Academic literature on the topic 'Numerosity adaptation'

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.

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.

AbstractIt has recently been reported that, like most sensory systems, numerosity is subject to adaptation. However, the effect seemed to be limited to numerosity estimation outside the subitizing range. In this study we show that low numbers, clearly in the subitizing range, are adaptable under conditions of high attentional load. These results support the idea that numerosity is detected by a perceptual mechanism that operates over the entire range of numbers, supplemented by an attention-based system for small numbers (subitizing).

Autism is known to be associated with major perceptual atypicalities. We have recently proposed a general model to account for these atypicalities in Bayesian terms, suggesting that autistic individuals underuse predictive information or priors. We tested this idea by measuring adaptation to numerosity stimuli in children diagnosed with autism spectrum disorder (ASD). After exposure to large numbers of items, stimuli with fewer items appear to be less numerous (and vice versa). We found that children with ASD adapted much less to numerosity than typically developing children, although their precision for numerosity discrimination was similar to that of the typical group. This result reinforces recent findings showing reduced adaptation to facial identity in ASD and goes on to show that reduced adaptation is not unique to faces (social stimuli with special significance in autism), but occurs more generally, for both parietal and temporal functions, probably reflecting inefficiencies in the adaptive interpretation of sensory signals. These results provide strong support for the Bayesian theories of autism.

The present dissertation investigated visual perception of numerosity. In the first part I reviewed the prominent literature about the topic. In the second chapter I described the first experiment, in which I measured confidence and reaction times to study the origins of the well-established visual and motor adaptation effects on numerosity perception. The results reinforce the evidence for a shared mechanism that encodes the quantity of both internally and externally generated events, and shows that the adaptation effects result from changes in sensory encoding, rather than perceptual decisions. More generally, in the study was introduced a novel and useful technique for investigating the mechanisms of numerosity adaptation and sensory adaptation in general. The third chapter investigated the effects of grouping cues on sensory precision of numerosity estimation. The results provide strong evidence that “grouping”, which can improve performance by up to 20%, can be induced by color and/or spatial proximity and occurs in temporal sequences as well as spatial arrays. In the fourth chapter I further examined the groupitizing phenomenon, by testing the hypothesis that the advantage provided by clustering stimuli relies on subitizing. This was achieved by manipulating attention, which is known to strongly affect the subitizing system. In the same chapter I discussed an additional explorative analysis on the relationship between calculation skills and estimation precision of grouped and ungrouped arrays. Taken together, the results showed that groupitizing is truly an attention-based process that leverages on the subitizing system. Furthermore, the outcome of the study suggested that measuring numerosity estimation thresholds with grouped stimuli may be a sensitive correlate of math abilities. In the fifth chapter I went on investigating the neural correlates of the groupitizing phenomenon with both a behavioral and a fMRI study. Similarly to the previous study I measured acuity in estimation of grouped and ungrouped stimuli and additionally I also examined whether the two tasks shared or not the same neural substrate. The results showed that the estimation of grouped and ungrouped stimuli activates similar regions in the right lateralized fronto-parietal network, however, only the presentation of grouped stimuli in the numerosity task elicited the additional activation of regions linked with calculations strategies, for instance the angular gyrus. Moreover, a multivariate pattern analysis showed that parietal activation patterns for individual numerosities could be accurately decoded in the parietal regions independently of the spatial arrangement of the stimuli. Finally, I correlated fMRI decoding accuracy of primary visual areas and angular gyrus with Wfs calculated in the grouped estimation task. Results suggested that the numerical representation in angular gyrus, but not in primary visual areas, is strongly linked with numerical performance and behavior. Overall, the results confirmed psychophysical studies highlighting that groupitizing shares the same regions and neural pattern mechanism of the estimation of ungrouped stimuli, but, furthermore, it also activates brain regions typically activated during calculation tasks. The last part of the dissertation is dedicated to investigating the link between numerosity precision, math abilities and a non-cognitive factor affecting mathematical learning: mathematical anxiety. To this aim, university students with low (< 25th percentile) and high (> 75th percentile) score in the Abbreviate Math Anxiety Scale were tested in multiple domains: a) math proficiency assessed using a standardized test (Mathematics Prerequisite for Psychometrics), b) visuo-spatial attention capacity, measured via a Multiple Object Tracking task, and c) the sensory precision for non-numerical quantities. The results confirmed previous studies showing that math abilities and numerosity precision correlate in subjects with high math anxiety. Furthermore, neither precision in size-discrimination nor visuo-spatial attentional capacity were found to correlate with math capacities. However, within the group with high MA the data also revealed a relationship between numerosity precision and math anxiety, with math anxiety playing a key role in mediating the correlation between participants’ numerosity precision and their math achievement. Taken together, this last study suggests an interplay between extreme levels of MA and sensory precision in the processing of non-symbolic numerosity, giving further insight into the processes (and the variables affecting these processes) behind the acquisition of formal mathematical abilities. In conclusion, the present work assessed the ability to perceive non-symbolic quantities in adults while providing new experimental evidence suggesting its perceptual nature and its link with cognitive and affective factors.

There is considerable controversy as to how the brain extracts numerosity information from a visual scene and as to how much attention is needed for this process. Traditionally, it has been assumed that visual enumeration is subserved by two functionally distinct mechanisms: the fast and accurate apprehension of 1 to about 4 items, a process termed “subitizing”, and the slow and error-prone appraisal of larger numerosities referred to as “estimation”. Further to a functional dichotomy between these two mechanisms, an attentional dichotomy has been proposed. Subitizing has been thought of as a pre-attentive and parallel process, whereas estimation is supposed to require serial attention. In this thesis, the hypothesis of a parallel and pre-attentive subitizing mechanism was tested. In the first part of the thesis to this aim, the amount of attention that could be allocated to an Estimation task was experimentally manipulated. We shown that numerosity estimation is composed by different and separable, sub- systems. Results indicated that subitizing strongly depends on attentional resources, while estimation of larger quantities does not. Exactly the same results were found when the attentional resources dedicated to the visual numerical estimation task were limited on other sensory modalities: indeed visual, auditory and also haptic attentional load strongly and similarly impair visual subitizing but much less high numbers. We also demonstrated that visual adaptation to numerosity, absent in the subitizing range under normal condition, emerges under attentional load with a magnitude of the effect highly comparable to that measured for high numbers. Moreover we first demonstrate that the ability to accurately map numbers onto space also depends on attentional resources, showing that the assumption that performance on the ‘numberline task’ is the direct reflection of the internal numeric representation form could be misleading. In last part of the thesis we study how number adaptation affects number perception in two different population; high-functioning autistic and typically developing children. We demostrated that ASD children discriminated numerosity with the same precision as the typical children, but showed much less (about half) the levels of adaptation to number than the control group. These new results show that adaptation, processes, fundamental for efficient processing of variable sensory inputs, is diminished in autism.