Maximal limits, waveform amplitude, and responses in individual neurons.
With dynamics similar to those described for activities across spatially-selective neurons, a maximal limit or threshold on weights ascribed to waveform amplitude, or changes in waveform amplitude, may govern when responses are evoked in individual, spatially-selective, neurons. When combined with values attributed to the opposite ear and other signal features, these weights may be viewed as proportional to the probability spiking in individual, spatially-selective, neurons.
Envelope amplitude weights contributing to the firing of individual spatially-selective neurons. The demonstration below is for a pair of 150 ms ‘lead/lag’ noise-bursts, passed through a 500 Hz auditory filter, when the ‘leading’ signal is spatialized to the right with an ITD of 0.25 ms and the ‘lagging’ signal is spatialized, after a 2.5 ms delay, to the left with an ITD of -0.25 ms.
The weights are generally strong (a) at the ‘leading’ signal’s onset when ITD favors the this signal’s ITD (0.25 ms) and (b) when amplitude is high in both signals and ITD favors neither signal (ITD ≈ 0). In contrast, weights are generally weak (a) after the ‘leading’ signal’s offset when ITD favors the ‘lagging’ signal’s ITD (-0.25 ms) or (b) when amplitude is low and ITD is fluctuating.
To understand how weights are computed, consider the amplitude modulated waveform (gray lines) and its amplitude envelope (dark circles) shown below in panel A. Principal outputs are envelope weights (panel B) ascribed incrementally to envelope amplitude values (At) using the logistic function shown in panel C.
When combined with parallel weights attributed to the opposite ear and other signal features, envelope weights (panel B) may be viewed as proportional to the probability spiking in individual spatially-selective neurons.
Changes in the logistic function (panel C) partly reflect new envelope amplitude values incrementally incorporated into variables summarizing all prior envelope amplitude values (average ≈ µ, standard deviation ≈ 𝜎 ; panel E).
More importantly, changes in the logistic function also reflect statistical weights (wtµ,𝜎, panel D) derived by accruing proportional increments of envelope weight in excess an upper weight limit.
- • Note that this incremental approach is akin to an iterative accrual of envelope weights, where each weight in excess of an upper weight limit is followed by a proportional decrement or decay of all prior weights.
Envelope weights and other measures derived from envelope amplitude values when the upper weight limit = 5
Envelope weights and other measures derived from envelope amplitude values when the upper weight limit = 2
Envelope weights and other measures derived from envelope amplitude values when the upper weight limit = 10
Notes:
- • ‘Lead/lag’ noise-pairs are typically associated with the ‘precedence effect.’ I hesitate to mention this, even in these notes, because the term carries an enormous amount of academic baggage. Another example of ‘persuasive writing’ leading to presumptuous dogma…
Igor Pro experiment file used to generate figures:
This experiment require the SpatialHearing XOP:
