A magnitude code common to numerosities and number symbols in human intraparietal cortex

Activation of the horizontal segment of the intraparietal sulcus (hIPS) has been observed in various number-processing tasks, whether numbers were conveyed by symbolic numerals (digits, number words) or by nonsymbolic displays (dot patterns). This suggests an abstract coding of numerical magnitude. Here, we critically tested this hypothesis using fMRI adaptation to demonstrate notation-independent coding of numerical quantity in the hIPS. Once subjects were adapted either to dot patterns or to Arabic digits, activation in the hIPS and in frontal regions recovered in a distance-dependent fashion whenever a new number was presented, irrespective of notation changes. This remained unchanged when analyzing the hIPS peaks from an independent localizer scan of mental calculation. These results suggest an abstract coding of approximate number common to dots, digits, and number words. They support the idea that symbols acquire meaning by linking neural populations coding symbol shapes to those holding nonsymbolic representations of quantities.     

A Two-Minute Paper-and-Pencil Test of Symbolic and Nonsymbolic Numerical Magnitude Processing Explains Variability in Primary School Children's Arithmetic Competence

Recently, there has been a growing emphasis on basic number processing competencies (such as the ability to judge which of two numbers is larger) and their role in predicting individual differences in school-relevant math achievement. Children’s ability to compare both symbolic (e.g. Arabic numerals) and nonsymbolic (e.g. dot arrays) magnitudes has been found to correlate with their math achievement. The available evidence, however, has focused on computerized paradigms, which may not always be suitable for universal, quick application in the classroom. Furthermore, it is currently unclear whether both symbolic and nonsymbolic magnitude comparison are related to children’s performance on tests of arithmetic competence and whether either of these factors relate to arithmetic achievement over and above other factors such as working memory and reading ability. In order to address these outstanding issues, we designed a quick (2 minute) paper-and-pencil tool to assess children’s ability to compare symbolic and nonsymbolic numerical magnitudes and assessed the degree to which performance on this measure explains individual differences in achievement. Children were required to cross out the larger of two, single-digit numerical magnitudes under time constraints. Results from a group of 160 children from grades 1–3 revealed that both symbolic and nonsymbolic number comparison accuracy were related to individual differences in arithmetic achievement. However, only symbolic number comparison performance accounted for unique variance in arithmetic achievement. The theoretical and practical implications of these findings are discussed which include the use of this measure as a possible tool for identifying students at risk for future difficulties in mathematics.     

The Mediating Relation between Symbolic and Nonsymbolic Foundations of Math Competence

This study investigated the relation between symbolic and nonsymbolic magnitude processing abilities with 2 standardized measures of math competence (WRAT Arithmetic and KeyMath Numeration) in 150 3^rd- grade children (mean age 9.01 years). Participants compared sets of dots and pairs of Arabic digits with numerosities 1–9 for relative numerical magnitude. In line with previous studies, performance on both symbolic and nonsymbolic magnitude processing was related to math ability. Performance metrics combining reaction and accuracy, as well as weber fractions, were entered into mediation models with standardized math test scores. Results showed that symbolic magnitude processing ability fully mediates the relation between nonsymbolic magnitude processing and math ability, regardless of the performance metric or standardized test.     

Numerical magnitude in the human parietal lobe; tests of representational generality and domain specificity

Behavioral evidence suggests that human adults have a single system for representing the numerical magnitude of both symbolic numbers (e.g., Arabic digits) and nonsymbolic number stimuli (e.g., dot arrays). Brain imaging studies have implicated a specific parietal region in symbolic number processing, leading to the influential hypothesis that this region is the locus of a dedicated, domain-specific number system. Here we evaluated a prediction of this hypothesis, that this region should be activated not only by symbolic but also nonsymbolic number processing. Using nonsymbolic stimuli, we tested for higher parietal activations for number than for nonnumber comparison tasks (experiment 1), fMRI adaptation for numerosity repetition (experiment 2), and greater fMRI increases with increasing task difficulty for number than nonnumber tasks (experiment 3). None of these predictions were supported by the data, posing a serious challenge to the hypothesis that a single, domain-specific parietal region underlies both symbolic and nonsymbolic number representation.     

