Manipulation of attention affects subitizing performance: A systematic review and meta-analysis.

Subitizing is the fast and accurate enumeration of small sets. Whether attention is necessary for subitizing remains controversial considering (1) subitizing is claimed to be "pre-attentive", and (2) existing experimental methods and results are inconsistent. To determine whether manipulations to attention demonstratively affect subitizing, the current study comprises a systematic review and meta-analysis. Results from fourteen studies (22 experiments, 35 comparisons) suggest that changes to attentional demands interferes with enumeration of small sets; leading to slower response times, lower accuracy, and poorer Weber acuity (p < .010; p < .001; p < .001; respectively)-notwithstanding a potential publication bias. A unifying framework is proposed to explain the role of attention in visual enumeration, with progressively greater attentional involvement from estimation to subitizing to counting. Our findings suggest attention is integral for subitizing and highlights the need to emphasise attentional mechanisms into neurocognitive models of numerosity processing. We also discuss the possible role of attention in numerical processing difficulties (e.g., dyscalculia).

Quantification of Competing Magnetic States and Switching Pathways in Curved Nanowires by Direct Dynamic Imaging.

For viable applications, spintronic devices based, for example, on domain wall motion need to be highly reliable with stable magnetization states and highly reproducible switching pathways transforming one state to another. The existence of multiple stable states and switching pathways in a system is a definitive barrier for device operation, yet rare and stochastic events are difficult to detect and understand. We demonstrate an approach to quantify competing magnetic states and stochastic switching pathways based on time-resolved scanning electron microscopy with polarization analysis, applied to the technologically relevant control of vortex domain wall chirality via field and curvature in curved wires. As a pump-probe technique, our analysis scheme nonetheless allows for the disentanglement of different occurring dynamic pathways, and we can even identify the rare events leading to changes from one magnetization switching pathway to another pathway via temperature- and geometry-dependent measurements. The experimental imaging is supported by micromagnetic simulations to reveal the mechanisms responsible for the change of the pathway. Together the results allow us to explain the origin and details of the domain wall chirality control and to quantify the frequency and the associated energy barriers of thermally activated changes of the states and switching pathways.

Spatial complexity facilitates ordinal mapping with a novel symbol set.

The representation of number symbols is assumed to be unique, and not shared with other ordinal sequences. However, little research has examined if this is the case, or whether properties of symbols (such as spatial complexity) affect ordinal learning. Two studies were conducted to investigate if the property of spatial complexity affects learning ordinal sequences. In Study 1, 46 adults made a series of judgements about two novel symbol sets (Gibson and Sunúz). The goal was to find a novel symbol set that could be ordered by spatial complexity. In Study 2, 84 adults learned to order nine novel symbols (Sunúz) with a paired comparison task, judging which symbol was 'larger' (whereby the larger symbol became physically larger as feedback), and were then asked to rank the symbols. Participants were assigned to either a condition where there was a relationship between spatial complexity and symbol order, or a condition where there was a random relationship. Of interest was whether learning an ordered list of symbols would be facilitated by the spatial complexity of the novel symbols. Findings suggest spatial complexity affected learning ability, and that pairing spatial complexity with relational information can facilitate learning ordinal sequences. This suggests that the implicit cognitive representation of number may be a more general feature of ordinal lists, and not exclusive to number per se.

Enumeration strategy differences revealed by saccade-terminated eye tracking.

Brain regions involved in saccadic eye movements partially overlap with a frontoparietal network implicated in encoding numerosities. Eye movement patterns may plausibly reflect strategic scanning behaviours to resolve the open-ended task of efficiently enumerating visual arrays. If so, these patterns may help explain individual differences in enumeration acuity in terms of well-understood visual attention mechanisms. Most enumeration eye-tracking paradigms, however, do not allow for direct manipulation of eye movement behaviours to test these claims. In the current study we terminated trials after a specified number of saccades to systematically probe the time course of enumeration strategies. Fifteen adults (11 naïve, 4 informed) enumerated random dot arrays under three conditions: (1) a novel saccade-terminated design where arrays were visible until one, two or four saccades had occurred; (2) a duration-terminated design where arrays were shown for 250, 500 or 1000 ms; and (3) a response-terminated design where arrays were visible until a response. Participants gave more accurate responses when enumerating saccade-terminated trials despite taking a similar time as in the duration-terminated trials. When participants were informed how trials would terminate, their saccade onset latencies shifted to match task demands. Rotating saccade vectors to align with salient image locations accounted for variability in the orientation of saccade trajectories. These findings (1) show a combination of stimulus-derived visual processing and task-based strategic demands account for enumeration eye movements patterns, (2) validate a novel saccade-contingent trial termination procedure for studying sequences of enumeration eye movements, and (3) highlight the need to include analyses of spatial and temporal eye movement patterns into models of visual enumeration strategies.

