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Research Report

Positive and negative congruency effects in masked priming:A neuro-computational model based on representation,attention, and conflict

Ahmad Sohrabia,b,⁎, Robert L. Westb,c

aDepartment of Psychology, University of Kurdistan, Sanandaj, IranbCarleton Cognitive Modeling Lab, Carleton University, Ottawa, CanadacDepartment of Psychology and Institute of Cognitive Science, Carleton University, Ottawa, Canada

A R T I C L E I N F O

⁎ Corresponding author. Department of PsychUniversity, Ottawa, Canada.

E-mail address: a.sohrabi@uok.ac.ir (A. So

0006-8993/$ – see front matter © 2009 Elsevidoi:10.1016/j.brainres.2009.07.004

A B S T R A C T

Article history:Accepted 1 July 2009Available online 14 July 2009

Studies on masked and unmasked priming have long shown reliable positive effects of thecongruent prime on target processing. Paradoxically, a negative effect has also been found,showing faster and more accurate responses in the incongruent compared to the congruenttrials. Positive effects have been found with a short time between the prime and the target,whilenegativeeffectshavebeen foundwitha long timebetween theprimeand the target. Thishas been modeled by assuming that the prime initiates a motor self-inhibitory process thatcauses these effects (Bowman,H., Schlaghecken, F., Eimer,M., 2006. A neural networkmodel ofinhibitory processes and cognitive control. Vis. Cogn. 13, 401–480). We have developed analternative explanation based on attentional neuro-modulation. In this paper we show thatattentional neuro-modulation can be used to model a wide range of findings in this area.

© 2009 Elsevier B.V. All rights reserved.

Keywords:Masked primingAttentionNumerical decisionComputational modelingCognitive control

1. Introduction

Masked priming method is based on the semantic primingparadigm, long known in the literature. In semantic priming(e.g., Meyer and Schvaneveldt, 1971), lexical decision (decidingif a string is a word or non-word) on a target word (e.g., NURSE)is faster when it is semantically related to a preceding primeword (e.g., DOCTOR prime) compared to a trial where theprime (e.g., CHAIR) is unrelated to the target (e.g., DOCTORprime). Similarly, in masked priming tasks, a brief maskedstimulus (the prime) can affect the decision on the stimulusthat follows (the target). A prime, a mask, and a target arepresented sequentially and the task is to make a decision onthe target. The result is usually a Positive Congruency Effect(PCE), also known as the positive compatibility effect. In PCE,

ology, University of Kurdis

hrabi).

er B.V. All rights reserved

the prime improves the decision (in terms of the speed andaccuracy) on the target if they are congruent and vice verse ifthey are incongruent (Marcel, 1983; Neumann and Klotz, 1994;Dehaene et al., 1998; Schlaghecken and Eimer, 2000). Forexample, participants were asked to press the left responsebutton when a female face was presented and to press theright response button when a male face was presented (Ennsand Oriet, 2007). When a female face was preceded by anotherfemale face, the task was performed faster than when afemale face was preceded by a male face, although the taskwas just to respond to the second face.

Conversely, a negative priming effect has been found,called the Negative Congruency Effect (NCE). This effect is alsoknown as the negative compatibility effect, where paradoxi-cally the prime improves the decision on the target if they are

tan, Sanandaj, Iran and Carleton Cognitive Modeling Lab, Carleton

.

Fig. 1 – The results of Simulation 1, SOA effect. (a) Modelingresults at seven levels of mask-target SOA, starting from 65cycles. EachSOA follows30 cycles after thepreviousone,withmask duration of 100 cycles. (b) The same result was shownby the congruencydifference (Incongruent−Congruent) in theseven SOAs. This is similar to the different lags in attentionalblink paradigm, showing a similar attentional basis forpriming and attentional blink.

