Human performance on the traveling salesman problem

Two experiments on performance on the traveling salesman problem (TSP) are reported. The TSP consists of finding the shortest path through a set of points, returning to the origin. It appears to be an intransigent mathematical problem, and heuristics have been developed to find approximate solutions. The first experiment used 10-point, the second, 20-point problems. The experiments tested the hypothesis that complexity of TSPs is a function of number of nonboundary points, not total number of points. Both experiments supported the hypothesis. The experiments provided information on the quality of subjects’ solutions. Their solutions clustered close to the best known solutions, were an order of magnitude better than solutions produced by three well-known heuristics, and on average fell beyond the 99.9th percentile in the distribution of random solutions. The solution process appeared to be perceptually based.     

The importance of the convex hull for human performance on the traveling salesman problem: a comment on MacGregor and Ormerod (1996)

MacGregor and Ormerod (1996) have presented results purporting to show that human performance on visually presented traveling salesman problems, as indexed by a measure of response uncertainty, is strongly determined by the number of points in the stimulus array falling inside the convex hull, as distinct from the total number of points. It is argued that this conclusion is artifactually determined by their constrained procedure for stimulus construction, and, even if true, would be limited to arrays with fewer than around 50 points.     

Parallel processing of the attributes of single stimuli

Three experiments are described, in which Ss had to decide whether or not single stimuli, varying along the dimensions of shape and color, satisfied a given criterion. In different conditions, the number of dimensions relevant to the criterion was varied. The first experiment indicates that simple interpretations of a standard Nickerson procedure are potentially artifactual. In the last two experiments, a design involving different difficulties of discrimination was used so that a serial interpretation of the results could be convincingly rejected, even for unpracticed Ss. These results strongly support the view that perceptually parallel processing normally occurs in the identification of single multidimensional stimuli. By this interpretation, apparently similar tasks may produce different patterns of results because of the use of different decision processes by the Ss.     

Properties of feature detectors for speech: Evidence from the effects of selective adaptation on dichotic listening

Two selective adaptation experiments were conducted in order to investigate certain properties of feature detector systems sensitive to the information underlying the voicing distinction (Experiment I) and the place of articulation distinction (Experiment II). The experimental paradigm combined binaural adaptation with a dichotic testing procedure. The stimuli were nonboundary, good exemplars of the respective phonetic categories. In both experiments, there was a systematic shift in performance following adaptation on those trials on which the stimulus in one ear had the adapted feature value and the stimulus in the other ear had the unadapted feature value. On these trials, the adapted feature value was relatively less effective in competing for processing with the unadapted value in the opposing ear (compared to preadaptation performance). Since these results were obtained using nonboundary stimuli, it was argued that (1) adaptation affects the relevant detector along its range of operation or sensitivity, and nof simply at the phonetic boundary, and that (2) information regarding the relative output level of the detector, as well as which detector was more strongly excited, must be available at the site of interaction of the two stimuli.

     

Binocular shape constancy from novel views: the role of a priori constraints

We tested shape constancy from novel views in the case of binocular viewing, using a variety of stimuli, including polyhedra, polygonal lines, and points in 3-D. The results of the psychophysical experiments show that constraints such as planarity of surface contours and symmetry are critical for reliable shape constancy. These results are consistent with the results obtained in our previous psychophysical experiments on shape constancy from novel views in the presence of a kinetic depth effect (Pizlo & Stevenson, 1999). On the basis of these results, we developed a new model of binocular shape reconstruction. The model is based on the assumption that binocular reconstruction is a difficult inverse problem, whose solution requires imposing a priori constraints on the family of possible interpretations. In the model, binocular disparity is used to correct monocularly reconstructed shape. The new model was tested on the same shapes as those used in the psychophysical experiments. The reconstructions produced by this model are substantially more reliable than the reconstructions produced by models that do not use constraints. Interestingly, monocular (but not binocular) reconstructions produced by this model correlate well with both monocular and binocular performance of human subjects. This fact suggests that binocular and monocular reconstructions of shapes in the human visual system involve similar mechanisms based on monocular shape constraints.     

