Fig 1.
Input targets (left) are processed in two stages: a unit-clipped sensory trace (center, clipping threshold represented by solid black line) followed by a threshold limited allocation of attentional resources (right, blinking threshold represented by dashed red line). Top: When input targets appear in close temporal succession (here, lag 3) the output of the attentional system is more likely to cross the blinking threshold (dashed red line) resulting in reduced detection of T2 (the attentional blink). Middle: When the temporal interval between targets is longer (here, lag 7), the overlap between their attentional loads is reduced, with a lower chance of crossing the blinking threshold. Bottom: When the two targets are even further apart (lag 15), each one creates a separate peak in the attentional load and the probability of triggering an attentional blink is negligible.
Table 1.
Model parameters.
Fig 2.
The attentional blink effect, model and typical data.
T2 detection probability for different T1-T2 lags. Typical empirical data, replotted from [4] (yellow). Model simulated detection probability averaged over N = 1, 000 repetitions (blue). An analytical calculation of the probability, using double exponential distribution was used to approximate the distribution of the maximal attentional load (red).
Fig 3.
When T2 appears immediately after T1 (lag-1, top), their overlap in the first processing stage is maximal, resulting in a stronger reduction of the sensory trace due to the clipping threshold (solid black line). This causes a decrease in the attentional load at the second processing stage (bottom axis) with a corresponding reduction in blinking probability. At lag-2 (bottom), the overlap in the first stage is smaller, resulting in less clipping of the sensory trace and a higher attentional load.
Fig 4.
Model behavior in mental noise parameter space.
(A) T2 detection probability for a T2-T1 lag of 4. (B) The model P3b amplitude defined in Eq 6, for a T2-T1 lag of 4. (C) lag-1 sparing probability as a function of mental noise activity parameters (mean and variance). The color indicates the probability of crossing the blinking threshold at lag 2 but not at lags 1 and 5. Blue and red crosses indicate (μ, σ) values at time 1 and 2 respectively, for which the model reproduces lag-1 sparing as well as the main findings of Slagter et al. [2], namely an increase of in T2 detection accuracy from 0.6±0.1 at time 1 to 0.8 or higher at time 2, and a reduction in T1-evoked P3b amplitudes by a factor of of 1.25–2. The green arrow connects the pair of mental noise parameter values at time 1 and 2 corresponding to the effects of mental training shown in Fig 5 below.
Fig 5.
Simulated and empirical effects of mental training on T1-evoked P3b amplitudes.
Left: T1-evoked P3b amplitude as a function of T2 detection (blink or no-blink), session (time 1 or time 2), and group (practitioners or novices). Meditation practitioners show a greater reduction in T1-evoked P3b amplitude compared to novices in no-blink vs blink trials at time 2 vs time 1. Right: Selective reduction in T1-evoked P3b amplitude in no-blink trials in the practitioner group. Mental noise mean and standard deviation levels (μ, σ), for practitioners: (17.5, 3.15) at time 1 and (14.5, 3.8) at time 2. For novices: (17, 3) at both times. Colors follow figure 3 in Slagter et al. [2], whose data is replotted here.
Fig 6.
Mental training induced modulation of attentional load reduces blink probability.
The attentional load profiles before and after meditation (right, blue and red traces respectively). The effects of meditation are modelled as a reduction in mental noise mean from 17.5 to 14.5 and an increase in mental noise standard deviation from 3.15 to 3.8.