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incongruent and vice verse if they are congruent (e.g.,Schlaghecken and Eimer, 2000, 2002, 2006; Eimer, 1999; Eimerand Schlaghecken, 1998, 2001, 2002; Lleras and Enns, 2004,2006; Verleger et al., 2004; Jaśkowski and Ślósarek, 2007). Forexample, participants were asked to press the left responsebuttonwhen a happy facewas presented and to press the rightbutton when an angry face was presented. Under someconditions (see below), when a happy face was preceded byan angry face, the response was paradoxically faster thanwhen a happy face was preceded by a happy face (Bennettet al., 2007). The PCE has been shownwith a short mask-targetStimulus Onset Asynchrony (SOA), while the NCE has beenshown with a longer mask-target SOA (e.g., 100 ms).

To explain these results, some researchers (Schlagheckenand Eimer, 2000; Eimer and Schlaghecken, 2003; Bowmanet al., 2006), based on Event Related Potential (ERP) measure-ments and computational modeling, argue that when SOA isshort, response selection can already take place during theinitial response activation phase; this is reflected as an earlyincrease of activation difference in Lateralized ReadinessPotential (LRP) for the congruent compared to incongruenttrials, and this should result in the congruency effects in theform of a PCE. When SOA is longer, responses have to beselected during the subsequent inhibitory phase. This inhibi-tory phase is reflected as a late decrease of activationdifference in LRP for congruent compared to incongruenttrials, and this should be demonstrated as a negative effect(i.e., NCE). In these studies, the reduction of activationdifference in LRP has been attributed to a motor self-inhibition, causing the NCE effect. The mask causes thisinhibition to be reversed, by removing the sensory evidencefor the corresponding response and initiating its suppression.

Across all studies the interaction between PCE and NCEand the manipulations in the experiments is complex.Therefore, computer simulations of potential models arerequired to see if the model can account for all the changes.Demonstrating the effectiveness of this approach, Bowmanet al. (2006) developed a neural network model of thisprocess that accounts for many findings in this area. Theirapproach, although it has not been applied to all of the dataseems, capable of explaining this phenomena (althoughminor modifications of the model might be required).However, with modeling it is important to establish ifother processes can achieve the same effect (Sloman, 2008;Taatgen and Anderson, 2008) to establish the differentpossibilities for explaining the phenomena. Different modelscan also suggest different possibilities in terms of the neuralprocesses involved. To this end, we created an alternativemodel using neuro-computational modeling. Unlike theBowman et al. (2006) model, our model is not based onmotor self-inhibition, instead it works through attentionalmodulation that can be affected by conflict. It shows theeffect of other factors such as degradation (Schlagheckenand Eimer, 2002), mask density (Eimer and Schlaghecken,2002), prime duration (Eimer and Schlaghecken, 2002), andthe finding that NCE decreases and eventually disappears orturns into a very small PCE (e.g., Jaśkowski and Ślósarek,2007; Sumner and Brandwood, 2008). Our goal with this wasto show an alternative modeling approach involving differ-ent cognitive functions.

2. Results

2.1. Simulation 1: mask-target SOA

This simulation was intended to model the effect of SOA,i.e., a PCE and an NCE with short and long mask-target SOAs,respectively (e.g., Schlaghecken and Eimer, 2000; Jaśkowskiand Ślósarek, 2007) with no changes in the parametersexcept the mask-target SOA. We used seven intervals of themask-target SOA (from 65 to 245, with 30 cycles interval) toshow the effect of SOA on priming pattern. The duration ofthe mask was 100 cycles (Dehaene et al., 1998), but differentmask durations have similar effects (as used in othersimulations, see Sohrabi, 2008).

In previous studies (e.g., Schlaghecken and Eimer, 2000;Eimer and Schlaghecken, 1998; Jaśkowski and Ślósarek, 2007),the NCE has been shown at long SOAs. As shown in Fig. 1a,here at the first SOA a PCE occurred (stronger PCE can be foundwith shorter SOAs), and at longer SOAs an NCE occurred. Then

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NCE and RTs slowly decreased and finally the effect becameslightly positive again. Human data from previous studiesshow that NCE decreases and eventually disappears or turnsinto a very small PCE (e.g., Jaśkowski and Ślósarek, 2007;Sumner and Brandwood, 2008).

