Optimization of noise-induced resonance mechanisms on co-evolutionary neurobiological networks
Final Report Abstract
The main objective of this project was to investigate the dynamics of specific noise-induced resonance phenomena, namely coherence resonance (CR) and self-induced stochastic resonance (SISR), and stochastic synchronization (SS) in co-evolutionary (adaptive) neural networks driven by spike-timing-dependent plasticity (STDP — describes how the synaptic weights get modified by repeated pairings of the pre-and post-synaptic membrane potentials with the sign and the degree of the modification dependent on the relative timing of the neurons firing) and/or homeostatic structural plasticity (HSP — describes the mechanisms that rewire connectivity between neurons over time by swapping synaptic connections between neurons while maintaining a particular type of topology). In the first part of the project, we examined the dynamics of two types of neural network behaviors, namely CR and SISR, in multiplex networks while considering the effects of STDP. Our findings demonstrate that the high degree of CR observed in one-layer networks exhibits greater robustness than SISR against network topology and STDP parameter variations. This contradicts the results presented by M.E. Yamakou and J. Jost (Phys. Rev. E 100, 022313, 2019), where SISR was more robust than CR against network parameter variations but in the absence of STDP. We also found that an increase in the temporal window of depression and a decrease in the potentiation adjusting rate parameter of STDP can significantly deteriorate the degree of SISR in one layer of the multiplex network. Interestingly, we found that this deteriorated degree of SISR in this particular layer can be improved significantly by multiplexing this layer with another exhibiting a high degree of CR or SISR and suitable inter-layer STDP parameter values. Furthermore, our results indicate for all inter-layer STDP parameter values, the enhancement of SISR based on the occurrence of SISR outperforms the one based on CR. We also found the optimal enhancement of SISR in one layer based on the occurrence of SISR in another layer occurs via long-term potentiation of the inter-layer synaptic weights. In comparison, optimal enhancement of SISR in one layer based on CR in another layer occurs via (long-term depression) of the inter-layer synaptic weights. An active research topic in theoretical neuroscience is to elucidate the functional interplay between noise-induced resonance phenomena and SS in information processing. Whether an optimal network and STDP configuration exist at which CR and SS are both pronounced is a fundamental question of interest that is still elusive. Such a configuration could allow the brain to process information efficiently by synergistically utilizing both phenomena. The second part of our research project examined the interplay between CR, SS, and STDP. We considered a small-world network of excitable Hodgkin–Huxley neurons driven by channel noise and STDP with an asymmetric Hebbian time window. Numerical results indicate specific network topology and STDP parameter intervals in which CR and SS can be simultaneously enhanced. In particular, it is found that at certain intermediate values of the average degree of the network, higher values of the potentiation adjusting rate of STDP, and lower values of the depression temporal window of STDP, the degrees of CR and SS can be both optimized. In the third phase of our project, we investigated the combined effect of HSP and STDP on CR. Specifically, we studied CR in smallworld and random adaptive networks of Hodgkin-Huxley neurons driven by STDP and HSP. Our numerical analysis revealed that the degree of CR strongly depends on several parameters, including the adjusting rate parameter P controlling STDP, the characteristic rewiring frequency parameter F controlling HSP, and the network topology parameters. We identified two robust behaviors in our study. Firstly, decreasing the P and F parameters led to higher degrees of CR in small-world and random networks provided that the synaptic time delay parameter τc has appropriate values. This effect was due to the weakening of synaptic weights and the slowing down of synapse swapping rates between neurons. Secondly, increasing the synaptic time delay τc induced multiple CR (MCR) in small-world and random networks. MCR manifests as multiple peaks in the degree of coherence as τc changes. This effect was more pronounced at smaller values of P and F . The findings of this project suggest that precise timing of noise-induced firing via CR, SS, and SISR in neural networks can be improved through optimal tuning of background noise, STDP rule, and network topology. Additionally, the combination of STDP and HSP can further enhance the time precision of noise-induced firing via CR, which is critical for efficient information processing and transfer in neural systems. These results offer insights into effective coding mechanisms and may have practical implications for designing ad hoc artificial neural circuits that utilize CR, SISR, and/or SS to optimize information processing and transfer. In addition to the abovementioned results, the project achieved three additional objectives that were not planned initially, leading to three other results in single neurons and non-adaptive neural networks. First, it was shown that the asymptotic matching of the e deterministic and stochastic escape timescales of trajectories perturbed by an α-stable L´vy process can induce a very strong SISR in a e memristive neuron. Moreover, it was shown that the degree of SISR induced by L´vy noise is not always higher than that of Gaussian e noise, depending on the L´vy noise parameters. Second, it was found that a poor degree of SISR in a non-adaptive three-neuron motif can be significantly improved by attaching an electrical or an excitatory chemical autapse to only one of the neurons. Lastly, it is demonstrated that, in contrast to previous literature that suggests network heterogeneity (diversity) can always be optimized to enhance CR and resonance effect in synchronization, the impact of diversity on SISR can only be antagonistic. This indicates that diversity’s ability to enhance or deteriorate a noise-induced resonance phenomenon depends on the underlying mechanism.
Publications
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Control of noise-induced coherent oscillations in three-neuron motifs. Cognitive Neurodynamics, 16(4), 941-960.
Bönsel, Florian; Krauss, Patrick; Metzner, Claus & Yamakou, Marius E.
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Lévy noise-induced self-induced stochastic resonance in a memristive neuron. Nonlinear Dynamics, 107(3), 2847-2865.
Yamakou, Marius E. & Tran, Tat Dat
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Diversity-induced decoherence. Physical Review E, 106(3).
Yamakou, Marius E.; Heinsalu, Els; Patriarca, Marco & Scialla, Stefano
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Optimal Resonances in Multiplex Neural Networks Driven by an STDP Learning Rule. Frontiers in Physics, 10.
Yamakou, Marius E.; Tran, Tat Dat & Jost, Jürgen
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Coherence resonance and stochastic synchronization in a small-world neural network: an interplay in the presence of spike-timing-dependent plasticity. Nonlinear Dynamics, 111(8), 7789-7805.
Yamakou, Marius E. & Inack, Estelle M.
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Combined effects of spike-timing-dependent plasticity and homeostatic structural plasticity on coherence resonance. Physical Review E, 107(4).
Yamakou, Marius E. & Kuehn, Christian