An ERP Study of the Processing of Common and Decimal Fractions: How Different They Are

This study explored event-related potential (ERP) correlates of common fractions (1/5) and decimal fractions (0.2). Thirteen subjects performed a numerical magnitude matching task under two conditions. In the common fraction condition, a nonsymbolic fraction was asked to be judged whether its magnitude matched the magnitude of a common fraction; in the decimal fraction condition, a nonsymbolic fraction was asked to be matched with a decimal fraction. Behavioral results showed significant main effects of condition and numerical distance, but no significant interaction of condition and numerical distance. Electrophysiological data showed that when nonsymbolic fractions were compared to common fractions, they displayed larger N1 and P3 amplitudes than when they were compared to decimal fractions. This finding suggested that the visual identification for nonsymbolic fractions was different under the two conditions, which was not due to perceptual differences but to task demands. For symbolic fractions, the condition effect was observed in the N1 and P3 components, revealing stimulus-specific visual identification processing. The effect of numerical distance as an index of numerical magnitude representation was observed in the P2, N3 and P3 components under the two conditions. However, the topography of the distance effect was different under the two conditions, suggesting stimulus specific semantic processing of common fractions and decimal fractions.     

Children’s Mapping between Non-Symbolic and Symbolic Numerical Magnitudes and Its Association with Timed and Untimed Tests of Mathematics Achievement

The ability to map between non-symbolic numerical magnitudes and Arabic numerals has been put forward as a key factor in children’s mathematical development. This mapping ability has been mainly examined indirectly by looking at children’s performance on a symbolic magnitude comparison task. The present study investigated mapping in a more direct way by using a task in which children had to choose which of two choice quantities (Arabic digits or dot arrays) matched the target quantity (dot array or Arabic digit), thereby focusing on small quantities ranging from 1 to 9. We aimed to determine the development of mapping over time and its relation to mathematics achievement. Participants were 36 first graders (M = 6 years 8 months) and 46 third graders (M = 8 years 8 months) who all completed mapping tasks, symbolic and non-symbolic magnitude comparison tasks and standardized timed and untimed tests of mathematics achievement. Findings revealed that children are able to map between non-symbolic and symbolic representations and that this mapping ability develops over time. Moreover, we found that children’s mapping ability is related to timed and untimed measures of mathematics achievement, over and above the variance accounted for by their numerical magnitude comparison skills.     

Multi-representation of symbolic and nonsymbolic numerical magnitude in Chinese number processing

Numerical information can be conveyed by either symbolic or nonsymbolic representation. Some symbolic numerals can also be identified as nonsymbolic quantities defined by the number of lines (e.g., I, II, III in Roman and -, =, ≡ in Japanese Kanji and Chinese). Here we report that such multi-representation of magnitude can facilitate the processing of these numerals under certain circumstances. In a magnitude comparison task judging 1 to 9 (except 5) Chinese and Arabic numerals presented at the foveal (at the center) or parafoveal (3° left or right of the center) location, multi-representational small-value Chinese numerals showed a processing advantage over single-representational Arabic numerals and large-value Chinese numerals only in the parafoveal condition, demonstrated by lower error rates and faster reaction times. Further event-related potential (ERP) analysis showed that such a processing advantage was not reflected by traditional ERP components identified in previous studies of number processing, such as N1 or P2p. Instead, the difference was found much later in a N400 component between 300-550 msec over parietal regions, suggesting that those behavioral differences may not be due to early processing of visual identification, but later processing of subitizing or accessing mental number line when lacking attentional resources. These results suggest that there could be three stages of number processing represented separately by the N1, P2p and N400 ERP components. In addition, numerical information can be represented simultaneously by both symbolic and nonsymbolic systems, which will facilitate number processing in certain situations.     