The error results can be found in Supplementary Fig. 1,showing that in short SOA, errors occurred mainly in theincongruent trials, and in long SOA these errors occurredmainly in the congruent trials (in forms of missing trials, i.e.,ML activation did not cross the threshold by the trialdeadline). Also, note the decrease in RTs throughout time inFig. 1a which is similar to previous experimental data (e.g.,Jaśkowski and Ślósarek, 2007), and the U-shaped curve of theRT difference (Fig. 1b), both of which result from recoveryfrom the attentional refractory period by AL (see Fig. 2). Fig. 1bshows the same results in Fig. 1a but using congruencydifference (i.e., incongruent−congruent mean RTs). It issimilar to the result of attentional blink paradigm, presum-ably showing a common attentional basis for attentionalblink (e.g., Nieuwenhuis et al., 2005) and priming effects in thecurrent study.

2.2. Simulation 2: stimulus degradation

A previous study (Schlaghecken and Eimer, 2002, Exp. 4) foundthat degradation of stimuli, by adding small randomdots to all

Fig. 2 – The changes in refractory period by increasing SOA.

Fig. 3 – Results of Simulation 2, degradation effect.(a) Degrading the prime and target with three levels of primeand target inputs in IL: 1 (no degradation), .85 (mediumdegradation), and .75 (high degradation), as well as anincrease in noise.With degraded unit activations NCE turnedinto PCE and RTs increased. (b) Degrading only the primeturned NCE to PCE but did not increase RTs.

stimuli, turns NCE into PCE. Here, the degradation of stimuliwas simulated by using lower input activation in IL (for bothprime and target) compared to the usual 1 and 0 andincreasing the noise of the prime and target in RL. Two levelsof degradation were created by using .85 (opposite unit .15)and .75 (opposite unit .25), while 1 (opposite unit 0) was used toencode an intact stimulus. For a better fit between simulationand human data, the noise of the prime and target units in RLwas increased from .2 to .3. The IL–RL strength for the primeand target was 2.5 and the mask-target SOA was 125 cycles.The model successfully simulated the human data as shownin Fig. 3a. With degradation, the NCE turned into PCE and RTswere increased by more degradation.

In another experiment in the same study (Schlagheckenand Eimer, 2002, Exp. 3), random dots were added to allstimuli, but the dots did not cover the target (presented aboveor below the target, randomly). In this case, while degradation

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turned the NCE into PCE, it did not increase the RTs. Forsimulating this experiment, a simulation was run identical tothe previous one but only the prime was degraded. The resultwas similar to the human data. As shown in Fig. 3b, if thetarget is not degraded the RTs do not increase (because it isstronger and is processed faster).

2.3. Simulation 3: mask density

It has been shown that themask needs to be dense enough at aspecific rate to cause NCE, and that decreasing the densitychanges NCE to PCE (e.g., Eimer and Schlaghecken, 2002),

Fig. 4 – Results of Simulations 3 (mask density) and 4(prime duration). (a) Four levels of mask density wereemployed: 1 (no mask), 2 (low density), 3 (medium density),and 4 (high density), simulated by IL mask unit inputs 0,.45, .55, and 1 compared to masks with ≥15, 10, 5, and 0random lines in human data, respectively (Eimer andSchlaghecken, 2002, Exp. 1). (b) Simulation results for threelevels of prime duration: 53 cycles (long), 48 cycles(medium), and 43 cycles (short), compared to 64, 32, and16 ms in human data (Eimer and Schlaghecken, 2002).Increasing the prime duration increased the NCE but afurther increase turned the NCE into PCE.

although beyond that it has no major effects. In this simula-tion,maskdensitywas simulatedby changing the inputs of themask units to .55 (medium density) and .45 (low density),instead of 1 (very high density, used in other simulationswhere usual mask was used). The IL–RL strength for the primeand target was 2.5 and themask-target SOAwas 125 cycles. Asshown in Fig. 4a, similar to human data (e.g., Eimer andSchlaghecken, 2002, Exp. 1) decreasing themaskdensity from1to .55 decreased NCE and then to .45 and 0 turned NCE to PCE(lowmask density and nomaskmight to invoke other types ofprocesses, not discussed here, but see Sohrabi, 2008).