The Importance of Ordinal Information in Interpreting Number/Letter Line Data.

The degree to which the ability to mark the location of numbers on a number-to-position (NP) task reflects a mental number line (MNL) representation, or a representation that supports ordered lists more generally, is yet to be resolved. Some argue that findings from linear equation modeling, often used to characterize NP task judgments, support the MNL hypothesis. Others claim that NP task judgments reflect strategic processes; while others suggest the MNL proposition could be extended to include ordered list processing more generally. Insofar as the latter two claims are supported, it would suggest a more nuanced account of the MNL hypothesis is required. To investigate these claims, 84 participants completed a NP and an alphabet-to-position task in which they marked the position of numbers/letters on a horizontal line. Of interest was whether: (1) similar judgment deviations from linearity occurred for number/letter stimuli; (2) left-to-right or right-to-left lines similarly, affected number/letter judgments; and (3) response times (RTs) differed as a function of number/letter stimuli and/or reverse/standard lines. While RTs were slower marking letter stimuli compared to number stimuli, they did not differ in the standard compared to the reverse number/letter lines. Furthermore, similar patterns of non-linear RTs were found marking stimuli on the number/letter lines, suggesting that similar strategic processes were at play. These findings suggest that a general mental representation may underlie ordered list processing and that a linear mental representation is not a unique feature of number per se. This is consistent with the hypothesis that number is supported by a representation that lends itself to processing ordered sequences in general.

Implications of Change/Stability Patterns in Children's Non-symbolic and Symbolic Magnitude Judgment Abilities Over One Year: A Latent Transition Analysis.

Non-symbolic magnitude abilities are often claimed to support the acquisition of symbolic magnitude abilities, which, in turn, are claimed to support emerging math abilities. However, not all studies find links between non-symbolic and symbolic magnitude abilities, or between them and math ability. To investigate possible reasons for these different findings, recent research has analyzed differences in non-symbolic/symbolic magnitude abilities using latent class modeling and has identified four different magnitude ability profiles residing within the general magnitude ability distribution that were differentially related to cognitive and math abilities. These findings may help explain the different patterns of findings observed in previous research. To further investigate this possibility, we (1) attempted to replicate earlier findings, (2) determine whether magnitude ability profiles remained stable or changed over 1 year; and (3) assessed the degree to which stability/change in profiles were related to cognitive and math abilities. We used latent transition analysis to investigate stability/changes in non-symbolic and symbolic magnitude abilities of 109 5- to 6-year olds twice in 1 year. At Time 1 and 2, non-symbolic and symbolic magnitude abilities, number transcoding and single-digit addition abilities were assessed. Visuospatial working memory (VSWM), naming numbers, non-verbal IQ, basic RT was also assessed at Time 1. Analysis showed stability in one profile and changes in the three others over 1 year. VSWM and naming numbers predicted profile membership at Time 1 and 2, and profile membership predicted math abilities at both time points. The findings confirm the existence of four different non-symbolic-symbolic magnitude ability profiles; we suggest the changes over time in them potentially reflect deficit, delay, and normal math developmental pathways.

Development of a scanning electron microscopy with polarization analysis system for magnetic imaging with ns time resolution and phase-sensitive detection.

Scanning electron microscopy with polarization analysis is a powerful lab-based magnetic imaging technique offering simultaneous imaging of multiple magnetization components and a very high spatial resolution. However, one drawback of the technique is the long required acquisition time resulting from the low inherent efficiency of spin detection, which has limited the applicability of the technique to certain quasi-static measurement schemes and materials with high magnetic contrast. Here we demonstrate the ability to improve the signal-to-noise ratio for particular classes of measurements involving periodic excitation of the magnetic structure via the implementation of a digital phase-sensitive detection scheme facilitated by the integration of a time-to-digital converter to the system. The modified setup provides dynamic imaging capabilities using selected time windows and finally full time-resolved imaging with a demonstrated time resolution of better than 2 ns.

Non-symbolic magnitudes are represented spatially: Evidence from a non-symbolic SNARC task.