Cross-cultural variation in the development of folk ecological reasoning

Two studies examined children's reasoning about biological kinds in populations that vary in formal education and direct experience with the natural world, a Western (urban U.S.) and a Non-Western population (Tanna, Vanuatu). Study 1 examined children's concepts of ecological relatedness between species (N = 97, 5–13-year-olds). U.S. children provided more taxonomic explanations than Ni-Vanuatu children, who provided more ecological, physiological, and utility explanations than U.S. children. Ecological explanations were most common overall and more common among older than younger children across cultures. In Study 2, children (N = 106, 6–11-year-olds) sorted pictures of natural kinds into groups. U.S. children were more likely than Ni-Vanuatu children to categorize a human as an animal and the tendency to group a human with other animals increased with age in the U.S. Despite substantial differences in cultural, educational, and ecological input, children in both populations privileged ecological reasoning. In contrast, taxonomic reasoning was more variable between populations, which may reflect differences in experience with formal education.     

Perception of sweetness in simple and complex taste stimuli by adults and children.

Currently, there is little information on the ability of children to analyse complex chemosensory stimuli in terms of the presence and magnitude of the components. The present study investigates this question by comparing the ability of 95 adults and 8- to 9-year-olds to estimate the sweetness of several concentrations of sucrose in water and in three foods, namely, orange drink, custard and shortbread biscuits, using a magnitude estimation procedure. The results indicated that similar response functions were produced by adults and children for the sweetness of aqueous solutions of sucrose, custard and biscuits, but not for orange juice, where the functions produced by both female and male children were significantly flatter than those of the adults. Stimulus context may have influenced the ratings of children in the no-sucrose and highest sucrose concentration conditions with two of the foods. The absence of differences between the response functions of the female and male children with all types of stimuli indicated that gender had no influence on their responses. It is concluded that, at mid-childhood, humans are capable of estimating the sweetness of sucrose in foods, but that they have a tendency to limit the range of numbers used in their estimates of sweetness at high concentrations of sucrose in some foods.     

Processing Demands Impact 3-Year-Olds’ Performance in a Spontaneous-Response Task: New Evidence for the Processing-Load Account of Early False-Belief Understanding

Prior to age four, children succeed in non-elicited-response false-belief tasks but fail elicited-response false-belief tasks. To explain this discrepancy, the processing-load account argues that the capacity to represent beliefs emerges in infancy, as indicated by early success on non-elicited-response tasks, but that children’s ability to demonstrate this capacity depends on the processing demands of the task and children’s processing skills. When processing demands exceed young children’s processing abilities, such as in standard elicited-response tasks, children fail despite their capacity to represent beliefs. Support for this account comes from recent evidence that reducing processing demands improves young children’s performance: when demands are sufficiently reduced, 2.5-year-olds succeed in elicited-response tasks. Here we sought complementary evidence for the processing-load account by examining whether increasing processing demands impeded children’s performance in a non-elicited-response task. 3-year-olds were tested in a preferential-looking task in which they heard a change-of-location false-belief story accompanied by a picture book; across children, we manipulated the amount of linguistic ambiguity in the story. The final page of the book showed two images: one that was consistent with the main character’s false belief and one that was consistent with reality. When the story was relatively unambiguous, children looked reliably longer at the false-belief-consistent image, successfully demonstrating their false-belief understanding. When the story was ambiguous, however, this undermined children’s performance: looking times to the belief-consistent image were correlated with verbal ability, and only children with verbal skills in the upper quartile of the sample demonstrated a significant preference for the belief-consistent image. These results support the processing-load account by demonstrating that regardless of whether a task involves an elicited response, children’s performance depends on the processing demands of the task and their processing skills. These findings also have implications for alternative, deflationary accounts of early false-belief understanding.     

