Architecture of the Model
In accordance with previous theoretical proposals 
here we propose that seriality in dual (or multiple) task performance results as a consequence of inhibition within the control networks needed for precise “routing” of information flow across a vast, virtually infinite, number of possible task configurations. To examine this hypothesis, we will explore dual-task performance in a recurrent network of spiking neurons capable of performing flexible routing of information according to specific task instructions. Contrary to previous computational work addressing flexible mapping 
, our objective is not to study flexible behavior per se
but to understand the conditions under which a computational model capable of flexible sensory-motor mapping shows patterns of interference when two tasks have to be performed simultaneously or in close succession 
Following classic experimental procedures of the PRP 
, the interference experiments we address here involve different sensory modalities, to avoid sources of interference in early sensory processing (with the exception of the last section, where we investigate the effects of masking). The model that we simulate is described in detail in the Materials and Methods
section and in . It includes two sensory modalities organized in a hierarchy in which each successive layer receives inputs from neurons of the previous layer thus generating progressively complex receptive fields. Within each hierarchical level, for simplicity we explore in detail only two distinct neural populations for each sensory modality, which correspond to the neural coding of the two task-relevant dimensions (red and orange populations in representing, for example, a high and low pitch sound, respectively). Other task-irrelevant stimuli were encoded by a large pool of non task-selective excitatory neurons (pink populations in ), as done in many other spiking networks modeling decision-making 
Each element in this sensory hierarchy is a canonical cortical circuit comprising excitatory pyramidal cells and local inhibitory cells, previously shown to be capable of performing elementary functions of working memory and decision making 
. Only excitatory pyramidal cells project with long-range connections to neurons higher and lower in the sensory hierarchy, while inhibitory neurons only project locally. Feedforward and feedback connections in the model differ both in the properties of the receptors that mediate the transmission as well as in their specificity 
. Feedforward connections are highly specific: Each neuron projects to a single homogeneous population in the next higher level. For simplicity, they are assumed to be all mediated by fast AMPA receptors, although in reality a small fraction of NMDA receptors would be expected. In the reciprocal direction, feedback connections are more broadly connected: each neuron sends non-specific feedback connections to all excitatory cells in the previous level 
. Again, for simplicity we assume that feedback transmission is mediated by slow NMDA receptors. Since the contribution of NMDA receptors to synaptic transmission varies with the level of postsynaptic depolarization, this ordering of glutamate receptors between the feedforward and feedback streams broadly assigns a driving role to the feedforward input and a modulatory one to the feedback, as in previous models 
Both sensory modalities project to a router which connects the sensory representations to a set of possible responses. Neurons in the router integrate sensory evidence and trigger a response when their activity reaches a threshold 
An explicit instruction - presented before the stimulus – sets the task for a given trial, i.e. specifies the specific mapping which indicates which response has to be executed when the stimulus is presented. The network that stores task instructions is referred throughout this work as the task-setting network. Excitatory populations in this network are activated by the presence of task-relevant stimuli in sensory areas and, through their patterns of projection to “router” neurons (see below), encode different stimulus-response mappings. As with the sensory modalities, we only simulate two task-setting populations which are sufficient for the experiments considered here.
An important aspect of our model is a circuit which we refer as the “router”. As in previous models of flexible decision making that do not rely on synaptic plasticity to dynamically adjust their behavior 
, task-setting neurons affect the decision process by gating a specific subset of “router” neurons, which implement the possible mappings between stimuli and responses. Here we assume a reduced ensemble of stimuli and responses and simply model as many selective populations in the router as there are combinations of stimuli and responses 
. Simulating a completely flexible network capable of mapping arbitrarily large stimulus and response sets, would require a high degree of overlap in the cortical representation implemented by task-setting and routing neurons. We will come back to this possibility and its possible implications for serial processing in the discussion.
