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The numerical Stroop task involves presenting participants with two digits that differ in physical size and numerical value and asking them to report which digit had the larger size or value while ignoring the other dimension. Previous studies show that participants have difficulty ignoring the irrelevant dimension and thus have implications on the automaticity of numerical processing. The present study investigates the automatic influence of numerical value on numerosity processing in a novel Stroop-like task. In two experiments, participants were presented with digits made of colored stripes and asked to identify the number of different colors. In both experiments, interference and facilitation effects were found, supporting the automaticity of symbolic number processing and its influence on numerosity processing. These findings expand upon previous research on numerical as well as counting Stroop tasks, and have potential implications for studying interference and basic numerical processing in children and clinical populations.

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Our visual environments are composed of an abundance of individual objects. The efficiency with which we can parse such rich environments is remarkable. Previous work suggests that this efficiency is partly explained by grouping mechanisms, which allow the visual system to process the objects that surround us as meaningful groups rather than individual entities. Here, we show that the grouping of objects in typically and meaningfully structured environments directly relates to a reduction of perceived complexity. In an object numerosity discrimination task, we showed participants pairs of schematic scene miniatures, in which objects were structured in typical or atypical ways and asked them to judge which scene consisted of more individual objects. Critically, participants underestimated the number of objects in typically structured compared with atypically structured scenes, suggesting that grouping based on typical object configurations reduces the perceived numerical complexity of a scene. In two control experiments, we show that this overestimation also occurs when the objects are presented on textured backgrounds, and that it is specific to upright scenes, indicating that it is not related to basic visual feature differences between typically and atypically structured scenes. Together, our results suggest that our visual surroundings appear less complex to the visual system than the number of objects in them makes us believe.

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Despite their young age, zebrafish larvae have a well-developed visual system and can distinguish between different visual stimuli. First, we investigated if the first visual surroundings the larvae experience during the first days after hatching shape their habitat preference. Indeed, these animals seem to "imprint" on the first surroundings they see and select visual stimuli accordingly at 7 days post fertilization (dpf). In particular, if zebrafish larvae experience a bar background just after hatching, they later on prefer bars over white stimuli, and vice versa. We then used this acquired preference for bars to investigate innate numerical abilities. We wanted to specifically test if the zebrafish larvae show real numerical abilities or if they rely on a lower-level mechanism-i.e. spatial frequency-to discriminate between two different numerosities. When we matched the spatial frequency in stimuli with different numbers of bars, the larvae reliably selected the higher numerosity. A previous study has ruled out that 7 dpf zebrafish larvae use convex hull, cumulative surface area and density to choose between two numerosities. Therefore, our results indicate that zebrafish larvae rely on real numerical abilities rather than other cues, including spatial frequency, when spontaneously comparing two sets with different numbers of bars.

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Accumulated functional magnetic resonance imaging (fMRI) and electroencephalography evidence indicate that numerosity is first processed in the occipito-parietal cortex. fMRI evidence also indicates right-lateralized processing of numerosity, but there is no consistent evidence from event-related potential (ERP) studies. This study investigated the ERP of numerosity processing in the left, right, and bilateral visual fields. The single-trial ERP-behavioral correlation was applied to show how the ERP was associated with behavioral responses. The results showed a significant early behavioral-ERP correlation on the right N1 component when stimuli were presented in the left visual field rather than in the right visual field. The behavioral ERP correlation was termed BN1. There was bilateral BN1 based on the reaction time or error rate, but the right BN1 was larger than that the left BN1 when the stimulus was present in the bilateral visual field. Therefore, this study provided a new neural marker for individual differences in processing numerosity and suggested that processing numerosity was supported by the right occipito-parietal cortex.

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The approximate number system (ANS) enables organisms to represent the approximate number of items in an observed collection, quickly and independently of natural language. Recently, it has been proposed that the ANS goes beyond representing natural numbers by extracting and representing rational numbers (Clarke & Beck, 2021a). Prior work demonstrates that adults and children discriminate ratios in an approximate and ratio-dependent manner, consistent with the hallmarks of the ANS. Here, we use a well-known "connectedness illusion" to provide evidence that these ratio-dependent ratio discriminations are (a) based on the perceived number of items in seen displays (and not just non-numerical confounds), (b) are not dependent on verbal working memory, or explicit counting routines, and (c) involve representations with a part-whole (or subset-superset) format, like a fraction, rather than a part-part format, like a ratio. These results vindicate key predictions of the hypothesis that the ANS represents rational numbers.

