Topographic numerosity maps cover subitizing and estimation ranges

Does the Cortical-Depth Dependence of the Hemodynamic Response Function Differ Between Age Groups?

Functional magnetic resonance imaging (fMRI) is a widely used tool to investigate the functional brain responses in living humans. Valid comparisons of fMRI results depend on consistency of the blood-oxygen-level-dependent (BOLD) hemodynamic response function (HRF). Although common statistical approaches assume a single HRF across the entire brain, the HRF differs across individuals, regions of the brain, and cortical depth. Here, we measure HRF properties in primary visual cortex (V1) using 7 T fMRI with ultra-high spatiotemporal resolution line-scanning (250 μm in laminar direction, sampled every 105 ms). Line-scanning allowed us to investigate age-related HRF changes as a function of cortical depth. Eleven young and eleven middle-aged healthy participants participated in the experiments. We estimated the HRFs using a smooth basis function deconvolution approach. We also compared the results with conventional resolutions. From these HRFs, we extracted properties related to response magnitude and temporal dynamics. The cortical depth dependent HRFs were similar to the HRFs extracted using conventional resolutions validating the cortical depth dependent approach. We found that the properties of the HRF in the two age groups are similar across cortical depth. In other words, the variance between participants is larger than the variance between age groups. This suggests that middle-aged individuals can participate in cortical depth dependent studies free of bias in HRF properties.

Hierarchical representations of relative numerical magnitudes in the human frontoparietal cortex

The ability to estimate numerical magnitude is essential for decision-making and is thought to underlie arithmetic skills. In humans, neural populations in the frontoparietal regions are tuned to represent numerosity. However, it remains unclear whether their response properties are fixed to a specific numerosity (i.e., absolute code) or dynamically scaled according to the range of numerosities relevant to the context (i.e., relative code). Here, using functional magnetic resonance imaging combined with multivariate pattern analysis, we uncover evidence that representations of relative numerosity coding emerge gradually as visual information processing advances in the frontoparietal regions. In contrast, the early sensory areas predominantly exhibit absolute coding. These findings indicate a hierarchical organization of relative numerosity representations that adapt their response properties according to the context. Our results highlight the existence of a context-dependent optimization mechanism in numerosity representation, enabling the efficient processing of infinite magnitude information with finite neural resources.

Feature-selective adaptation of numerosity perception

Perceptual adaptation has been widely used to infer the existence of numerosity detectors, enabling animals to quickly estimate the number of objects in a scene. Here, we investigated, in humans, whether numerosity adaptation is influenced by stimulus feature changes as previous research suggested that adaptation is reduced when the colour of adapting and test stimuli did not match. We tested whether such adaptation reduction is due to unspecific novelty effects or changes of stimuli identity. Numerosity adaptation was measured for stimuli matched or unmatched for low-level (colour, luminance, shape and motion) or high-level (letters' identity and face emotions) features. Robust numerosity adaptation occurred in all conditions, but it was reduced when adapting and test stimuli differed for colour, luminance and shape. However, no reduction was observed between moving and still stimuli, a readable change that did not affect the item's identity. Similarly, changes in letters' spatial rotations or face features did not affect adaptation magnitude. Overall, changes in stimulus identity defined by low-level features, rather than novelty in general, determined the strength of the adaptation effects, provided these changes were readily noticeable. These findings suggest that numerosity mechanisms operate on categorized items in addition to the total quantity of the set.

The calculating brain

The human brain possesses neural networks and mechanisms enabling the representation of numbers, basic arithmetic operations, and mathematical reasoning. Without the ability to represent numerical quantity and perform calculations, our scientifically and technically advanced culture would not exist. However, the origins of numerical abilities are grounded in an intuitive understanding of quantity deeply rooted in biology. Nevertheless, more advanced symbolic arithmetic skills require a cultural background with formal mathematical education. In the past two decades, cognitive neuroscience has seen significant progress in understanding the workings of the calculating brain through various methods and model systems. This review begins by exploring the mental and neuronal representations of nonsymbolic numerical quantity and then progresses to symbolic representations acquired in childhood. During arithmetic operations (addition, subtraction, multiplication, and division), these representations are processed and transformed according to arithmetic rules and principles, leveraging different mental strategies and types of arithmetic knowledge that can be dissociated in the brain. Although it was once believed that number processing and calculation originated from the language faculty, it is now evident that mathematical and linguistic abilities are primarily processed independently in the brain. Understanding how the healthy brain processes numerical information is crucial for gaining insights into debilitating numerical disorders, including acquired conditions like acalculia and learning-related calculation disorders such as developmental dyscalculia.

