Weaker number sense accounts for impaired numerosity perception in dyscalculia: Behavioral and computational evidence.

Impaired numerosity perception in developmental dyscalculia (low "number acuity") has been interpreted as evidence of reduced representational precision in the neurocognitive system supporting non-symbolic number sense. However, recent studies suggest that poor numerosity judgments might stem from stronger interference from non-numerical visual information, in line with alternative accounts that highlight impairments in executive functions and visuospatial abilities in the etiology of dyscalculia. To resolve this debate, we used a psychophysical method designed to disentangle the contribution of numerical and non-numerical features to explicit numerosity judgments in a dot comparison task and we assessed the relative saliency of numerosity in a spontaneous categorization task. Children with dyscalculia were compared to control children with average mathematical skills matched for age, IQ, and visuospatial memory. In the comparison task, the lower accuracy of dyscalculics compared to controls was linked to weaker encoding of numerosity, but not to the strength of non-numerical biases. Similarly, in the spontaneous categorization task, children with dyscalculia showed a weaker number-based categorization compared to the control group, with no evidence of a stronger influence of non-numerical information on category choice. Simulations with a neurocomputational model of numerosity perception showed that the reduction of representational resources affected the progressive refinement of number acuity, with little effect on non-numerical bias in numerosity judgments. Together, these results suggest that impaired numerosity perception in dyscalculia cannot be explained by increased interference from non-numerical visual cues, thereby supporting the hypothesis of a core number sense deficit. RESEARCH HIGHLIGHTS: A strongly debated issue is whether impaired numerosity perception in dyscalculia stems from a deficit in number sense or from poor executive and visuospatial functions. Dyscalculic children show reduced precision in visual numerosity judgments and weaker number-based spontaneous categorization, but no increasing reliance on continuous visual properties. Simulations with deep neural networks demonstrate that reduced neural/computational resources affect the developmental trajectory of number acuity and account for impaired numerosity judgments. Our findings show that weaker number acuity in developmental dyscalculia is not necessarily related to increased interference from non-numerical visual cues.

Measuring temporal bias in sequential numerosity comparison.

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.

Prediction of rehabilitation induced motor recovery after stroke using a multi-dimensional and multi-modal approach.

Background: Stroke is a debilitating disease affecting millions of people worldwide. Despite the survival rate has significantly increased over the years, many stroke survivors are left with severe impairments impacting their quality of life. Rehabilitation programs have proved to be successful in improving the recovery process. However, a reliable model of sensorimotor recovery and a clear identification of predictive markers of rehabilitation-induced recovery are still needed. This article introduces the cross-modality protocols designed to investigate the rehabilitation treatment's effect in a group of stroke survivors. Methods/design: A total of 75 stroke patients, admitted at the IRCCS San Camillo rehabilitation Hospital in Venice (Italy), will be included in this study. Here, we describe the rehabilitation programs, clinical, neuropsychological, and physiological/imaging [including electroencephalography (EEG), transcranial magnetic stimulation (TMS), and magnetic resonance imaging (MRI) techniques] protocols set up for this study. Blood collection for the characterization of predictive biological biomarkers will also be taken. Measures derived from data acquired will be used as candidate predictors of motor recovery. Discussion/summary: The integration of cutting-edge physiological and imaging techniques, with clinical and cognitive assessment, dose of rehabilitation and biological variables will provide a unique opportunity to define a predictive model of recovery in stroke patients. Taken together, the data acquired in this project will help to define a model of rehabilitation induced sensorimotor recovery, with the final aim of developing personalized treatments promoting the greatest chance of recovery of the compromised functions.

Math computerized games in the classroom: A number line training in primary school children.

Several studies have shown that the number line can be a useful tool to support early numeracy development. Here, we conducted a school-based training study to evaluate the effectiveness of the software "The Number Line" ("La Linea Dei Numeri"; Tressoldi and Peroni, 2013) in improving children's mathematical skills. We randomly allocated 10 classes of first, second and third graders (N=183) to one of three experimental groups: one group played with The Number Line; the second group played with Labyrinth, a computerized game designed to train attention skills; the third group had no intervention (business-as-usual). At the end of the first training phase, children in The Number Line group completed another training phase playing with Labyrinth, whereas the other two groups played with The Number Line. After playing with The Number Line, all groups displayed more accuracy when placing numbers in the number line task. However, we observed no evident improvement in other mathematical skills. These results suggest that specific training effects emerge even in the school context, although transfer to other numerical skills may be harder to achieve.