As with all other neurons in the network, task-setting neurons are entailed with self excitation and lateral inhibition. Excitatory neurons in the task-setting network are connected to the router through NMDA connections. When an excitatory population of the task-setting network is in an “active” state it excites the subset of neurons in the router receiving inputs from task relevant sensory populations and connecting them to the appropriate motor populations. A neuron in the router which receives excitation from task-setting neurons is set in a mode of integration in which it can accumulate sensory information (Text S1,A
). This architecture also serves as a selection mechanism, assuring that task-irrelevant stimuli that are represented in sensory cortex do not elicit any output ().
Single-trial dynamics for task relevant and irrelevant stimuli.
Response execution is triggered in response selection networks (motor 1 and 2 in ) by a set of bursting neurons that signal a threshold-crossing of the input received from the integrating neurons, modeled as in previous work by Wang and collaborators 
To ensure that the network did not enter in a response perseveration mode (Figure S1
), we implemented an inhibition of return mechanism 
typical of a control network. After response execution, response neurons feed back to inhibit the sensory, routing and task-setting neurons involved in the task (similar to the “termination” signals in Dehaene and Changeux, 1997 
and recently observed in single-cell recordings in awake behaving monkeys performing a sequential task 
This architecture ensured that the network did not respond spontaneously, to irrelevant stimuli or to mappings different than those set by the explicit task-instruction and that it did not show perseveration of responses to task-relevant stimuli. We emphasize that here we have not investigated how a large repertoire of tasks can be encoded with a finite number of neurons. Rather, we ensure that the network has stable performance for a small number of tasks and then explore the operation of this network during dual-task performance.
Our simulations of dual task experiments showed that when both tasks were close together in time, response order could be reversed on a fraction of trials so that the first response was given to the stimulus that was presented second (Figure S2
). This coincides with experimental observation in task-interference experiments when the response order is not fixed 
. Here we wanted to explore a comparatively simpler situation, typically studied in psychophysical experiments, in which participants are explicitly told to respond to two tasks in a specific order, as fast as possible. This required the implementation of a task-setting network 
that determined the order of the tasks. The task-setting network was bistable. It was composed of two excitatory populations that projected to the inhibitory population of the other task. Three hundred milliseconds before the presentation of the first stimulus, excitatory neurons in the order-setting network are activated by a brief (100 ms) external input. Due to the strong self-recurrent connections, the network maintains high levels of activity after removal of the external input and tonically inhibits T2 neurons in the task-setting network. When the response to T1 is emitted, inhibition from the router resets the order-network permitting the activation of T2 task setting-neurons (Text S1,B
In summary, we generated a network based on a large-scale implementation of simple canonical neuronal circuits endowed with self-recurrence and lateral inhibition. The network has a hierarchical sensory organization which ultimately feeds stochastic evidence to “router” neurons which (if activated by a specific task-setting context) both accumulate evidence towards a motor decision and route sensory input to the relevant motor neurons.
Time Course of Neural Activations during Single-Task Performance
Each stimulus has four features. The four populations encoding low-level features of a stimulus receive a brief pulse of constant current during stimulus presentation (100 ms). This initial impulse generates a transient response in the earliest input neurons (), which increase their firing rate from the default level of around 2 Hz to around 40 Hz. This transient response initiates a wave of activation that propagates through the network 
. Each layer works as an integrator of the previous layer and thus the neural response becomes increasingly expanded in time as one progress in the hierarchy. At the highest level, recurrent connections are strong enough to assure a very low decay rate of stimulus information, resulting in an effective form of working memory as observed in several areas of occipito-temporal and frontal cortex 
The last stage in the sensory hierarchy projects to the router using AMPA receptors. Neurons in the router also receive currents from task-setting neurons, but these projections use NMDA receptors. These NMDA currents control the recurrence in the router, and they determine the degree of integration of AMPA currents. As a result of this architecture, neurons in the router act as detectors of the conjunction of stimulus presence and task relevance as observed in 
. A neuron which receives task-setting currents integrates the sensory input rapidly (), while a neuron that does not integrates the input only partially (). Thus, task-setting neurons accomplish their role by assuring that the wave in the sensory system initiated by an irrelevant stimulus does not trigger a response. The integration process continues until a threshold is crossed, which is signaled by a nonlinear response: a powerful burst of spikes in the motor network (). The activation of these response neurons, in turn, initiates a cascade of feed-back inhibition that resets activation in task-related neurons 
Time Course of Neural Activations during Dual-Task Performance
The principal aim of this paper is to explore the operation of the model in a classic dual-task paradigm: the psychologically refractory period (PRP), widely studied in the psychophysical literature. We explored the response of the model with two different stimuli, presented simultaneously or at a short stimulus onset asynchrony (SOA). When the separation between stimuli (SOA) is much longer than the response time to the first task (RT1), the neural activations associated with the first and second task do not interfere with each other and the observed dynamics is similar to that observed during single-task performance ().
