Unconscious Number Discrimination in the Human Visual System

Identifying conceptual neural responses to symbolic numerals

The goal of measuring conceptual processing in numerical cognition is distanced by the possibility that neural responses to symbolic numerals are influenced by physical stimulus confounds. Here, we targeted conceptual responses to parity (even versus odd), using electroencephalogram (EEG) frequency-tagging with a symmetry/asymmetry design. Arabic numerals (2-9) were presented at 7.5 Hz in 50 s sequences; odd and even numbers were alternated to target differential, 'asymmetry' responses to parity at 3.75 Hz (7.5 Hz/2). Parity responses were probed with four different stimulus sets, increasing in intra-numeral stimulus variability, and with two control conditions composed of non-conceptual numeral alternations. Significant asymmetry responses were found over the occipitotemporal cortex to all conditions, even for the arbitrary controls. The large physical-differences control condition elicited the largest response in the stimulus set with the lowest variability (one font). Only in the stimulus set with the highest variability (20 drawn, coloured exemplars/numeral) did the response to parity surpass both control conditions. These findings show that physical differences across small sets of Arabic numerals can strongly influence, and even account for, automatic brain responses. However, carefully designed control conditions and highly variable stimulus sets may be used towards identifying truly conceptual neural responses.

Spontaneous supra-modal encoding of number in the infant brain

The core knowledge hypothesis postulates that infants automatically analyze their environment along abstract dimensions, including numbers. According to this view, approximate numbers should be encoded quickly, pre-attentively, and in a supra-modal manner by the infant brain. Here, we directly tested this idea by submitting the neural responses of sleeping 3-month-old infants, measured with high-density electroencephalography (EEG), to decoders designed to disentangle numerical and non-numerical information. The results show the emergence, in approximately 400 ms, of a decodable number representation, independent of physical parameters, that separates auditory sequences of 4 vs. 12 tones and generalizes to visual arrays of 4 vs. 12 objects. Thus, the infant brain contains a number code that transcends sensory modality, sequential or simultaneous presentation, and arousal state.

Early neural markers for individual difference in mathematical achievement determined from rational number processing

The neural markers for individual differences in mathematical achievement have been studied extensively using magnetic resonance imaging; however, high temporal resolution electrophysiological evidence for individual differences in mathematical achievement require further elucidation. This study evaluated the event-related potential (ERP) when 48 college students with high or low mathematical achievement (HA vs. LA) matched non-symbolic and symbolic rational numbers. Behavioral results indicated that HA students had better performance in the discretized non-symbolic matching, although the two groups showed similar performances in the continuous matching. ERP data revealed that even before non-symbolic stimulus presentation, HA students had greater Bereitschaftspotential (BP) amplitudes over posterior central electrodes. After the presentation of non-symbolic numbers, HA students had larger N1 amplitudes at 160 ms post-stimulus, over left-lateralized parieto-occipital electrodes. After the presentation of symbolic numbers, HA students displayed more profound P1 amplitudes at 100 ms post-stimulus, over left parietal electrodes. Furthermore, larger BP and N1 amplitudes were associated with the shorter reaction times, and larger P1 amplitudes corresponded to lower error rates. The BP effect could indicate preparation processing, and early left-lateralized N1 and P1 effects could reflect the non-symbolic and symbolic number processing along the dorsal neural pathways. These results suggest that the left-lateralized P1 and N1 components elicited by matching non-symbolic and symbolic rational numbers can be considered as neurocognitive markers for individual differences in mathematical achievement.

AVNC: Attention-Based VGG-Style Network for COVID-19 Diagnosis by CBAM

(Aim) To detect COVID-19 patients more accurately and more precisely, we proposed a novel artificial intelligence model. (Methods) We used previously proposed chest CT dataset containing four categories: COVID-19, community-acquired pneumonia, secondary pulmonary tuberculosis, and healthy subjects. First, we proposed a novel VGG-style base network (VSBN) as backbone network. Second, convolutional block attention module (CBAM) was introduced as attention module into our VSBN. Third, an improved multiple-way data augmentation method was used to resist overfitting of our AI model. In all, our model was dubbed as a 12-layer attention-based VGG-style network for COVID-19 (AVNC) (Results) This proposed AVNC achieved the sensitivity/precision/F1 per class all above 95%. Particularly, AVNC yielded a micro-averaged F1 score of 96.87%, which is higher than 11 state-of-the-art approaches. (Conclusion) This proposed AVNC is effective in recognizing COVID-19 diseases.

Perceived number is not abstract

To support the claim that the approximate number system (ANS) represents rational numbers, Clarke and Beck (C&B) argue that number perception is abstract and characterized by a second-order character. However, converging evidence from visual illusions and psychophysics suggests that perceived number is not abstract, but rather, is perceptually interdependent with other magnitudes. Moreover, number, as a concept, is second-order, but number, as a percept, is not.