You Seem Certain but You Were Wrong Before: Developmental Change in Preschoolers’ Relative Trust in Accurate versus Confident Speakers

The present study tested how preschoolers weigh two important cues to a person’s credibility, namely prior accuracy and confidence, when deciding what to learn and believe. Four- and 5-year-olds (N = 96) preferred to believe information provided by a confident rather than hesitant individual; however, when confidence conflicted with accuracy, preschoolers increasingly favored information from the previously accurate but hesitant individual as they aged. These findings reveal an important developmental progression in how children use others’ confidence and prior accuracy to shape what they learn and provide a window into children’s developing social cognition, scepticism, and critical thinking.     

Binocular Depth Judgments on Smoothly Curved Surfaces

Binocular disparity is an important cue to depth, allowing us to make very fine discriminations of the relative depth of objects. In complex scenes, this sensitivity depends on the particular shape and layout of the objects viewed. For example, judgments of the relative depths of points on a smoothly curved surface are less accurate than those for points in empty space. It has been argued that this occurs because depth relationships are represented accurately only within a local spatial area. A consequence of this is that, when judging the relative depths of points separated by depth maxima and minima, information must be integrated across separate local representations. This integration, by adding more stages of processing, might be expected to reduce the accuracy of depth judgements. We tested this idea directly by measuring how accurately human participants could report the relative depths of two dots, presented with different binocular disparities. In the first, Two Dot condition the two dots were presented in front of a square grid. In the second, Three Dot condition, an additional dot was presented midway between the target dots, at a range of depths, both nearer and further than the target dots. In the final, Surface condition, the target dots were placed on a smooth surface defined by binocular disparity cues. In some trials, this contained a depth maximum or minimum between the target dots. In the Three Dot condition, performance was impaired when the central dot was presented with a large disparity, in line with predictions. In the Surface condition, performance was worst when the midpoint of the surface was at a similar distance to the targets, and relatively unaffected when there was a large depth maximum or minimum present. These results are not consistent with the idea that depth order is represented only within a local spatial area.     

Graphical Aids to the Estimation and Discrimination of Uncertain Numerical Data

This research investigates the performance of graphical dot arrays designed to make discrimination of relative numerosity as effortless as possible at the same time as making absolute (quantitative) numerosity estimation as effortful as possible. Comparing regular, random, and hybrid (randomized regular) configurations of dots, the results indicate that both random and hybrid configurations reduce absolute numerosity estimation precision, when compared with regular dots arrays. However, discrimination of relative numerosity is significantly more accurate for hybrid dot arrays than for random dot arrays. Similarly, human subjects report significantly lower levels of subjective confidence in judgments when using hybrid dot configurations as compared with regular configurations; and significantly higher levels of subjective confidence as compared with random configurations. These results indicate that data graphics based on the hybrid, randomized-regular configurations of dots are well-suited to applications that require decisions to be based on numerical data in which the absolute quantities are less certain than the relative values. Examples of such applications include decision-making based on the outputs of empirically-based mathematical models, such as health-related policy decisions using data from predictive epidemiological models.     

How many deaths can be prevented by newborn screening for congenital adrenal hyperplasia?

BACKGROUND/AIMS: Congenital adrenal hyperplasia (CAH) is increasingly being included in newborn screening programs. Screening can prevent neonatal mortality in children with salt-wasting CAH, but the number of deaths prevented is not known. Cost-effectiveness analyses of screening require estimates of the probability of mortality in CAH. METHODS: We reviewed the literature to identify cohort studies of children with CAH ascertained clinically in the absence of screening. We abstracted the numbers of infant deaths attributable to CAH. We also addressed sex ratios among children with clinically detected CAH and the contribution of ascertainment bias to unbalanced ratios. RESULTS: The evidence suggests a probability of infant death due to adrenal crises in salt-wasting CAH of 4% or less in contemporary advanced economies without screening for CAH. This is lower than previous estimates, although the rate of mortality could be considerably higher in populations with limited clinical awareness or access. CONCLUSION: Although screening for CAH is conducted in a number of countries, further research is still needed to provide reliable estimates on the numbers of prevented deaths, along with evidence-based assessments of the potential benefits, harms, and costs of screening.     