2.4. Simulation 4: prime duration

Prime duration has an important role in the priming effect.Stimuli with longer duration have stronger representationsand also activate more attentional responses. It has beenshown that increasing the prime duration increases NCE tosome extent and turns it to PCE after a specific rate (Eimer andSchlaghecken, 2002). The current simulation shows thepriming effects for three prime durations: 43, 48, and 53cycles. The IL–RL strength for the prime and target was 2.5 andthe mask-target SOA was 125 cycles.

As shown in Fig. 4b, increasing the prime duration causedlarger NCE, but a further increase turned it into PCE.Interestingly, increasing the prime duration does not decreaseRTs and even has an opposite effect, similar to human data(e.g., Eimer and Schlaghecken, 2002, Exp. 2) (longer durationmight invoke other types of processes, not discussed here, butsee Sohrabi, 2008).

3. Discussion

The positive and negative congruency effects (PCE and NCE)found in previous studies (Dehaene et al., 1998; Schlagheckenand Eimer, 2000, 2002, 2006; Eimer, 1999; Eimer and Schla-ghecken, 1998, 2001, 2002; Lleras and Enns, 2004, 2006; Verlegeret al., 2004; Jaśkowski and Ślósarek, 2007) was simulated bymanipulating the time between prime and target (i.e., mask-target SOAs), with no other changes in the model. Consistentwith human data, PCE and NCE were found with short andlong mask-target SOA, respectively. When the mask-targetSOA was short (as with short mask-target SOA in Simulation1), the correct response could be made easily, and primarilywith the initial activation of the prime followed by thecongruent target (not happened with incongruent trials) andattentional boost. When the delay between them was longer(as with longer mask-target SOAs in Simulation 1), the primeactivation decayed and the second phase of attention (for thetarget) was not strong enough to activate the target quickly.This happened because attention showed a phasic responsewith a refractory period. The conflict, measured based on theincongruency in the stimuli relationship, decreased the effectof the refractory period by putting the second phase ofattention (to the target) in a tonic mode, enhancing theprocessing of the incongruent trials where conflict occurred.This was not the case in the congruent trials. Therefore, asmentioned, when the prime-target SOA was short, thepriming pattern was positive (i.e., PCE). On the other hand,

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when the prime-target SOAwas longer, the priming effect wasinverted (i.e., NCE).

The model also showed the effects of other factors on thesize and direction of priming such as prime duration, stimulusdegradation, and mask density. For example, a prime withlonger duration and less degradation had a strong representa-tion that caused a large NCE when the target came late (and alarge PCE when it came). The model also showed thatdecreasing the activation of input units (e.g., from binary, 1and 0, to real normalized numbers, .9 and .1, or less, forsimulating stimulus degradation) turns NCE into PCE. Thissupports the idea that the NCE is not caused merely by adecrease in the incoming perceptual information but by adecrease in the representation strength. In the current model,degradation was simulated by less incoming information (andhigher noise) and the strength was implemented by connec-tion weights between input and representation layers for bothprime and target. The involvement of an attentional bottle-neck in the decisional rather than perceptional processes hasbeen proposed previously (Sigman and Dehaene, 2005).

The current model, in addition to being biologicallycompelling, showed many dynamic effects in RT and errorpatterns that have not been shown previously (such as thechanges in RT and the size of priming effects through time).Themodel is based on previousmodels that have been used tosimulate different tasks such as target detection and simpledecisions in monkeys and humans (Gilzenrat et al., 2002;Usher et al., 1999; Usher and Davelaar, 2002; Nieuwenhuis etal., 2005). The present model is similar to some other previousneuro-computational models, especially those employed tosimulate the attentional blink (Mathis and Mozer, 1996;Nieuwenhuis et al., 2005). In thesemodels blink for the secondtarget occurs at lag 2 (after 100ms from the first target) and noblink occurs at lag 1 (if the second target is presented during100 ms after the first target), related to NCE and PCE in thecurrent model, respectively.

