Common variant at 16p11.2 conferring risk of psychosis.

Epidemiological and genetic data support the notion that schizophrenia and bipolar disorder share genetic risk factors. In our previous genome-wide association study, meta-analysis and follow-up (totaling as many as 18 206 cases and 42 536 controls), we identified four loci showing genome-wide significant association with schizophrenia. Here we consider a mixed schizophrenia and bipolar disorder (psychosis) phenotype (addition of 7469 bipolar disorder cases, 1535 schizophrenia cases, 333 other psychosis cases, 808 unaffected family members and 46 160 controls). Combined analysis reveals a novel variant at 16p11.2 showing genome-wide significant association (rs4583255[T]; odds ratio=1.08; P=6.6 × 10(-11)). The new variant is located within a 593-kb region that substantially increases risk of psychosis when duplicated. In line with the association of the duplication with reduced body mass index (BMI), rs4583255[T] is also associated with lower BMI (P=0.0039 in the public GIANT consortium data set; P=0.00047 in 22 651 additional Icelanders).

Combining graded categories: membership and typicality.

Forming a conjoint category (square tables) from constituent categories (squares and tables) has traditionally been modeled by formal set intersection. In this traditional view, in which categories are treated as precisely defined sets, an item is a member of the conjoint category if and only if it is a member of both constituent categories. However, as is now widely believed, many categories should be treated as graded, with members that vary in typicality and boundaries that are inexact. In the present article, it is argued that set intersection is inappropriate for combining graded categories. The authors propose an alternative formal mechanism in which a conjoint category is constructed from constituent categories by forming a joint distribution of values. The proposed model accounts for both membership and typicality of instances in conjoint categories, but only when the constituent categories are independent, or the relation between them is known.

Categories and particulars: prototype effects in estimating spatial location.

A model of category effects on reports from memory is presented. The model holds that stimuli are represented at 2 levels of detail: a fine-grain value and a category. When memory is inexact but people must report an exact value, they use estimation processes that combine the remembered stimulus value with category information. The proposed estimation processes include truncation at category boundaries and weighting with a central (prototypic) category value. These processes introduce bias in reporting even when memory is unbiased, but nevertheless may improve overall accuracy (by decreasing the variability of reports). Four experiments are presented in which people report the location of a dot in a circle. Subjects spontaneously impose horizontal and vertical boundaries that divide the circle into quadrants. They misplace dots toward a central (prototypic) location in each quadrant, as predicted by the model. The proposed model has broad implications; notably, it has the potential to explain biases of the sort described in psychophysics (contraction bias and the bias captured by Weber's law) as well as symmetries in similarity judgments, without positing distorted representations of physical scales.

Linguistic and non-linguistic spatial categorization.

Three experiments examine the relation between linguistic and non-linguistic categorization of spatial relations. We compare linguistic and non-linguistic responses to the same spatial stimuli. Contrary to earlier claims in the literature (Hayward, W. G. & Tarr, M. J. (1995). Spatial language and spatial representation. Cognition, 55, 39-84), we find that linguistic and non-linguistic spatial categories do not correspond. Rather, they appear to have an inverse relation such that the prototypes of linguistic categories, such as 'above', are boundaries in non-linguistic spatial categorization. Evidence for this inverse relation comes from linguistic acceptability judgments and the pattern of bias in participants' reproductions of location. Our findings suggest that while linguistic and non-linguistic spatial organization rely on a common underlying structure, that structure may play different roles in the two organizational systems.

Bias in spatial location due to categorization: comment on Tversky and Schiano.

B. Tversky and D. J. Schiano (1989) reported bias in reproducing the angle of a line in an "ell" frame. When no conceptual interpretation of the task was given, they argued that the bias was due to a perceptual process that produced an apparent tilt in the line (D. J. Schiano & B. Tversky, 1992). We propose that J. Huttenlocher, L. V. Hedges, and S. Duncan's (1991) model of category effects on estimates of stimulus values provides a better explanation of this bias. Two experiments are presented that examine these alternative views. The results show effects of the orientation of the frame and of an interference task on bias that are more consistent with J. Huttenlocher et al.'s model than with the perceptual explanation adopted by D. J. Schiano and B. Tversky.

Memory for day of the week: a 5 + 2 day cycle.

People use a variety of schemes to keep track of time. One such scheme is the week, with its 7 distinctly named days. This article examines memory for day of the week and its relation to memory for time of day and for elapsed time (number of days). Data are presented from a study in which people answered a set of interview questions about the time of occurrence of a particular event. Two issues are addressed. The first issue concerns the way different temporal schemes are organized in relation to each other in memory. Memory for day of the week is independent of other aspects of temporal memory. The second issue concerns whether the week is organized hierarchically into either weekday periods or weekend periods or both. The weekday period forms a distinct 5-day unit within the 7-day weekly cycle. The present data, together with those from the authors' earlier work, suggest that the time an event occurred is encoded in relation to a set of separate temporal scripts (e.g., daily and weekly) and that such scripts may be hierarchically organized.