Distinct serial dependence between small and large numerosity processing

The serial dependence effect (SDE) is a perceptual bias where current stimuli are perceived as more similar to recently seen stimuli, possibly enhancing the stability and continuity of visual perception. Although SDE has been observed across many visual features, it remains unclear whether humans rely on a single mechanism of SDE to support numerosity processing across two distinct numerical ranges: subitizing (i.e., small numerosity processing, likely related to early object recognition) and estimation (i.e., large numerosity processing, likely related to ensemble numerosity extraction). Here, we show that subitizing and estimation exhibit distinct SDE patterns. Subitizing is characterized by an asymmetric SDE, whereas estimation demonstrates a symmetric SDE. Specifically, in subitizing, the SDE occurs only when the current magnitude is smaller than the previous magnitude but not when it is larger. In contrast, the SDE in estimation is present in both scenarios. We propose that these differences arise from distinct underlying mechanisms. A perceptual mechanism-namely, a 'temporal hysteresis' account, can explain the asymmetrical SDE in subitizing since object individuation resources are easily activated but resistant to deactivation. Conversely, a combination of perceptual and post-perceptual mechanisms can account for the SDEs in estimation, as both perceptual and post-perceptual interference can reduce the SDEs. Critically, a novel type of SDE characterized by reduced processing precision is found in subitizing only, implying that the continuity and stability of numerical processing can be dissociable in dynamic situations where numerical information is integrated over time. Our findings reveal the multifaceted nature of SDE mechanisms and suggest their engagement with cognitive modules likely subserving different functionalities.

Securin Regulates the Spatiotemporal Dynamics of Separase

Separase is a key regulator of the metaphase to anaphase transition with multiple functions. Separase cleaves cohesin to allow chromosome segregation and localizes to vesicles to promote exocytosis in mid-anaphase. The anaphase promoting complex/cyclosome (APC/C) activates separase by ubiquitinating its inhibitory chaperone, securin, triggering its degradation. How this pathway controls the exocytic function of separase has not been investigated. During meiosis I, securin is degraded over several minutes, while separase rapidly relocalizes from kinetochore structures at the spindle and cortex to sites of action on chromosomes and vesicles at anaphase onset. The loss of cohesin coincides with the relocalization of separase to the chromosome midbivalent at anaphase onset. APC/C depletion prevents separase relocalization, while securin depletion causes precocious separase relocalization. Expression of non-degradable securin inhibits chromosome segregation, exocytosis, and separase localization to vesicles but not to the anaphase spindle. We conclude that APC/C mediated securin degradation controls separase localization. This spatiotemporal regulation will impact the effective local concentration of separase for more precise targeting of substrates in anaphase.

Single-cell level deconvolution, convolution, and clustering in spatial transcriptomics by aligning spot level transcriptome to nuclear morphology

In spot-based spatial transcriptomics, spots that are of the same size and printed at the fixed location cannot precisely capture the actual randomly located single cells, therefore failing to profile the transcriptome at the single-cell level. The current studies primarily focused on enhancing the spot resolution in size via computational imputation or technical improvement, however, they largely overlooked that single-cell resolution, i.e., resolution in cellular or even smaller size, does not equal single-cell level. Using both real and simulated spatial transcriptomics data, we demonstrated that even the high-resolution spatial transcriptomics still has a large number of spots partially covering multiple cells simultaneously, revealing the intrinsic non-single-cell level of spot-based spatial transcriptomics regardless of spot size. To this end, we present STIE, an EM algorithm that aligns the spatial transcriptome to its matched histology image-based nuclear morphology and recovers missing cells from up to ~70% gap area between spots via the nuclear morphological similarity and neighborhood information, thereby achieving the real single-cell level and whole-slide scale deconvolution/convolution and clustering for both low- and high-resolution spots. On both real and simulation spatial transcriptomics data, STIE characterizes the cell-type specific gene expression variation and demonstrates the outperforming concordance with the single-cell RNAseq-derived cell type transcriptomic signatures compared to the other spot- and subspot-level methods. Furthermore, STIE enabled us to gain novel insights that failed to be revealed by the existing methods due to the lack of single-cell level, for instance, lower actual spot resolution than its reported spot size, the additional contribution of cellular morphology to cell typing beyond transcriptome, unbiased evaluation of cell type colocalization, superior power of high-resolution spot in distinguishing nuanced cell types, and spatially resolved cell-cell interactions at the single-cell level other than spot level. The STIE code is publicly available as an R package at https://github.com/zhushijia/STIE.

