A phase transition model for the speed-accuracy trade-off in response time experiments

Most models of response time (RT) in elementary cognitive tasks implicitly assume that the speed-accuracy trade-off is continuous: When payoffs or instructions gradually increase the level of speed stress, people are assumed to gradually sacrifice response accuracy in exchange for gradual increases in response speed. This trade-off presumably operates over the entire range from accurate but slow responding to fast but chance-level responding (i.e., guessing). In this article, we challenge the assumption of continuity and propose a phase transition model for RTs and accuracy. Analogous to the fast guess model (Ollman, 1966), our model postulates two modes of processing: a guess mode and a stimulus-controlled mode. From catastrophe theory, we derive two important predictions that allow us to test our model against the fast guess model and against the popular class of sequential sampling models. The first prediction--hysteresis in the transitions between guessing and stimulus-controlled behavior--was confirmed in an experiment that gradually changed the reward for speed versus accuracy. The second prediction--bimodal RT distributions--was confirmed in an experiment that required participants to respond in a way that is intermediate between guessing and accurate responding.     

Bunched sequential information

It is known that the logic BI of bunched implications is a logic of resources. Many studies have reported on the applications of BI to computer science. In this paper, an extension BIS of BI by adding a sequence modal operator is introduced and studied in order to formalize more fine-grained resource-sensitive reasoning. By the sequence modal operator of BIS, we can appropriately express “sequential information” in resource-sensitive reasoning. A Gentzen-type sequent calculus SBIS for BIS is introduced, and the cut-elimination and decidability theorems for SBIS are proved. An extension of the Grothendieck topological semantics for BI is introduced for BIS, and the completeness theorem with respect to this semantics is proved. The cut-elimination, decidability and completeness theorems for SBIS and BIS are proved using some theorems for embedding BIS into BI.     

Walk this way: approaching bodies can influence the processing of faces

A highly familiar type of movement occurs whenever a person walks towards you. In the present study, we investigated whether this type of motion has an effect on face processing. We took a range of different 3D head models and placed them on a single, identical 3D body model. The resulting figures were animated to approach the observer. In a first series of experiments, we used a sequential matching task to investigate how the motion of an approaching person affects immediate responses to faces. We compared observers’ responses following approach sequences to their performance with figures walking backwards (receding motion) or remaining still. Observers were significantly faster in responding to a target face that followed an approach sequence, compared to both receding and static primes. In a second series of experiments, we investigated long-term effects of motion using a delayed visual search paradigm. After studying moving or static avatars, observers searched for target faces in static arrays of varying set sizes. Again, observers were faster at responding to faces that had been learned in the context of an approach sequence. Together these results suggest that the context of a moving body influences face processing, and support the hypothesis that our visual system has mechanisms that aid the encoding of behaviourally-relevant and familiar dynamic events.     

Asymmetrical retention functions for sequences of light flashes or tone bursts in the rat

In Experiment 1, rats were trained in a symbolic delayed matching-to-sample task to discriminate sample stimuli that consisted of sequences of magazine light flashes. The intertrial interval was illuminated by the houselight for Group Light, and it was dark for Group Dark. Retention functions exhibited a choose-many response bias when the delay interval was illuminated by the houselight in both groups, and no consistent response bias when the delay interval was dark. In Experiment 2, rats were trained to discriminate sample stimuli that consisted of sequences of tone bursts. During delay testing, a different tone (i.e., different frequency and location than the sample tone) was present or absent during the delay interval. The retention functions exhibited a significant choose-many bias when tone was present during the delay and a choose-few bias when tone was absent. Asymmetrical retention functions for tone burst and light flash sequences are due to the similarity between the stimulus conditions of the delay interval and the modality of the sequential event being discriminated. These results are consistent with an instructional ambiguity explanation of response biases in memory for number.     

A new secretary problem with rank-based selection and cardinal payoffs

We present an extension of the secretary problem in which the decision maker (DM) sequentially observes up to n applicants whose values are random variables X₁,X₂,…,X_n drawn i.i.d. from a uniform distribution on [0,1]. The DM must select exactly one applicant, cannot recall released applicants, and receives a payoff of x_t, the realization of X_t, for selecting the tth applicant. For each encountered applicant, the DM only learns whether the applicant is the best so far. We prove that the optimal policy dictates skipping the first sqrt(n)-1 applicants, and then selecting the next encountered applicant whose value is a maximum.     

A new dynamical model of brainstorming: Linear, nonlinear, continuous (simultaneous) and impulsive (sequential) cases

In this paper, we extended the linear dynamical model of [Brown, V., Paulus, P. B. (1996). A simple dynamic model of social factors in group brainstorming. Small Group Research, 27, 91-114] on two accounts. First, we modelled the sequential type brainstorming using impulsive differential equations by treating each category as an impulse and tested its validity in the two experiments that investigated and demonstrated the beneficial effects of sequential priming and memory in individual brainstorming. Finally, we considered the nonlinear case of brainstorming in writing or brainwriting where dyads exchanged their ideas in a written format and that eliminated negative factors occurring in oral brainstorming (e.g., evaluation apprehension, free-riding, production blocking) and enhanced the upward performance matching, and conducted the second experiment in order to test its validity in this paradigm with the effects of sequential priming and memory. Comparisons showed good agreement between results of experiments and those of the mathematical model.     