A core proposition in numerical cognition is numbers are represented spatially. Evidence for this proposition comes from the "spatial numerical association of response codes" effect (SNARC) in which faster responses are made by the left/right hand judging whether one of a pair of Arabic digits is smaller/larger than the other. Less is known if a similar SNARC effect exists for non-symbolic magnitudes; and research that has been conducted used stimuli which could be translated into symbolic terms. To overcome this limitation, we employed a referent-to-target judgment paradigm in which a referent dot array (n = 30 dots) was follow by a second array of dots (e.g., n = 45 or 15 dots)-participants judged if the second array contained fewer or more dots than the referent array. Dot arrays with fewer dots were judged more quickly with the left hand compared to the right hand (i.e., a SNARC effect). Not all participants demonstrated a SNARC effect, however. Neither visuospatial working memory nor math ability was associated with the presence/absence of a non-symbolic SNARC effect. Implications of the non-symbolic SNARC effect for accounts of numerical cognition are discussed.

Variability in Single Digit Addition Problem-Solving Speed Over Time Identifies Typical, Delay and Deficit Math Pathways.

We assessed the degree to which the variability in the time children took to solve single digit addition (SDA) problems longitudinally, predicted their ability to solve more complex mental addition problems. Beginning at 5 years, 164 children completed a 12-item SDA test on four occasions over 6 years. We also assessed their (1) digit span, visuospatial working memory, and non-verbal IQ, and (2) the speed with which they named single numbers and letters, as well the speed enumerating one to three dots as a measure of subitizing ability. Children completed a double-digit mental addition test at the end of the study. We conducted a latent profile analysis to determine if there were different SDA problem solving response time (PRT) variability patterns across the four test occasions, which yielded three distinct PRT variability patterns. In one pattern, labeled a typical acquisition pathway, mean PRTs were relatively low and PRT variability diminished over time. In a second pattern, label a delayed pathway, mean PRT and variability was high initially but diminished over time. In a third pattern, labeled a deficit pathway, mean PRT and variability remained relatively high throughout the study. We investigated the degree to which the three SDA PRT variability pathways were associated with (1) different cognitive ability measures, and (2) double-digit mental addition abilities. The deficit pathway differed from the typical and delayed pathway on the subitizing measure only, but not other measures; and the latter two pathways also differed from each other on the subitizing but not other measures. Double-digit mental addition problem solving success differed between each of the three pathways, and mean PRT variability differed between the typical and the delayed and deficit pathways. The latter two pathways did not differ from each other. The findings emphasize the value of examining individual differences in problem-solving PRT variability longitudinally as an index of math ability, and highlight the important of subitizing ability as a diagnostic index of math ability/difficulties.

Culture-Independent Prerequisites for Early Arithmetic.

In numerate societies, early arithmetic development is associated with visuospatial working memory, executive functions, nonverbal intelligence, and magnitude-comparison abilities. To what extent do these associations arise from cultural practices or general cognitive prerequisites? Here, we administered tests of these cognitive abilities (Corsi Blocks, Raven's Colored Progressive Matrices, Porteus Maze) to indigenous children in remote northern Australia, whose culture contains few counting words or counting practices, and to nonindigenous children from an Australian city. The indigenous children completed a standard nonverbal addition task; the nonindigenous children completed a comparable single-digit addition task. The correlation matrices among variables in the indigenous and nonindigenous children showed similar patterns of relationships, and parallel regression analyses showed that visuospatial working memory was the main predictor of addition performance in both groups. Our findings support the hypothesis that the same cognitive capacities promote competence for learners in both numerate and nonnumerate societies.

[Formula: see text]A longitudinal analysis of the attention networks in 6- to 11-year-old children.

Attention is critical for everyday functioning. Posner and Petersen's model of attention describes three neural networks involved in attention control-the alerting network for arousal, the orienting network for selecting sensory input and reorienting attention, and the executive network for the regulatory control of attention. No longitudinal research has examined relative change in these networks in children. A modified version of the attention network task (ANT) was used to examine changes in the three attention networks, three times over 12 months, in 114 6-, 8- and 10-year-olds. Findings showed that the alerting network continued to develop over this period, the orienting network had stabilized by 6 years, and the conflict network had largely stabilized by 7 years. The reorienting of attention was also assessed using invalid cues, which showed a similar developmental trajectory to the orienting attention network and had stabilized by 6 years. The results confirm that age 6 to 7 years is a critical period in the development of attention, in particular executive attention. The largest improvement over the evaluation period was between 6 and 7 years; however, subtle changes were found in attention beyond 8 years of age.

Sustained attention to a predictable, unengaging Go/No-Go task shows ongoing development between 6 and 11 years.