Low discriminative power of WISC cognitive profile in developmental dyscalculia.

BACKGROUND: The role of domain-general cognitive abilities in the etiology of Developmental Dyscalculia (DD) is a hotly debated issue. AIMS: In the present study, we tested whether WISC-IV cognitive profiles can be useful to single out DD. METHODS AND PROCEDURES: Using a stringent 2-SD cutoff in a standardized numeracy battery, we identified children with DD (N = 43) within a clinical sample referred for assessment of learning disability and compared them in terms of WISC cognitive indexes to the remaining children without DD (N = 100) employing cross-validated logistic regression. OUTCOMES AND RESULTS: Both groups showed higher Verbal Comprehension and Perceptual Reasoning than Working Memory and Processing Speed, and DD scores were generally lower. Predictive accuracy of WISC indexes in identifying DD individuals was low (AUC = 0.67) and it dropped to chance level in discriminating DD from selected controls (N = 43) with average math performance but matched on global IQ. The inclusion of a visuospatial memory score as an additional predictor did not improve classification accuracy. CONCLUSIONS AND IMPLICATIONS: These results demonstrate that cognitive profiles do not reliably discriminate DD from non-DD children, thereby weakening the appeal of domain-general accounts.

Severe Developmental Dyscalculia Is Characterized by Core Deficits in Both Symbolic and Nonsymbolic Number Sense.

A long-standing debate concerns whether developmental dyscalculia is characterized by core deficits in processing nonsymbolic or symbolic numerical information as well as the role of domain-general difficulties. Heterogeneity in recruitment and diagnostic criteria make it difficult to disentangle this issue. Here, we selected children (n = 58) with severely compromised mathematical skills (2 SD below average) but average domain-general skills from a large sample referred for clinical assessment of learning disabilities. From the same sample, we selected a control group of children (n = 42) matched for IQ, age, and visuospatial memory but with average mathematical skills. Children with dyscalculia showed deficits in both symbolic and nonsymbolic number sense assessed with simple computerized tasks. Performance in the digit-comparison task and the numerosity match-to-sample task reliably separated children with developmental dyscalculia from controls in cross-validated logistic regression (area under the curve = .84). These results support a number-sense-deficit theory and highlight basic numerical abilities that could be targeted for early identification of at-risk children as well as for intervention.

Pupil size as a robust marker of attentional bias toward nicotine-related stimuli in smokers.

Spatial attention can be magnetically attracted by behaviorally salient stimuli. This phenomenon occasionally conflicts with behavioral goals, leading to maladaptive consequences, as in the case of addiction, in which attentional biases have been described and linked with clinically meaningful variables, such as craving level or dependence intensity. Here, we sought to probe the markers of attentional priority in smokers through eye-tracking measures, by leveraging the established link between eye movements and spatial attention. We were particularly interested in potential markers related to pupil size, because pupil diameter reflects a range of autonomic, affective, and cognitive/attentional reactions to behaviorally significant stimuli and is a robust marker of appetitive and aversive learning. We found that changes in pupil size to nicotine-related visual stimuli could reliably predict, in cross-validated logistic regression, the smoking status of young smokers (showing pupil constriction) better than more traditional proxy measures. The possibility that pupil constriction may reflect a bias toward central vision, for example, attentional capture, is discussed in terms of sensory tuning with respect to nicotine-related stimuli. Pupil size was more sensitive at lower nicotine dependence levels, and at increased abstinence time (though these two variables were collinear). We conclude that pupillometry can provide a robust marker for attentional priority computation and useful indications regarding motivational states and individual attitudes toward conditioned stimuli.

Number estimation in Down syndrome: Cognition or experience?

