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Nt (e.g., photoreceptor noise and retinal ganglion cell channel noise, respectively), then the two kinds of noise will likely be uncorrelated in a feedforward circuit like we model here. Lateral input from other channels, which we usually do not look at, could potentially introduce dependence in between upstream and downstream noise. Feedback connections operating on timescales within a single-integration window could also potentially introduce correlations between additive upstream and downstream noises. Nonetheless, even though such connections may be crucial in cortical circuits, they are not substantial in the sensory circuits that inspired this model, so we assume independent upstream and downstream noise in this function. For additional biological interpretation of your model, see Discussion. We begin by studying a model of a single pathway. We then take into account how two pathways operating in parallel ought to divide the stimulus space to most effectively code inputs. These models are constructed of two parallel pathways of your single pathway motif PubMed ID:http://www.ncbi.nlm.nih.gov/pubmed/20190722 (Fig 1C), with the addition that noise might be correlated Dabigatran (ethyl ester hydrochloride) biological activity across both pathways. The study of two parallel channels is motivated by the fact that a specific location of visual space is commonly encoded by paired ON and OFF channels with otherwise comparable functional properties, but similar parallel processing occurs all through early sensory systems and in some cortical areas [29, 31, 32]. We will return to further discussion of parallel pathways within the second half of the Outcomes.Optimal coding tactics for single pathwaysWe commence using the case of a single pathway. For simplicity, we commence with circumstances in which among the 3 noise sources dominates over the other individuals. Considering circumstances in which a single noise source dominates isolates the distinct effects of every noise source around the optimal nonlinearity. We then show that these same effects govern how the 3 noise sources compete in setting the optimal nonlinearity when they are all of comparable magnitude. Upstream noise decreases slope of optimal nonlinearity to encode broader selection of inputs. In Fig two, we plot the optimal nonlinearities for circumstances in which among the list of noise sources dominates the others. For every noise supply, we show final results for smaller, intermediate, and big values of the signal-to-noise ratio (SNR) of model responses. Importantly, the SNR is matched inside columns of Fig two, permitting to get a direct comparison with the effects of distinctive noise sources. We present each analytical outcomes (dashed lines) for optimal nonlinearities constrained only by the assumption of fixed dynamic range, and outcomes utilizing parametrized nonlinearities of a sigmoidal type (solid lines). We show only optimal “ON” nonlinearities (nonlinearities that improve response strength as stimulus strength increases) in this sectionPLOS Computational Biology | DOI:ten.1371/journal.pcbi.1005150 October 14,5 /How Efficient Coding Is determined by Origins of NoiseFig 2. Optimal nonlinearities when 1 noise source dominates, identified by minimizing the mean squared error (MSE) of a linear estimator. Every single row shows 3 separate instances in which a single source of noise dominates. The dominant noise supply is indicated by the highlighted source in the circuit schematics left of each and every row. The all round degree of noise is quantified by the signal-to-noise ratio (SNR), that is fixed in each column. The SNR is largest within the leftmost column and smallest inside the rightmost column; i.e., the strength of the noise inc.