Integrating velocity,time, and distance information: A developmental study

The development of understanding the relationships between velocity, time, and distance was investigated in three tasks. In each task, values of two dimensions were given, and 5-year-olds, 10-year-olds, and adults had to infer values of the third dimension. These inferences were made in all age groups. The integration rules were found to depend upon age and task. In the distance = time × velocity task, all age groups obeyed the normative multiplication rule. In the time = distance ÷ velocity task, the two older age groups obeyed the normative division rule, but the 5-year-olds shifted to a simpler subtraction rule. In the velocity = distance ÷ time task, which was the most difficult, the two older age groups simplified to use of a subtraction rule, and the 5-year-olds simplified even further to use of a distance-only rule. The knowledge level revealed for young children contrasts sharply with results from previous studies using Piagetian choice tasks, which apparently investigate selective attention to one dimension rather than conceptual understanding of relations.     

Further Tests of Schmidt’s Schema Theory

The present study investigated the generalizability of Schmidt’s (1975) schema theory to an open-skill (Poulton, 1957) situation. Subjects attempted to time a preferred-hand button press so that it was coincident with the lighting of the last of a series of runway lights whose apparent velocity was 4023 mm/sec. Prior to five trials of performance on the criterion task, subjects received 40 trials in which they either (a) watched (low response requirements) or (b) responded with the nonpreferred hand (high response requirements) to a stimulus moving at (a) a constant (2235, 3129, 4917, or 5812 mm/sec) velocity (low stimulus variability) or (b) different velocities (high stimulus variability) from trial to trial. Subjects receiving high stimulus variability and high response requirements during training had significantly lower absolute error on the criterion task than did those in the other conditions. The results were discussed in terms of the type of practice which facilitates development of a schema rule for coincident-timing situations.     

The 'extrapolated center of mass' concept suggests a simple control of balance in walking

Next to position x and velocity v of the whole body center of mass (CoM) the 'extrapolated center of mass' (XcoM) can be introduced: xi = chi + nu/omega 0, where omega 0 is a constant related to stature. Based on the inverted pendulum model of balance, the XcoM enables to formulate the requirements for stable walking in a relatively simple form. In a very simple walking model, with the effects of foot roll-over neglected, the trajectory of the XcoM is a succession of straight lines, directed in the line from center of pressure (CoP) to the XcoM at the time of foot contact. The CoM follows the XcoM in a more sinusoidal trajectory. A simple rule is sufficient for stable walking: at foot placement the CoP should be placed at a certain distance behind and outward of the XcoM at the time of foot contact. In practice this means that a disturbance which results in a CoM velocity change Deltav can be compensated by a change in foot position (CoP) equal to Deltav/omega 0 in the same direction. Similar simple rules could be formulated for starting and stopping and for making a turn.     

Further tests of Schmidt's schema theory: development of a schema rule for a coincident timing task

The present study investigated the generalizability of Schmidt's (1975) schema theory to an open-skill (Poulton, 1957) situation. Subjects attempted to time a preferred-hand button press so that it was coincident with the lighting of the last of a series of run way lights whose apparent velocity was 4023 mm/sec. Prior to five trials of performance on the criterion task, subjects received 40 trials in which they either (a) watched (low response requirements) or (b) responded with the nonpreferred hand (high response requirements) to a stimulus moving at (a) a constant (2235, 3129, 4917, or 5812 mm/sec) velocity (low stimulus variability) or (b) different velocities (high stimulus variability) from trial to trial. Subjects receiving high stimulus variability and high response requirements during training had significantly lower absolute error on the criterion task than did those in the other conditions. The results were discussed in terms of the type of practice which facilitates development of a schema rule for coincident-timing situations.     

Self-organizing continuous attractor network models of hippocampal spatial view cells

Single neuron recording studies have demonstrated the existence of hippocampal spatial view neurons which encode information about the spatial location at which a primate is looking in the environment. These neurons are able to maintain their firing even in the absence of visual input. The standard neuronal network approach to model networks with memory that represent continuous spaces is that of continuous attractor networks. It has recently been shown how idiothetic (self-motion) inputs could update the activity packet of neuronal firing for a one-dimensional case (head direction cells), and for a two-dimensional case (place cells which represent the place where a rat is located). In this paper, we describe three models of primate hippocampal spatial view cells, which not only maintain their spatial firing in the absence of visual input, but can also be updated in the dark by idiothetic input. The three models presented in this paper represent different ways in which a continuous attractor network could integrate a number of different kinds of velocity signal (e.g., head rotation and eye movement) simultaneously. The first two models use velocity information from head angular velocity and from eye velocity cells, and make use of a continuous attractor network to integrate this information. A fundamental feature of the first two models is their use of a 'memory trace' learning rule which incorporates a form of temporal average of recent cell activity. Rules of this type are able to build associations between different patterns of neural activities that tend to occur in temporal proximity, and are incorporated in the model to enable the recent change in the continuous attractor to be associated with the contemporaneous idiothetic input. The third model uses positional information from head direction cells and eye position cells to update the representation of where the agent is looking in the dark. In this case the integration of idiothetic velocity signals is performed in the earlier layer of head direction cells.     

