The Cognitive Mechanisms of the SNARC Effect: An Individual Differences Approach

Access to mental representations of smaller vs. larger number symbols is associated with leftward vs. rightward spatial locations, as represented on a number line. The well-replicated SNARC effect (Spatial-Numerical Association of Response Codes) reveals that simple decisions about small numbers are facilitated when stimuli are presented on the left, and large numbers facilitated when on the right. We present novel evidence that the size of the SNARC effect is relatively stable within individuals over time. This enables us to take an individual differences approach to investigate how the SNARC effect is modulated by spatial and numerical cognition. Are number-space associations linked to spatial operations, such that those who have greater facility in spatial computations show the stronger SNARC effects, or are they linked to number semantics, such that those showing stronger influence of magnitude associations on number symbol decisions show stronger SNARC effects? Our results indicate a significant correlation between the SNARC effect and a 2D mental rotation task, suggesting that spatial operations are at play in the expression of this effect. We also uncover a significant correlation between the SNARC effect and the distance effect, suggesting that the SNARC is also related to access to number semantics. A multiple regression analysis reveals that the relative contributions of spatial cognition and distance effects represent significant, yet distinct, contributions in explaining variation in the size of the SNARC effect from one individual to the next. Overall, these results shed new light on how the spatial-numerical associations of response codes are influenced by both number semantics and spatial operations.     

Size matters: non-numerical magnitude affects the spatial coding of response

It is known that small and large numbers facilitate left/right respectively (the SNARC effect). Recently, it has been proposed that numerical magnitude is just one example of a range of quantities, which have a common cognitive/neural representation. To investigate this proposition, response congruency effects were explored for stimuli which differed according to their: (a) numerical size, (b) physical size, (c) luminance, (d) conceptual size and (e) auditory intensity. In a series of experiments, groups of undergraduate participants made two-alternative forced choice discriminations with their left or right hands. There were clear interactions between magnitude and responding hand whereby right hand responses were faster for stimuli with (a) large numbers, (b) large physical size, (c) low luminance, and (d) a reference to large objects. There was no congruency effect for the auditory stimuli. The data demonstrate that the response congruency effect observed for numbers also occurs for a variety of other non-numerical visual quantities. These results support models of general magnitude representation and suggest that the association between magnitude and the left/right sides of space may not be related to culture and/or directional reading habits.     

Numbers in the Blind's “Eye”

Background

Although lacking visual experience with numerosities, recent evidence shows that the blind perform similarly to sighted persons on numerical comparison or parity judgement tasks. In particular, on tasks presented in the auditory modality, the blind surprisingly show the same effect that appears in sighted persons, demonstrating that numbers are represented through a spatial code, i.e. the Spatial-Numerical Association of Response Codes (SNARC) effect. But, if this is the case, how is this numerical spatial representation processed in the brain of the blind?

Principal Findings

Here we report that, although blind and sighted people have similarly organized numerical representations, the attentional shifts generated by numbers have different electrophysiological correlates (sensorial N100 in the sighted and cognitive P300 in the blind).

Conclusions

These results highlight possible differences in the use of spatial representations acquired through modalities other than vision in the blind population.     

Digit ratio (2D:4D) and the spatial representation of magnitude

Digit ratio (as a putative indicator of prenatal androgen exposure) is related to a range of sexually dimorphic abilities, including spatial skills and mathematical ability. This study examined a phenomenon known as the SNARC effect (Spatial Numerical Association of Response Codes), which is taken as evidence of a mental representation of magnitude along a left-right-oriented number line, with low magnitudes associated with the left side of space, and high numbers with the right side of space. Participants made a parity judgement of numbers with responses made with a left key to odd numbers and a right key to even numbers. This was reversed for a second block of trials. Response times to numbers one to nine with both the right and left hand were calculated, and regression analyses conducted to analyse whether lower magnitudes were responded to faster with the left hand and higher magnitudes with the right hand. Participants with lower (more masculine) digit ratios on the right hand showed a stronger SNARC effect compared to participants with high digit ratios. This pattern of results was also found when the analyses were conducted separately for men and women. Results from left hand digit ratios indicated that only low digit ratio females showed a significant SNARC effect. These findings add to a growing literature on the relationship between digit ratio and cognitive abilities; in this case, simple cognitive representations that are accessed automatically rather than complex skills such as mental rotation or "mathematics" where a variety of solution strategies may be utilised.     

