Groupitizing modifies neural coding of numerosity.

Numerical estimation of arrays of objects is faster and more accurate when items can be clustered into groups, a phenomenon termed "groupitizing." Grouping can facilitate segregation into subitizable "chunks," each easily estimated, then summed. The current study investigates whether spatial grouping of arrays drives specific neural responses during numerical estimation, reflecting strategies such as exact calculation and fact retrieval. Fourteen adults were scanned with fMRI while estimating either the numerosity or shape of arrays of items, either randomly distributed or spatially grouped. Numerosity estimation of both classes of stimuli elicited common activation of a right lateralized frontoparietal network. Grouped stimuli additionally recruited regions in the left hemisphere and bilaterally in the angular gyrus. Multivariate pattern analysis showed that classifiers trained with the pattern of neural activations read out from parietal regions, but not from the primary visual areas, can decode different numerosities both within and across spatial arrangements. The behavioral numerical acuity correlated with the decoding performance of the parietal but not with occipital regions. Overall, this experiment suggests that the estimation of grouped stimuli relies on the approximate number system for numerosity estimation, but additionally recruits regions involved in calculation.

Uncertainty and Prior Assumptions, Rather Than Innate Logarithmic Encoding, Explain Nonlinear Number-to-Space Mapping.

Mapping number to space is natural and spontaneous but often nonveridical, showing a clear compressive nonlinearity that is thought to reflect intrinsic logarithmic encoding of numerical values. We asked 78 adult participants to map dot arrays onto a number line across nine trials. Combining participant data, we confirmed that on the first trial, mapping was heavily compressed along the number line, but it became more linear across trials. Responses were well described by logarithmic compression but also by a parameter-free Bayesian model of central tendency, which quantitatively predicted the relationship between nonlinearity and number acuity. To experimentally test the Bayesian hypothesis, we asked 90 new participants to complete a color-line task in which they mapped noise-perturbed color patches to a "color line." When there was more noise at the high end of the color line, the mapping was logarithmic, but it became exponential with noise at the low end. We conclude that the nonlinearity of both number and color mapping reflects contextual Bayesian inference processes rather than intrinsic logarithmic encoding.

Numerosity adaptation partly depends on the allocation of implicit numerosity-contingent visuo-spatial attention.

Like other perceptual attributes, numerosity is susceptible to adaptation. Nevertheless, it has never been fully investigated whether adaptation to numerosity is fully perceptual in nature or if it stems from the mixed influence of perception and attention. In the present work, we addressed this point throughout three separate experiments aiming at investigating the potential role played by visuo-spatial attentional mechanisms in shaping numerosity perception and adaptation. In Experiments 1 and 2, we showed that the magnitude of numerosity adaptation can be strongly influenced by the distribution of numerosity-contingent visuo-spatial attentional resources during the adaptation period. Results from Experiment 1 revealed a robust reduction of adaptation magnitude whenever a second numerical stimulus was presented in a diametrically opposite location from that of the adaptor, despite this second adapter being neutral as matched in numerosity with the following stimulus displayed in that location. In Experiment 2, we showed that this reduction in adaptation did not occur in cases where the second stimulus was not numerical, suggesting that attentional resources specifically related to numerosity information accounts for the results of Experiment 1. Finally, in Experiment 3, we showed that uninformative visuo-spatial cues shape numerosity discrimination judgments both at baseline and during adaptation. Taken together, our results seem to indicate that visuo-spatial attention plays a relevant role in numerosity perception and that adaptation to numerosity is actively influenced by this cognitive process.

Implicit visuospatial attention shapes numerosity adaptation and perception.

The perception of numerical quantities is susceptible to adaptation: after inspecting a numerous dot array for a few seconds a subsequent dot array is grossly underestimated. In a recent work we showed that the mere appearance of an additional numerically neutral stimulus significantly reduces the adaptation magnitude. Here we demonstrate that this reduction is likely due to a numerosity underestimation of the adaptor caused by a change of numerosity-related attentional resources deployed on the adapting stimulus. In Experiment 1 we replicated previous findings revealing a robust reduction of numerosity adaptation when an additional adaptor (even if neutral) was displayed. In Experiment 2 we used the method of magnitude estimation to demonstrate that numerosity is underestimated whenever a second task-irrelevant numerical stimulus appears on screen. Furthermore we demonstrated that the same experimental manipulations were not effective in modulating orientation adaptation magnitude as well as orientation estimation accuracy. Our results support the hypothesis of a tight relationship between numerosity perception and implicit visuospatial attention and corroborate the notion that numerosity adaptation depends on perceived rather than physical numerosity. However the lack of an effect of visuospatial attentional deployment for orientation perception suggests that attention might differently shape adaptation aftereffects for different features along the visual hierarchy.