Perceptual anticipation in handwriting: the role of implicit motor competence

In two experiments, perceptual anticipation--that is, the observer's ability to predict the course of dynamic visual events--in the case of handwriting traces was investigated. Observers were shown the dynamic display of the middle letter l excerpted from two cursive trigrams (lll or lln) handwritten by one individual. The experimental factor was the distribution of the velocity along the trace, which was controlled by a single parameter, beta. Only for one value of this parameter (beta = 2/3) did the display comply with the two-thirds power law, which describes how tangential velocity depends on curvature in writing movements. The task was to indicate the trigram from which the trace was excerpted--that is, to guess the letter that followed the specific instance of the l that had been displayed. In Experiment 1, the no answer option was available. Experiment 2 adopted a forced-choice response rule. Responses were never reinforced. When beta = 2/3, the rate of correct guesses was high (Experiment 1, P?correct? = .69; Experiment 2, P?correct? = .78). The probability of a correct answer decreased significantly for both smaller and larger values of beta, with wrong answers becoming predominant at the extremes of the range of variation of this parameter. The results are consistent with the hypothesis that perceptual anticipation of human movements involves comparing the perceptual stimulus with an internal dynamic representation of the ongoing event.     

'Squaring' is better at predicting plaid motion than the vector average or intersection of constraints

How do humans combine the velocity information from two moving gratings (plaids) to detect pattern motion direction?-We are still unable to answer this question. The 'intersection of constraints' rule (IOC-Adelson and Movshon, 1982 Nature 300 523-525), and the 'vector average' rule (VA-Wilson et al, 1992 Visual Neuroscience 9 79-97) have both been supported by results in the plaid literature, but could these results be predicted by a 'squaring' nonlinearity that now forms part of several influential spatiotemporal energy models (Wilson et al 1992, loco cit.; Lu and Sperling, 1995 Vision Research 35 2697-2722; Simoncelli and Heeger, 1998 Vision Research 38 743-761)? Spatiotemporal energy in these models predicts directions other than those predicted by standard spatiotemporal energy models and may underlie the results that support the combination rules. The two combination rules and predictions from 'squaring' were tested under identical conditions. In the first three experiments a plaid was randomly presented in one of 45 different orientations, and observers were asked to remember the direction. The stimulus was then replaced by an oriented line indicating the direction predicted by one of the hypotheses. The observer was unaware which hypothesis had generated the line and was asked to make a same/different judgment. Results showed that the 'squaring' hypothesis was better at predicting perceived direction than either the IOC or VA.     

What makes the windows task difficult for young children: rule inference or rule use?

The windows task is difficult for young children. In this task, a child is shown two boxes with windows revealing that one is empty, whereas the other contains a treat. The child is asked to point to a box for an opponent to look in. The child then "wins" the contents of the other box (the treat). To pass the task, the child must use a rule such as "point to the empty box." But crucially, because the child is not told this rule by the experimenter, he or she must first infer it. Therefore, the windows task has two distinct requirements: (a) infer the rule "point to the empty box" and, once the rule is inferred, (b) use the rule by holding it in mind while inhibiting the prepotent response of pointing to the treat. In this study, the authors sought to determine which of these two requirements was responsible for poor performance on the windows task. They compared the performance of 3(1/2)-year-olds (N=40) on four tasks: the standard windows task, a version of the windows task that required rule use but not rule inference, and two versions of the day-night task that also required rule use but not rule inference. The relative performance on these four tasks and the pattern of correlations among them suggested that children had difficulty in inferring a rule that enables them to pass the task, whereas they had little difficulty in using the rule. Little evidence was obtained to suggest that the standard windows task requires inhibition.     

