scholarly journals Grouping effects in numerosity perception under prolonged viewing conditions

2018 ◽  
Author(s):  
Leo Poom ◽  
Marcus Lindskog ◽  
Anders Winman ◽  
Ronald van den Berg
Keyword(s):  
Spatial Organization ◽  
Spatial Clustering ◽  
Number Sense ◽  
Single Group ◽  
Dynamic Nature ◽  
Free Viewing ◽  
Grouping Effect ◽  
Dot Motion ◽  
Numerosity Estimation ◽  
Numerosity Perception

ABSTRACTHumans can estimate numerosities – such as the number sheep in a flock – without deliberate counting. A number of biases have been identified in these estimates, which seem primarily rooted in the spatial organization of objects (grouping, symmetry, etc). Most previous studies on the number sense used static stimuli with extremely brief exposure times. However, outside the laboratory, visual scenes are often dynamic and freely viewed for prolonged durations (e.g., a flock of moving sheep). The purpose of the present study is to examine grouping-induced numerosity biases in stimuli that more closely mimic these conditions. To this end, we designed two experiments with limited-dot-lifetime displays (LDDs), in which each dot is visible for a brief period of time and replaced by a new dot elsewhere after its disappearance. The dynamic nature of LDDs prevents subjects from counting even when they are free-viewing a stimulus under prolonged presentation. Subjects estimated the number of dots in arrays that were presented either as a single group or were segregated into two groups by spatial clustering, dot size, dot color, or dot motion. Grouping by color and motion reduced perceived numerosity compared to viewing them as a single group. Moreover, the grouping effect sizes between these two features were correlated, which suggests that the effects may share a common, feature-invariant mechanism. Finally, we find that dot size and total stimulus area directly affect perceived numerosity, which makes it difficult to draw reliable conclusions about grouping effects induced by spatial clustering and dot size. Our results provide new insights into biases in numerosity estimation and they demonstrate that the use of LDDs is an effective method to study the human number sense under prolonged viewing.

scholarly journals Numerosity representation in a deep convolutional neural network

2021 ◽  
Vol 15 ◽  
pp. 183449092110126
Author(s):  
Cihua Zhou ◽  
Wei Xu ◽  
Yujie Liu ◽  
Zhichao Xue ◽  
Rui Chen ◽  
...  
Keyword(s):  
Neural Network ◽  
Mathematical Knowledge ◽  
Animal Species ◽  
Number Sense ◽  
Future Research ◽  
Deep Convolutional Neural Networks ◽  
Visual Stream ◽  
Explicit Training ◽  
Numerosity Estimation ◽  
Numerosity Perception

Enumerating objects in the environment (i.e., “number sense”) is crucial for survival in many animal species, and foundational for the construction of more abstract and complex mathematical knowledge in humans. Perhaps surprisingly, deep convolutional neural networks (DCNNs) spontaneously emerge a similar number sense even without any explicit training for numerosity estimation. However, little is known about how the number sense emerges, and the extent to which it is comparable with human number sense. Here, we examined whether the numerosity underestimation effect, a phenomenon indicating that numerosity perception acts upon the perceptual number rather than the physical number, can be observed in DCNNs. In a typical DCNN, AlexNet, we found that number-selective units at late layers operated on the perceptual number, like humans do. More importantly, this perceptual number sense did not emerge abruptly, rather developed progressively along the hierarchy in the DCNN, shifting from the physical number sense at early layers to perceptual number sense at late layers. Our finding hence provides important implications for the neural implementation of number sense in the human brain and advocates future research to determine whether the representation of numerosity also develops gradually along the human visual stream from physical number to perceptual number.

scholarly journals Visual numerosity estimation is based on anisotropic representations of visual space

2021 ◽  
Author(s):  
Miao Li ◽  
Bert Reynvoet ◽  
Bilge Sayim
Keyword(s):  
Visual Field ◽  
Convex Hull ◽  
Visual Fields ◽  
Spatial Vision ◽  
Visual Space ◽  
Stimulus Features ◽  
Numerosity Estimation ◽  
Numerosity Perception ◽  
Average Eccentricity ◽  
Shed Light