Notation-dependent and -independent representations of numbers in the parietal lobes

It is a commonly held view that numbers are represented in an abstract way in both parietal lobes. This view is based on failures to find differences between various notational representations. Here we show that by using relatively smaller voxels together with an adaptation paradigm and analyzing subjects on an individual basis it is possible to detect specialized numerical representations. The current results reveal a left/right asymmetry in parietal lobe function. In contrast to an abstract representation in the left parietal lobe, the numerical representation in the right parietal lobe is notation dependent and thus includes nonabstract representations. Our results challenge the commonly held belief that numbers are represented solely in an abstract way in the human brain.     

Oscillatory Brain Activity Reveals Linguistic Prints in the Quantity Code

Number representations change through education, although it is currently unclear whether and how language could impact the magnitude representation that we share with other species. The most prominent view is that language does not play any role in modulating the core numeric representation involved in the contrast of quantities. Nevertheless, possible cultural hints on the numerical magnitude representation are currently on discussion focus. In fact, the acquisition of number words provides linguistic input that the quantity system may not ignore. Bilingualism offers a window to the study of this question, especially in bilinguals where the two number wording systems imply also two different numerical systems, such as in Basque-Spanish bilinguals. The present study evidences linguistic prints in the core number representational system through the analysis of EEG oscillatory activity during a simple number comparison task. Gamma band synchronization appears when Basque-Spanish bilinguals compare pairs of Arabic numbers linked through the Basque base-20 wording system, but it does not if the pairs are related through the base-10 system. Crucially, this gamma activity, originated in a left fronto-parietal network, only appears in bilinguals who learned math in Basque and not in equivalent proficiency bilinguals who learned math in Spanish. Thus, this neural index reflected in gamma band synchrony appears to be triggered by early learning experience with the base-20 numerical associations in Basque number words.     

Effects of black mustard population size on the taxonomic composition of pollinators

In plant species that are pollinated by a variety of animal species, spatial and temporal variability in the taxonomic composition of those pollinators may cause spatial and temporal variability in selection on floral traits. While temporal variation in pollinator composition has been widely reported, spatial variability, particularly on a local scale, has been studied less frequently; nevertheless, available evidence suggests that local spatial variability may be a widespread feature of plant-pollinator interactions. In addition, the causes of this spatial variability are poorly known. This study was undertaken to quantify variability in the taxonomic composition of pollinators visiting local populations of black mustard, Brassica nigra, and to determine some of the causes of this variability. Simultaneous observations were conducted in seven pairs of black mustard populations. The members of each pair were in close spatial proximity but differed in number of plants. Larger plant populations were visited by significantly greater numbers of honey bees and significantly fewer small bees than small populations on a per-plant basis. There was also a trend toward greater syrphid fly visitation in small populations. The increased numbers of honey bees at large plant populations is probably due to their ability to recruit long distances to the most rewarding plant populations. The lower number of small bees at large plant populations may be due to competition from honey bees and/or spreading a constant number of small bees over the larger number of plants in large populations.This paper is dedicated to the memory of George Eickwort     

Effect of immobilized laminin on karyotypic variability in two karyotypically different variants of the indian muntjac skin fibroblast cell line

The numerical and structural karyotypic variability has been investigated in MTs of the markerless cell line of Indian muntjac skin fibroblasts, as well as in its karyotypic variant MT^D cultivated on a laminin 2/4 coated surface. In the MT cell line preincubated in serum-free medium for 2.5 and 1.0 h, then cultivated on a laminin-coated surface in serum-containing medium for one, two, and three days, the character of cell distribution for the chromosome number has changed. These changes involve a significant decrease in the frequency of cells with modal numbers of chromosomes and an increase in frequency of cells with lower chromosome numbers. Some new additional structural variants of the karyotype (SVK) appeared. The observed alterations seem to be due to disturbances of the chromosome segregation and the establishment of a new advantageous balanced karyotypic structure. In the karyotypic variant MT^D differing from MT by an increased number of dicentrics (telomeric associations) cultivated under the same conditions, the character of cell distribution for the chromosome number did not change. In the MT cell line, the frequency of chromosomal aberrations did not change relative to control variants. In the karyotypic variant MT^D under the same conditions, the frequency of chromosomal aberrations significantly increased after three days mainly due to the formation of dicentrics. These results confirm the conclusion that, like aneuploidy, the formation of dicentrics in markerless cell lines appears to be the way in which the cell population adapts to unfavorable environmental factors. Possible reasons for differences in the character of the numerical and structural karyotypic variability between the MT cell line and its karyotypic variant MT^D are discussed.     