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Numerous studies have consistently demonstrated the presence of the approximate number system (ANS) throughout development. Research has also revealed that visual cues may influence the ANS acuity, which may change with age. However, most studies have drawn conclusions based on performance differences between incongruent and congruent trials, which may be confounded by an individual's ability to inhibit interference. Therefore, to examine the developmental changes of the impact of visual cues on ANS acuity, we utilized congruent trials with varying visual cues. Our sample comprised Chinese children from grade one to grade five. We manipulated the salience of numerical cues (numerical ratio) and visual cues (dot size) in a non-symbolic numerosity comparison task. The results revealed a discernible leap in development from first to third grade and first to fifth grade; however, this upward trajectory did not persist into the transition from third to fifth grade, where no appreciable advancement was observed. Moreover, we observed different effects of visual cues on the dot-comparison task depending on the numerical cues and age. Specifically, visual cues (i.e., dot size) only facilitated ANS acuity in older school-aged children when numerical cues were weakened. The results indicate the presence of two distinct magnitude representational systems-one for the numerical dimension and another for the non-numerical dimension-during development.

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While several methods have been proposed to assess the influence of continuous visual cues in parallel numerosity estimation, the impact of temporal magnitudes on sequential numerosity judgments has been largely ignored. To overcome this issue, we extend a recently proposed framework that makes it possible to separate the contribution of numerical and non-numerical information in numerosity comparison by introducing a novel stimulus space designed for sequential tasks. Our method systematically varies the temporal magnitudes embedded into event sequences through the orthogonal manipulation of numerosity and two latent factors, which we designate as "duration" and "temporal spacing". This allows us to measure the contribution of finer-grained temporal features on numerosity judgments in several sensory modalities. We validate the proposed method on two different experiments in both visual and auditory modalities: results show that adult participants discriminated sequences primarily by relying on numerosity, with similar acuity in the visual and auditory modality. However, participants were similarly influenced by non-numerical cues, such as the total duration of the stimuli, suggesting that temporal cues can significantly bias numerical processing. Our findings highlight the need to carefully consider the continuous properties of numerical stimuli in a sequential mode of presentation as well, with particular relevance in multimodal and cross-modal investigations. We provide the complete code for creating sequential stimuli and analyzing participants' responses.

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We have previously shown that after few seconds of adaptation by finger-tapping, the perceived numerosity of spatial arrays and temporal sequences of visual objects displayed near the tapping region is increased or decreased, implying the existence of a sensorimotor numerosity system (Anobile et al., 2016). To date, this mechanism has been evidenced only by adaptation. Here, we extend our finding by leveraging on a well-established covariance technique, used to unveil and characterize 'channels' for basic visual features such as colour, motion, contrast, and spatial frequency. Participants were required to press rapidly a key a specific number of times, without counting. We then correlated the precision of reproduction for various target number presses between participants. The results showed high positive correlations for nearby target numbers, scaling down with numerical distance, implying tuning selectivity. Factor analysis identified two factors, one for low and the other for higher numbers. Principal component analysis revealed two bell-shaped covariance channels, peaking at different numerical values. Two control experiments ruled out the role of non-numerical strategies based on tapping frequency and response duration. These results reinforce our previous reports based on adaptation, and further suggest the existence of at least two sensorimotor number channels responsible for translating symbolic numbers into action sequences.

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Vittorio Benussi (1878-1927) is known for numerous studies on optical illusions, visual and haptic perception, spatial and time perception. In Padova, he had a brilliant student who carefully worked on the topic of how people estimate numerosity, Silvia De Marchi (1897-1936). Her writings have never been translated into English before. Here we comment on her work and life, characterized also by the challenges faced by women in academia. The studies on perception of numerosity from her thesis were published as an article in 1929. We provide a translation from Italian, a redrawing of its 23 illustrations and of the graphs. It shows an original experimental approach and an anticipation of what later became known as magnitude estimation.