Apical amplification-a cellular mechanism of conscious perception?

We present a theoretical view of the cellular foundations for network-level processes involved in producing our conscious experience. Inputs to apical synapses in layer 1 of a large subset of neocortical cells are summed at an integration zone near the top of their apical trunk. These inputs come from diverse sources and provide a context within which the transmission of information abstracted from sensory input to their basal and perisomatic synapses can be amplified when relevant. We argue that apical amplification enables conscious perceptual experience and makes it more flexible, and thus more adaptive, by being sensitive to context. Apical amplification provides a possible mechanism for recurrent processing theory that avoids strong loops. It makes the broadcasting hypothesized by global neuronal workspace theories feasible while preserving the distinct contributions of the individual cells receiving the broadcast. It also provides mechanisms that contribute to the holistic aspects of integrated information theory. As apical amplification is highly dependent on cholinergic, aminergic, and other neuromodulators, it relates the specific contents of conscious experience to global mental states and to fluctuations in arousal when awake. We conclude that apical dendrites provide a cellular mechanism for the context-sensitive selective amplification that is a cardinal prerequisite of conscious perception.

The Number Sense Represents (Rational) Numbers

On a now orthodox view, humans and many other animals possess a "number sense," or approximate number system (ANS), that represents number. Recently, this orthodox view has been subject to numerous critiques that question whether the ANS genuinely represents number. We distinguish three lines of critique-the arguments from congruency, confounds, and imprecision-and show that none succeed. We then provide positive reasons to think that the ANS genuinely represents numbers, and not just non-numerical confounds or exotic substitutes for number, such as "numerosities" or "quanticals," as critics propose. In so doing, we raise a neglected question: numbers of what kind? Proponents of the orthodox view have been remarkably coy on this issue. But this is unsatisfactory since the predictions of the orthodox view, including the situations in which the ANS is expected to succeed or fail, turn on the kind(s) of number being represented. In response, we propose that the ANS represents not only natural numbers (e.g. 7), but also non-natural rational numbers (e.g. 3.5). It does not represent irrational numbers (e.g. √2), however, and thereby fails to represent the real numbers more generally. This distances our proposal from existing conjectures, refines our understanding of the ANS, and paves the way for future research.

Automatic Processing of Numerosity in Human Neocortex Evidenced by Occipital and Parietal Neuromagnetic Responses

Humans and other animal species are endowed with the ability to sense, represent, and mentally manipulate the number of items in a set without needing to count them. One central hypothesis is that this ability relies on an automated functional system dedicated to numerosity, the perception of the discrete numerical magnitude of a set of items. This system has classically been associated with intraparietal regions, however accumulating evidence in favor of an early visual number sense calls into question the functional role of parietal regions in numerosity processing. Targeting specifically numerosity among other visual features in the earliest stages of processing requires high temporal and spatial resolution. We used frequency-tagged magnetoencephalography to investigate the early automatic processing of numerical magnitudes and measured the steady-state brain responses specifically evoked by numerical and other visual changes in the visual scene. The neuromagnetic responses showed implicit discrimination of numerosity, total occupied area, and convex hull. The source reconstruction corresponding to the implicit discrimination responses showed common and separate sources along the ventral and dorsal visual pathways. Occipital sources attested the perceptual salience of numerosity similarly to both other implicitly discriminable visual features. Crucially, we found parietal responses uniquely associated with numerosity discrimination, showing automatic processing of numerosity in the parietal cortex, even when not relevant to the task. Taken together, these results provide further insights into the functional roles of parietal and occipital regions in numerosity encoding along the visual hierarchy.

A robust electrophysiological marker of spontaneous numerical discrimination

Humans have a Number Sense that enables them to represent and manipulate numerical quantities. Behavioral data suggest that the acuity of numerical discrimination is predictively associated with math ability-especially in children-but some authors argued that its assessment is problematic. In the present study, we used frequency-tagged electroencephalography to objectively measure spontaneous numerical discrimination during passive viewing of dot or picture arrays in healthy adults. During 1-min sequences, we introduced periodic numerosity changes and we progressively increased the magnitude of such changes every ten seconds. We found significant brain synchronization to the periodic numerosity changes from the 1.2 ratio over medial occipital regions, and amplitude strength increased with the numerical ratio. Brain responses were reliable across both stimulus formats. Interestingly, electrophysiological responses also mirrored performances on a number comparison task and seemed to be linked to math fluency. In sum, we present a neural marker of numerical acuity that is passively evaluated in short sequences, independent of stimulus format and that reflects behavioural performances on explicit number comparison tasks.