Morphometric and genetic divergence among populations ofNeotinea ustulata (Orchidaceae) with different flowering phenologies

The terrestrial orchid speciesNeotinea ustulata has recently been split into two subspecies, differing remarkably in their flowering time, but only slightly in morphological characteristics, which makes their taxonomic status uncertain. We have analyzed morphometric and genetic differences between the early- and late-flowering populations in Central Europe. Our results on morphology are ambiguous. Indirect gradient analysis has not shown a distinct separation of early- and late-flowering individuals in the ordination space. However, according to MANOVA, populations of early- and late-flowering plants can be distinguished by plant height, leaf length, numbers of basal (rosette) and stem leaves and even better by certain ratios of these numbers. All genetic analyses, on the other hand, are definite and consistently distinguish two groups. Random amplified polymorphic DNA (RAPD) markers have shown that the early- and late-flowering populations differ significantly from one another. Principal coordinate analysis (PCoA) based on presence/absence matrix of RAPD bands separated the two groups, implying that the difference in flowering phenology could form an effective barrier to gene exchange. Partitioning of genetic diversity in analysis of molecular variance (AMOVA) has shown that the genetic divergence between the two groups, early- and late-flowering populations, is somewhat greater (33%) than the genetic variability among populations within particular group (23%). Using the Mantel test, we found that genetic differentiation coefficients between populations closely correspond to their geographic distribution. After elimination of the effect of sample origin from the model, direct gradient analysis (RDA) has shown that the early- and late-flowering groups differ significantly in their RAPD spectra. To conclude, our results indicate the presence of two genetically and phenologically distinct taxa, but the weak morphological differentiation supports the taxonomic rank of variety rather than subspecies.     

Processing ordinality and quantity: the case of developmental dyscalculia

In contrast to quantity processing, up to date, the nature of ordinality has received little attention from researchers despite the fact that both quantity and ordinality are embodied in numerical information. Here we ask if there are two separate core systems that lie at the foundations of numerical cognition: (1) the traditionally and well accepted numerical magnitude system but also (2) core system for representing ordinal information. We report two novel experiments of ordinal processing that explored the relation between ordinal and numerical information processing in typically developing adults and adults with developmental dyscalculia (DD). Participants made "ordered" or "non-ordered" judgments about 3 groups of dots (non-symbolic numerical stimuli; in Experiment 1) and 3 numbers (symbolic task: Experiment 2). In contrast to previous findings and arguments about quantity deficit in DD participants, when quantity and ordinality are dissociated (as in the current tasks), DD participants exhibited a normal ratio effect in the non-symbolic ordinal task. They did not show, however, the ordinality effect. Ordinality effect in DD appeared only when area and density were randomized, but only in the descending direction. In the symbolic task, the ordinality effect was modulated by ratio and direction in both groups. These findings suggest that there might be two separate cognitive representations of ordinal and quantity information and that linguistic knowledge may facilitate estimation of ordinal information.     

Intraspecific variation in the comb structure ofPolistes dominulusi parameters,maturation, nest size and cell arrangement

Summary The intraspecific variability of the nest structures ofPolistes dominulus is described quantitatively. Several variables already used in the literature (e.g. wall expenditure and diameter ratio) are reexamined and a number of new ones are suggested. Variables are analyzed with respect to their dependency on the size and the maturation of the colony.The analyses were based on mathematical functions deduced for ideal nest growth. In the examined species, the numbers of outer walls and buildable cells do not differ significantly from those calculated for the ideal growth, demonstrating that the real nests are close to the ideal round form. P. dominulus builds compact and well-centered nests. The shape of the comb remains compact during the maturation of the nest. The eccentricity changes during maturation: it is significantly greater in the mature stage than in younger combs.Analysis reveals that the wasps prefer to initiate a new cell in a position where it will have at least three neighbors. The nests in different age groups not only differed in height, but were also under the control of three different constraints: the structure itself, the large larvae and indirectly the meconium.     

