The interplay between spatial and non-spatial grouping cues over approximate number perception.

Humans and animals share the cognitive ability to quickly extract approximate number information from sets. Main psychophysical models suggest that visual approximate numerosity relies on segmented units, which can be affected by Gestalt rules. Indeed, arrays containing spatial grouping cues, such as connectedness, closure, and even symmetry, are underestimated compared to ungrouped arrays with equal low-level features. Recent evidence suggests that non-spatial cues, such as color-similarity, also trigger numerosity underestimation. However, in natural vision, several grouping cues may coexist in the scene. Notably, conjunction of grouping cues (color and closure) reduces perceived numerosity following an additive rule. To test whether the conjunction-effect holds for other Gestalt cues, we investigated the effect of connectedness and symmetry over numerosity perception both in isolation and, critically, in conjunction with luminance similarity. Participants performed a comparison-task between a reference and a test stimulus varying in numerosity. In Experiment 1, test stimuli contained two isolated groupings (connectedness or luminance), a conjunction (connectedness and luminance), and a neutral condition (no groupings). Results show that point of subjective equality was higher in both isolated grouping conditions compared to the neutral condition. Furthermore, in the conjunction condition, the biases from isolated grouping cues added linearly, resulting in a numerosity underestimation equal to the sum of the isolated biases. In Experiment 2 we found that conjunction of symmetry and luminance followed the same additive rule. These findings strongly suggest that both spatial and non-spatial isolated cues affect numerosity perception. Crucially, we show that their conjunction effect extends to symmetry and connectedness.

Spatial frequency equalization does not prevent spatial-numerical associations.

There is an intense debate surrounding the origin of spatial-numerical associations (SNAs), according to which small numbers are mapped onto the left side of the space and large numbers onto the right. Despite evidence suggesting that SNAs would emerge as an innate predisposition to map numerical information onto a left-to-right spatially oriented mental representation, alternative accounts have challenged these proposals, maintaining that such a mapping would be the result of a mere spatial frequency (SF) coding of any visual image. That is, any smaller or larger array of objects would naturally contain more low or high SF information and, accordingly, each hemisphere would be preferentially tuned only for one SF range (e.g., right hemisphere tuned for low SF and left hemisphere tuned for high SF). This would determine the typical SNA (e.g., faster RTs for small numerical arrays with the left hand and for large numerical arrays with the right hand). To directly probe the role of SF coding in SNAs, we tested participants in a typical dot-arrays comparison task with two numerical sets: one in which SFs were confounded with numerosity (Experiment 1) and one in which the full SF power spectrum was equalized across all stimuli, keeping this cue uninformative about numerosity (Experiment 2). We found that SNAs emerged in both experiments, independently of whether SF was confounded or not with numerosity. Taken together, these findings suggest that SNAs cannot simply originate from SF power spectrum alone, and, thus, they rule out the brain's asymmetric SF tuning as a primary cause of such an effect.

Number is not just an illusion: Discrete numerosity is encoded independently from perceived size.

While seminal theories suggest that nonsymbolic visual numerosity is mainly extracted from segmented items, more recent views advocate that numerosity cannot be processed independently of nonnumeric continuous features confounded with the numerical set (i.e., such as the density, the convex hull, etc.). To disentangle these accounts, here we employed two different visual illusions presented in isolation or in a merged condition (e.g., combining the effects of the two illusions). In particular, in a number comparison task, we concurrently manipulated both the perceived object segmentation by connecting items with Kanizsa-like illusory lines, and the perceived convex-hull/density of the set by embedding the stimuli in a Ponzo illusion context, keeping constant other low-level features. In Experiment 1, the two illusions were manipulated in a compatible direction (i.e., both triggering numerical underestimation), whereas in Experiment 2 they were manipulated in an incompatible direction (i.e., with the Ponzo illusion triggering numerical overestimation and the Kanizsa illusion numerical underestimation). Results from psychometric functions showed that, in the merged condition, the biases of each illusion summated (i.e., largest underestimation as compared with the conditions in which illusions were presented in isolation) in Experiment 1, while they averaged and competed against each other in Experiment 2. These findings suggest that discrete nonsymbolic numerosity can be extracted independently from continuous magnitudes. They also point to the need of more comprehensive theoretical views accounting for the operations by which both discrete elements and continuous variables are computed and integrated by the visual system.