Humans can estimate the number of visually displayed items without counting. This capacity of numerosity perception has often been attributed to a dedicated system to estimate numerosity, or alternatively to the exploitation of various stimulus features, such as density, convex hull, the size of items and occupancy area. The distribution of the presented items is usually not varied with eccentricity in the visual field. However, our visual fields are highly asymmetric, and to date, it is unclear how inhomogeneities of the visual field impact numerosity perception. Besides eccentricity, a pronounced asymmetry is the radial-tangential anisotropy. For example, in crowding, radially placed flankers interfere more strongly with target perception than tangentially placed flankers. Similarly, in redundancy masking, the number of perceived items in repeating patterns is reduced when the items are arranged radially but not when they are arranged tangentially. Here, we investigated whether numerosity perception is subject to the radial-tangential anisotropy of spatial vision to shed light on the underlying topology of numerosity perception. Observers were presented with varying numbers of discs and asked to report the perceived number. There were two conditions. Discs were predominantly arranged radially in the “radial” condition and tangentially in the “tangential” condition. Additionally, the spacing between discs was scaled with eccentricity. Physical properties, such as average eccentricity, average spacing, convex hull, and density were kept as similar as possible in the two conditions. Radial arrangements were expected to yield underestimation compared to tangential arrangements. Consistent with the hypothesis, numerosity estimates in the radial condition were lower compared to the tangential condition. Magnitudes of radial alignment (as well as predicted crowding strength) correlated with the observed numerosity estimates. Our results demonstrate a robust radial-tangential anisotropy, suggesting that the topology of spatial vision determines numerosity estimation. We suggest that asymmetries of spatial vision should be taken into account when investigating numerosity estimation.

Geographical Psychology

2016 ◽  
Vol 25 (6) ◽  
pp. 393-398 ◽  
Author(s):  
Peter J. Rentfrow ◽  
Markus Jokela
Keyword(s):  
Spatial Organization ◽  
Spatial Clustering ◽  
Health Indicators ◽  
Well Being ◽  
Individual Characteristics ◽  
Psychological Characteristics ◽  
Future Research ◽  
Organization Studies ◽  
Psychological Phenomena ◽  
Multilevel Studies

There is geographical variation in the ways in which people think, feel, and behave. How are we to understand the causes and consequences of such variation? Geographical psychology is an emerging subarea of research concerned with the spatial organization of psychological phenomena and how individual characteristics, social entities, and physical features of the environment contribute to their organization. Studies at multiple levels of analysis have indicated that social influence, ecological influence, and selective migration are key mechanisms that contribute to the spatial clustering of psychological characteristics. Investigations in multiple countries have shown that the psychological characteristics common in particular regions are respectively linked to important political, economic, and health indicators. Furthermore, results from large multilevel studies have shown that the psychological characteristics of individuals interact with features of the local environment to impact psychological development and well-being. Future research is needed to better understand the scale and impact of person-environment associations over time.

Numbers in action

2021 ◽  
Vol 44 ◽  
Author(s):  
David C. Burr ◽  
Giovanni Anobile ◽  
Elisa Castaldi ◽  
Roberto Arrighi
Keyword(s):  
Perception And Action ◽  
Number Sense ◽  
Action Preparation ◽  
Numerosity Estimation ◽  
And Control

Abstract 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.

scholarly journals Topology-defined units in numerosity perception

2015 ◽  
Vol 112 (41) ◽  
pp. E5647-E5655 ◽  
Author(s):  
Lixia He ◽  
Ke Zhou ◽  
Tiangang Zhou ◽  
Sheng He ◽  
Lin Chen
Keyword(s):  
Number Sense ◽  
Color Contrast ◽  
Intraparietal Sulcus ◽  
Tuning Curves ◽  
Visual Property ◽  
Numerosity Judgment ◽  
Wide Range ◽  
Color Similarity ◽  
Equality Judgment ◽  
Numerosity Perception

What is a number? The number sense hypothesis suggests that numerosity is “a primary visual property” like color, contrast, or orientation. However, exactly what attribute of a stimulus is the primary visual property and determines numbers in the number sense? To verify the invariant nature of numerosity perception, we manipulated the numbers of items connected/enclosed in arbitrary and irregular forms while controlling for low-level features (e.g., orientation, color, and size). Subjects performed discrimination, estimation, and equality judgment tasks in a wide range of presentation durations and across small and large numbers. Results consistently show that connecting/enclosing items led to robust numerosity underestimation, with the extent of underestimation increasing monotonically with the number of connected/enclosed items. In contrast, grouping based on color similarity had no effect on numerosity judgment. We propose that numbers or the primitive units counted in numerosity perception are influenced by topological invariants, such as connectivity and the inside/outside relationship. Beyond the behavioral measures, neural tuning curves to numerosity in the intraparietal sulcus were obtained using functional MRI adaptation, and the tuning curves showed that numbers represented in the intraparietal sulcus were strongly influenced by topology.