Arithmetic Memory Is Modality Specific

In regards to numerical cognition and working memory, it is an open question as to whether numbers are stored into and retrieved from a central abstract representation or from separate notation-specific representations. This study seeks to help answer this by utilizing the numeral modality effect (NME) in three experiments to explore how numbers are processed by the human brain. The participants were presented with numbers (1–9) as either Arabic digits or written number words (Arabic digits and dot matrices in Experiment 2) at the first (S1) and second (S2) stimuli. The participant’s task was to add the first two stimuli together and verify whether the answer (S3), presented simultaneously with S2, was correct. We hypothesized that if reaction time (RT) at S2/S3 depends on the modality of S1 then numbers are retrieved from modality specific memory stores. Indeed, RT depended on the modality of S1 whenever S2 was an Arabic digit which argues against the concept of numbers being stored and retrieved from a central, abstract representation.     

An evaluation of transfer suppression phenomenon at different stages of learning-set formation

Three groups of three rhesus monkeys each trained to varying levels of object discrimination learning-set formation were tested for reversal-learning proficiency. Training consisted in presenting discrimination problems by the usual learning-set procedure; whereas reversal-learning proficiency was tested by presenting the reversal problems along with control problems according to the usual learning-set procedure and also according to the serial learning procedure. No substantial change in negative interproblem transfer effects was observed as a result of learning-set proficiency, as reversed-problem performance remained significantly poorer than control-problem performance at all the levels. Learning of a reversed problem was not found to be in any way related to anS's correct or incorrect response on its first acquisition trial.     

External quality assessment in gynaecological cytology: The Trent Region experience

A Department of Health Executive Letter stated in 1998 that the principal function of external quality assessment (EQA) is educational. Subsequently, in England, it has no longer been acceptable to assess performance in gynaecological cytology by proficiency testing. This paper describes the EQA scheme in gynaecological cytology that has been run by the Trent Regional Gynaecological Pathology Quality Assurance Group for the NHS Cervical Screening Programme (NHSCSP) since 1998. It conforms as closely as possible to the recommendations published by the Department of Health Working Group on Histopathology EQA Accreditation, and replaced the national proficiency testing protocol. The educational value of the scheme is derived predominantly from a numerical score which provides confidential and quantitative feedback to all participants. Personal performance monitoring occurs as a secondary function. For primary screeners and checkers, this is based purely on the distinction between negative, inadequate and abnormal smears. For pathologists, personal performance monitoring also includes grading of abnormalities. The EQA has been designed so that all professional groups participate in a manner that closely mimics normal practice. Only slides that have achieved an 80% consensus amongst participants are used in the EQA. Substandard performance has been defined as those participants with scores falling below the 2.5%ile. The paper describes the EQA in detail and illustrates its use by means of the second round results. The EQA protocol developed within Trent and described in this paper has contributed to proposals contained in the current national EQA in gynaecological cytology for the NHSCSP. In particular this paper highlights the effectiveness of the scoring system contained within the Trent and National EQA protocols.     

Are binary synapses superior to graded weight representations in stochastic attractor networks?

Synaptic plasticity is an underlying mechanism of learning and memory in neural systems, but it is controversial whether synaptic efficacy is modulated in a graded or binary manner. It has been argued that binary synaptic weights would be less susceptible to noise than graded weights, which has impelled some theoretical neuroscientists to shift from the use of graded to binary weights in their models. We compare retrieval performance of models using both binary and graded weight representations through numerical simulations of stochastic attractor networks. We also investigate stochastic attractor models using multiple discrete levels of weight states, and then investigate the optimal threshold for dilution of binary weight representations. Our results show that a binary weight representation is not less susceptible to noise than a graded weight representation in stochastic attractor models, and we find that the load capacities with an increasing number of weight states rapidly reach the load capacity with graded weights. The optimal threshold for dilution of binary weight representations under stochastic conditions occurs when approximately 50% of the smallest weights are set to zero.     

