632 BOTVINICK.BRAVER.BARCH.CARTER,AND COHEN a third set o ndition of the Stoop task isa g.and in fact the byinhibtC through the co enting letter s blan the 3- ontrolsenalcoitagr m the olor-naming task. weaken or-naming uni e tn ng inte nd thus to high .Here.he assumes an activati on equal to the curer also trar stable I ACC on (partial inp activation during incong ntedintewod-unitrlayrerof In the w d-rea n uers of e nalneuroinmaging A oral studies (. troop interf ence effect if in one are ran esuls.canbctndc tood as de the final outcome in the word for sedtotheword-readingtask)The Carter ()s full wordsand paths by which reache ently.Be oral set of other words (e.g the FSin Fmight tivate FIST),the ls when were rare.Eve vord un ciated with wor y ng the input.For word stems,pro trials were rare. two units ese wor Simulation IB:Stem Completion ter units associal function.Using the approach taken in Simu tion task odelsimdlation2Bmhepeeataniclkealocontain 632 BOTVINICK, BRAVER, BARCH, CARTER, AND COHEN illustration of how the idea of conflict monitoring can be used to explain this finding. When an element is added to an existing model of a typical response override task, acting to transform the occurrence of conflict into an activation-based signal, a pattern is observed across conditions that parallels that observed in ACC activation studies. The color-naming condition of the Stroop task is a classic example of controlled information processing, and in fact, the Cohen and Huston (1994) model was originally proposed as a basic model of control function. Control is implemented here through the color-naming and word-reading units, insofar as these units bias information flow through the rest of the system in accordance with task demands. It is interesting that varying the control signal coming from these units impacts the degree to which conflict occurs during stimulus processing. In simulations of the color-naming task, specifically, weakening the input from the color-naming unit on incompatible trials leads to increasing inter￾ference between color and word inputs and, thus, to higher peak energy.5 This aspect of the model's behavior fits well with the idea that conflict might serve as an indicator of insufficient control, as it means that conflict is most likely to occur when control is weak. It also translates into a testable prediction: If ACC activation reflects conflict detection, then, on the basis of the model, ACC activation during incongruent trials in the Stroop task should vary inversely with the strength of control, defined as the effort to attend exclusively to color. We recently tested this prediction in a functional neuroimaging study (Carter et al., 2000). Here, the strength of top-down control was influenced indirectly by manipulating trial-type frequency. As shown by a number of behavioral studies (e.g., Lindsay & Jacoby, 1994; Logan & Zbrodoff, 1979), participants display a smaller Stroop interference effect if incongruent trials are frequent than if they are rare. In our terms, frequent incongruent trials lead to a high-control state (a tight focus on the color-naming task as opposed to the word-reading task). The Carter et al. (2000) study exploited this phenomenon to test for the predicted relationship between control state and ACC activation. Participants performed the Stroop task while undergoing fMRI. Trial-type frequency was varied across blocks; in one half of the blocks, incongruent trials occurred frequently, in the other half, relatively infrequently. Be￾havioral results confirmed the expected effect of trial-type fre￾quency on control state. Participants were faster on incompatible trials when these were frequent than when they were rare. Event￾related scan acquisition allowed evaluation of the time course of ACC activation on individual trials. As predicted, peak activation on incongruent trials differed as a function of trial-type frequency, with greater activity occurring during blocks where incompatible trials were rare. Simulation IB: Stem Completion As in response override tasks, we have attributed ACC engage￾ment in underdetermined responding tasks to the engagement of a conflict monitoring function. Using the approach taken in Simu￾lation 1A, this proposal was tested against a relevant model of information processing, in this case a model of the stem comple￾tion task. Method. Stem completion can be simulated using the interactive acti￾vation (IA) model of word reading introduced by McClelland and Rumel￾hart (1981; Rumelhart & McClelland, 1982), illustrated in Figure 2 (left). The model consists of three interconnected sets of processing units. External input is applied to a layer encoding featural elements—vertical, horizontal, and diagonal line segments—from which individual letters are constructed. Activation feeds forward from this feature layer to a layer of units representing individual letters. This layer connects to a third set of units, each standing for an individual four-letter word. Between layers, compatible units (e.g., the unit for the letter A in the first slot and the word unit for ALSO) are connected by excitatory weights, and incompatible ones by inhibitory weights. There are also symmetrical inhibitory connections between each pair of units in the word layer. Stem completion can be simulated in the IA model by presenting letters in the first two positions, leaving the third and fourth slots blank. Given such input, the model completes it, settling into a final state dominated by a word unit (and corresponding letter units) representing a word beginning with the two letters presented, similar to what would have resulted had all four letters of the word been present. As in Simulation 1A, a conflict monitoring element was added to the underlying model. Here, the conflict monitoring unit takes its input from the units in the word layer and assumes an activation equal to the current level of energy in that layer. In order to account for the finding of ACC activation in association with stem completion, the activity of the conflict monitoring unit was evaluated during simulations of both stem completion (partial input) and word reading (full input). A total of 20 words were chosen at random from the corpus represented in the word-unit layer of the model. In the word-reading condition, each word was presented in full to the feature layer. In the stem-completion condition, only the first two letters of each word were presented, with the last two slots receiving no input. As in Simulation 1A, energy was measured at regular intervals throughout each trial. Results. Results are shown in Figure 2 (right). Whereas pre￾senting a full word led to only a fleeting rise in energy, stem presentation led to much greater and sustained levels of energy. As in Simulation 1A, these results can be understood as deriving from the different degrees of crosstalk involved in the two task condi￾tions. Although the final outcome in the word layer is similar for full words and word stems, the paths by which the network reaches its final representation entail quite different amounts of crosstalk. For full words, the process is fairly straightforward. The input for each letter activates its corresponding feature units and letter unit. The selected letter units together strongly activate one word unit. Although subgroups of letters might also weakly activate a small set of other words (e.g., the FIS in FISH might activate FIST), the support for the fully specified word is stronger, and this word unit quickly dominates the word layer. The small increase in energy associated with word reading corresponds to the minor conflict among words partially matching the input. For word stems, pro￾cessing unfolds differently. Initially, the input activates one letter unit in each of the first two letter positions. These two units together activate a wide range of word units (FI_ will activate FISH, FIND, FINE, FIRE, etc.). These word units compete through inhibitory interconnections, also sending activation to the letter units associated with them in the third and fourth positions of the letter layer. Although this conflict is ultimately resolved in 5 The effects of varying task-unit input were first explored in an earlier version of the model by Cohen et al. (1990). Usher and Cohen (2000) have replicated and extended these findings in the context of the Cohen and Huston (1994) model. Simulation 2B in the present article also contains relevant findings