The most interesting situation is for SOA values close to or shorter than RT1 (, SOA
100ms) in which case the two waves of activation evoked by each stimulus partially interfere. In the model, this interference does not occur at the sensory level: even at short SOA, while a first target T1 is being processed, sensory neurons associated with the second target T2 still initiate a wave of activations which is very similar to that in the single-task condition. However, due to competition between task-setting neurons, the routing neurons of T2 are not gated and hence do not integrate sensory information while T1 is being processed. In this instance there is a very interesting dissociation: local-recurrence in the sensory hierarchy is sufficient to maintain T2 stimulus information, but this information is not piped to the motor response and awaits liberation of the router. This constitutes a key aspect of this network – during a temporary waiting period, T2 has to be maintained in a “local memory” which does not propagate throughout the network. After the response to the first task has been executed, the T1 pathway is reset and Task 2 setting neurons activate, gating the router neurons of T2 and allowing them to begin to integrate information about the second incoming stimulus. Thus, the shift in the locus of “task-related attention” (which information is amplified in sensory areas and routed to response networks) is the natural consequence of the progression of the task in the router and task-setting network.
Neural activations during dual-task performance.
Note that the second key aspect of our network is that routing neurons of T1 and T2 cannot be simultaneously activated. In our network this is controlled through a competition between task setting neurons, but a similar result would be obtained if this competition would be implemented by lateral inhibition between routing neurons. This would occur, for example, if the number of possible mappings largely exceeds the number of neurons in the router so that routing can only occur by a distributed assembly of active cells. We will come back to this possibility in the discussion.
In the interference regime, the network includes groups of neurons with very different response properties (); the existence of these different types of neuronal firing patterns constitutes a key prediction of our simulations. Early sensory neurons show a response which is essentially unaffected by interference, reflecting fully parallel behavior. In contrast, the motor and task-setting neurons are strictly serial, only showing strong activation after task 1 has been completed. The behavior of the router neurons is intermediate; they are mostly serial, but can undergo moderate integration (insufficient to boost a response) before completion of T1. Interestingly, late sensory neurons act as a buffer. They have an onset which is locked to the stimulus and are active until the response, so that they hold a memory of T2 which is retrieved when the router becomes available. This population of neurons is therefore engaged in different components of the task; first, a transient response which results in stimulus encoding, and second, a later memory trace which is eventually broadcasted to the motor neurons involved in the second task.
All the previous analysis relied on spiking activity. Recently, much effort has been devoted to understand the relevance of complementary measures of brain function such as synaptic currents, local field potentials, and induced oscillations. Our neuronal network has the potential to study these measures.