Compact integer-programming models for extracting subsets of stimuli from confusion matrices

This paper presents an integer linear programming formulation for the problem of extracting a subset of stimuli from a confusion matrix. The objective is to select stimuli such that total confusion among the stimuli is minimized for a particular subset size. This formulation provides a drastic reduction in the number of variables and constraints relative to a previously proposed formulation for the same problem. An extension of the formulation is provided for a biobjective problem that considers both confusion and recognition in the objective function. Demonstrations using an empirical interletter confusion matrix from the psychological literature revealed that a commercial branch-and-bound integer programming code was always able to identify optimal solutions for both the single-objective and biobjective formulations within a matter of seconds. A further extension and demonstration of the model is provided for the extraction of multiple subsets of stimuli, wherein the objectives are to maximize similarity within subsets and minimize similarity between subsets.     

Generating nonsymbolic number stimuli

Studies investigating nonsymbolic numbers (e.g., dot arrays) are confronted with the problem that changes in numerosity are always accompanied by changes in the visual properties of the stimulus. It is therefore debated whether the visual properties of the stimulus rather than number can explain the results obtained in studies investigating nonsymbolic number processing. In this report, we present a program (available at ; note that the program is designed to work with the Psychophysics Toolbox in MATLAB) that exports information about the visual properties of stimuli that co-vary with number (area extended, item size, total surface, density, and circumference). Consequently, insight into the relation between the visual properties of the stimulus and numerical distance can be achieved, and post hoc analyses can be conducted to directly reveal whether numerical distance or (some combinations of) the visual properties of a stimulus could be the most likely candidate underlying the results. Here, we report data that demonstrate the program’s usefulness for research on nonsymbolic number stimuli.     

Visual representations of dynamic actions from static pictures

We investigated how subjects used their knowledge of biomechanical constraints when judging whether different items were in balance or in the process of falling, as a function of their angle of slant. In the first experiment, the stimuli were pictures of postures of a human body, of a wooden mannequin, and of a skeleton. The results show that for these 3 items, fall responses appeared for a smaller slant angle for a backward slant than for a forward one. This difference may reflect the influence of biomechanical constraints. To verify whether the asymmetry of the responses to the mannequin and the skeleton was genuine or due to some semantic context effect, a second experiment was run with only pictures of a wooden mannequin. The same asymmetry was observed. In a third experiment, falling judgments were obtained for pictures of a human body and of a structurally comparable artifactual object. The asymmetry of the fall responses appeared only for the human body.     

Memory and learning for visual signals in time and space

Vision is often characterized as a spatial sense, but what does that characterization imply about the relative ease of processing visual information distributed over time rather than over space? Three experiments addressed this question, using stimuli comprising random luminances. For some stimuli, individual items were presented sequentially, at 8 Hz; for other stimuli, individual items were presented simultaneously, as horizontal spatial arrays. For temporal sequences, subjects judged whether each of the last four luminances matched the corresponding luminance in the first four; for spatial arrays, they judged whether each of the right-hand four luminances matched the corresponding left-hand luminance. Overall, performance was far better with spatial presentations, even when the entire spatial array was presented for just tens of milliseconds. Experiment 2 demonstrated that there was no gain in performance from combining spatial and temporal information within a single stimulus. In a final experiment, particular spatial arrays or temporal sequences were made to recur intermittently, interspersed among, non-recurring stimuli. Performance improved steadily as particular stimulus exemplars recurred, with spatial and temporal stimuli being learned at equivalent rates. Logistic regression identified several shortcut strategies that subjects may have exploited while performing our task.     

Initial outcomes of an augmented competing stimulus assessment

Competing stimulus assessments (CSAs) are designed to identify stimuli that, when made freely available, reduce problem behavior. Although CSAs have demonstrated utility, identifying competing stimuli can be difficult for some individuals. The current study describes outcomes from an augmented CSA (A-CSA) for 6 consecutively encountered cases with treatment-resistant subtypes of automatically maintained problem behavior. When test stimuli were made freely available, only between 0 and 1 effective competing stimuli were identified for each case. Prompting and response blocking were temporarily employed in succession to promote engagement with stimuli and disrupt problem behavior. When those procedures were withdrawn and stimuli made freely available, the number of effective competing stimuli increased in all 6 cases. Findings suggest that procedures designed to promote engagement and disrupt problem behavior may allow the A-CSA to be a platform not only for identifying competing stimuli, but also for actively establishing competing stimuli.     