The simple way we chose to implement conflict was notmeant to represent all executive functions. However, its two-state nature, while simple, is relevant to the binary or rule-based processes of executive functions (e.g., O'Reilly, 2006).The role of conflict has been supported by the previous studies(e.g., Botvinick et al., 2001; Dehaene et al., 2003). Furthermore,the dynamic response in the model is consistent with the ERPresult of themotor cortex (Eimer and Schlaghecken, 2003), thatshows an earlier dominance of neural activation in thecongruent condition (reflected as PCE) and a later dominanceof the incongruent condition (reflected as NCE, see alsoSupplementary Fig. 2 online). A change in priming effectshas been reported in diseases such as schizophrenia (Dehaeneet al., 2003) and Parkinson's (Seiss and Praamstra, 2004).

Fig. 5 – Thearchitecture of themodel. The ILprojects to theRL.TheRLexcitatesAL,CL, andML (notshown). TheALmodulatesall other layers except IL. The CL changes the AL responsemode in the event of conflict. Note that different connectionsare depicted with different arrows: –♦ modulatory; –● conflictmonitoring;r self-excitationand lateral excitation; ●–● Lateralinhibition; –a Feed-forward activation.

4. Experimental procedures

The processing elements in the model are a few neurons withself-excitation, lateral inhibition, and accumulative activationthat have a strong computational power in simulating basicneural and cognitive processes (e.g., Usher et al., 1999; Brownand Holmes, 2001; Usher and McClelland, 2001; Usher andDavelaar, 2002; Gilzenrat et al., 2002). It has been demon-

strated that these types of reduced models can resemble theneural computation of a large group of neurons (e.g., Wongand Wang, 2006).

The model (Fig. 5) is a multi-layer dynamic neural modelthat consists of a feed-forward component for perceptuo-motor processing from the Input Layer (IL) to an intermediatelayer, called Representation Layer (RL), and from there to theCognitive Layer (CL) and Motor Layer (ML, not shown in Fig. 5).The stimulus type (numerals and symbols) and distance (closeand far) are encoded by their strength of representation,simulated by connection weights between IL and RL. Decreas-ing the weights is intended to make the representationsweaker or less direct (i.e., harder) and increasing theweights isintended to make the representations stronger or more direct(i.e., easier). Another assumption is that the cognitive proces-sing, including the response, is modulated by attention. TheAttentional layer (AL) corresponds to attentional modulation,that is supposed to be a model of Locus Coeruleus (LC) thatpotentiates cortical areas through norepinephrine (Aston-Jones and Cohen, 2005). The executive attention is onlymodelled through its effects on AL, using a Cognitive Layer(henceforth, CL) for conflict monitoring. The CL effect on ALsimulates direct cortical projections to LC (Aston-Jones and

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Cohen, 2005). The CL and ML are affected by both prime andtarget. The ML is not shown in Fig. 5 for the sake of simplicity,but its architecture is identical to CL, with the exception that itsends no outputs to AL, is slower, and noisier (see Table 1).

Each condition in a simulation consists of 20,000 trials (200independent blocks of 100 trials each, with congruent andincongruent trials counterbalanced randomly within eachblock). A single trial takes 1100 cycles. Each block starts with500 cycles without changes in IL to let the units in other layersreach a steady state of activation. Similarly the Inter-TrialInterval (ITI) for each trial is 500 cycles, which allows theactivation of units to return to baseline following theresponses. The prime is presented by clamping one of thetwo units in the IL to 1, intended to be left or right in the case ofarrows. The mask units in IL are set to 1 at the time of maskpresentation and are otherwise set to 0. Therefore, therecognition of the stimuli is implemented with a localizedrepresentation, for example, the left unit is turned on whenthe stimulus points left in the case of arrows; otherwise theright unit is turned on. Accordingly, as will be described below,in a congruent trial the two corresponding units (e.g., the leftunit of the prime and target in IL) is set to 1 or 0 at the time ofstimulus presentation, while in an incongruent trial, one ofthe two relevant units of the prime or target is set to 1 and theother to 0 (or to real normalized values, e.g., .75 and .25, insome simulations for specific reasons such as stimulusdegradation or mask density).