C(i,j) matrix: a better numerical characterization for graphical representations of biological sequences

We find that the traditional numerical characterizations of biological sequences, such as E matrix, D/D matrix, L/L matrix and their "high order" matrices, have their limitations to characterize the biological sequences exactly, but they are widely used to analyze the biological sequences. Here, we propose a better numerical characterization for graphical representations of biological sequences, C(i,j) matrix. It is associated with the curvature of every point and has many advantages: (1) It can characterize the graphical representations for DNA sequences exactly, because it can overcome the limitation of the traditional matrices. (2) If we choose an appropriate fixed point, we can make the elements of the C(i,j) matrix less than or equal to 1.     

Effect of laminin on karyotypic variability in cell line of Indian muntjac skin fibroblasts

The numerical and structural karyotypic variability has been investigated in the Indian muntjac skin fibroblasts cell line M and karyotypic variant of this line M' on cultivation on a laminin 2/4 coated surface. In cell line M, cultivated on the laminin-coated surface for 4 and 14 days, and in karyotypic variant M', cultivated for 2, 4 and 14 days, the character of cell distribution for the chromosome number has changed. These changes involve a significant decrease in frequency of cells with model numbers of chromosomes, and an increase in frequency of cells with lower chromosome numbers. As a result, new modal chromosome numbers form. The frequency of cells with 4 chromosomes increases significantly; as a rule, such cells are absent in the control cell variants. Many new additional structural variants of the karyotype (SVK) appear. Detachment of cells M' from the laminin-coated surface followed by a 2 day cultivation on a hydrophilic surface, commonly used for routine cell cultivation, does not restore the control cell distribution for chromosomal number. The frequency of chromosomal aberrations on cultivation of the laminin-coated surface does not change relatively to controls. The observed alterations seem to be due to both disturbances of mitotic apparatus and selection of SVK, which are more advantageous to changed culture conditions of the cell population.     

Maize ears sculptured in 12th and 13th centuryA.D. India as indicators of pre-columbian diffusion

Evidence for the presence of maize (Lea. mays, Poaceae) in India prior to traditional European contact is found in stone sculptures of maize ears in the 12th and 13th century (and earlier) Hoysala temples in southern India near Mysore. These “ears” present the morphology of maize in such intricate and specifically variable representations that it would have been impossible for sculptors to have imagined the variability consistently and realistically without large numbers of actual maize ears as models. No other natural model could supply this variability. We should search for other crops and cultural artifacts that would have diffused with maize across the oceans before 1492 A.D.     

Protection against reactive oxygen species during mouse preimplantation embryo development: role of EDTA, oxygen tension, catalase, superoxide dismutase and pyruvate

Oxidative damage due to the production of reactive oxygen species (ROS) is one of a number of culture-induced stresses which may compromise preimplantation embryo development in vitro. Ethylenediaminetetraacetic acid (EDTA), reduced oxygen tension, superoxide dismutase (SOD) and catalase (CAT) offer protection against oxidative stress, but few attempts have been made to determine which of these agents, or which combination, is the most effective. In particular, no systematic investigation of their actions and interactions has been made using a multifactorial experimental design. Murine zygotes were cultured in the presence or absence of 10 miccroM EDTA, SOD (100-7,000 U/ml) and CAT (50-100 U/ml) at atmospheric (20%) and reduced (5%) oxygen tensions. Blastocyst formation and hatching rates (at various time points), and cell numbers were recorded, whilst parallel groups of embryos had their consumption of pyruvate, a hydrogen peroxide scavenger, measured. All parameters interacted significantly and affected blastocyst formation, hatching rate and cell numbers but the effect of EDTA was the most pronounced. There were beneficial effects of 5% O2, CAT and SOD, while 20% O2 had a deleterious effect on development. EDTA improved blastocyst formation and hatching rates but paradoxically led to a reduction in cell number. 5% O2 was the next most significant parameter to enhance embryo development and also increased cell numbers. No differences in pyruvate uptake were apparent between the various treatment groups. The results suggest that embryo culture in EDTA-free medium under 5% O2 provides the most practical and physiological conditions for in vitro murine embryo culture.