S1 Text - Dendritic Pooling of Noisy Threshold Processes Can Explain Many Properties of a Collision-Sensitive Visual Neuron

Pooling of Noisy Threshold Units—Mathematical Considerations In this section, a closed expression for Eq (14) is derived, which is used for fitting the n-ψ-model to neuronal recordings in Section D in S1 Text. Noise in the Excitatory Pathway In this section the impact of excitatory noise on the predictions of n-ψ is studied, where the same threshold smoothing mechanism is used for the excitatory and the inhibitory synaptic input. This is to say that threshold smoothing is applied simultaneously to the excitatory and inhibitory pathway. It turns out that the predictions of n-ψ are reasonably robust with this configuration. Integration time constant dt and nrelax In this section, the influence of the number of relaxation time steps nrelax and that of the integration time constant dt is studied. Specifically, corresponding values of nrelax and dt are determined such that n-ψ operates close to the equilibrium solution Eq (10). The exact values are important as they were shown to influence the location of the LGMD’s predicted response peak [19]. Fitting the n-ψ and the η-Function to Neuronal Recordings The n-ψ-model is fit to several recording curves from different studies. The fits are juxtaposed with those of the η-function. Goodness of fit measures are provided as well, and some fitting results of the predecessor model Ψ are also shown. This section presents the results of previously published studies in the same fitting framework. A common fitting framework enables a meaningful comparison of the respective predictions of the η-function and the n-ψ-model. List of Symbols A list with mathematical symbols along with corresponding brief descriptions are provided in this section. Pooling of Noisy Threshold Units—Mathematical Considerations In this section, a closed expression for Eq (14) is derived, which is used for fitting the n-ψ-model to neuronal recordings in Section D in S1 Text. Noise in the Excitatory Pathway In this section the impact of excitatory noise on the predictions of n-ψ is studied, where the same threshold smoothing mechanism is used for the excitatory and the inhibitory synaptic input. This is to say that threshold smoothing is applied simultaneously to the excitatory and inhibitory pathway. It turns out that the predictions of n-ψ are reasonably robust with this configuration. Integration time constant dt and nrelax In this section, the influence of the number of relaxation time steps nrelax and that of the integration time constant dt is studied. Specifically, corresponding values of nrelax and dt are determined such that n-ψ operates close to the equilibrium solution Eq (10). The exact values are important as they were shown to influence the location of the LGMD’s predicted response peak [19]. Fitting the n-ψ and the η-Function to Neuronal Recordings The n-ψ-model is fit to several recording curves from different studies. The fits are juxtaposed with those of the η-function. Goodness of fit measures are provided as well, and some fitting results of the predecessor model Ψ are also shown. This section presents the results of previously published studies in the same fitting framework. A common fitting framework enables a meaningful comparison of the respective predictions of the η-function and the n-ψ-model. List of Symbols A list with mathematical symbols along with corresponding brief descriptions are provided in this section. (PDF)