The units in each layer make connections, via excitatoryweights, to their corresponding units in other layers. Theactivations of these units (except IL) are calculated by asigmoid (logistic) function of the incoming information, and asmall amount of random noise. The RL sends excitatoryactivities to ML and CL continuously but activates AL only if aunit of the prime or target reaches a designated threshold of.62. Similarly, when one of the two units in the ML reaches thesame designated threshold it triggers a manual response (i.e.,initiating a hand movement). When AL is activated and its

Table 1 – Parameters in themodel, fixed for all simulations,unless otherwise mentioned.

WXiIi (IL to RL) [P and T] andWYiXi (RL to ML) [P and T]

2.5 and 1.5

WXiIi (IL to RL) [M] andWYiXi (RL to CL) [P and T]

1.5 and 1

WXiXi (RL) [P and T], WXiXi (RL) [M],WYiYi (CL), and WYiYi (ML)

1.5, 1.25, 1, and .9

WXiXj (RL) and WYiYj (ML and CL) 1 and 1WXiXj (RL) [M to P and T]and WXiIj (IL to RL)

.75 and .33

K (AL) 4.52θx, θy (AL), θx (RL), θy (CL),and θy (ML)

1.25, 1.5, .5, .85, and 2

b,c, ax and ay (AL) 4, 1–3, 2, and 3λx, λg, and λy (AL) .92, .98, and .996λ (CL), λ (ML), and λ (RL) .75, .925, and .95σ (CL), σ (RL) [P and T], σ (ML)and σ (RL) [M]

.025, .2, .25, and 1.25

IL = Input Layer; RL = Representation Layer; CL = Cognitive Layer;ML = Motor Layer; AL = Attentional Layer; P = Prime; T = Target;M = Mask.

activation reaches a threshold, it starts modulating informa-tion processing in RL, CL, and ML by making the activationfunction of their units steeper (Servan-Schreiber et al., 1990;see Supplementary Fig. 3 online).

4.1. Modeling details

As shown in Fig. 5, the IL encodes the prime, themask, and thetarget, and projects to RL through excitatory connections. Forthe sake of simplicity, prime and target, as well as an identicalmask for each (shown as a single unit in Fig. 5, for the sake ofsimplicity) was implemented in two separate paths. The IL–RLweights for prime and target were 2.5 in all simulations. Allunits in RL have a self-excitation connection, intended tosimulate mutual excitation among a group of neurons.Connections between mutual units (for prime and target andto the mask) from IL to RL have small cross-talks (see Table 1),indicating feature overlaps or similarities among stimuli. Theunits also have lateral inhibition with neighboring unitswithin the same layer.

The mask units are activated after the prime and beforethe target for a specific time. They have lateral inhibitionwith prime and target. The lateral inhibition has beenproposed as a good way to simulate masking (Wiesstein,1968; Rolls and Tovee, 1994). In addition to lateral inhibition,the model simulates the similarity of the mask to the primeand target through a lateral excitation from mask to theprime and target. This connection plays a role using thislateral excitation and can affect ML and AL (and CL),indirectly, through its effect on both prime and target.Moreover, the prime and target units, but not the mask,have feed-forward projections into the ML, CL, and AL layers.Therefore, the mask acquires meaning through its relation-ship with the prime and target. Because it comes right afterthe prime, it can activate the prime through its excitation. So,it can act partially like the prime when it is similar to it andincrease the attentional responses to it, helping it to staylonger. But, on the other hand, its inhibitory effect usuallydominates its excitatory effect and interrupts the prime,causing it to decay faster. This interplay depends on thesimilarity of the mask to the prime and target (Sohrabi, 2008).

The units in all layers (except IL and AL) receive additiveGaussian noise (zero mean and variance σ), intended asgeneral, irrelevant incoming activities. The activations in themodel are represented using units with real valued activitylevels. The units excite and inhibit each other throughweighted connections. Activation propagates through thenetwork when the IL is clamped with input patterns, leadingto a final response. As will be described below, the states ofunits in RL, ML, and CL are adopted in a method similar to anoisy, leaky, integrator algorithm (Usher andMcClelland, 2001,see also Usher et al., 1999; Brown and Holmes, 2001; Usher andDavelaar, 2002;Gilzenrat et al., 2002). These typesofmodels arenoisy versions of previous connectionist models (Anderson etal., 1977; McClelland, 1979; McClelland and Rumelhart, 1981).