scholarly journals Gene selection for optimal prediction of cell position in tissues from single-cell transcriptomics data

2020 ◽  
Vol 3 (11) ◽  
pp. e202000867 ◽  
Author(s):  
Jovan Tanevski ◽  
Thin Nguyen ◽  
Buu Truong ◽  
Nikos Karaiskos ◽  
Mehmet Eren Ahsen ◽  
...  
Keyword(s):  
Single Cell ◽  
Spatial Organization ◽  
Gene Selection ◽  
Spatial Information ◽  
Spatial Clustering ◽  
Spatial Location ◽  
Spatial Arrangement ◽  
Fish Embryo ◽  
Hybridization Data ◽  
Silver Standard

Single-cell RNA-sequencing (scRNAseq) technologies are rapidly evolving. Although very informative, in standard scRNAseq experiments, the spatial organization of the cells in the tissue of origin is lost. Conversely, spatial RNA-seq technologies designed to maintain cell localization have limited throughput and gene coverage. Mapping scRNAseq to genes with spatial information increases coverage while providing spatial location. However, methods to perform such mapping have not yet been benchmarked. To fill this gap, we organized the DREAM Single-Cell Transcriptomics challenge focused on the spatial reconstruction of cells from the Drosophila embryo from scRNAseq data, leveraging as silver standard, genes with in situ hybridization data from the Berkeley Drosophila Transcription Network Project reference atlas. The 34 participating teams used diverse algorithms for gene selection and location prediction, while being able to correctly localize clusters of cells. Selection of predictor genes was essential for this task. Predictor genes showed a relatively high expression entropy, high spatial clustering and included prominent developmental genes such as gap and pair-rule genes and tissue markers. Application of the top 10 methods to a zebra fish embryo dataset yielded similar performance and statistical properties of the selected genes than in the Drosophila data. This suggests that methods developed in this challenge are able to extract generalizable properties of genes that are useful to accurately reconstruct the spatial arrangement of cells in tissues.

scholarly journals Numerosity Comparison, Estimation and Proportion Estimation Abilities May Predict Numeracy and Cognitive Reflection in Adults

2021 ◽  
Vol 15 ◽  
Author(s):  
Midori Tokita ◽  
Sumire Hirota
Keyword(s):  
Cognitive Abilities ◽  
Number System ◽  
Cognitive Mechanisms ◽  
Cognitive Reflection Test ◽  
Comparison Task ◽  
Cognitive Reflection ◽  
Japanese Adults ◽  
Proportion Estimation ◽  
Numerosity Estimation ◽  
Numerosity Perception

This study explores whether and how different tasks associated with approximate number system (ANS) ability are related to numeracy and cognitive reflection in adults. We conducted an online experiment using a sample of 300 Japanese adults aged 20–39. Participants were given three ANS tasks (numerosity comparison, numerosity estimation, and proportion estimation) as well as Rasch-based numeracy scale and cognitive reflection test, and we tested the correlation among the measures of these tasks. We explored the hypothesis that the typical measures used to gauge ANS ability, numerosity comparison and numerosity estimation may mediate different cognitive mechanisms in adults. We also introduced a task measuring proportion estimation, added because such estimation requires numerosity perception and the ability to map symbolic numerals. Our findings suggest that there is a weak, but significant correlation among the three ANS-related tasks. Moreover, there is a significant relationship between each of these measures and the numeracy and CRT score, suggesting that the ANS-related ability may be associated with higher cognitive abilities such as numeracy and cognitive reflection. In addition, we found that performances on the numerosity and proportion estimation are more clearly related to CRT score than the numerosity comparison task.

scholarly journals Spatially distributed representation of taste quality in the gustatory insular cortex of awake behaving mice