We first explored whether input currents in the router could be more informative than spiking activity of T2 processing stages. We measured input currents to the router at different processing stages of T2: Spontaneous activity, S2 queuing (memory phase), and S2 routing. During queuing, currents in the router reflected a steady level of activity which was significantly larger than during spontaneous activity (Figure S3
). Thus, during this regime, subthreshold activity in the router is tightly coupled to spiking activity of late sensory neurons. During the routing stage, synaptic current activity ramps, coupling to the progression of spiking activity in the router. An interesting observation was that this pattern was virtually identical for all receptor currents (NMDA, AMPA and GABA). Although the input from the task-setting network is carried by NMDA-receptors, the local amplification in the router circuit also engages AMPA currents and the NMDA specificity is lost very rapidly (Figure S3
The task-switching circuit was endowed with high efficiency inhibition to achieve rapid switching from one task-setting program to another. This endowed the task-setting circuit with high frequency oscillations as can be seen in the raster plots of . Since the task-setting circuit drives the router, we asked how these oscillations propagate into the network and whether measures of oscillatory activity could be more informative than simply spiking activity to identify distinct processing stages from neuronal responses. We analyzed the spectrogram of sensory, routing and task setting T2 neurons throughout the trial (Figure S4
). Responses were locked to RT1. Both router and task setting neurons showed clear event-related spectrograms, as seen for firing rates. The spectral content of the responses of both populations are quite distinct: task-setting circuit activity occurs in high-frequency bands (peaking around 70 Hz) while router neurons, which act as slow integrators, display low-frequency responses (~20 Hz). Router neurons do not inherit high frequency oscillations of the driving task-setting neurons because these connections are mostly mediated through NMDA receptors which have a slow time constant.
Rhythmic activity in the sensory neurons showed distinct oscillatory activity during buffering and routing (Figure S4
, left panel). During routing, responses of sensory neurons showed high power in the 40–60 Hz range while during routing they were more broad band and showed an increase in lower-frequency activity. Firing rates of sensory neurons during buffering and routing were not different (). Spike density coherence between sensory and router neurons also showed distinct profiles during distinct phases of task processing: phase coherence was not-significant during spontaneous activity, it showed significant coupling for low frequencies during routing and broad-band coherence during T2 queuing (Figure S5
Response Times in Dual-Task Performance
An appealing aspect of the PRP paradigm () is that it is associated with a large number of chronometric observations. We explored whether the network shows a behavior in accordance with these observations including the dependence of mean RT (and RT distributions) with SOA and the differential effects of pre and post-bottleneck manipulations.
Mean response times: fingerprints of dual-task interference.
Specifically, the main experimental characteristics of the PRP phenomenon are 
- RT2 shows a linear decrease with slope of −1 for short SOA and a slope of 0 for large SOA
- RT1 is typically unaffected by SOA
- Pre-bottleneck manipulations (experimental factors that affect sensory processing) additively affect both RT1 and RT2 inside the interference range when the first task is being manipulated. When the second task is manipulated, under-additive effects are seen at short SOA, due to the absorption of pre-bottleneck components while T2 is being queued by T1 processing
- Bottleneck manipulations (experimental factors that affect the difficulty of the S-R mapping) additively affect the task that is being manipulated
- RT distributions are long-tailed (Wald-type distributions)
- RT2 tightly covaries with RT1, but only for short SOA (i.e. in the interference regime)
- RT2 variance increases as SOA decreases, since it accumulates the variability of both RT1 and RT2 in the interference regime
We first explored the main effects of the PRP (without specific task manipulations) by simulating an experiment in which two stimuli were presented at an SOA which varied between 0 and 800 ms, sampled at [0, 50, 100, 150, 200, 250, 300, 400, 500, 600, 700, 800] ms (). Response times were defined as the time interval between the onset of the stimulus signaling each task and the peak of the motor burst. The network virtually made no mistakes (error rates were less than 0.1% for both tasks), which was expected given that the two different stimuli have non-overlapping representations in each sensory modality. We observed that the network behavior captured all the predictions listed above ( and ). RT1 was unaffected by SOA (). Although, the presentation of the second stimulus provides input to the task-setting neurons of T2, this network is configured in a winner-take-all mode and the top-down control of T1 over the router neurons is virtually unaffected by the incoming stimuli. Thus, S2 was never strong enough to overwrite T1 in the task setting network as long as this task was ongoing.
Response time distributions in dual-task execution.
Second, we observed the classic RT2 profile with varying SOA values: An initial decrease with a slope of −1 (). This indicates that T2 completion is strictly serial even though some aspects of T2 processing are carried out in parallel with T1 (). As SOA increased and reached the average value of RT1, the two tasks became increasingly independent. The stochasticity of the system (see below for an analysis of RT distributions) assured that this elbow –i.e. the regime in which RT2 becomes independent of SOA was not sharp and thus RT2 showed a curved decay which reached a horizontal asymptote after about 300 ms, as observed in human psychophysics ().