BACKGROUND: The ability to place numbers on a visual "number line" is a hallmark of the understanding of numerical magnitude and it is a strong predictor of mathematical achievement. AIM: We examined whether the performance in the number line estimation task is more driven by mental age or experience with numbers in a sample of Italian children with Down syndrome (DS). METHOD AND PROCEDURE: Sixty-three children with DS (Mmonths = 128.62, SD = 30.73) and sixty-three typically developing children (Mmonths = 54.98, SD = 6.34) matched one to one for mental age completed number line estimation tasks and other tests to assess their numerical knowledge. OUTCOMES AND RESULTS: No significant differences emerged between the two groups in terms of accuracy of positioning numbers on the 1-10 and 1-20 interval. In addition, the accuracy on the 1-10 interval was related to the ability to recognize numbers, while the accuracy on the 1-20 line was related to the ability to compare magnitudes. CONCLUSION AND IMPLICATION: Results suggest that in individuals with DS the linear mapping of numbers is driven by mental age, but the accuracy of positioning numbers is also shaped by the experience with symbolic numbers. Therefore, the improvement of numerical estimation abilities should be a target of intervention programs.

Influences of hand action on the processing of symbolic numbers: A special role of pointing?

Embodied and grounded cognition theories state that cognitive processing is built upon sensorimotor systems. In the context of numerical cognition, support to this framework comes from the interactions between numerical processing and the hand actions of reaching and grasping documented in skilled adults. Accordingly, mechanisms for the processing of object size and location during reach and grasp actions might scaffold the development of mental representations of numerical magnitude. The present study exploited motor adaptation to test the hypothesis of a functional overlap between neurocognitive mechanisms of hand action and numerical processing. Participants performed repetitive grasping of an object, repetitive pointing, repetitive tapping, or passive viewing. Subsequently, they performed a symbolic number comparison task. Importantly, hand action and number comparison were functionally and temporally dissociated, thereby minimizing context-based effects. Results showed that executing the action of pointing slowed down the responses in number comparison. Moreover, the typical distance effect (faster responses for numbers far from the reference as compared to close ones) was not observed for small numbers after pointing, while it was enhanced by grasping. These findings confirm the functional link between hand action and numerical processing, and suggest new hypotheses on the role of pointing as a meaningful gesture in the development and embodiment of numerical skills.

Recovery of neural dynamics criticality in personalized whole-brain models of stroke.

The critical brain hypothesis states that biological neuronal networks, because of their structural and functional architecture, work near phase transitions for optimal response to internal and external inputs. Criticality thus provides optimal function and behavioral capabilities. We test this hypothesis by examining the influence of brain injury (strokes) on the criticality of neural dynamics estimated at the level of single participants using directly measured individual structural connectomes and whole-brain models. Lesions engender a sub-critical state that recovers over time in parallel with behavior. The improvement of criticality is associated with the re-modeling of specific white-matter connections. We show that personalized whole-brain dynamical models poised at criticality track neural dynamics, alteration post-stroke, and behavior at the level of single participants.

A common neural substrate for number comparison, hand reaching and grasping: A SDM-PSI meta-analysis of neuroimaging studies.

The reliance of number processing on sensorimotor mechanisms involved in hand action has been extensively documented by behavioural studies. Nonetheless, where and how the computations of number and hand action interact in the brain has received limited attention. In this study we investigated the brain networks underlying symbolic number comparison and the hand action of reaching and grasping, capitalizing on functional imaging studies meta-analyzed with the seed-based d mapping with permutation of subject images meta-analytic method (SDM-PSI). The main objective was to test whether and to what extent symbolic number processing recruits the same sensorimotor network involved in the hand action of reaching and grasping. We included 42 studies (756 participants) adopting symbolic number comparison tasks and 58 studies (867 participants) investigating hand reaching and hand grasping. The conjunction analysis of brain networks common to number processing, reaching, and grasping revealed spatial convergence over frontoparietal areas. Specifically, four clusters were identified, in and around the left and right intraparietal sulci, in the left precentral gyrus, and in the supplementary motor area. The degree of overlap was extensive, since the reach/grasp network mostly included the number areas. A qualitative analysis of functional characterization capitalizing on the Neurosynth database depicted a strong multifunctionality of the regions of overlap between numbers and hand action: these brain areas were also associated to a variety of functions within the domains of memory and imagery, visuospatial attention, and language. Overall, these results characterize the neuroanatomical substrate of the interaction between reaching, grasping, and symbolic number comparison.