2020 ◽  
Author(s):  
Ke Chen ◽  
Joshua F. Kogan ◽  
Alfredo Fontanini
Keyword(s):  
Spatial Organization ◽  
Spatial Clustering ◽  
Spatial Scales ◽  
Piriform Cortex ◽  
Insular Cortex ◽  
Multiple Spatial Scales ◽  
Somatosensory Cortices ◽  
Conflicting Evidence ◽  
Sensory Features ◽  
Spatially Distributed

SUMMARYVisual, auditory and somatosensory cortices are topographically organized, with neurons responding to similar sensory features clustering in adjacent portions of the cortex. Such topography has not been observed in the piriform cortex, whose responses to odorants are sparsely distributed across the cortex. The spatial organization of taste responses in the gustatory insular cortex (GC) is currently debated, with conflicting evidence from anesthetized rodents pointing to alternative and mutually exclusive models. Here, we rely on calcium imaging to determine how taste and task-related variables are represented in the superficial layers of GC of alert, licking mice. Our data show that the various stimuli evoke sparse responses from a combination of broadly and narrowly tuned neurons. Analysis of the distribution of responses over multiple spatial scales demonstrates that taste representations are distributed across the cortex, with no sign of spatial clustering or topography. Altogether, data presented here support the idea that the representation of taste qualities in GC of alert mice is sparse and distributed, analogous to the representation of odorants in piriform cortex.

scholarly journals Spatial organization of the transcriptome in individual neurons

2020 ◽  
Author(s):  
Guiping Wang ◽  
Cheen-Euong Ang ◽  
Jean Fan ◽  
Andrew Wang ◽  
Jeffrey R. Moffitt ◽  
...  
Keyword(s):  
Spatial Organization ◽  
Spatial Clustering ◽  
Super Resolution ◽  
Distribution Patterns ◽  
Synaptic Activity ◽  
Spatial Profiling ◽  
Multiple Length Scales ◽  
Neuronal Functions ◽  
Genome Scale ◽  
Micrometer Scale

AbstractNeurons are highly polarized cells with complex neurite morphology. Spatial organization and local translation of RNAs in dendrites and axons play an important role in many neuronal functions. Here we performed super-resolution spatial profiling of RNAs inside individual neurons at the genome scale using multiplexed error-robust fluorescence in situ hybridization (MERFISH), and mapped the spatial organization of up to ∼4,200 RNA species (genes) across multiple length scales, ranging from sub-micrometer to millimeters. Our data generated a quantitative intra-neuronal atlas of RNAs with distinct transcriptome compositions in somata, dendrites, and axons, and revealed diverse sub-dendritic distribution patterns of RNAs. Moreover, our spatial analysis identified distinct groups of genes exhibiting specific spatial clustering of transcripts at the sub-micrometer scale that were dependent on protein synthesis and differentially dependent on synaptic activity. Overall, these data provide a rich resource for characterizing the subcellular organization of the transcriptome in neurons with high spatial resolution.

scholarly journals Fast saccadic eye-movements in humans suggest that numerosity perception is automatic and direct

2020 ◽  
Vol 287 (1935) ◽  
pp. 20201884
Author(s):  
Elisa Castaldi ◽  
David Burr ◽  
Marco Turi ◽  
Paola Binda
Keyword(s):  
Neural Circuit ◽  
Numerical Range ◽  
Reaction Times ◽  
Saccadic Eye Movements ◽  
Separate Experiment ◽  
Vocal Responses ◽  
Oculomotor Responses ◽  
Numerosity Estimation ◽  
Numerosity Perception ◽  
Study Participants

Fast saccades are rapid automatic oculomotor responses to salient and ecologically important visual stimuli such as animals and faces. Discriminating the number of friends, foe, or prey may also have an evolutionary advantage. In this study, participants were asked to saccade rapidly towards the more numerous of two arrays. Participants could discriminate numerosities with high accuracy and great speed, as fast as 190 ms. Intermediate numerosities were more likely to elicit fast saccades than very low or very high numerosities. Reaction-times for vocal responses (collected in a separate experiment) were slower, did not depend on numerical range, and correlated only with the slow not the fast saccades, pointing to different systems. The short saccadic reaction-times we observe are surprising given that discrimination using numerosity estimation is thought to require a relatively complex neural circuit, with several relays of information through the parietal and prefrontal cortex. Our results suggest that fast numerosity-driven saccades may be generated on a single feed-forward pass of information recruiting a primitive system that cuts through the cortical hierarchy and rapidly transforms the numerosity information into a saccade command.

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