Numbers in action.

To understand the number sense, we need to understand its function. We argue that numerosity estimation is fundamental not only for perception, but also preparation and control of action. We outline experiments that link numerosity estimation with action, pointing to a generalized numerosity system that serves both perception and action preparation.

Adaptation to hand-tapping affects sensory processing of numerosity directly: evidence from reaction times and confidence.

Like most perceptual attributes, the perception of numerosity is susceptible to adaptation, both to prolonged viewing of spatial arrays and to repeated motor actions such as hand-tapping. However, the possibility has been raised that adaptation may reflect response biases rather than modification of sensory processing. To disentangle these two possibilities, we studied visual and motor adaptation of numerosity perception while measuring confidence and reaction times. Both sensory and motor adaptation robustly distorted numerosity estimates, and these shifts in perceived numerosity were accompanied by similar shifts in confidence and reaction-time distributions. After adaptation, maximum uncertainty and slowest response-times occurred at the point of subjective (rather than physical) equality of the matching task, suggesting that adaptation acts directly on the sensory representation of numerosity, before the decisional processes. On the other hand, making reward response-contingent, which also caused robust shifts in the psychometric function, caused no significant shifts in confidence or reaction-time distributions. These results reinforce evidence for shared mechanisms that encode the quantity of both internally and externally generated events, and advance a useful general technique to test whether contextual effects like adaptation and serial dependence really affect sensory processing.

Simultaneous and sequential subitizing are separate systems, and neither predicts math abilities.

Small quantities of visual objects can be rapidly estimated without error, a phenomenon known as subitizing. Larger quantities can also be rapidly estimated, but with error, and the error rate predicts math abilities. This study addressed two issues: (a) whether subitizing generalizes over modalities and stimulus formats and (b) whether subitizing correlates with math abilities. We measured subitizing limits in primary school children and adults for visual and auditory stimuli presented either sequentially (sequences of flashes or sounds) or simultaneously (visual presentations, dot arrays). The results show that (a) subitizing limits for adults were one item larger than those for primary school children across all conditions; (b) subitizing for simultaneous visual stimuli (dots) was better than that for sequential stimuli; (c) subitizing limits for dots do not correlate with subitizing limits for either flashes or sounds; (d) subitizing of sequences of flashes and subitizing of sequences of sounds are strongly correlated with each other in children; and (e) regardless of stimuli sensory modality and format, subitizing limits do not correlate with mental calculation or digit magnitude knowledge proficiency. These results suggest that although children can subitize sequential numerosity, simultaneous and temporal subitizing may be subserved by separate systems. Furthermore, subitizing does not seem to be related to numerical abilities.

Blood oxygen level-dependent activation of the primary visual cortex predicts size adaptation illusion.

In natural scenes, objects rarely occur in isolation but appear within a spatiotemporal context. Here, we show that the perceived size of a stimulus is significantly affected by the context of the scene: brief previous presentation of larger or smaller adapting stimuli at the same region of space changes the perceived size of a test stimulus, with larger adapting stimuli causing the test to appear smaller than veridical and vice versa. In a human fMRI study, we measured the blood oxygen level-dependent activation (BOLD) responses of the primary visual cortex (V1) to the contours of large-diameter stimuli and found that activation closely matched the perceptual rather than the retinal stimulus size: the activated area of V1 increased or decreased, depending on the size of the preceding stimulus. A model based on local inhibitory V1 mechanisms simulated the inward or outward shifts of the stimulus contours and hence the perceptual effects. Our findings suggest that area V1 is actively involved in reshaping our perception to match the short-term statistics of the visual scene.

A generalized sense of number.

Much evidence has accumulated to suggest that many animals, including young human infants, possess an abstract sense of approximate quantity, a number sense. Most research has concentrated on apparent numerosity of spatial arrays of dots or other objects, but a truly abstract sense of number should be capable of encoding the numerosity of any set of discrete elements, however displayed and in whatever sensory modality. Here, we use the psychophysical technique of adaptation to study the sense of number for serially presented items. We show that numerosity of both auditory and visual sequences is greatly affected by prior adaptation to slow or rapid sequences of events. The adaptation to visual stimuli was spatially selective (in external, not retinal coordinates), pointing to a sensory rather than cognitive process. However, adaptation generalized across modalities, from auditory to visual and vice versa. Adaptation also generalized across formats: adapting to sequential streams of flashes affected the perceived numerosity of spatial arrays. All these results point to a perceptual system that transcends vision and audition to encode an abstract sense of number in space and in time.