Response time variability (RTV) is a useful measure of sustained attention; however, little is known about developmental changes in RTV at different temporal frequencies. Thirty-five 6-year-olds, 31 8-year-olds, and 37 10-year-olds completed the fixed-sequence Sustained Attention to Response Task on three occasions, six months apart. Fast Fourier Transform and ex-Gaussian analyses of response time (RT) data assessed momentary fluctuations in RT, gradual changes in RT, and very long responses, thought to reflect attentional control fluctuations, slow-shifting arousal, and infrequent lapses in attention, respectively. A half-by-half analysis measured within-occasion time-on-task effects. The 10-to 11-year-olds performed with less momentary fluctuations in RT, fewer long responses, and fewer commission and omission errors than the younger groups. This group performed well in the first half of the task but showed time-on-task effects on measures of momentary fluctuations in RT, very long responses, target sensitivity (d'), and commission errors. The 6- to 7-year-olds performed less well than the older groups, and showed time-on-task effects, on almost all measures. The 8- to- 9-year-olds mostly performed at an intermediate level compared with the other groups; however, this group performed with a similar level of momentary fluctuations in RT and very long responses as the 6- to 7-year-olds. These findings indicate that there is ongoing maturation of various aspects of sustained attention on a predictable task, with a period of relative stability in performance between 8 and 9 years of age.

Ultra-large non-volatile modulation of magnetic moments in PbZr0.2Ti0.8O3/MgO/La0.7Sr0.3MnO3 heterostructure at room temperature via interfacial polarization mediation.

Multiferroic hybrid structures PbZr0.2Ti0.8O3 (PZT)/La0.7Sr0.3MnO3 (LSMO) and PZT/MgO/LSMO were epitaxially deposited on (001) Nb:SrTiO3 crystals. Crystallinity and ferroelectric domain structures were investigated for the PZT/LSMO heterostructure. Interestingly, relatively high non-volatile magnetoelectric coupling effects were observed in both heterostructures at room temperature. The change of chemical valence for Mn and Ti at the PZT/MgO/LSMO interface may play a dominant role rather than external strain or orbital reconstruction, which lead to a large modulation of the magnetization. Correspondingly, the transport behavior of the PZT/MgO/LSMO heterostructure is investigated to confirm the role of oxygen vacancies motion. Our result indicates that the PZT/MgO/LSMO heterostructure have a promising application for future high-density non-volatile memories.

Taking a(c)count of eye movements: Multiple mechanisms underlie fixations during enumeration.

We habitually move our eyes when we enumerate sets of objects. It remains unclear whether saccades are directed for numerosity processing as distinct from object-oriented visual processing (e.g., object saliency, scanning heuristics). Here we investigated the extent to which enumeration eye movements are contingent upon the location of objects in an array, and whether fixation patterns vary with enumeration demands. Twenty adults enumerated random dot arrays twice: first to report the set cardinality and second to judge the perceived number of subsets. We manipulated the spatial location of dots by presenting arrays at 0°, 90°, 180°, and 270° orientations. Participants required a similar time to enumerate the set or the perceived number of subsets in the same array. Fixation patterns were systematically shifted in the direction of array rotation, and distributed across similar locations when the same array was shown on multiple occasions. We modeled fixation patterns and dot saliency using a simple filtering model and show participants judged groups of dots in close proximity (2°-2.5° visual angle) as distinct subsets. Modeling results are consistent with the suggestion that enumeration involves visual grouping mechanisms based on object saliency, and specific enumeration demands affect spatial distribution of fixations. Our findings highlight the importance of set computation, rather than object processing per se, for models of numerosity processing.

Evidence of substantial development of inhibitory control and sustained attention between 6 and 8years of age on an unpredictable Go/No-Go task.

Inhibitory control and sustained attention are important cognitive abilities; however, their developmental trajectories remain unclear. In total, 35 6-year-olds, 32 8-year-olds, and 37 10-year-olds performed a Go/No-Go task; this required frequent responding to stimuli with infrequent inhibition to a target that appeared unpredictably. Children performed this task three times over 12months. Response time variability and accuracy measures, linked to inhibition and sustained attention, were assessed. Specifically, fast Fourier transform and ex-Gaussian analyses of response time data provided several measures of response time variability; these measures are thought to represent different components of sustained attention. The 6-year-olds performed less well than the older groups on most measures. The 8-year-olds exhibited greater momentary fluctuations in response time and made more long responses than the 10-year-olds; otherwise, there were few differences between the two older groups. Response inhibition and sustained attention developed significantly between 6 and 8years of age, with subtle changes in attentional control between 8 and 11years of age.

TEMA and Dot Enumeration Profiles Predict Mental Addition Problem Solving Speed Longitudinally.