Based on typical experimental procedures, we then explored the effect of different manipulations on the first and second task on mean response times, and their interaction with SOA ().
First we investigated the effect of changing the complexity of sensory processing. In a number comparison task, changing the notation (for instance replacing the digit 3 by the word three
) results in an increase in response time which is absorbed during the PRP (i.e., more elaborate sensory processing of S2 can occur while central processing for T2 is blocked by the processing of task 1, therefore not increasing RT2 at short SOA) 
. A simple model of word recognition predicts that complex combinations of characters are encoded in successive layers of a feed-forward scheme 
. To model this experimental factor in our network, we simply added an additional processing level in the sensory hierarchy. We first applied this manipulation to task 1, and observed an additive effect on RT1, which did not depend on the SOA (). This effect propagated to RT2 in the interference regime. This shows that the network functions strictly in a first-come first-served basis. Manipulating the second task affected RT2 for long SOA values, but had no effect at short SOA (), indicating that the additional sensory processing can be carried out in parallel with T1 processing. This absorption of pre-bottleneck manipulations constitutes one of the critical predictions of theoretical models of the PRP (Text S1,C
We then explored another important manipulation which affects the complexity of the sensory-motor mapping, i.e. the amount of sensory evidence in favor of the correct decision. In experiments in which a decision is taken on an analog variable (movement, intensity, numerosity, size etc…) the two competing stimuli can be made arbitrarily close, rendering the decision progressively more difficult. This results in increased errors and RTs, and attractor dynamic networks have been very successful in modeling these phenomena 
. This distance
manipulation in a PRP setup results in a bottleneck manipulation which is not absorbed in the PRP. Here, as conventionally done, we modulated the amount of evidence by changing the relative input currents of each of the two competing sensory populations (). We applied this manipulation to the first task, and observed an increase in RT1 unaffected by SOA (). This effect propagated to RT2 in the interference regime. When the manipulation was applied to the task performed second (), the first task was unaffected but the second task showed an additive effect not absorbed at short SOA values. This effect is what would be expected from bottleneck manipulations. The statistical significance of these observations was evaluated with a series of ANOVAs using the R software package (http://www.r-project.org/
) (Table S1
The response times histogram for SOA
0 ms is displayed in . The results of the model capture an important experimental observation that the variability in RT2 is higher at short SOA, as RT2 accumulates the variability of both tasks. Response times for T2 become faster and less variable as SOA increases, as seen by plotting the cumulative response time distributions for varying SOA () 
. Interference and seriality are also observed in the scatter plots of RT1 vs. RT2, for different SOA values: for short SOA values RT2 is tightly correlated to RT1 indicating that RT2 is sequentially locked to Task 1 completion. For long SOA values, RT1 and RT2 become independent measures ().
Effects of Noise and Oscillatory Inputs on Response Times
The previous results showed that our model can explain the precise shape of response time distributions in dual-task performance. Here we investigate the underlying physiological markers which result in such distributions, i.e. the relation between neuronal and response time variability. All neurons in the model receive strong background Poisson inputs, which assures a spontaneous activity of 2–5 spikes/s. We hypothesized that in trials in which input noise in the sensory neurons coincides with stimulus presentation (presented for 100 ms) response times would be faster. We also hypothesized that in the case of low-frequency noise (~5Hz), the coincidence effect of external-stimulus and internal noise fluctuations, should manifest in a phase-locking relation of stimulus presentation to internal rhythms, as observed in both psychophysical 
and neurophysiological 
We first used a general linear regression model to investigate how noise fluctuations affected response times in the PRP. The explanatory (independent) variables were external noise fluctuations for each population group and temporal bin, and the response (dependent) variable was either RT1 () or RT2 ().
Response time sensitivity to stochastic fluctuations and low-frequency oscillations.
