# Biological Basis of the PoissonBinauralVM.mod Code The provided code is designed to simulate a **binaural inhomogeneous Poisson process** within the realm of computational neuroscience. This simulation is specifically applied to understand how auditory stimuli are processed in a bilaterally symmetrical way, mimicking the function of a biological auditory system. Here are the key biological elements and their relevance: ## Binaural Hearing - **Binaural Processing**: The code simulates auditory processing by considering stimuli from both ears (binaural hearing), which is crucial for sound localization—determining the direction of a sound source. Binaural processing allows for differences in timing (phase) and amplitude (intensity) of sound signals coming from each ear to be integrated by the brain, leading to spatial hearing capabilities. - **Von Mises Distributions**: The model uses von Mises probability distributions for each ear (ipsilateral and contralateral). These distributions are analogous to Gaussian distributions on a circular domain and are often used to model inhomogeneities in periodic data such as phase information in auditory signals. ## Neural Representations - **Phase Information**: The code includes parameters `stimPhaseIpsi` and `stimPhaseContra`, which represent the phase of the stimulus for the ipsilateral (same side) and contralateral (opposite side) ears, respectively. This phase information is critical for understanding interaural time differences (ITDs) that the auditory system uses to localize sound. - **Firing Rates**: The parameter `stimRate` and the resulting variable `stimProb` reflect the rate of neural firing in response to the auditory stimuli. This is indicative of the action potential generation in real neural circuits that can vary depending on stimulus properties. ## Biological Noise Modeling - **Poisson Process**: The choice of a Poisson process mimics the probabilistic nature of neuronal firing. Neurons are known to emit action potentials (spikes) in a stochastic manner, especially in response to certain types of continuous stimuli like sound. ## Bessel Functions and Von Mises Approximation - **Circular Data**: The approximation of Bessel functions and the calculation of `kappa` are used to adjust the degree of concentration or "peakedness" of the von Mises distribution. This allows the simulation to represent how tightly or loosely neuron firing corresponds to the phase angles of auditory stimuli, akin to how biological neurons might tune to specific frequencies and phases. ## Procedural Elements - **Initialization and Clocking**: The `prerun` procedure and `NET_RECEIVE` block are used to manage the timing and probabilistic initiation of the auditory stimulus response, analogous to how biological neurons might reset or adjust their firing rates in preparation for processing incoming stimuli. In summary, this code encapsulates a computational model designed to replicate the ability of the auditory system to detect and process binaural auditory stimuli by leveraging probabilistic firing processes. By using von Mises distributions and Poisson processes, it effectively captures critical aspects of how the auditory brainstem might engage with incoming sounds at a neural population level for sound localization and spatial auditory perception.