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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2405.13508 |
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| _version_ | 1866910623417237504 |
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| author | Stubenrauch, Jakob Lindner, Benjamin |
| author_facet | Stubenrauch, Jakob Lindner, Benjamin |
| contents | We consider a dynamic system that is driven by an intensity-modulated Poisson process with intensity $Λ(t)=λ(t)+\varepsilonν(t)$. We derive an exact relation between the input-output cross-correlation in the spontaneous state ($\varepsilon=0$) and the linear response to the modulation ($\varepsilon>0$). If $\varepsilon$ is sufficiently small, linear response theory captures the full response. The relation can be regarded as a variant of the Furutsu-Novikov theorem for the case of shot noise. As we show, the relation is still valid in the presence of additional independent noise. Furthermore, we derive an extension to Cox-process input, which provides an instance of colored shot noise. We discuss applications to particle detection and to neuroscience. Using the new relation, we obtain a fluctuation-response-relation for a leaky integrate-and-fire neuron. We also show how the new relation can be used in a remote control problem in a recurrent neural network. The relations are numerically tested for both stationary and non-stationary dynamics. Lastly, extensions to marked Poisson processes and to higher-order statistics are presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_13508 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Furutsu-Novikov--like cross-correlation--response relations for systems driven by shot noise Stubenrauch, Jakob Lindner, Benjamin Disordered Systems and Neural Networks Biological Physics We consider a dynamic system that is driven by an intensity-modulated Poisson process with intensity $Λ(t)=λ(t)+\varepsilonν(t)$. We derive an exact relation between the input-output cross-correlation in the spontaneous state ($\varepsilon=0$) and the linear response to the modulation ($\varepsilon>0$). If $\varepsilon$ is sufficiently small, linear response theory captures the full response. The relation can be regarded as a variant of the Furutsu-Novikov theorem for the case of shot noise. As we show, the relation is still valid in the presence of additional independent noise. Furthermore, we derive an extension to Cox-process input, which provides an instance of colored shot noise. We discuss applications to particle detection and to neuroscience. Using the new relation, we obtain a fluctuation-response-relation for a leaky integrate-and-fire neuron. We also show how the new relation can be used in a remote control problem in a recurrent neural network. The relations are numerically tested for both stationary and non-stationary dynamics. Lastly, extensions to marked Poisson processes and to higher-order statistics are presented. |
| title | Furutsu-Novikov--like cross-correlation--response relations for systems driven by shot noise |
| topic | Disordered Systems and Neural Networks Biological Physics |
| url | https://arxiv.org/abs/2405.13508 |