We simulated 900 trials of the PRP for an SOA of 50 ms. For each trial, the population average of
- dynamic gating variable mediating background AMPA currents (see Materials and Methods
section) - was measured every 1 ms, assigning a value of 0 if its value exceeded the median value over all trials, and a value of 1 otherwise, independently for each population and time step. Independent variables were obtained by averaging these values within windows of 100 ms. Similar populations - for example, all neurons in the first level of the sensory hierarchy selective to the same stimulus - were averaged together. A positive regression coefficient means that higher activity of a group of neurons leads to faster responses.
The time-course of the coefficients of the regression () showed a very clear temporal organization. For Task-1 sensory neurons (), fluctuations in the first sensory level which were coincident with stimulus presentations were highly predictive of RT1. On the contrary, fluctuations beyond this window were essentially independent of response time. In successive stages of the hierarchy the window of correlation was delayed.
As we showed previously, RT2 variability accumulates RT1 variability (due to changes in the onset of the routing of T2) and intrinsic variability of the T2 routing process. To understand the impact of noise on each of these processes, we measured the time-course of the noise input to Task-2 responding neurons locked to the response to Task 1 (). Significant noise contributions were observed before the integration onset (, upper panel), suggesting that although sensory integration is delayed during the PRP, fluctuations in the memory trace of S2 during T2 queuing or before have an influence on RT2.
Thus, spontaneous Poisson-noise fluctuations were effective when they coincided in time with external stimulus currents. If noise currents were carried by low-frequency oscillations 
this effect could result in phase locking of RTs to the rhythmic oscillatory activity. We tested explicitly this possibility by running single-task simulations where excitatory neurons in the first sensory level received a low-frequency (5 Hz), low-amplitude (0.06% of the external background noise), oscillatory input. This additional input resulted in a small synchronous fluctuation on top of the large external background input. The phase of the stimulus onset relative to the background rhythm was varied across trials in order to study its effects on average response times and their distributions (). The relative phase between stimulus onset and rhythmic background activity had a marked effect on response times, compatible with recent experimental findings 
and theoretical proposals 
linking low-frequency oscillations to attentional selection. Our model provides a simple physiological explanation of why phase-locking stimulus to low-frequency oscillations may result in shorter response times. When the phase is such that the peak of noise fluctuations coincides with stimulus presentation, the stimulus is enhanced and this reduces response time. On the contrary, when stimulus presentation coincides with the valley of noise oscillations, input to the router is less effective and response times are longer.
From the PRP to the Attentional Blink
Behavioral experiments which have combined the basic features of different manifestations of central processing such as the PRP (two rapid responses) or the attentional blink (extinction of a second rapidly presented stimulus) have suggested that both forms of processing limitations may arise in part from a common bottleneck 
. The main differences between the PRP and the AB is that in the PRP a speeded response is required to the first target and, most importantly, that in the AB the visibility of the second target is reduced, generally by masking it or by embedding it in a rapid visual serial presentation (RSVP).
To evaluate whether our model could, without modification, also account for AB experiments, we studied the effect of a mask applied after T2. The mask was modeled as a brief stimulation of non-specific excitatory cells in the first layer of the sensory hierarchy, thus modeling the activation of a neural representation competing with the target T2 
. The mask lasted 100 ms and was presented immediately following T2. In the majority of AB experiments, both T2 and the T1 are masked. Here, for direct comparison with the PRP simulations, we considered a special AB case in which the T1's fleetingness is obtained by virtue of its weak strength, rather than masking 
We simulated 100 trials at each SOA value, varying the SOA between 50 and 500 ms at 50 ms intervals. In contrast to the previous PRP simulations, when the SOA between T1 and T2 was short we observed a small (but significant) number of errors and, most importantly, a large number of trials in which the network failed to respond to T2 (). For simplicity and to follow the convention of prior experimental work, we refer to trials in which the network responds correctly as seen
, and those in which it fails to respond as unseen
. For example, at SOA
50 ms we obtained 49±5% seen
trials, 47±4.99% unseen
trials, and 4±1.96% errors; for SOA
500 ms, we obtained 90±3% seen
trials, 9±2.86% unseen
trials, and 1±0.01% errors. As observed in the Attentional Blink and in mixed AB-PRP paradigms, the brief mask after T2 is only effective when T2 is presented within a short temporal window – typically of around 500 ms – following T1 presentation.