Preschool Children’s Behavioral Tendency toward Social Indirect Reciprocity

Social indirect reciprocity seems to be crucial in enabling large-scale cooperative networks among genetically unrelated individuals in humans. However, there are relatively few studies on social indirect reciprocity in children compared to adults. Investigating whether young children have a behavioral tendency toward social indirect reciprocity will help us understand how and when the fundamental ability to form cooperative relationships among adults is acquired. Using naturalistic observation at a nursery school, this study examined whether 5- to 6-year-olds show a behavioral tendency to engage in social indirect reciprocity in response to their peers’ prosocial behavior toward a third party. The results revealed that bystander children tended to display prosocial behavior toward their peers more frequently after observing these peers’ prosocial behavior toward third-party peers, compared with control situations; this suggests that 5- to 6-year-olds may have an essential behavioral tendency to establish social indirect reciprocity when interacting with peers in their daily lives. In addition, bystanders tended to display affiliative behavior after observing focal children’s prosocial behavior. In other words, observing peers’ prosocial behavior toward third-party peers evoked bystanders’ positive emotions toward the helpers. Considering both the present results and previous findings, we speculate that in preschoolers, such positive emotions might mediate the increase in the bystander’s prosocial behavior toward the helper. In addition, an intuitional emotional process plays an important role in the preschooler’s behavioral tendency toward social indirect reciprocity in natural interactions with peers.     

Identification of a novel nuclear domain

For most known nuclear domains (ND), specific functions have been identified. In this report we used murine mAbs and human autoantibodies to investigate precisely circumscribed structures 0.2-0.3 micron in diameter which appear as "nuclear dots" distributed throughout the nucleoplasm. Nuclear dots are metabolically stable and resistant to nuclease digestion and salt extraction. The localization of nuclear dots is separate from kinetochores, centromeres, sites of mRNA processing and tRNA synthesis, nuclear bodies, and chromosomes. The nuclear dots, therefore, represent a novel ND. Nuclear dots break down as cells enter metaphase and reassemble at telophase. In interphase cells, nuclear dots are frequently "paired," and some are visible as "doublets" when stained with one particular antiserum. The number of dot doublets increased when quiescent cells were stimulated with serum although the total number of dots did not change substantially. One of the antigens was identified as a protein with a molecular mass of approximately 55 kD showing three charge isomers in the pI range of 7.4 to 7.7. Autoantibodies affinity purified from this nuclear dot protein (NDP-55) show nuclear dots exclusively. Nuclear dot-negative rat liver parenchymal cells became positive after chemical hepatectomy, suggesting involvement of the NDP-55 in the proliferative state of cells.     

Does assignment of orientation to dot patterns reveal optimization processes in the visual system?

Sixty subjects were tested to assign orientation to ten dot patterns differing in their overall form and the number of dots in the pattern. The patterns were presented in four different positions in the visual field and their orientation was estimated in two ways. It was demonstrated that the assignment of orientation did not depend on the position of the pattern in the visual field as well as on the method of estimation used. A quantitative measure for the elongation of a dot pattern is proposed which correlates with the degree of ambiguity in orientation estimation. The greater the elongation the smaller the standard deviation of the estimates given. The distributions of the estimates for the ten patterns were analyzed. It was shown that they can be presented as superpositions of two or more groups of normally distributed estimates determined by some salient characteristics of the stimuli. Data are discussed from the point of view that assignment of orientation to dot patterns reveals the existence of optimization mechanisms in human brain that extract perceptual invariants from external stimulation.     