Electrophysiological correlates of temporal numerosity adaptation.

Introduction: Much research has revealed the human visual system is capable to estimate numerical quantities, rapidly and reliably, in both the spatial and the temporal domain. This ability is highly susceptible to short-term plastic phenomena related to previous exposure to visual numerical information (i.e., adaptation). However, while determinants of spatial numerosity adaptation have been widely investigated, little is known about the neural underpinnings of short-term plastic phenomena related to the encoding of temporal numerical information. In the present study we investigated the electrophysiological correlates of temporal numerosity adaptation. Methods: Participants were asked to estimate the numerosity of a test sequence of flashes after being exposed to either a high or low numerous adapting sequence. Behavioral results confirmed the expected underestimation of test stimulus when this was preceded by a high numerous sequence as compared to when preceded by a low numerous sequence. Results: Electrophysiological data revealed that this behavior was tightly linked to the amplitude of the steady-state visual evoked (ssVEP) response elicited by the test stimulus. When preceded by a high numerous sequence, the test stimulus elicited larger ssVEP responses as compared to when preceded by a low numerous sequence with this pattern being robustly correlated with behavior. Finally, topographical maps showed that this difference was mostly evident across two antero-posterior distributed clusters of electrodes and correlated with changes in functional connectivity. Discussion: Taken together, our results suggest that visual plastic phenomena related to the encoding of temporal numerosity information reflect changes in rhythmic evoked activity that are likely related to long range communications between distinct brain regions.

Drivers' performance assessment approaching pedestrian crossings through the analysis of the speed and perceptive data recorded during on-field tests.

Pedestrian fatalities in road accidents represent one of the biggest causes of death in the world despite the great efforts that have been made to decrease the involvement of vulnerable road users in road accidents. Literature analysis revealed the presence of several studies aimed at investigating the phenomenon and proposing strategies to improve pedestrian safety, but this is still not enough to considerably reduce the number of pedestrians killed on the road. In this context, with the aim to take a step forward in the topic, this paper describes a naturalistic driving assessment carried out in Firenze aimed at evaluating the effect of different pedestrian crossing configurations on the drivers' behavior, especially concerning the reduction of the speeding phenomenon approaching a pedestrian crossing. The experiment was conducted on a section of an urban collector road within the Firenze suburban area. Crucially, over the past few years, different traffic calming interventions have been implemented along this street. Among the different traffic calming countermeasures, both the presence of a traffic light and trapezoidal deflection have been considered to assess their effect on drivers' behavior, also with reference to specific aspects related to the drivers' perception. During the experiment, thirty-six users drove their own vehicles along the street, encountering different pedestrian crossing configurations. During the driving speed, deceleration and ocular fixation were recorded. This study shows the difference in drivers' behavior in response to different traffic calming countermeasures. It demonstrates also that the raised pedestrian crossing caused a significant effect on reducing the speed approaching a pedestrian crossing. Moreover, it is observed that, when perceptive countermeasures are present, the drivers' behavior changes only if the pedestrian crossing configuration is perceived in foveal vision; suggesting that the correct identification of the configuration is crucial to implement a congruent and safe driving behavior.

Reshaping the peripersonal space in virtual reality.

Peripersonal space (PPS) is defined as the space that lies within reach. Previous research revealed that PPS can be dynamically reshaped with the use of tools extending the arm's reach. Here we investigated whether PPS reshaping depends on the kind of selected tool and/or the motor routine associated with its use. Participants carried out a visuo-tactile detection task in an immersive VR environment that allowed to measure the PPS size before and after a short period of tools use. In Experiment 1, participants had to pull or push objects towards or away from themselves using a shovel. In Experiment 2, they were required to either hammer or shoot an avatar placed in the Extrapersonal space. We found, for the first time in a VR environment, that a period of pull training was effective in enlarging the PPS, a result that replicates and expands previous findings carried out in real life conditions. However, no significant change in PPS size was achieved for training with other tools and motor routines. Our results suggest that the reshaping of PPS is a complex phenomenon in which the kind of interaction between the agent, the targets and the exploited motor routines all play a critical role.