Velocity perception for sounds moving in frequency space

In three experiments, we considered the relative contribution of frequency change (Δf) and time change (Δt) to perceived velocity (Δf/Δt) for sounds that moved either continuously in frequency space (Experiment 1) or in discrete steps (Experiments 2 and 3). In all the experiments, participants estimated “how quickly stimuli changed in pitch” on a scale ranging from 0 (not changing at all) to 100 (changing very quickly). Objective frequency velocity was specified in terms of semitones per second (ST/s), with ascending and descending stimuli presented on each trial at one of seven velocities (2, 4, 6, 8, 10, 12, and 14 ST/s). Separate contributions of frequency change (Δf) and time change (Δt) to perceived velocity were assessed by holding total Δt constant and varying Δf or vice versa. For tone glides that moved continuously in frequency space, both Δf and Δt cues contributed approximately equally to perceived velocity. For tone sequences, in contrast, perceived velocity was based almost entirely on Δt, with surprisingly little contribution from Δf. Experiment 3 considered separate judgments about Δf and Δt in order to rule out the possibility that the results of Experiment 2 were due to the inability to judge frequency change in tone sequences.     

Does rule recursion make melodies easier to reproduce? If not, what does?

Two experiments examined the effects of variations in melodic rule structure and rhythm upon the ability of musically sophisticated listeners to reproduce auditory patterns. These experiments were designed to evaluate different theoretical perspectives on auditory pattern perception and the role of rule structure in perceiving and remembering. Predictions of a coding model, which emphasizes the impact of rule recursion, were contrasted with those of an accent model, which emphasizes the relative timing of melodic and temporal accents. Effects of recursive (hierarchical) and nonrecursive (linear) rule arrangements were studied in contexts where pattern contour differences were controlled for. Rhythm was also varied. Measured pauses were inserted between certain tones to make a rhythm compatible or incompatible with melodic rule phrases. Experiment 1 showed that pattern simplicity was determined not by rule recursive codes, but by the number and timing of contour changes and melodic rule breaks. Experiment 2 examined additional effects of rhythm on listeners' response to rule recursion and melodic phrasing in melodies of equivalent contour. Although modest effects of rule recursion appeared, these effects were again outweighed by large performance differences due to the relative timing of changes in contour and melodic rule structure. Implications of the accent model for dynamic attending are discussed in the context of a new proposal involving temporal phasing of accents.     

Delayed rule following

Although the elements of a fully stated rule (discriminative stimulus [S(D)], some behavior, and a consequence) can occur nearly contemporaneously with the statement of the rule, there is often a delay between the rule statement and the S(D). The effects of this delay on rule following have not been studied in behavior analysis, but they have been investigated in rule-like settings in the areas of prospective memory (remembering to do something in the future) and goal pursuit. Discriminative events for some behavior can be event based (a specific setting stimulus) or time based. The latter are more demanding with respect to intention following and show age-related deficits. Studies suggest that the specificity with which the components of a rule (termed intention) are stated has a substantial effect on intention following, with more detailed specifications increasing following. Reminders of an intention, too, are most effective when they refer specifically to both the behavior and its occasion. Covert review and written notes are two effective strategies for remembering everyday intentions, but people who use notes appear not to be able to switch quickly to covert review. By focusing on aspects of the setting and rule structure, research on prospective memory and goal pursuit expands the agenda for a more complete explanation of rule effects.     

Matching and naming objects by shape or function: age and context effects in preschool children

Three experiments tested preschoolers' use of abstract principles to classify and label objects by shape or function. Three- and 4-year-olds were instructed to match objects by shape or function. Four-year-olds readily adopted either rule, but 3-year-olds followed only the shape rule. Without a rule, 4-year-olds tended to match by shape unless object function was shown during matching (Experiment 2). Three-year-olds' ability to use a function rule was tested in several conditions (re-presenting functions; reminders to "use the rule"; repeating rule on every trial). None induced consistent function matching (Experiment 3). Supplemental memory and verbal tasks showed that 3-year-olds have trouble using function as an abstract basis of comparison. Naming data, however, show that preschoolers are learning that object labels are based on function. The results show preschoolers' growing flexibility in adopting abstract generalization rules and growing knowledge of conventions for extending words.     

Parsing silhouettes: the short-cut rule.

Many researchers have proposed that, for the purpose of recognition, human vision parses shapes into component parts. Precisely how is not yet known. The minima rule for silhouettes (Hoffman & Richards, 1984) defines boundary points at which to parse but does not tell how to use these points to cut silhouettes and, therefore, does not tell what the parts are. In this paper, we propose the short-cut rule, which states that, other things being equal, human vision prefers to use the shortest possible cuts to parse silhouettes. We motivate this rule, and the well-known Petter's rule for modal completion, by the principle of transversality. We present five psychophysical experiments that test the short-cut rule, show that it successfully predicts part cuts that connect boundary points given by the minima rule, and show that it can also create new boundary points.     