Distinct neuronal representation of small and large numbers in the human medial temporal lobe

Whether small numerical quantities are represented by a special subitizing system that is distinct from a large-number estimation system has been debated for over a century. Here we show that two separate neural mechanisms underlie the representation of small and large numbers. We performed single neuron recordings in the medial temporal lobe of neurosurgical patients judging numbers. We found a boundary in neuronal coding around number 4 that correlates with the behavioural transition from subitizing to estimation. In the subitizing range, neurons showed superior tuning selectivity accompanied by suppression effects suggestive of surround inhibition as a selectivity-increasing mechanism. In contrast, tuning selectivity decreased with increasing numbers beyond 4, characterizing a ratio-dependent number estimation system. The two systems with the coding boundary separating them were also indicated using decoding and clustering analyses. The identified small-number subitizing system could be linked to attention and working memory that show comparable capacity limitations.

Implicit Processing of Numerical Order: Evidence from a Continuous Interocular Flash Suppression Study

Processing the ordered relationships between sequential items is a key element in many cognitive abilities that are important for survival. Specifically, order may play a crucial role in numerical processing. Here, we assessed the existence of a cognitive system designed to implicitly evaluate numerical order, by combining continuous flash suppression with a priming method in a numerical enumeration task. In two experiments and diverse statistical analysis, targets that required numerical enumeration were preceded by an invisibly ordered or non-ordered numerical prime sequence. The results of both experiments showed that enumeration for targets that appeared after an ordered prime was significantly faster, while the ratio of the prime sequences produced no significant effect. The findings suggest that numerical order is processed implicitly and affects a basic cognitive ability: enumeration of quantities.

Towards functional spin-echo BOLD line-scanning in humans at 7T

OBJECTIVE

Neurons cluster into sub-millimeter spatial structures and neural activity occurs at millisecond resolutions; hence, ultimately, high spatial and high temporal resolutions are required for functional MRI. In this work, we implemented a spin-echo line-scanning (SELINE) sequence to use in high spatial and temporal resolution fMRI.

MATERIALS AND METHODS

A line is formed by simply rotating the spin-echo refocusing gradient to a plane perpendicular to the excited slice and by removing the phase-encoding gradient. This technique promises a combination of high spatial and temporal resolution (250 μm, 500 ms) and microvascular specificity of functional responses. We compared SELINE data to a corresponding gradient-echo version (GELINE).

RESULTS

We demonstrate that SELINE showed much-improved line selection (i.e. a sharper line profile) compared to GELINE, albeit at the cost of a significant drop in functional sensitivity.

DISCUSSION

This low functional sensitivity needs to be addressed before SELINE can be applied for neuroscientific purposes.

Visual P2p component responds to perceived numerosity

Numerosity perception is a key ability for human and non-human species, probably mediated by dedicated brain mechanisms. Electrophysiological studies revealed the existence of both early and mid-latency components of the Electrophysiological (EEG) signal sensitive to numerosity changes. However, it is still unknown whether these components respond to physical or perceived variation in numerical attributes. We here tackled this point by recording electrophysiological signal while participants performed a numerosity adaptation task, a robust psychophysical method yielding changes in perceived numerosity judgments despite physical numerosity invariance. Behavioral measures confirmed that the test stimulus was consistently underestimated when presented after a high numerous adaptor while perceived as veridical when presented after a neutral adaptor. Congruently, EEG results revealed a potential at around 200 ms (P2p) which was reduced when the test stimulus was presented after the high numerous adaptor. This result was much prominent over the left posterior cluster of electrodes and correlated significantly with the amount of adaptation. No earlier modulations were retrievable when changes in numerosity were illusory while both early and mid-latency modulations occurred for physical changes. Taken together, our results reveal that mid-latency P2p mainly reflects perceived changes in numerical attributes, while earlier components are likely to be bounded to the physical characteristics of the stimuli. These results suggest that short-term plastic mechanisms induced by numerosity adaptation may involve a relatively late processing stage of the visual hierarchy likely engaging cortical areas beyond the primary visual cortex. Furthermore, these results also indicate mid-latency electrophysiological correlates as a signature of the internal representation of numerical information.