In a typical masked trial or epoch, one of the prime units inthe IL is turned on and the network is left active for 43 cycles.Then the mask units in IL are turned on for 100 cycles,followed by turning on the target input in IL for 200 cycles. Thisis similar to a trial in the experiment, except no forward mask

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is presented, for the sake of simplicity. The prime and targetunits in the IL are used to represent the stimulus features (i.e.,direction or magnitude). However, as mentioned before, therecognition of the stimuli is not implemented in detail, but isencoded as a binary code, i.e., 1 is used for the left unit if itpoints left, and 0 is used for the opposite (reciprocal) unit. Inthe congruent condition, the RL units of the prime and targetat the same side (left or right randomly) are turned on (1) or off(0) in each trial at the time of stimulus presentation. Bycontrast, in the incongruent condition, the two units at theopposite sides are turned on and the other two are left off, withrandom selection of the two possible cases. The RL is governedby a modified version of previous models (Usher and McClel-land, 2001; see also Usher et al., 1999, Usher and Davelaar,2002; Gilzenrat et al., 2002), which is calculated with discreteintegrational time steps using the dynamic equation:

Xi t + 1ð Þ = kxX tð Þ+ 1� kxð Þf ½WXiXi Xi tð Þ +WXiIi Ii tð Þ�WXiXj Xj tð Þ � hXi + nXi�:

ð1Þ

Likewise, ML and CL are modelled in a similar way with theirinputs coming from RL:

Yi t + 1ð Þ = kyY tð Þ+ 1� ky� �

f ½WYiYi Yi tð Þ +WYiXi Xi tð ÞÞ�WYiYj Yj tð Þ � hYi + nYi�

: ð2Þ

In Eqs. (1) and (2), X and Y denote the activity of units throughtime t. W is the weight of the connections between units, I isthe input, and the subscripts i and j are indexes of the units.The three weight parameters in the brackets correspond torecurrent self-excitation, feed-forward excitation, and lateralinhibition, respectively. However, for the sake of simplicity inEq. 1, the lateral excitation from mask units to the prime andtarget, WXiXj Xj(t), and the cross-talk in prime and target toreciprocal units andmask units,WXiIj Ij(t), are not present. Theterm θ is the bias, the term ξ is noise, and ƒ is a sigmoidfunction (see Eq. (3) and Supplementary Fig. 3 online). Theterm λ represents neural decay (Amit and Tsodyks, 1991)which is related to the discrete integrational time steps in theunderlying equation (Usher and Davelaar, 2002). This char-acterizes neuronal gating with a fast rise followed by a slowdecay (Wang, 1999).

The ALmodulates other layers by changing their activationfromsigmoid toward binary responses (Servan-Schreiber et al.,1990; Cohen et al., 1990; Gilzenrat et al., 2002; Nieuwenhuiset al., 2005). The activation function, ƒ, transfers the net input,X, of a unit, and modulatory gain, g, to its activity state,implementing the firing rate of aneuronor themean firing rateof a group of neurons (Supplementary Fig. 3 online):

f Xð Þ = 1= 1 + exp �Xgð Þð Þ: ð3ÞA conflict-monitoringmeasurementwas employed to take theactivations of the units in the CL layer to adjust phasic andtonic responsemodes of AL. The CL itself may be equivalent toa “convergence zone” (Damasio, 1990) that combines differentinformation (here from the prime and target). It may partiallyinvolve the temporal lobe, but the conflict is supposed tomostly be involved in the Anterior Cingulate Cortex (ACC) andadjacent prefrontal areas (e.g., Botvinick et al., 1999; Dehaene

et al., 2003). The activation of the CL unitswas used tomeasuretheHopfield energy function between units (Hopfield, 1982), asused previously (Botvinick et al., 2001). One way to measureconflict is to calculate it as the co-activation of incompatiblerepresentations (Botvinick et al., 2001). So, conflict can bedefined as the concurrent activation of the competing unitsand as the joint effect of both prime and target in CL. Hopfieldenergy can be calculated as

E = � :5 XtWX

= � :5 X1 X2½ � 0 �1�1 0

� �X1X2

� � ð4Þ

where E denotes energy, X denotes the activity of a unit, Wis the weight of the connection between units, and thesubscripts 1 and 2 are indexes of the two units.