Morphology versus molecules: sexing Red-winged Blackbird nestlings

ABSTRACT.   Past studies of offspring sex ratios in birds have often relied on sexually size dimorphic species where nestling sex could be determined based on weight at a given age. DNA-based sexing techniques allow us to assess the accuracy of those techniques and to refine them for use when costs or convenience make DNA methods impractical. Using nestling Red-winged Blackbirds ( Agelaius phoeniceus ) whose sex was determined using DNA, we compared sex ratios obtained using different morphological criteria. Conservative criteria from previous studies were completely accurate, but allowed sexing of few nestlings younger than 8 d old, and were more successful for sexing males than females. A new method was developed that allowed accurate sexing of nestlings beginning at day 6 posthatching and was less biased relative to known sex ratios. Using 11 years of data, the conservative method left an average of 55% of nestlings and 36% of fledglings unsexed, compared to 31% and 9% using the new method. Furthermore, the male bias in sex ratio estimates using the conservative method was greater, both absolutely and relative to estimates based on the new method, when the proportion of unsexed nestlings (because they were not weighed when older) was higher. Thus, estimates of population sex ratios will be more accurate as the number of nestlings measured on day 8 or older increases. However, if some nestlings that were not weighed past day 7 fledge, the new method allows more of those individuals to be sexed than the conservative method, and the population sex ratio estimate should be more reliable. Although our approach should apply to other sexually dimorphic species, the criteria used must be developed based on such species-specific attributes as growth patterns and degree of hatching asynchrony.     

A Mixture Model for Quantum Dot Images of Kinesin Motor Assays

Summary We introduce a nearly automatic procedure to locate and count the quantum dots in images of kinesin motor assays. Our procedure employs an approximate likelihood estimator based on a two‐component mixture model for the image data; the first component has a normal distribution, and the other component is distributed as a normal random variable plus an exponential random variable. The normal component has an unknown variance, which we model as a function of the mean. We use B‐splines to estimate the variance function during a training run on a suitable image, and the estimate is used to process subsequent images. Parameter estimates are generated for each image along with estimates of standard errors, and the number of dots in the image is determined using an information criterion and likelihood ratio tests. Realistic simulations show that our procedure is robust and that it leads to accurate estimates, both of parameters and of standard errors.     

Comparative study of the abundance of various bacterial morphotypes in an eutrophic freshwater environment determined by AODC and TEM

Transmission electron microscopy (TEM) and epifluorescence microscopy were used to obtain comparative measurements of total bacterial counts, and to enumerate abundances of various bacterial morphotypes in an eutrophic freshwater habitat. Although particulate matter would have been expected to interfere with counting by obscuring large areas of the electron microscope grids, estimates of total bacterial abundance made by TEM were on average 1.2 times greater than those obtained using the acridine orange direct counting method (AODC). However, the precision of the AODC method was greater than that for TEM, with a coefficient of variation (C.V.) of 4.0% versus 8.8%, respectively. The total bacterial abundance ranged from 1.1 to 3.2 x 10(6) ml(-1). As was the case for total bacterial density, the numbers of rod- and vibrio-shaped cells were lower when counted in the epifluorescence microscope, indicating the presence of potential starvation forms or ultramicrobacteria. Greatest variations in counts made by TEM and AODC were found for filamentous and coccoid bacteria. Counts of filamentous bacteria made by AODC were only about half of those detected by TEM. In contrast, cocci were on average 1.5 times greater when counted by AODC compared to TEM estimates. Both counting differences were probably caused by the morphology and low density of filamentous and coccoid bacteria (1.7 and 1.4 x 10(5) ml(-1), respectively), which led to an uneven distribution on polycarbonate filters as well as on electron microscope grids. Besides, cocci might easily be mistaken for large viral particles when counted by AODC. Hence, the study supports the use of TEM over AODC for obtaining accurate estimates of total bacterial abundance and especially bacterial morphotypes in natural waters.