Berlin 2024 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 20: Statistical Physics of Biological Systems I (joint session DY/BP)
DY 20.7: Vortrag
Dienstag, 19. März 2024, 11:30–11:45, BH-N 334
Furutsu-Novikov theorem for shot-noise driven systems — •Jakob Stubenrauch1,2 and Benjamin Lindner1,2 — 1Physics Department of Humboldt University Berlin, Newtonstraße 15, 12489 Berlin, Germany — 2Bernstein Center for Computational Neuroscience Berlin, Philippstraße 13, Haus 2, 10115 Berlin, Germany
We consider an arbitrary system (later exemplified by a spiking neuron) that is driven by an intensity-modulated Poisson process with intensity λ(t)=λ0+ε s(t). We derive an exact relation between the input-output cross-correlation in the spontaneous state (ε=0) and the response function for a weak time-dependent modulation of the input intensity (ε>0). This can be regarded as a variant of the famous Furutsu-Novikov theorem (FNT) for the case of shot noise. Neurons in networks fluctuate spontaneously and respond if stimulated. Spontaneous fluctuations and response properties are linked, in correspondence to the fluctuation-dissipation theorem, as has recently been shown (Lindner, 2022). Such relations constrain the signal-to-noise ratio, they can be used to fit models, and to advance theories. However, for the biologically relevant case of shot-noise driven neurons, such relations have not been reported yet. As we demonstrate, we can use the new FNT to obtain a fluctuation-response-relation between the spontaneous fluctuations of a neuron’s output and its systematic response to a time-dependent stimulus, extending the approach of (Lindner, 2022) from Gaussian noise to shot noise. The relations are numerically tested and their limitation to Poissonian input exemplified for the important example of a leaky integrate-and-fire neuron with alpha synapses.
Keywords: Stochastic processes; Linear response theory; Spiking neurons; Statistical physics of neural networks