As noted above, CL combines prime and target activationsand measures conflict between its two units. When one CLunit is active and the other is inactive, conflict is low.However, when both units are active concurrently, the conflictis high. Instead of directly and dynamically measuringactivations in the CL units for measuring conflict (McClureet al., 2005), those activations are converted to 1 if they areequal to or greater than .5, and to 0 otherwise (i.e., using athreshold function). Also, E>.5 is considered as a conflict,otherwise as no conflict. When the activation of a prime ortarget unit in RL reaches the designated threshold, .62, the ALis activated with a phasic or tonic mode, depending on theabsence or presence of conflict in CL. The change in ALresponse mode usually occurs by the presentation of a targetthat is incongruent with the prime.

Here the AL is modelled using a reduced or abstractedversion of LC neurons in aWillson–Cowan type of system (e.g.,Wilson and Cowan, 1972) adopted recently (Usher andDavelaar, 2002) (there are similar models and detailed imple-mentations of this type of attention (Gilzenrat et al., 2002;Usher et al., 1999; Brown et al., 2004; Nieuwenhuis et al., 2005):

X t + 1ð Þ = kxX tð Þ+ 1� kxð Þf c axX tð Þ � bY tð Þ + Ix tð Þ � hxð Þ½ �;

Y t + 1ð Þ = kyY tð Þ+ 1� ky� �

f c ayX tð Þ � hy� �� �

;

G t + 1ð Þ = kgG tð Þ + 1� kg� �

X tð Þ:

ð5Þ

where ƒ is again a sigmoid function (as in Eq. (3)), X is the fastvariable representing AL activity and Y is a slow auxiliaryvariable, together simulating excitatory/inhibitory neurongroups in the LC (Usher and Davelaar, 2002). The X and Yvariables have decay parameters λx and λy, excitatory/inhibitory coefficients, ax and ay, as well as thresholds θxand θy, respectively. The G variable is the output of the AL,which is based on X. The g (used in Eq. (3)) is computed fromG: g=G ⁎K. The AL modulates other layers when g crosses athreshold, 1. Its activity modes can be phasic or tonicdepending on the conflict state, low or high, respectively. Inall conditions the CL can change the AL mode according tothe conflict between prime and target (i.e., using within-trialconflict). The phasic and tonic modes of AL responses areimplemented using high or low c value (3 or 1) (see Eq. (5)).The c value is 3 at the beginning of each trial (for the prime),but it is set to 1 (for the target) if conflict occurs.

131B R A I N R E S E A R C H 1 2 8 9 ( 2 0 0 9 ) 1 2 4 – 1 3 2

The number of computer simulation cycles from the targetonset until one of the ML units reached a designated thresh-old, .62, was considered as RT. A constant, as other sensoryandmotor processes, could be added to this RT, to increase thematch between simulation and human data. The modelshowed different types of errors including wrong responses(late errors), premature incorrect responses called early errors,premature correct responses called pre-hits (reaching thethreshold before the target presentation), and misses (failingto cross the threshold by the trial deadline). However, to focuson the main idea (i.e., RT result that is most consistent indifferent studies), the model was set up to not produce thesetypes of error responses frequently (usually about 1%, seeSupplementary Fig. 3 online, as an example). For all simula-tions, parameters in Table 1 were used, and were fixed in allsimulations unless otherwise mentioned.

Acknowledgments

This study was supported by Carleton University, CarletonCognitive Modeling Lab, and University of Kurdistan. AuthorsthankAndrewBrook, John Logan, and Friederike Schlagheckenfor their comments.

Appendix A. Supplementary data

Supplementary data associated with this article can be found,in the online version, at doi:10.1016/j.brainres.2009.07.004.

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