Neurocognitive Assessment of Mathematics-Related Capacities in Neurosurgical Patients.

A precise neuropsychological assessment is of the utmost importance for neurosurgical patients undergoing the surgical excision of cerebral lesions. The assessment of mathematical abilities is usually limited to arithmetical operations while other fundamental visuo-spatial aspects closely linked to mathematics proficiency, such as the perception of numerical quantities and geometrical reasoning, are completely neglected. We evaluated these abilities with two objective and reproducible psychophysical tests, measuring numerosity perception and non-symbolic geometry, respectively. We tested sixteen neuro-oncological patients before the operation and six after the operation with classical neuropsychological tests and with two psychophysical tests. The scores of the classical neuropsychological tests were very heterogeneous, possibly due to the distinct location and histology of the tumors that might have spared (or not) brain areas subserving these abilities or allowed for plastic reorganization. Performance in the two non-symbolic tests reflected, on average, the presumed functional role of the lesioned areas, with participants with parietal and frontal lesions performing worse on these tests than patients with occipital and temporal lesions. Single-case analyses not only revealed some interesting exceptions to the group-level results (e.g., patients with parietal lesions performing well in the numerosity test), but also indicated that performance in the two tests was independent of non-verbal reasoning and visuo-spatial working memory. Our results highlight the importance of assessing non-symbolic numerical and geometrical abilities to complement typical neuropsychological batteries. However, they also suggest an avoidance of reliance on an excessively rigid localizationist approach when evaluating the neuropsychological profile of oncological patients.

Optimal encoding of interval timing in expert percussionists.

We measured temporal reproduction in human subjects with various levels of musical expertise: expert drummers, string musicians, and non-musicians. While duration reproduction of the non-percussionists showed a characteristic central tendency or regression to the mean, drummers responded veridically. Furthermore, when the stimuli were auditory tones rather than flashes, all subjects responded veridically. The behavior of all three groups in both modalities is well explained by a Bayesian model that seeks to minimize reproduction errors by incorporating a central tendency prior, a probability density function centered at the mean duration of the sample. We measured separately temporal precision thresholds with a bisection task; thresholds were twice as low in drummers as in the other two groups. These estimates of temporal precision, together with an adaptable Bayesian prior, predict well the reproduction results and the central tendency strategy under all conditions and for all subject groups. These results highlight the efficiency and flexibility of sensorimotor mechanisms estimating temporal duration.

The symmetry-induced numerosity illusion depends on visual attention.

Symmetry is an important and strong cue we rely on to organize the visual world. Although it is at the basis of objects segmentation in a visual scene, it can sometimes bias our perception. When asked to discriminate numerical quantities between symmetric and asymmetric arrays, individuals tend to underestimate the number of items in the symmetric stimuli. The reason for this underestimation is currently unknown. In this study we investigated whether the symmetry-induced numerosity underestimation depends on perceptual grouping mechanisms by depriving attentional resources. Twenty-six adults judged the numerosity of dot arrays arranged symmetrically or randomly, while ignoring a visual distractor (single task) or while simultaneously judging its color and orientation (dual-task). Diverting attention to the concurrent color-orientation conjunction task halved the symmetry-induced numerosity underestimation. Taken together these results showed that the bias in numerosity perception of symmetric arrays depends-at least partially-on attentional resources and suggested that it might originate from the recruitment of attentional dependent incremental grouping mechanisms.

The role of non-numerical information in the perception of temporal numerosity.

Numerosity perception refers to the ability to make rapid but approximate estimates of the quantity of elements in a set (spatial numerosity) or presented sequentially (temporal numerosity). Whether numerosity is directly perceived or indirectly recomputed from non-numerical features is a highly debated issue. In the spatial domain, area and density have been suggested as the main parameters through which numerosity would be recomputed. In the temporal domain, stimuli duration and temporal frequency could be similarly exploited to retrieve numerosity. By adapting a psychophysical technique previously exploited in the spatial domain, we investigated whether temporal visual numerosity is directly perceived. Adult participants observed sequences of visual impulses sampled from a stimulus space spanning several levels of temporal frequency and duration (and hence numerosity), and then reproduced the sequence as accurately as possible via a series of keypresses. Crucially, participants were not asked to reproduce any particular property (such as number of impulses) but were free to choose any available cue (such as total duration, or temporal frequency). The results indicate that while the overall sequence duration was barely considered, numerosity and temporal frequency were both spontaneously used as the main cues to reproduce the sequences, with a slight but significant dominance of numerosity. Overall, the results are in line with previous literature suggesting that numerosity is directly encoded, even for temporal sequences, but a non-numerical feature (temporal frequency) is also used in reproducing sequences.