Quantity judgments of sequentially presented food items by capuchin monkeys (Cebus apella)

Recent assessments have shown that capuchin monkeys, like chimpanzees and other Old World primate species, are sensitive to quantitative differences between sets of visible stimuli. In the present study, we examined capuchins’ performance in a more sophisticated quantity judgment task that required the ability to form representations of food quantities while viewing the quantities only one piece at a time. In three experiments, we presented monkeys with the choice between two sets of discrete homogeneous food items and allowed the monkeys to consume the set of their choice. In Experiments 1 and 2, monkeys compared an entirely visible food set to a second set, presented item-by-item into an opaque container. All monkeys exhibited high accuracy in choosing the larger set, even when the entirely visible set was presented last, preventing the use of one-to-one item correspondence to compare quantities. In Experiment 3, monkeys compared two sets that were each presented item-by-item into opaque containers, but at different rates to control for temporal cues. Some monkeys performed well in this experiment, though others exhibited near-chance performance, suggesting that this species’ ability to form representations of food quantities may be limited compared to previously tested species such as chimpanzees. Overall, these findings support the analog magnitude model of quantity representation as an explanation for capuchin monkeys’ quantification of sequentially presented food items.

First and second language vowel perception in early bilinguals

Previous research has shown that the perception of speech sounds is strongly influenced by the internal structure of maternal language categories. Specifically, it has been shown that stimuli judged as good exemplars of a phonemic category are more difficult to discriminate from similar sounds than bad exemplars from equally similar sounds. This effect seems to be restricted to phonemes present in the maternal language, and is acquired in the first months of life. The present study investigates the malleability of speech acquisition by analysing the discrimination capacities for L2 phonemes in highly proficient Spanish-Catalan bilinguals born in monolingual families. In Experiment I subjects were required to give goodness of fit judgments to establish the best exemplars corresponding to three different vowel categories (Catalan /e/ and /ε/ Spanish /e/). In Experiments 2 and 3, bilinguals were asked to perform a discrimination task with materials in their maternal language (Exp. 2) and in their second language (Exp. 3). Results reveal that bilinguals show a reduced discrimination capacity only for good exemplars of their maternal language, but not for good exemplars of their second language. The same pattern of results was obtained in Experiment 4, using a within-subjects design and a bias-free discrimination measure (d'). These findings support the hypothesis that phonemic categories are not only acquired early in life, but under some circumstances, the acquisition of new phonemic categories can be seriously compromised, in spite of early and extensive exposure to L2.     

Strategic navigation of two-dimensional alley mazes: comparing capuchin monkeys and chimpanzees

Planning is an important component of cognition that contributes, for example, to efficient movement through space. In the current study we presented novel two-dimensional alley mazes to four chimpanzees and three capuchin monkeys to identify the nature and efficiency of planning in relation to varying task parameters. All the subjects solved more mazes without error than expected by chance, providing compelling evidence that both species planned their choices in some manner. The probability of making a correct choice on mazes designed to be more demanding and presented later in the testing series was higher than on earlier, simpler mazes (chimpanzees), or unchanged (capuchin monkeys), suggesting microdevelopment of strategic choice. Structural properties of the mazes affected both species' choices. Capuchin monkeys were less likely than chimpanzees to take a correct path that initially led away from the goal but that eventually led to the goal. Chimpanzees were more likely to make an error by passing a correct path than by turning onto a wrong path. Chimpanzees and one capuchin made more errors on choices farther in sequence from the goal. Each species corrected errors before running into the end of an alley in approximately 40% of cases. Together, these findings suggest nascent planning abilities in each species, and the prospect for significant development of strategic planning capabilities on tasks presenting multiple simultaneous or sequential spatial relations. The computerized maze paradigm appears well suited to investigate movement planning and spatial perception in human and nonhuman primates alike.     

Memory for sequences of tone bursts in the rat: Reliance on temporal cues and evidence for an instructional ambiguity explanation of the choose-few effect

Two groups of rats were trained in a symbolic delayed matching-to-sample task with a 0-s delay to discriminate sample stimuli that consisted of sequences of tone bursts. For one group, sequences varied in number with total sequence duration controlled. For the other group, total sequence duration, sum of the tone durations, and sum of the gap durations were all controlled. The former group of rats acquired the discrimination, but the latter group of rats were not able to learn the discrimination with the additional temporal cues controlled. Retention functions for the group that acquired the discrimination exhibited a choose-many bias at the 1-s delay and a choose-few bias at the 8-s delay regardless of the similarity in the intertrial interval and delay interval illumination condition. The asymmetrical retention functions appeared to be due to instructional ambiguity which resulted from the similarity of the delay interval to temporal features of the tone burst sequence, such as the gap between tone bursts and the total duration of tone. In Experiment 2, diagnostic tests provided evidence that rats discriminated the sequences of tone bursts by timing and summing the duration of individual tone bursts rather than using an event switch to count tones. Like pigeons, rats use multiple temporal features rather than number to discriminate sequences of successive events.