Visual field asymmetries in numerosity processing

A small number of objects can be rapidly and accurately enumerated, whereas a larger number of objects can only be approximately enumerated. These subitizing and estimation abilities, respectively, are both spatial processes relying on extracting information across spatial locations. Nevertheless, whether and how these processes vary across visual field locations remains unknown. Here, we examined if enumeration displays asymmetries around the visual field. Experiment 1 tested small number (1–6) enumeration at cardinal and non-cardinal peripheral locations while manipulating the spacing among the objects. Experiment 2 examined enumeration at cardinal locations in more detail while minimising crowding. Both experiments demonstrated a Horizontal-Vertical Asymmetry (HVA) where performance was better along the horizontal axis relative to the vertical. Experiment 1 found that this effect was modulated by spacing with stronger asymmetry at closer spacing. Experiment 2 revealed further asymmetries: a Vertical Meridian Asymmetry (VMA) with better enumeration on the lower vertical meridian than on the upper and a Horizontal Meridian Asymmetry (HMA) with better enumeration along the left horizontal meridian than along the right. All three asymmetries were evident for both subitizing and estimation. HVA and VMA have been observed in a range of visual tasks, indicating that they might be inherited from early visual constraints. However, HMA is observed primarily in mid-level tasks, often involving attention. These results suggest that while enumeration processes can be argued to inherit low-level visual constraints, the findings are, parsimoniously, consistent with visual attention playing a role in both subitizing and estimation.

Assessing the ecological validity of numerosity-selective neuronal populations with real-world natural scenes

Animals and humans are able to quickly and effortlessly estimate the number of items in a set: their numerosity. Numerosity perception is thought to be critical to behavior, from feeding to escaping predators to human mathematical cognition. Virtually, all scientific studies on numerosity mechanisms use well controlled but artificial stimuli to isolate the numerosity dimension from other physical quantities. Here, we probed the ecological validity of these artificial stimuli and evaluate whether an important component in numerosity processing, the numerosity-selective neural populations, also respond to numerosity of items in real-world natural scenes. Using 7T MRI and natural images from a wide range of categories, we provide evidence that the numerosity-tuned neuronal populations show numerosity-selective responses when viewing images from a real-world natural scene. Our findings strengthen the role of numerosity-selective neurons in numerosity perception and provide an important link to their function in numerosity perception in real-world settings.

Intracranial recordings show evidence of numerosity tuning in human parietal cortex

Numerosity is the set size of a group of items. Numerosity perception is a trait shared across numerous species. Numerosity-selective neural populations are thought to underlie numerosity perception. These neurons have been identified primarily using electrical recordings in animal models and blood oxygen level dependent (BOLD) functional magnetic resonance imaging (fMRI) in humans. Here we use electrical intracranial recordings to investigate numerosity tuning in humans, focusing on high-frequency transient activations. These recordings combine a high spatial and temporal resolution and can bridge the gap between animal models and human recordings. In line with previous studies, we find numerosity-tuned responses at parietal sites in two out of three participants. Neuronal populations at these locations did not respond to other visual stimuli, i.e. faces, houses, and letters, in contrast to several occipital sites. Our findings further corroborate the specificity of numerosity tuning of in parietal cortex, and further link fMRI results and electrophysiological recordings.

Attention drives human numerosity-selective responses

Numerosity, the set size of a group of items, helps guide behavior and decisions. Previous studies have shown that neural populations respond selectively to numerosities. How numerosity is extracted from the visual scene is a longstanding debate, often contrasting low-level visual with high-level cognitive processes. Here, we investigate how attention influences numerosity-selective responses. The stimuli consisted of black and white dots within the same display. Participants' attention was focused on either black or white dots, while we systematically changed the numerosity of black, white, and total dots. Using 7 T fMRI, we show that the numerosity-tuned neural populations respond only when attention is focused on their preferred numerosity, irrespective of the unattended or total numerosities. Without attention, responses to preferred numerosity are suppressed. Unlike traditional effects of attention in the visual cortex, where attention enhances already existing responses, these results suggest that attention is required to drive numerosity-selective responses.

