticipatory collision-free velocity model is introduced. Compared to the original velocity model, the new model reduces the occurrence of gridlocks and reproduces the movement of pedestrians more realistically. For a quantitative description of the phenomenon, the definition of an order parameter is used to describe the formation of lanes at transient states and to show that the proposed model compares relatively well with experimental data. Furthermore, the model is validated by the experimental fundamental diagrams of bidirectional flows.
In this paper, a systematic synthesis approach is proposed for achieving negative group delay responses using lossy coupling matrix. It is mathematically proved that, for a passive and reciprocal network, loss is the necessary condition to realize a negative group delay. Also, the optimum strategy is to place zeros and poles of the transfer function both on the left complex plane. A closed-form relation between the group delay and magnitude is then derived based on this strategy, and followed by a complete synthesis approach using coupling matrix. Two numerical and one experimental examples are finally given to illustrate the proposed synthesis method.
The design of reliable indicators to anticipate critical transitions in complex systems is an im portant task in order to detect a coming sudden regime shift and to take action in order to either prevent it or mitigate its consequences. We present a data-driven method based on the estimation of a parameterized nonlinear stochastic differential equation that allows for a robust anticipation of critical transitions even in the presence of strong noise levels like they are present in many real world systems. Since the parameter estimation is done by a Markov Chain Monte Carlo approach we have access to credibility bands allowing for a better interpretation of the reliability of the results. By introducing a Bayesian linear segment fit it is possible to give an estimate for the time horizon in which the transition will probably occur based on the current state of information. This approach is also able to handle nonlinear time dependencies of the parameter controlling the transition. In general the method could be used as a tool for on-line analysis to detect changes in the resilience of the system and to provide information on the probability of the occurrence of a critical transition in future.
In physics of living systems, a search for relationships of a few macroscopic variables that emerge from many microscopic elements is a central issue. We evolved gene regulatory networks so that the expression of target genes (partial system) is insensitive to environmental changes. Then, we found the expression levels of the remaining genes autonomously increase as a plastic response. Negative proportionality was observed between the average changes in target and remnant genes, reflecting reciprocity between the macroscopic robustness of homeostatic genes and plasticity of regulator genes. This reciprocity follows the lever principle, which was satisfied throughout the evolutionary course, imposing an evolutionary constraint.
Neural avalanches are collective firings of neurons that exhibit emergent scale-free behavior. Understanding the nature and distribution of these avalanches is an important element in understanding how the brain functions. We study a model of neural avalanches for which the dynamics are governed by neutral theory. The neural avalanches are defined using causal connections between the firing neurons. We analyze the scaling of causal neural avalanches as the critical point is approached from the absorbing phase. By using cluster analysis tools from percolation theory, we characterize the critical properties of the neural avalanches. We identify the tuning parameters consistent with experiments. The scaling hypothesis provides a unified explanation of the power laws which characterize the critical point. The critical exponents characterizing the avalanche distributions and divergence of the response functions are consistent with the predictions of the scaling hypothesis. We use a universal scaling function for the avalanche profile to find that the firing rates for avalanches of different durations show data collapse after appropriate rescaling. We also find data collapse for the avalanche distribution functions, which is stronger evidence of criticality than just the existence of power laws. Critical slowing-down and power law relaxation of avalanches is observed as the system is tuned to its critical point. We discuss how our results motivate future empirical studies of criticality in the brain.
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