Parsing silhouettes: The short-cut rule

Many researchers have proposed that, for the purpose of recognition, human vision parses shapes into component parts. Precisely how is not yet known. The minima rule for silhouettes (Hoffman & Richards, 1984) defines boundary points at which to parse but does not tell how to use these points to cut silhouettes and, therefore, does not tell what the parts are. In this paper, we propose the short-cut rule, which states that, other things being equal, human vision prefers to use the shortest possible cuts to parse silhouettes. We motivate this rule, and the well-known Petter’s rule for modal completion, by the principle of transversality. We present five psychophysical experiments that test the short-cut rule, show that it successfully predicts part cuts that connect boundary points given by the minima rule, and show that it can also create new boundary points.     

迫选规则体验法: 检验规范性和描述性风险决策理论的新尝试

为寻求检验规范性和描述性风险决策理论的通用标准, 本研究以期望价值理论和齐当别抉择模型为例, 探讨了“迫选规则体验法”的适用性。被试为120名大学生, 实验任务为要求被试分别完成自主决策(采用未知规则: 真规则)和规则迫选决策(遵循给定规则: 假规则)任务, 并对决策后的情感和认可程度进行评定。研究发现: (1) 被试在自主决策条件下比在规则迫选条件下体验到的正性情感程度更强, 负性情感的程度更弱; (2) 被试在自主决策与规则迫选决策两种条件下做出的相同决策越多, 该被试对迫选规则更加认可并体验到的正性情感程度越强, 负性情感的程度越弱; (3) 与期望价值理论相比, 齐当别抉择模型可能符合更多决策者的实际决策规则。这些结果表明, 作为检验规范性和描述性风险决策理论的新尝试, 迫选规则体验法可能更有助于回答“决策者实际采用的决策规则是什么”的问题。     

Hypothesis-testing strategies: Why two goals are better than one

An intriguing finding in the hypothesis-testing literature concerns a large increase in the proportion of subjects who discover a rule when they are asked to determine two rules rather than that rule alone. This finding is based on Wason's (1960) “2 4 6” task, in which subjects try to discover a rule (ascending numbers) by generating and testing number triples. They are initially given an example (“2, 4, 6”) of the rule that leads to overly specific hypotheses. With single-goal (SG) instructions, subjects try to discover the correct rule and are told whether each triple proposed fits the rule. With dual-goal (DG) instructions, correct and incorrect categories are labelled, respectively, as DAX and MED. Subjects try to discover both rules and are told whether each proposed triple is DAX or MED. Two explanations of why DG subjects do better at rule discovery than SG subjects are tested: the quantity of information and the testing of complementary rules using the prevalent positive-test strategy. Results support the latter explanation: DG subjects outperform SG subjects only if they know the rules are complementary, and that SG subjects' performance does not improve when required to test more triples before announcing their first rule. A third explanation, the positivity of the linguistic label of the feedback, is ruled out. Understanding the superiority of DG instructions might suggest a general method for enhancing rule discovery.     

Optimization of sample size in controlled experiments: The CLAST rule

Sequential rules are explored in the context of null hypothesis significance testing. Several studies have demonstrated that the fixed-sample stopping rule, in which the sample size used by researchers is determined in advance, is less practical and less efficient than sequential stopping rules. It is proposed that a sequential stopping rule called CLAST (composite limited adaptive sequential test) is a superior variant of COAST (composite open adaptive sequential test), a sequential rule proposed by Frick (1998). Simulation studies are conducted to test the efficiency of the proposed rule in terms of sample size and power. Two statistical tests are used: the one-tailed t test of mean differences with two matched samples, and the chi-square independence test for twofold contingency tables. The results show that the CLAST rule is more efficient than the COAST rule and reflects more realistically the practice of experimental psychology researchers.     

Sugaring o'er the devil: Moral superiority and group identification help individuals downplay the implications of ingroup rule‐breaking

We examined how a group's claim to moral superiority influences evaluations of rule‐breaking by ingroup members. Moral superiority was manipulated among researchers (Study 1) and British citizens (Study 2), after which group members were presented with ingroup rule‐breakers: a researcher violating ethical rules (Study 1) and British soldiers abusing Iraqi prisoners (Study 2). In both studies, higher and lower identifiers in the control condition perceived the rule‐breaking as equally damaging, evaluated the rule‐breakers equally negatively and recommended equally harsh punishments. When the group had taken the moral high ground, lower identifiers perceived the rule‐breaking as more damaging than did higher identifiers. In addition, higher identifiers evaluated the rule‐breakers less negatively and recommended more lenient punishments. Results of mediation analyses demonstrated that negative evaluations of, and recommended punishment for, the rule‐breakers were explained by the perceived damage that their behaviour caused to the ingroup. Theoretical and practical implications are discussed. Copyright © 2011 John Wiley & Sons, Ltd.