Spontaneous representation of numerosity zero in a deep neural network for visual object recognition

Conceiving "nothing" as a numerical value zero is considered a sophisticated numerical capability that humans share with cognitively advanced animals. We demonstrate that representation of zero spontaneously emerges in a deep learning neural network without any number training. As a signature of numerical quantity representation, and similar to real neurons from animals, numerosity zero network units show maximum activity to empty sets and a gradual decrease in activity with increasing countable numerosities. This indicates that the network spontaneously ordered numerosity zero as the smallest numerical value along the number line. Removal of empty-set network units caused specific deficits in the network's judgment of numerosity zero, thus reflecting these units' functional relevance. These findings suggest that processing visual information is sufficient for a visual number sense that includes zero to emerge and explains why cognitively advanced animals with whom we share a nonverbal number system exhibit rudiments of numerosity zero.

The role of neural tuning in quantity perception

Perception of quantities, such as numerosity, timing, and size, is essential for behavior and cognition. Accumulating evidence demonstrates neurons processing quantities are tuned, that is, have a preferred quantity amount, not only for numerosity, but also other quantity dimensions and sensory modalities. We argue that quantity-tuned neurons are fundamental to understanding quantity perception. We illustrate how the properties of quantity-tuned neurons can underlie a range of perceptual phenomena. Furthermore, quantity-tuned neurons are organized in distinct but overlapping topographic maps. We suggest that this overlap in tuning provides the neural basis for perceptual interactions between different quantities, without the need for a common neural representational code.

Laminar processing of numerosity supports a canonical cortical microcircuit in human parietal cortex

As neural signals travel through the visual hierarchy, spatial precision decreases and specificity for stimulus features increases.^1-4 A similar hierarchy has been found for laminar processing in V1, where information from the thalamus predominantly targets the central layers, while spatial precision decreases and feature specificity increases toward superficial and deeper layers.^5-17 This laminar processing scheme is proposed to represent a canonical cortical microcircuit that is similar across the cortex.^11,18-21 Here, we go beyond early visual cortex and investigate whether processing of numerosity (the set size of a group of items) across cortical depth in the parietal association cortex follows this hypothesis. Numerosity processing is implicated in many tasks such as multiple object tracking,²² mathematics,^23-25 decision making,²⁶ and dividing attention.²⁷ Neurons in the parietal association cortex are tuned to numerosity, with both a preferred numerosity tuning and tuning width (i.e., specificity).^28-30 We quantified preferred numerosity responses across cortical depth in the parietal association cortex with ultra-high field fMRI and population receptive field-based numerosity modeling.^1,28,31 We find that numerosity responses sharpen, i.e., become increasingly specific, moving away from the central layers. This suggests that the laminar processing scheme for numerosity processing in the parietal cortex is similar to primary visual cortex, providing support for the canonical cortical microcircuit hypothesis beyond primary visual cortex.

Individualized cognitive neuroscience needs 7T: Comparing numerosity maps at 3T and 7T MRI

The field of cognitive neuroscience is weighing evidence about whether to move from the current standard field strength of 3 Tesla (3T) to ultra-high field (UHF) of 7T and above. The present study contributes to the evidence by comparing a computational cognitive neuroscience paradigm at 3T and 7T. The goal was to evaluate the practical effects, i.e. model predictive power, of field strength on a numerosity task using accessible pre-processing and analysis tools. Previously, using 7T functional magnetic resonance imaging and biologically-inspired analyses, i.e. population receptive field modelling, we discovered topographical organization of numerosity-selective neural populations in human parietal cortex. Here we show that these topographic maps are also detectable at 3T. However, averaging of many more functional runs was required at 3T to reliably reconstruct numerosity maps. On average, one 7T run had about four times the model predictive power of one 3T run. We believe that this amount of scanning would have made the initial discovery of the numerosity maps on 3T highly infeasible in practice. Therefore, we suggest that the higher signal-to-noise ratio and signal sensitivity of UHF MRI is necessary to build mechanistic models of the organization and function of our cognitive abilities in individual participants.