Different math indices can be used to assess math potential at school entry. We evaluated whether standardized math achievement (TEMA-2 performance), core number abilities (dot enumeration, symbolic magnitude comparison), non-verbal intelligence (NVIQ) and visuo-spatial working memory (VSWM), in combination or separately, predicted mental addition problem solving speed over time. We assessed 267 children's TEMA-2, magnitude comparison, dot enumeration, and VSWM abilities at school entry (5 years) and NVIQ at 8 years. Mental addition problem solving speed was assessed at 6, 8, and 10 years. Longitudinal path analysis supported a model in which dot enumeration performance ability profiles and previous mental addition speed predicted future mental addition speed on all occasions, supporting a componential account of math ability. Standardized math achievement and NVIQ predicted mental addition speed at specific time points, while VSWM and symbolic magnitude comparison did not contribute unique variance to the model. The implications of using standardized math achievement and dot enumeration ability to index math learning potential at school entry are discussed.

Cognitive factors affecting children's nonsymbolic and symbolic magnitude judgment abilities: A latent profile analysis.

Early math abilities are claimed to be linked to magnitude representation ability. Some claim that nonsymbolic magnitude abilities scaffold the acquisition of symbolic (Arabic number) magnitude abilities and influence math ability. Others claim that symbolic magnitude abilities, and ipso facto math abilities, are independent of nonsymbolic abilities and instead depend on the ability to process number symbols (e.g., 2, 7). Currently, the issue of whether symbolic abilities are or are not related to nonsymbolic abilities, and the cognitive factors associated with nonsymbolic-symbolic relationships, remains unresolved. We suggest that different nonsymbolic-symbolic relationships reside within the general magnitude ability distribution and that different cognitive abilities are likely associated with these different relationships. We further suggest that the different nonsymbolic-symbolic relationships and cognitive abilities in combination differentially predict math abilities. To test these claims, we used latent profile analysis to identify nonsymbolic-symbolic judgment patterns of 124, 5- to 7-year-olds. We also assessed four cognitive factors (visuospatial working memory [VSWM], naming numbers, nonverbal IQ, and basic reaction time [RT]) and two math abilities (number transcoding and single-digit addition abilities). Four nonsymbolic-symbolic ability profiles were identified. Naming numbers, VSWM, and basic RT abilities were differentially associated with the different ability profiles and in combination differentially predicted math abilities. Findings show that different patterns of nonsymbolic-symbolic magnitude abilities can be identified and suggest that an adequate account of math development should specify the inter-relationship between cognitive factors and nonsymbolic-symbolic ability patterns.

Number-specific and general cognitive markers of preschoolers' math ability profiles.

Different number-specific and general cognitive markers have been claimed to underlie preschoolers' math ability. It is unclear, however, whether similar/different cognitive markers, or combinations of them, are associated with different patterns of emerging math abilities (i.e., different patterns of strength and weakness). To examine this question, 103 preschoolers (40-60 months of age) completed six math tasks (count sequence, object counting, give a number, naming numbers, ordinal relations, and arithmetic), three number-specific markers of math ability (dot enumeration, magnitude comparison, and spontaneous focusing on numerosity), and four general markers (working memory, response inhibition, attention, and vocabulary). A three-step latent profile modeling procedure identified five math ability profiles that differed in their patterns of math strengths and weaknesses; specifically, the profiles were characterized by (a) excellent math ability on all math tasks, (b) good arithmetic ability, (c) good math ability but relatively poor count sequence recitation ability, (d) average ability on all math tasks, and (e) poor ability on all math tasks. After controlling for age, only dot enumeration and spontaneous focusing on numerosity were associated with the math ability profiles, whereas vocabulary was also marginally significant, and these markers were differentially associated with different profiles; that is, different cognitive markers were associated with different patterns of strengths and weaknesses in math abilities. Findings are discussed in terms of their implications for the development of math cognition.

Observation of room-temperature magnetic skyrmions and their current-driven dynamics in ultrathin metallic ferromagnets.

Magnetic skyrmions are topologically protected spin textures that exhibit fascinating physical behaviours and large potential in highly energy-efficient spintronic device applications. The main obstacles so far are that skyrmions have been observed in only a few exotic materials and at low temperatures, and fast current-driven motion of individual skyrmions has not yet been achieved. Here, we report the observation of stable magnetic skyrmions at room temperature in ultrathin transition metal ferromagnets with magnetic transmission soft X-ray microscopy. We demonstrate the ability to generate stable skyrmion lattices and drive trains of individual skyrmions by short current pulses along a magnetic racetrack at speeds exceeding 100 m s(-1) as required for applications. Our findings provide experimental evidence of recent predictions and open the door to room-temperature skyrmion spintronics in robust thin-film heterostructures.