Why do categories affect stimulus judgment?

The authors tested a model of category effects on stimulus judgment. The model holds that the goal of stimulus judgment is to achieve high accuracy. For this reason, people place inexactly represented stimuli in the context of prior information, captured in categories, combining inexact fine-grain stimulus values with prior (category) information. This process can be likened to a Bayesian statistical procedure designed to maximize the average accuracy of estimation. If people follow the proposed procedure to maximize accuracy, their estimates should be affected by the distribution of instances in a category. In the present experiments, participants reproduced one-dimensional stimuli. Different prior distributions were presented. The experiments verified that people's stimulus estimates are affected by variations in a prior distribution in such a manner as to increase the accuracy of their stimulus reproductions.

A mental model for early arithmetic.

The authors examined young children's ability to solve nonverbal calculation problems in which they must determine how many items are in a hidden array after items have been added into or taken away from it. Earlier work showed that an ability to reliably solve such problems emerges earlier than verbal calculation ability but did not examine when it first appears. The authors propose that the ability to solve such problems involves domain-general symbolic processes similar to those involved in symbolic play and the use of physical models. Hence the ability to calculate should appear at about 2 years and should be related to overall level of intellectual competence. The authors show that the ability to reliably solve nonverbal calculation tasks emerges only after 2 years of age and that performance on nonverbal calculation problems is highly related to overall level of intellectual competence in children between 3 and 4 years of age.

Reports of elapsed time: bounding and rounding processes in estimation.

The present article concerns the way temporal information is represented in memory and the processes used in estimating when events occurred. In particular, we examine the sources of bias in reports of the time that has elapsed since a target event occurred. We find that reported times are less than actual times. Evidence is presented that this forward bias is not a result of misrepresentation of elapsed time in memory, but rather reflects two factors that arise in constructing reports from inexact information in memory. One factor is subjects' imposition of an upper boundary on reports, reflecting their notion of what would constitute reasonable answers to the question asked. This boundary truncates the distribution of reports, producing forward bias. The other factor is subjects' use of rounded (prototypic) values; these values, although stated in days, actually represent larger temporal categories (e.g., 14, 21, 30, 60 days ago). The distance between rounded values increases as the temporal categories become larger. Because of decreasing precision in memory and this increase in the distance between rounded values, a broader range of values is rounded down than up, thus producing forward bias.

Numerical abstraction in infants: another look.

This article examines an important finding from the literature on infant numerical competence. The finding, reported by P. Starkey, E. S. Spelke, and R. Gelman (1990), was that infants looked longer toward a visual display that was equal in number to an auditory set. In Experiment 1, when the procedures described by P. Starkey et al. were followed and duration was held constant across auditory sequences that varied in number, infants looked longer toward the display that was not numerically equivalent to the auditory set. In Experiment 2, when the rate and duration of the auditory sequences were varied randomly within infants, no significant preference for either the equivalent or nonequivalent visual display was shown. These results raise questions about P. Starkey et al.'s claims that infants can represent the numerosity of sets in different modalities and then perform one-one correspondence computations over them.

Early fraction calculation ability.

Three- to 7-year-olds' ability to calculate with whole-number, fraction, and mixed-number amounts was tested using a nonverbal task in which an amount was displayed and then hidden (J. Huttenlocher, N. C. Jordan, & S. C. Levine, 1994). Next, an amount was added to or subtracted from the hidden amount. The child's task was to determine the hidden amount that resulted from the transformation. Although fraction problems were more difficult than whole-number problems, competence on all problem types emerged in the early childhood period. Furthermore, there were striking parallels between the development of whole-number and fraction calculation. This is inconsistent with the hypothesis that early representations of quantity promote learning about whole numbers but interfere with learning about fractions (e.g., R. Gelman, 1991; K. Wynn, 1995, 1997).

Early sex differences in spatial skill.

This study investigated sex differences in young children's spatial skill. The authors developed a spatial transformation task, which showed a substantial male advantage by age 4 years 6 months. The size of this advantage was no more robust for rotation items than for translation items. This finding contrasts with studies of older children and adults, which report that sex differences are largest on mental rotation tasks. Comparable performance of boys and girls on a vocabulary task indicated that the male advantage on the spatial task was not attributable to an overall intellectual advantage of boys in the sample.

Calculation abilities in young children with different patterns of cognitive functioning.