Nonsymbolic numerosity in sets with illusory-contours exploits a context-sensitive, but contrast-insensitive, visual boundary formation process.

The visual mechanisms underlying approximate numerical representation are still intensely debated because numerosity information is often confounded with continuous sensory cues (e.g., texture density, area, convex hull). However, numerosity is underestimated when a few items are connected by illusory contours (ICs) lines without changing other physical cues, suggesting in turn that numerosity processing may rely on discrete visual input. Yet, in these previous works, ICs were generated by black-on-gray inducers producing an illusory brightness enhancement, which could represent a further continuous sensory confound. To rule out this possibility, we tested participants in a numerical discrimination task in which we manipulated the alignment of 0, 2, or 4 pairs of open/closed inducers and their contrast polarity. In Experiment 1, aligned open inducers had only one polarity (all black or all white) generating ICs lines brighter or darker than the gray background. In Experiment 2, open inducers had always opposite contrast polarity (one black and one white inducer) generating ICs without strong brightness enhancement. In Experiment 3, reverse-contrast inducers were aligned but closed with a line preventing ICs completion. Results showed that underestimation triggered by ICs lines was independent of inducer contrast polarity in both Experiment 1 and Experiment 2, whereas no underestimation was found in Experiment 3. Taken together, these results suggest that mere brightness enhancement is not the primary cause of the numerosity underestimation induced by ICs lines. Rather, a boundary formation mechanism insensitive to contrast polarity may drive the effect, providing further support to the idea that numerosity processing exploits discrete inputs.

The ratio effect in visual numerosity comparisons is preserved despite spatial frequency equalisation.

How non-symbolic numerosity is visually extracted remains a matter of intense debate. Most evidence suggests that numerosity is directly extracted on individual objects following Weber's law, at least for a moderate numerical range. Alternative accounts propose that, whatever the range, numerosity is indirectly derived from summary texture-statistics of the raw image such as spatial frequency (SF). Here, to disentangle these accounts, we tested whether the well-known behavioural signature of numerosity encoding (ratio effect) is preserved despite the equalisation of the SF content. In Experiment 1, participants had to select the numerically larger of two briefly presented moderate-range numerical sets (i.e., 8-18 dots) carefully matched for SF; the ratio between numerosities was manipulated by levels of increasing difficulty (e.g., 0.66, 0.75, 0.8). In Experiment 2, participants performed the same task, but they were presented with both the original and SF equalised stimuli. In both experiments, the results clearly showed a ratio-dependence of the performance: numerosity discrimination became harder and slower as the ratio between numerosities increased. Moreover, this effect was found to be independent of the stimulus type, although the overall performance was better with the original rather than the SF equalised stimuli (Experiment 2). Taken together, these findings indicate that the power spectrum per se cannot explain the main behavioural signature of Weber-like encoding of numerosities (the ratio effect), at least over the tested numerical range, partially challenging alternative indirect accounts of numerosity processing.

Non-symbolic numerosity encoding escapes spatial frequency equalization.

The exact visual mechanisms underpinning the approximate number system are still debated. Recent evidence suggests that numerosity is extracted on segmented visual objects, at least for a moderate numerical range (e.g., < 100 items), whereas alternative models rather propose that numerosity is derived from low-level features (e.g., power spectrum) of an unsegmented image, independently from the range. Here, to disentangle these accounts, we generated stimuli that were equalized for spatial frequency amplitude spectrum and luminance across sets of moderate range numerosities (e.g., 9-15 dots), while independently manipulating the perceived item segmentation by connecting dots with illusory contours (ICs). In Experiment 1, participants performed a numerical discrimination task, in which they had to select the numerically larger between two stimuli: a reference stimulus (always 12 dots) and a test stimulus (from 9 to 15 dots) containing 0, 2 or 4 pairs of dots grouped by ICs lines. In Experiment 2, participants were presented only the test stimulus and performed an estimation task. Results clearly showed that in both experiments participants' performance followed well-known numerical signatures (e.g., distance effect and scalar variability), with numerosity that was underestimated as the illusory connections increased. Crucially, this was found despite spatial frequencies and luminance were kept constant across all the experimental stimuli and these variables were thus uninformative about numerosity. Taken together, these findings indicate that power spectrum in its own cannot explain numerical processing. Rather, visual segmentation mechanisms may be crucial in such processing at least for a moderate numerosity range.