Perception of biomechanical motions by infants: implementation of various processing constraints

Geometry informs us that there exist a large number of possible connectivity patterns consistent with a point-light display of a person walking. Yet there is only one pattern consistent with a "stick figure" representation of the human form, and that pattern is uniquely specified by those pairwise connections that remain locally rigid. In this study, sensitivity to local rigidity in biomechanical displays was investigated in 3- and 5-month-old infants. The results of Experiment 1 revealed that by 5 months of age, infants discriminate a locally rigid point-light walker display from one in which local rigidity is perturbed. In Experiment 2 we tested infants' sensitivity to the same stimuli when those stimuli were inverted. Contrary to the preceding experiment, the results revealed no evidence of discrimination. Taken together, these findings suggest that infants are sensitive to local rigidity in biomechanical displays but that this sensitivity is orientation specific. Possible mechanisms for this specificity are discussed in the context of additional constraints on the processing of biomechanical displays.     

The forced-choice paradigm and the perception of facial expressions of emotion

The view that certain facial expressions of emotion are universally agreed on has been challenged by studies showing that the forced-choice paradigm may have artificially forced agreement. This article addressed this methodological criticism by offering participants the opportunity to select a none of these terms are correct option from a list of emotion labels in a modified forced-choice paradigm. The results show that agreement on the emotion label for particular facial expressions is still greater than chance, that artifactual agreement on incorrect emotion labels is obviated, that participants select the none option when asked to judge a novel expression, and that adding 4 more emotion labels does not change the pattern of agreement reported in universality studies. Although the original forced-choice format may have been prone to artifactual agreement, the modified forced-choice format appears to remedy that problem.     

The effect of different methods to construct non-symbolic stimuli in numerosity estimation and comparison

Numerosity estimation and comparison tasks are often used to measure the acuity of the approximate number system (ANS), a mechanism which allows extracting numerosity from an array of dots independently from several visual cues (e.g. area extended by the dots). This idea is supported by studies showing that numerosity can be processed while these visual cues are controlled for. Different methods to construct dot arrays while controlling their visual cues have been proposed in the past. In this paper, these methods were contrasted in an estimation and a comparison task. The way of constructing the dot arrays had little impact on estimation. In contrast, in the comparison task, participants' performance was significantly influenced by the method that was used to construct the arrays of dots, indicating better performance when the visual cues of the dot arrays (partly) co-varied with numerosity. The present study therefore shows that estimates of ANS acuity derived from comparison tasks are inconsistent and dependent on how the stimuli are constructed. This makes it difficult to compare studies which utilised different methods to construct the dot arrays in numerosity comparison tasks. In addition, these results question the currently held view of the ANS as capable of robustly extracting numerosity independently from visual cues.     

Sensitivity to Crossover Constraints During Native and Non-native Pronoun Resolution

We report the results from two experiments examining native and non-native German speakers’ sensitivity to crossover constraints on pronoun resolution. Our critical stimuli sentences contained personal pronouns in either strong (SCO) or weak crossover (WCO) configurations. Using eye-movement monitoring during reading and a gender-mismatch paradigm, Experiment 1 investigated whether a fronted wh-phrase would be considered as a potential antecedent for a pronoun intervening between the wh-phrase and its canonical position. Both native and non-native readers initially attempted coreference in WCO but not in SCO configurations, as evidenced by early gender-mismatch effects in our WCO conditions. Experiment 2 was an offline antecedent judgement task whose results mirrored the SCO/WCO asymmetry observed in our reading-time data. Taken together, our results show that the SCO constraint immediately restricts pronoun interpretation in both native and non-native comprehension, and further suggest that SCO and WCO constraints derive from different sources.     

Sex differences and the factor of time in solving Vandenberg and Kuse mental rotation problems

In accounting for the well-established sex differences on mental rotation tasks that involve cube stimuli of the Shepard and Metzler (Shepard & Metzler, 1971) kind, performance factors are frequently invoked. Three studies are presented that examine performance factors. In Study 1, analyses of the performance of a large number of subjects (n=1765) that performed the Vandenberg and Kuse (1976) mental rotation test (MRT) under standard conditions showed that the magnitude of the sex differences increases as subjects proceed through the sequence of problems, and that fewer females than males reach the last problems in a problem set. This supports the role of time constraints in sex differences on the MRT. Study 2 compared the magnitude of sex differences for subjects (n=212) who did the MRT under standard conditions (T1), and with double the time (T2) allowed for the test. No significant reduction in the magnitude of sex differences was observed-even though the overall scores under T2 increased markedly for both sexes. Study 3 examined the suggestion by that mental rotation differences arise because females spend more time than males in assuring that stimuli that do not match do indeed not match, with no sex differences for matching stimuli. This hypothesis was not supported for a sample of 20 males and 26 females. We conclude that performance factors may play a role in sex difference on mental rotation tasks, but do not account for all of the differences.     