Similar effect of running on visual and auditory time perception in the ranges of milliseconds and seconds.

Introduction: The ability to accurately encode events' duration is of critical importance for almost all everyday activities, yet numerous factors have been reported to robustly distort time perception. One of these is physical activity (i.e., running, walking) but, partly due to the variety of methodologies employed, a full comprehension of the role of exercise on the encoding of time has still to be achieved. Methods: Here we tackle the issue with a multifaceted approach by measuring the effect of vigorous running with a time generalization task for visual and auditory stimuli in the range of milliseconds (0.2-0.8 s) as well as seconds (1-4 s). At baseline, participants performed both the encoding and decoding at rest while in the experimental conditions the decoding was performed while running. Results: Our results indicate that physical activity in both duration ranges (sub-second and seconds) was expanded during running regardless of the sensory modality used to present the stimuli. Despite this generalized effect of running on perceived duration, we found evidence for the existence of independent timing mechanisms: (1) the perceptual biases induced by running in the two temporal regimes were uncorrelated, (2) sensory precision levels (Weber fraction) were higher for stimuli in the seconds range, (3) sensory precision levels were higher for auditory than for visual stimuli, but only within the sub-second range. Discussion: Overall, our results support previous findings suggesting (at least partially) separate timing mechanisms for short/long durations and for visual and auditory stimuli. However, they also indicate that physical activity affects all these temporal modules, suggesting a generalized interaction-via generalized and shared resources-between the motor system and the brain time mechanisms.

Top-down determinants of the numerosity-time interaction.

Previous studies have reported that larger visual stimuli are perceived as lasting longer than smaller ones. However, this effect disappears when participants provide a qualitative judgment, by stating whether two stimuli have the "same or different" duration, instead of providing an explicit quantitative judgment (which stimulus lasts longer). Here, we extended these observations to the interaction between the numerosity of visual stimuli, i.e. clouds of dots, and their duration. With "longer vs shorter" responses, participants judged larger numerosities as lasting longer than smaller ones, both when the responses were related to the order (Experiment 1) or color (Experiment 4) of stimuli. In contrast, no similar effect was found with "same vs different" responses (Experiment 2) and in a time motor reproduction task (Experiment 3). The numerosity-time interference in Experiment 1 and Experiment 4 was not due to task difficulty, as sensory precision was equivalent to that of Experiment 2. We conclude that in humans the functional interaction between numerosity and time is not guided, in the main, by a shared bottom-up mechanism of magnitude coding. Rather, high-level and top-down processes involved in decision-making and guided by the use of "magnitude-related" response codes play a crucial role in triggering interference among different magnitude domains.

EEG signature of grouping strategies in numerosity perception.

The moment we see a group of objects, we can appreciate its numerosity. Our numerical estimates can be imprecise for large sets (>4 items), but they become much faster and more accurate if items are clustered into groups compared to when they are randomly displaced. This phenomenon, termed groupitizing, is thought to leverage on the capacity to quickly identify groups from 1 to 4 items (subitizing) within larger sets, however evidence in support for this hypothesis is scarce. The present study searched for an electrophysiological signature of subitizing while participants estimated grouped numerosities exceeding this range by measuring event-related potential (ERP) responses to visual arrays of different numerosities and spatial configurations. The EEG signal was recorded while 22 participants performed a numerosity estimation task on arrays with numerosities in the subitizing (3 or 4) or estimation (6 or 8) ranges. In the latter case, items could be spatially arranged into subgroups (3 or 4) or randomly scattered. In both ranges, we observed a decrease in N1 peak latency as the number of items increased. Importantly, when items were arranged to form subgroups, we showed that the N1 peak latency reflected both changes in total numerosity and changes in the number of subgroups. However, this result was mainly driven by the number of subgroups to suggest that clustered elements might trigger the recruitment of the subitizing system at a relatively early stage. At a later stage, we found that P2p was mostly modulated by the total numerosity in the set, with much less sensitivity for the number of subgroups these might be segregated in. Overall, this experiment suggests that the N1 component is sensitive to both local and global parcelling of elements in a scene suggesting that it could be crucially involved in the emergence of the groupitizing advantage. On the other hand, the later P2p component seems to be much more bounded to the global aspects of the scene coding the total number of elements while being mostly blind to the number of subgroups in which elements are parsed.