This study examined the arithmetic calculation abilities of kindergarten and first-grade children with different patterns of cognitive functioning: children with low language but adequate spatial abilities (Low Language; n = 33, male = 42%); children with low spatial but adequate language abilities (Low Spatial; n = 21, male = 42%); children with general delays (Delayed; n = 21, male = 48%); and children with no language or spatial impairments (Nonimpaired; n = 33, male = 48%). Each child was given a series of addition and subtraction calculations presented as nonverbal problems, story problems, and number-fact problems. Story problems and number-fact problems require mastery of conventional verbal symbols, whereas nonverbal problems do not. The findings show that nonverbal, story, and number-fact problem formats are differentially sensitive to variation in cognitive ability. The Low Language group performed significantly worse than the Nonimpaired group on story problems but not on nonverbal problems or number-fact problems. The Delayed group performed significantly worse than the Nonimpaired group on nonverbal problems as well as on story problems but not on number-fact problems. The Low Spatial group did not differ significantly from the Nonimpaired group on any of the three problem types, although the overall performance of these children was weaker. When we adjusted for finger use on number-fact problems, the Nonimpaired group outperformed both the Low Language and the Delayed groups but not the Low Spatial group. Thus, the finding that the Low Language and Delayed groups perform as well as the Nonimpaired group on number-fact problems is attributable to their greater finger use.

Language input and language growth.

This report is concerned with the sources of language development in the child. We have found a substantial relation between naturally occurring variations in children's language environments and their language skills, both at the earliest stages of language development and later, at 5 and 6 years of age. Our studies show that children's language development is related to the speech they hear at home and the speech they hear at school. Although much more work remains to be done, it is clear that differences in language input within the normal range are causally related to the growth of children's vocabularies and their syntactic skills.

Environmental input and cognitive growth: a study using time-period comparisons.

In this study, we examined the relation of input to cognitive growth in a single population of children. We studied 4 domains: Language, Spatial Operations, Concepts, and Associative Memory. Four groups of children drawn from the same population were tested in October of kindergarten, April of kindergarten, October of first grade, and April of first grade. These time points are 6 months apart, but they span periods that differ in amount of school input children receive. Much greater growth was found over time periods with greater amounts of school input (October to April) than over time periods with less school input (April to October) for Language, Spatial Operations, and Concepts, but not for Associative Memory. These findings suggest that amount of input is causally related to cognitive growth in particular domains.

Category effects on estimates of stimuli: perception or reconstruction?

The present study examined a common category effect that has been reported in the literature: the tendency for estimates of individual stimuli to be biased toward the central value of the presented set of stimuli. Both encoding and reconstruction accounts of this central-tendency effect are considered. Plain vertical lines and vertical lines embedded in the Müller-Lyer illusion were estimated while still in view or from memory. Although bias due to the Müller-Lyer illusion remained constant across the two conditions, bias due to the context set (category) occurred only when stimuli were estimated from memory. The results suggest that the category bias occurs at a later stage of processing than the Müller-Lyer effect and offer support for a reconstruction account of category effects on stimulus estimation.

Development of calculation abilities in young children.

This study investigates the development of skills for solving verbally and nonverbally presented calculation problems in children between 4 and 6 years of age. Identical addition and subtraction calculations were presented in three problem-type formats: nonverbal problems, story problems, and number-fact problems. The nonverbal problems involved presenting sets of physical referents that were then transformed either by adding or removing elements. The child saw the initial set and the number of elements that were added or removed, but not the final set. The task was to construct an array that contained the number of elements in the final set. The story problems and number-fact problems were presented orally, without props. Results indicate that children as young as 4 years of age have some success on the nonverbal problems, showing that they can transform sets by adding or subtracting elements. In contrast, children do not achieve comparable levels of success on the story problems or number-fact problems until 5 1/2 to 6 1/2 years of age. Moreover, throughout the age range tested, children performed better on nonverbal problems than on either story problems or number-fact problems. These results suggest that children's earliest ability to add and subtract is based on experiences combining and separating sets of objects in the world and that this ability precedes the development of conventional verbal methods of calculating.

Basing categorization on individuals and events.

Exemplar, prototype, and connectionist models typically assume that events constitute the basic unit of learning and representation in categorization. In these models, each learning events updates a statistical representation of a category independently of other learning events. An implication is that events involving the same individual affect learning independently and are not integrated into a single structure that represents the individual in an internal model of the world. A series of experiments demonstrates that human subjects track individuals across events, establish representations of them, and use these representations in categorization. These findings are consistent with "representationalism," the view that an internal model of the world constitutes a physical level of representation in the brain, and that the brain does not simply capture the statistical properties of events in an undifferentiated dynamical system. Although categorization is an inherently statistical process that produces generalization, pattern completion, frequency effects, and adaptive learning, it is also an inherently representational process that establishes an internal model of the world. As a result, representational structures evolve in memory to track the histories of individuals, accumulate information about them, and simulate them in events.

Do preschool children recognize auditory-visual numerical correspondences?

The present study investigated the ability of 3- and 4-year-old children to perform tasks which require matching sets of sounds to numerically equivalent visual displays. We found that 3-year-olds performed at chance on the auditory-visual matching task, while 4-year-olds performed significantly above chance. There is evidence that mastery of the linguistic counting system is related to success on this task. These findings are unexpected given previous research reporting that 6-8-month-olds can detect the numerical equivalence between a set of sounds and items in a visual display.