Effects of attentional shifts along the vertical axis on number processing: An eye-tracking study with optokinetic stimulation.

Previous studies suggest that associations between numbers and space are mediated by shifts of visuospatial attention along the horizontal axis. In this study, we investigated the effect of vertical shifts of overt attention, induced by optokinetic stimulation (OKS) and monitored through eye-tracking, in two tasks requiring explicit (number comparison) or implicit (parity judgment) processing of number magnitude. Participants were exposed to black-and-white stripes (OKS) that moved vertically (upward or downward) or remained static (control condition). During the OKS, participants were asked to verbally classify auditory one-digit numbers as larger/smaller than 5 (comparison task; Exp. 1) or as odd/even (parity task; Exp. 2). OKS modulated response times in both experiments. In Exp.1, upward attentional displacement decreased the Magnitude effect (slower responses for large numbers) and increased the Distance effect (slower responses for numbers close to the reference). In Exp.2, we observed a complex interaction between parity, magnitude, and OKS, indicating that downward attentional displacement slowed down responses for large odd numbers. Moreover, eye tracking analyses revealed an influence of number processing on eye movements both in Exp. 1, with eye gaze shifting downwards during the processing of small numbers as compared to large ones; and in Exp. 2, with leftward shifts after large even numbers (6,8) and rightward shifts after large odd numbers (7,9). These results provide evidence of bidirectional links between number and space and extend them to the vertical dimension. Moreover, they document the influence of visuo-spatial attention on processing of numerical magnitude, numerical distance, and parity. Together, our findings are in line with grounded and embodied accounts of numerical cognition.

A novel stroke lesion network mapping approach: improved accuracy yet still low deficit prediction.

Lesion network mapping estimates functional network abnormalities caused by a focal brain lesion. The method requires embedding the volume of the lesion into a normative functional connectome and using the average functional magnetic resonance imaging signal from that volume to compute the temporal correlation with all other brain locations. Lesion network mapping yields a map of potentially functionally disconnected regions. Although promising, this approach does not predict behavioural deficits well. We modified lesion network mapping by using the first principal component of the functional magnetic resonance imaging signal computed from the voxels within the lesioned area for temporal correlation. We measured potential improvements in connectivity strength, anatomical specificity of the lesioned network and behavioural prediction in a large cohort of first-time stroke patients at 2-weeks post-injury (n = 123). This principal component functional disconnection approach localized mainly cortical voxels of high signal-to-noise; and it yielded networks with higher anatomical specificity, and stronger behavioural correlation than the standard method. However, when examined with a rigorous leave-one-out machine learning approach, principal component functional disconnection approach did not perform better than the standard lesion network mapping in predicting neurological deficits. In summary, even though our novel method improves the specificity of disconnected networks and correlates with behavioural deficits post-stroke, it does not improve clinical prediction. Further work is needed to capture the complex adjustment of functional networks produced by focal damage in relation to behaviour.

Visual exploration dynamics are low-dimensional and driven by intrinsic factors.

When looking at visual images, the eyes move to the most salient and behaviourally relevant objects. Saliency and semantic information significantly explain where people look. Less is known about the spatiotemporal properties of eye movements (i.e., how people look). We show that three latent variables explain 60% of eye movement dynamics of more than a hundred observers looking at hundreds of different natural images. The first component explaining 30% of variability loads on fixation duration, and it does not relate to image saliency or semantics; it approximates a power-law distribution of gaze steps, an intrinsic dynamic measure, and identifies observers with two viewing styles: static and dynamic. Notably, these viewing styles were also identified when observers look at a blank screen. These results support the importance of endogenous processes such as intrinsic dynamics to explain eye movement spatiotemporal properties.

Learning Numerosity Representations with Transformers: Number Generation Tasks and Out-of-Distribution Generalization.