From the PRP to the attentional blink: masking effects on visibility.
For short SOA values, the network exhibits a highly stochastic behavior: the same configuration of stimuli and SOA may lead to seen
responses depending on the inner state of the network. shows the time-course of activity of a representative seen
trial and reveals the cause of the blink. In the unseen
trial, RT1 was longer and thus at the moment in which inhibition of T2 task-setting neurons was released, T2 sensory activation had faded out. As a consequence, T2 task-setting neurons failed to respond and this impeded the integration and routing of T2. This can also be seen when averaging across all trials (for an SOA of 100 ms) according to whether the network responded or failed to respond to T2 (). T2 non-responded trials resulted – on average - from a delayed response of the T1 task setting neurons. This observation establishes a concrete prediction for the dynamics of routing neurons in a AB experiment and is consistent with physiological and behavioral experiments which have shown that the extent of T1 processing has an impact on T2 visibility 
, in accordance with the behavior of the sequential bottleneck model.
The interpretation of our results is that the mask results in an accelerated exponential fading of the representation of T2 stimulus in short-term memory 
. As a result, if the waiting time of T2 is too long, due to the concurrent processing of T1, the remaining activation is insufficient to ignite the router and task-setting neurons and the network fails to respond to T2. Consistent with this interpretation, we verified that early responses evoked by the second stimulus in seen
trials showed a small, but significant effect in the amplitude – but not in the latency - of the transient responses when compared to unseen
trials (). These small fluctuations are strongly amplified in the router and task-setting neurons, which show an almost all-or-none difference (). This result is consistent with electrophysiological experiments of the blink and the PRP which have observed a modest effect in early sensory components and a massive all-or-none effect in late P3 components 
A series of experimental observations have shown that the AB is attenuated (i.e. the probability of seeing T2 increases) with increased T1 strength. For example, the blink is attenuated when a blank is placed after T1, i.e. masking is delayed 
. This observation is in contradiction with pure T1–T2 competition models of the AB since these models predict the opposite effect: increased T1 strength should result in a reduced likelihood of perceiving T2 
. However, it seems compatible with our network operation, since a stronger T1 stimulus should result in a faster conclusion of Task 1, increasing the probability of retrieving the second stimulus before it has fade out.
We examined this hypothesis performing two different simulations. First, we increased the strength of T1 by 10% relative to the previous PRP and AB simulations. This resulted in an attenuated AB for the second task (76±4% correct vs. 49±5% correct without the manipulation; p-value <0.0005; 100 trials at a fixed SOA of 50 ms). Despite perfect performance for T1 in these simulations, RT1 was smaller when T1 was stronger (with strong T1: RT1
318±5 ms; without the manipulation: RT1
396±9 ms; p-value<0.0005). Thus increasing T1 strength decreases RT1 and increases the probability of retrieving the second stimulus.
The second manipulation, conversely, involved masking the first target T1, simulating the most typical AB paradigm in which both T1 and T2 are masked. As for the first manipulation, 100 trials were simulated at a fixed SOA of 50 ms and we now added a mask identical to the one previously used for T2. In this condition, performance in the first task was still accurate (92±3% correct) while T2 visibility was decreased significantly (26±4% correct). This effect can be understood by the increased latency of the inhibitory signal following routing of T1, which increased RT1 from 396±9 ms in the unmasked condition to 869±50 ms when T1 was masked.
In summary, our simulations show that T1 manipulations that facilitate the first task and therefore reduce its duration have the effect of reducing the attentional blink for T2, as experimentally observed 
. Since RT1 is typically not measured in most AB tasks, where the task is to covertly commit T1 to memory for delayed report, only the reduced blink for T2 would have been noticed experimentally – but our network suggests that, if RT1 was measured by an on-line task, then the reduced AB would be replication and would be mediated by a faster RT1.