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Groupitizing is a well-established strategy in numerosity perception that enhances speed and sensory precision. Building on the ATOM theory, Anobile proposed the sensorimotor numerosity system, which posits a strong link between number and action. Previous studies using motor adaptation technology have shown that high-frequency motor adaptation leads to underestimation of numerosity perception, while low-frequency adaptation leads to overestimation. However, the impact of motor adaptation on groupitizing, and whether visual motion adaptation produces similar effects, remain unclear. In this study, we investigate the persistence of the advantage of groupitizing after motor adaptation and explore the effects of visual motion adaptation. Surprisingly, our findings reveal that proprioceptive motor adaptation weakens the advantage of groupitizing, indicating a robust effect of motor adaptation even when groupitizing is employed. Moreover, we observe a bidirectional relationship, as groupitizing also weakens the adaptation effect. These results highlight the complex interplay between motor adaptation and groupitizing in numerosity perception. Furthermore, our study provides evidence that visual motion adaptation also has an adaptation effect, but does not fully replicate the effects of proprioceptive motor adaptation on groupitizing. In conclusion, our research underscores the importance of groupitizing as a valuable strategy in numerosity perception, and sheds light on the influence of motion adaptation on this strategy.

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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.

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Introduction: Associating multimodal information is essential for human cognitive abilities including mathematical skills. Multimodal learning has also attracted attention in the field of machine learning, and it has been suggested that the acquisition of better latent representation plays an important role in enhancing task performance. This study aimed to explore the impact of multimodal learning on representation, and to understand the relationship between multimodal representation and the development of mathematical skills. Methods: We employed a multimodal deep neural network as the computational model for multimodal associations in the brain. We compared the representations of numerical information, that is, handwritten digits and images containing a variable number of geometric figures learned through single- and multimodal methods. Next, we evaluated whether these representations were beneficial for downstream arithmetic tasks. Results: Multimodal training produced better latent representation in terms of clustering quality, which is consistent with previous findings on multimodal learning in deep neural networks. Moreover, the representations learned using multimodal information exhibited superior performance in arithmetic tasks. Discussion: Our novel findings experimentally demonstrate that changes in acquired latent representations through multimodal association learning are directly related to cognitive functions, including mathematical skills. This supports the possibility that multimodal learning using deep neural network models may offer novel insights into higher cognitive functions.

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Numerosity perception is a fundamental and innate cognitive function shared by both humans and many animal species. Previous research has primarily focused on exploring the spatial and functional consistency of neural activations that were associated with the processing of numerosity information. However, the inter-individual variability of brain activations of numerosity perception remains unclear. In the present study, with a large-sample functional magnetic resonance imaging (fMRI) dataset (n = 460), we aimed to localize the functional regions related to numerosity perceptions and explore the inter-individual, hemispheric, and sex differences within these brain regions. Fifteen subject-specific activated regions, including the anterior intraparietal sulcus (aIPS), posterior intraparietal sulcus (pIPS), insula, inferior frontal gyrus (IFG), inferior temporal gyrus (ITG), premotor area (PM), middle occipital gyrus (MOG) and anterior cingulate cortex (ACC), were delineated in each individual and then used to create a functional probabilistic atlas to quantify individual variability in brain activations of numerosity processing. Though the activation percentages of most regions were higher than 60%, the intersections of most regions across individuals were considerably lower, falling below 50%, indicating substantial variations in brain activations related to numerosity processing among individuals. Furthermore, significant hemispheric and sex differences in activation location, extent, and magnitude were also found in these regions. Most activated regions in the right hemisphere had larger activation volumes and activation magnitudes, and were located more lateral and anterior than their counterparts in the left hemisphere. In addition, in most of these regions, males displayed stronger activations than females. Our findings demonstrate large inter-individual, hemispheric, and sex differences in brain activations related to numerosity processing, and our probabilistic atlas can serve as a robust functional and spatial reference for mapping the numerosity-related neural networks.

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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.