Identification of Real and Artifactual Moderators of Effect Size in Meta-Analysis

This article argues that while meta-analytic studies are widely used in psychological literature, heterogeneity and the potential for confounding remain major problems in the interpretation of meta-analytic study results. The article demonstrates the use of exploratory analysis including graphical methods prior to meta-analysis, and introduces a methodology to screen for artifactual effects. These procedures are illustrated on effect size data comparing depression treatment outcome from psychotherapy versus pharmacotherapy. Results support prior findings of a nonsignificant difference in effect size between the two treatments. They also support findings that treatment type accounts for only a very small proportion of outcome variance. However, the results indicate that some previously reported covariates of depression treatment outcome may be artifactual.     

数学能力与问句位置对小学生数学结构不良应用题表征的影响

对小学四年级高低数学能力学生各40名,呈现问句前置和问句后置两种形式的结构不良应用题,探讨两种被试在问句前置时对应用题的内在表征形式倾向.结果发现,两种被试在问句前置时阅读条件句的总时间比问句后置时显著降低,解题时间显著降低,但高能力被试阅读有关条件句的时间在总阅读时间中的比例显著增高,解答成绩显著提高,而低能力被试相关时间比反而显著下降、解答成绩没有显著提高.这表明,高能力被试建构问题模型与情境模型,而低能力被试只建构问题模型.     

Perceptual reference points for form and orientation in young infants: anchors or magnets?

In some domains, certain stimuli are especially salient and efficiently encoded and are referred to as reference points. One current issue concerns whether reference points are associated with regions of increased or decreased discriminability and function as either perceptual anchors or magnets. In two experiments utilizing the familiarization/novelty-preference procedure, the question of whether 3- to 4-month-old infants' representations of form and orientation information are structured by perceptual reference points and whether such reference points serve as anchors or magnets is examined. In Experiment 1, infants displayed above-chance discrimination performance for pairs of form stimuli that were equivalently distinct on a physical basis, but only when one member of each pair was a "good" form (i.e., diamond, square, or triangle). In Experiment 2, infants displayed above-chance discrimination performance for pairs of stimuli differing by 7.5 degrees of orientation, but only when one member of each pair was either horizontal or vertical. The combined results from the two experiments suggest that "simple" gestalts and main axes (i.e., horizontal and vertical) serve as perceptual anchors in young infants' representations of form and orientation information.     

Shaping of rule-governed behaviour

Over an experimental session of 80 trials, subjects counted brief auditory stimuli ("clicks") in stimulus presentation periods and indicated the number counted by pressing a key the corresponding number of times in subsequent response periods. "Correct" answers resulted in feedback. Unknown to the subjects, the feedback criterion was based on speed of pressing rather than on the correct number of presses. Speed of pressing was modified by response consequences when feedback was made dependent on pressing faster or slower than baseline speed. Modification of speed occurred independently of rules and without the subjects' ability to describe contingency or response requirements. The results suggest that non-verbal contingencies may have a shaping effect on non-salient and non-described attributes of rule-governed behaviour, and it is argued that this may be an important control mechanism of low-level behavioural attributes that are unlikely to be guided by verbal discriminative stimuli.     

Effects of Interspersing Rate on Student Preferences for Mathematics Assignments

This study investigated the extent to which interspersing effects are consistent with the effects of reinforcement on predicting students preferences for mathematics assignments. Students were exposed to 4 pairs of assignments. Each assignment pair contained a control assignment with 15 problems requiring multiplication of a three digit number by a two digit number, and an experimental assignment consisting of 15 similar multiplication problems plus additional brief one-digit by one-digit multiplication problems interspersed at four different rates (i.e., no interspersing, every other, every third, or every fifth problem) across assignment pairs. Performance data were collected for accuracy, total problem completion rate and target problem completion rate. In addition to performance data, students were asked to rate each assignment with regard to relative difficulty, time, effort to complete, and preference between assignments for homework. Results suggest that although interspersing rates do not affect accuracy, they do affect problem completion rate, and student preferences for academic assignments. Discussion focuses on interspersing rate and schedules of reinforcement with emphasis on both applied and theoretical implications.