One of the most rapidly advancing areas of deep learning research aims at creating models that learn to disentangle the latent factors of variation from a data distribution. However, modeling joint probability mass functions is usually prohibitive, which motivates the use of conditional models assuming that some information is given as input. In the domain of numerical cognition, deep learning architectures have successfully demonstrated that approximate numerosity representations can emerge in multi-layer networks that build latent representations of a set of images with a varying number of items. However, existing models have focused on tasks requiring to conditionally estimate numerosity information from a given image. Here, we focus on a set of much more challenging tasks, which require to conditionally generate synthetic images containing a given number of items. We show that attention-based architectures operating at the pixel level can learn to produce well-formed images approximately containing a specific number of items, even when the target numerosity was not present in the training distribution.

Extraordinary claims, extraordinary evidence? A discussion.

Roberts (2020, Learning & Behavior, 48[2], 191-192) discussed research claiming honeybees can do arithmetic. Some readers of this research might regard such claims as unlikely. The present authors used this example as a basis for a debate on the criterion that ought to be used for publication of results or conclusions that could be viewed as unlikely by a significant number of readers, editors, or reviewers.

Effects of Orthographic Consistency on Bilingual Reading: Human and Computer Simulation Data.

English serves as today's lingua franca, a role not eased by the inconsistency of its orthography. Indeed, monolingual readers of more consistent orthographies such as Italian or German learn to read more quickly than monolingual English readers. Here, we assessed whether long-lasting bilingualism would mitigate orthography-specific differences in reading speed and whether the order in which orthographies with a different regularity are learned matters. We studied high-proficiency Italian-English and English-Italian bilinguals, with at least 20 years of intensive daily exposure to the second language and its orthography and we simulated sequential learning of the two orthographies with the CDP++ connectionist model of reading. We found that group differences in reading speed were comparatively bigger with Italian stimuli than with English stimuli. Furthermore, only Italian bilinguals took advantage of a blocked presentation of Italian stimuli compared to when stimuli from both languages were presented in mixed order, suggesting a greater ability to keep language-specific orthographic representations segregated. These findings demonstrate orthographic constraints on bilingual reading, whereby the level of consistency of the first learned orthography affects later learning and performance on a second orthography. The computer simulations were consistent with these conclusions.

The secret life of predictive brains: what's spontaneous activity for?

Brains at rest generate dynamical activity that is highly structured in space and time. We suggest that spontaneous activity, as in rest or dreaming, underlies top-down dynamics of generative models. During active tasks, generative models provide top-down predictive signals for perception, cognition, and action. When the brain is at rest and stimuli are weak or absent, top-down dynamics optimize the generative models for future interactions by maximizing the entropy of explanations and minimizing model complexity. Spontaneous fluctuations of correlated activity within and across brain regions may reflect transitions between 'generic priors' of the generative model: low dimensional latent variables and connectivity patterns of the most common perceptual, motor, cognitive, and interoceptive states. Even at rest, brains are proactive and predictive.

Sensorimotor, Attentional, and Neuroanatomical Predictors of Upper Limb Motor Deficits and Rehabilitation Outcome after Stroke.

The rehabilitation of motor deficits following stroke relies on both sensorimotor and cognitive abilities, thereby involving large-scale brain networks. However, few studies have investigated the integration between motor and cognitive domains, as well as its neuroanatomical basis. In this retrospective study, upper limb motor responsiveness to technology-based rehabilitation was examined in a sample of 29 stroke patients (18 with right and 11 with left brain damage). Pretreatment sensorimotor and attentional abilities were found to influence motor recovery. Training responsiveness increased as a function of the severity of motor deficits, whereas spared attentional abilities, especially visuospatial attention, supported motor improvements. Neuroanatomical analysis of structural lesions and white matter disconnections showed that the poststroke motor performance was associated with putamen, insula, corticospinal tract, and frontoparietal connectivity. Motor rehabilitation outcome was mainly associated with the superior longitudinal fasciculus and partial involvement of the corpus callosum. The latter findings support the hypothesis that motor recovery engages large-scale brain networks that involve cognitive abilities and provides insight into stroke rehabilitation strategies.