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Many sensory brain areas are organized as topographic maps where neural response preferences change gradually across the cortical surface. Within association cortices, 7-Tesla fMRI and neural model-based analyses have also revealed many topographic maps for quantities like numerosity and event timing, often in similar locations. Numerical and temporal quantity estimations also show behavioral similarities and even interactions. For example, the duration of high-numerosity displays is perceived as longer than that of low-numerosity displays. Such interactions are often ascribed to a generalized magnitude system with shared neural responses across quantities. Anterior quantity responses are more closely linked to behavior. Here, we investigate whether common quantity representations hierarchically emerge by asking whether numerosity and timing maps become increasingly closely related in their overlap, response preferences, and topography. While the earliest quantity maps do not overlap, more superior maps overlap increasingly. In these overlapping areas, some intraparietal maps have consistently correlated numerosity and timing preferences, and some maps have consistent angles between the topographic progressions of numerosity and timing preferences. However, neither of these relationships increases hierarchically like the amount of overlap does. Therefore, responses to different quantities are initially derived separately, then progressively brought together, without generally becoming a common representation. Bringing together distinct responses to different quantities may underlie behavioral interactions and allow shared access to comparison and action planning systems.

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Our everyday perceptual experiences are grounded in the integration of information within and across our senses. Due to this direct behavioural relevance, cross-modal integration retains a certain degree of contextual flexibility, even to social relevance. However, how social relevance modulates cross-modal integration remains unclear. To investigate possible mechanisms, Experiment 1 tested the principles of audio-visual integration for numerosity estimation by deriving a Bayesian optimal observer model with perceptual prior from empirical data to explain perceptual biases. Such perceptual priors may shift towards locations of high salience in the stimulus space. Our results showed that the tendency to over- or underestimate numerosity, expressed in the frequency and strength of fission and fusion illusions, depended on the actual event numerosity. Experiment 2 replicated the effects of social relevance on multisensory integration from Scheller & Sui, 2022 JEP:HPP, using a lower number of events, thereby favouring the opposite illusion through enhanced influences of the prior. In line with the idea that the self acts like a prior, the more frequently observed illusion (more malleable to prior influences) was modulated by self-relevance. Our findings suggest that the self can influence perception by acting like a prior in cue integration, biasing perceptual estimates towards areas of high self-relevance.

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Everyday experiences suggest that a container, such as a box of cereal, can convey pertinent information about the nature and quantity of its content. This study investigated how well people can judge large quantities of objects in a container through haptic perception. Stimuli consisted of plastic drinking straws cut to "small" (1.5 cm) or "big" (4.5 cm) pieces contained in plastic food containers. Participants performed both a magnitude estimation of the number of objects and a direct estimation of the proportion of the container perceived to be filled with objects. Overall, participants demonstrated considerable accuracy for both tasks and irrespective of the size of the content. Post-experiment interviews revealed three potential strategies. Participants either focused on the container's contents, the excess space in the container, or the perceived weight of the container (content).

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There are many situations in which we interact with collections of objects, from a crowd of people to a bowl of blackberries. There is an experience of the quantity of these items, although not a precise number, and we have this impression quickly and effortlessly. It can be described as an expressive property of the whole. In the literature, the study of this sense of numerosity has a long history, which is reviewed here with examples. I argue that numerosity is a direct perceptual experience, and that all experiences of numerosity, not only estimations, are affected by perceptual organisation.

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Everyday experiences suggest that a container, such as a box of chocolate sprinkles, can convey pertinent information about the nature of its content. Despite the familiarity of the experience, we do not know whether people can perceive the number of objects in the container from touch alone and how accurately they can do so. In three experiments, participants handled containers holding between one and five objects and verbally estimated their number. Containers were small cardboard jewelry boxes, and objects were round beads of varying diameter and weight. Any useful visual and auditory cues were precluded. Experiment 1 demonstrated very accurate performance, provided the objects were of sufficient weight. Experiment 2 demonstrated that withholding information about the possible number of objects inside the container does not affect accuracy at a group level but does produce occasional overestimations at an individual level. Experiment 3 demonstrated that removing the weight cue leads to systematic underestimations but does not eliminate people's ability to distinguish between different numbers of objects in the container. This study contributes to a growing picture that container haptics is surprisingly capable.

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