Visual illusions as a tool to hijack numerical perception: Disentangling nonsymbolic number from its continuous visual properties.

The past few years have witnessed a fervent theoretical debate about the exact visual mechanisms supporting nonsymbolic number processing. The idea that quantity information is extracted through a primitive visual segmentation algorithm has been challenged by recent models, which rather tap on low-level features confounded with numerosity (i.e., density, convex hull, or total area). Here we used an original manipulation based on visual illusions to disentangle whether visual numerosity processing operates over discrete units or rather over continuous variables. In particular, we generated a set of stimuli composed by open inducers (e.g., like a pac-man shape) that simulate physical connections with Kanizsa-like illusory contours (ICs). Test sets contained pairs of collinear open inducers items that prompted 0 IC, 2 IC, or 4 IC lines connecting 2 objects. Critically, low-level visual features were fully controlled across connectedness levels. We found a systematic underestimation as we increased the IC connections when participants had to select the larger between 2 sets of objects (Experiment 1) but not in the case of aligned closed inducers preventing illusory lines (Experiments 2A and 2B). We also found a systematic numerosity underestimation when both IC connections and continuous features (e.g., convex hull) were independently manipulated in test stimuli (Experiment 3). Finally, these results were shown to be task independent because the same effects of IC connections were replicated in an estimation task (Experiment 4). Taken together, our findings indicate that numerosity perception relies on basic visual-segmentation mechanisms, pointing out the need of new theoretical frameworks integrating both continuous and discrete perceptual number signals. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Approximate number sense theory or approximate theory of magnitude?

Leibovich et al. argue that the evidence in favor of a perceptual mechanism devoted to the extraction of numerosity from visual collections is unsatisfactory and propose to replace it with an unspecific mechanism capturing approximate magnitudes from continuous dimensions. We argue that their representation of the evidence is incomplete and that their theoretical proposal is too vague to be useful.

High Ca2+ Influx During Traumatic Brain Injury Leads to Caspase-1-Dependent Neuroinflammation and Cell Death.

We investigated the hypothesis that high Ca2+ influx during traumatic brain injury induces the activation of the caspase-1 enzyme, which triggers neuroinflammation and cell apoptosis in a cell culture model of neuronal stretch injury and an in vivo model of fluid percussion injury (FPI). We first established that stretch injury causes a rapid increase in the intracellular Ca2+ level, which activates interleukin-converting enzyme caspase-1. The increase in the intracellular Ca2+ level and subsequent caspase-1 activation culminates into neuroinflammation via the maturation of IL-1ß. Further, we analyzed caspase-1-mediated apoptosis by TUNEL staining and PARP western blotting. The voltage-gated sodium channel blocker, tetrodotoxin, mitigated the stretch injury-induced neuroinflammation and subsequent apoptosis by blocking Ca2+ influx during the injury. The effect of tetrodotoxin was similar to the caspase-1 inhibitor, zYVAD-fmk, in neuronal culture. To validate the in vitro results, we demonstrated an increase in caspase-1 activity, neuroinflammation and neurodegeneration in fluid percussion-injured animals. Our data suggest that neuronal injury/traumatic brain injury (TBI) can induce a high influx of Ca2+ to the cells that cause neuroinflammation and cell death by activating caspase-1, IL-1ß, and intrinsic apoptotic pathways. We conclude that excess IL-1ß production and cell death may contribute to neuronal dysfunction and cognitive impairment associated with TBI.

Traumatic brain injury induced matrix metalloproteinase2 cleaves CXCL12α (stromal cell derived factor 1α) and causes neurodegeneration.

Traumatic brain injury (TBI), even at mild levels, can activate matrix metalloproteinases (MMPs) and the induction of neuroinflammation that can result in blood brain barrier breakdown and neurodegeneration. MMP2 has a significant role in neuroinflammation and neurodegeneration by modulating the chemokine CXCL12α (stromal cell derived factor SDF-1α) signaling pathway and the induction of apoptosis. SDF-1α is responsible for cell proliferation and differentiation throughout the nervous system and is also implicated in various neurodegenerative illnesses. We hypothesized that TBI leads to MMP2 activation and cleavage of the N-terminal 4 amino acid residues of CXCL12α with generation of the highly neurotoxic fragment SDF-1(5-67). Using an in vitro stretch-injury model of rat neuronal cultures and the in vivo fluid percussion injury (FPI) model in rats, we found that oxidative stress has a significant role in the activation of MMP2. This is initiated by the induction of free radical generating enzyme NADPH oxidase 1 (NOX1). Induction of NOX1 correlated well with the signatures of oxidative stress marker, 4HNE in the injured neuronal cultures and cerebral cortex of rats. Further, using MMP2 siRNA and pharmacological MMP2 inhibitor, ARP100, we established the neurodegenerative role of MMP2 in cleaving SDF-1α to a neurotoxic fragment SDF-1(5-67). By immunofluorescence, western blotting and TUNEL experiments, we show the cleaved form of SDF leads to apoptotic cell death in neurons. This work identifies a new potential therapeutic target to reduce the complications of brain damage in TBI.

Individual differences in non-symbolic numerical abilities predict mathematical achievements but contradict ATOM.

BACKGROUND: A significant debate surrounds the nature of the cognitive mechanisms involved in non-symbolic number estimation. Several studies have suggested the existence of the same cognitive system for estimation of time, space, and number, called "a theory of magnitude" (ATOM). In addition, researchers have proposed the theory that non-symbolic number abilities might support our mathematical skills. Despite the large number of studies carried out, no firm conclusions can be drawn on either topic. METHODS: In the present study, we correlated the performance of adults on non-symbolic magnitude estimations and symbolic numerical tasks. Non-symbolic magnitude abilities were assessed by asking participants to estimate which auditory tone lasted longer (time), which line was longer (space), and which group of dots was more numerous (number). To assess symbolic numerical abilities, participants were required to perform mental calculations and mathematical reasoning. RESULTS: We found a positive correlation between non-symbolic and symbolic numerical abilities. On the other hand, no correlation was found among non-symbolic estimations of time, space, and number. CONCLUSIONS: Our study supports the idea that mathematical abilities rely on rudimentary numerical skills that predate verbal language. By contrast, the lack of correlation among non-symbolic estimations of time, space, and number is incompatible with the idea that these magnitudes are entirely processed by the same cognitive system.

Accurate determination of succinimide degradation products using high fidelity trypsin digestion peptide map analysis.

We report an efficient, high fidelity trypsin digestion method for peptide map analysis. This method minimizes artifacts caused by the sample preparation process, and we show its utility for the accurate determination of succinimide formation in a degraded monoclonal antibody product. A basic charge variant was detected by imaged capillary isoelectric focusing and was shown with reduced antigen binding and biological activity. Samples were reduced under denaturing conditions at pH 5.0, and digestion of the reduced protein with porcine trypsin was performed at pH 7.0 for 1 h. Following reversed phase high-performance liquid chromatography and online mass spectrometric analysis, succinimide formation was identified at Asp30 in the light chain. This result contrasts with the observation of only iso-Asp and Asp residues under conventional sample preparation conditions, which are therefore concluded to be artificially generated. The Asp30 residue is seen in the cocrystal structure model to participate in favorable charge interaction with an antigen molecule. Formation of succinimide and the resulting loss of negative charge are therefore hypothesized to be the degradation mechanism. After treatment of the degraded antibody sample to mildly alkaline pH conditions, we observed only Asp residue as the succinimide hydrolysis product and concurrent recovery of biological activity.