Unconscious Integration of Categorical Relationship of Two Subliminal Numbers in Comparison with "5"

Many studies have shown that the brain can process subliminal numerals, i.e., participants can categorize a subliminal number into two categories: greater than 5 or less than 5. In the context of many studies on the unconscious integration of multiple subliminal stimuli, the issue of whether multiple subliminal numbers can be integrated is contentious. The same-different task is regarded as a perfect tool to explore unconscious integration. In the two experiments reported, we used a same-different task in which a pair of masked prime numbers was followed by a pair of target numbers, and participants were asked to decide whether the two target numbers were on the same (both smaller or larger than 5) or different sides (one smaller, the other larger than 5) of 5 in magnitude. The results indicated that the prime numbers could be categorized unconsciously, which was reflected by the category priming effect, and that the unconscious category relationship of the two prime numbers could affect the judgment on the category relationship of the two target numbers, as reflected by the response priming effect. The duration of the prime-to-target interstimulus interval (ISI) was also manipulated, showing a positive compatibility effect (PCE) of category priming and a negative compatibility effect (NCE) of response priming no matter whether the ISI was short (50 ms) or long (150 ms). The NCE, which occurred when the prime-to-target ISI was relatively short in this study, contradicted the conventional view but was consistent with previous results of unconscious integration based on an attention modulation mechanism. Importantly, this study provided evidence for the still-under-debate issue of numerical information integration.

Transcoding of French numbers for first- and second-language learners in third grade

Transcoding is the process of translating between spoken and written numbers, and it is correlated with other mathematical skills. In the present study, we investigated the link between French number writing of 49 students in the third grade (aged 7-9 years) and their language skills. Transcoding in French is of particular interest because the spoken number language system does not completely correspond to that of the written digits (e.g., quatre-vingt-dix [four-twenty-ten] and 90). We hypothesised that the complex linguistic structure of spoken numbers in French would be challenging for students who are learning to transcode. First and second French-language learners' accuracy and errors were recorded during a writing task of 3- to 7-digit numbers. Children also completed linguistic tests (e.g., receptive vocabulary, receptive syntax). Results showed that first- and second-language learners did not differ in their transcoding accuracy. Number size, decade complexity of stimulus number words in French (i.e., numbers containing a complex decade, operationalized as a number between soixante-dix, 70, and quatre-vingt-dix-neuf, 99), and receptive vocabulary predicted children's French transcoding skills. Students were more likely to produce errors (e.g., 68 or 6018 for 78) when they transcoded complex decade numbers compared with simple decade numbers. When an error was made on the complex decade portion of a number, it was likely a lexical error. In conclusion, third graders, both first- and second-language learners, found complex decade numbers challenging and their performance was related to their general vocabulary skills.

Central lymph nodes in frozen sections can effectively guide extended lymph node resection for papillary thyroid carcinoma

OBJECTIVES

The scope of lateral neck lymph node dissection (LND) in papillary thyroid carcinoma (PTC) remains controversial. Our research aimed to explore the value of central lymph node metastasis (CLNM) in frozen sections for predicting neck lateral lymph node metastasis (NLLNM) and to guide clinical surgeons in performing surgical lymph node dissection.

PATIENTS

A total of 275 patients with PTC with suspected 'Cervical lymph node metastasis (LNM, including CLNM and NLLNM)' underwent unilateral or bilateral thyroidectomy and an intraoperative frozen diagnosis of central lymph nodes (LNs), as well as central and neck lateral LND. Validity indices and consistency of central LNs in frozen sections were calculated. In total, 216 patients then met the inclusion criteria and were enrolled in the follow-up study. The clinical and pathological data of the patients were retrospectively analyzed. The relationship between the number, metastatic diameter, and the ratio of CLNM to NLLNM was investigated.

RESULTS

CLNM in frozen and paraffin-embedded sections was associated with NLLNM. Univariate and multivariate analyses revealed the following risk factors for NLLNM metastasis: maximum diameter, total number, and ratio of metastatic LNs. A significant result was obtained when a cut-off value of 2.050 mm for the maximum metastatic diameter, 5.5 in the total number, and 0.5342 for the CLNM ratio level was used. Interaction term analyses showed that the association between the number of CLNM and NLLNM differed according to maximum diameter.

CONCLUSION

Central LNs in frozen sections accurately predicted NLLNM. In patients with PTC with >5 CLNMs, ≥2 and ≤5 CLNMs and maximum metastatic diameter > 2 mm, neck lateral LND should be considered. Our findings will facilitate the identification of patients who are likely to benefit from extended lateral neck LND.

How understanding and strengthening brain networks can contribute to elementary education

Imaging the human brain during the last 35 years offers potential for improving education. What is needed is knowledge on the part of educators of all types of how this potential can be realized in practical terms. This paper briefly reviews the current level of understanding of brain networks that underlie aspects of elementary education and its preparation for later learning. This includes the acquisition of reading, writing and number processing, improving attention and increasing the motivation to learn. This knowledge can enhance assessment devices, improve child behavior and motivation and lead to immediate and lasting improvements in educational systems.

Subject-verb agreement inflection in Arabic-speaking individuals with Down syndrome

This research examines the production of subject-verb agreement inflection in person, number, and gender in Urban Jordanian Arabic-speaking individuals with Down syndrome (DS). Third person singular masculine, third person singular feminine, and third person plural suffixes (3MS/3FS/3P) were investigated to achieve this objective. The research involved 60 participants, 30 males and 30 females, enrolled in Nazik Al Hariri Welfare Center for Special Education in Amman. The participants were divided into three groups by age, kindergarten 2 (7.1 to 12.5), school-age (13.10 to 17.6), and vocational training (18.3 to 27.3). Data were collected via a picture-naming task. The results showed that verb agreement constitutes a severe problem in individuals with DS. All three age groups showed some degree of language decline. The 3MS form was the most used and the most accurate form by the three DS groups (48.5%), followed by the 3FS (35.3%) and the 3P (22.8%). A significant finding of this study is that the acquisition of agreement for person, number, and gender by the DS groups is associated with inconsistency and atypical asynchrony. In addition, the results show that age significantly affects the DS groups' production of subject-verb agreement. Thus, the study recommends early intervention for the verb system and subject-verb agreement.

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.

Spider Angioma Number and Location as Potential Prognostic Indicators in Chronic Liver Disease: A Case Report

Spider angiomas (SAs) are a well-known physical exam feature found in patients with chronic liver disease. While SAs are thought to correspond with a higher risk of mortality in chronic liver disease (CLD) patients, only few studies have been done to assess the number and location of SAs as prognostic indicators. We present a case of a 64-year-old patient with decompensated CLD who was found to have three SAs on physical exam. The patient presented to the inpatient service at a community hospital in Miami, Florida. He had experienced previous esophageal varices banding, had a Model for End-Stage Liver Disease (MELD) score of 31, and needed large-volume paracentesis due to significant ascites. It was determined that he had a very poor prognosis and was in need of a liver transplant. We suggest that more research is necessary to determine if there is a prognostic importance to the number and location of SAs in patients with CLD, as earlier interventions could potentially lead to improvements in outcomes through this physical exam finding.

Spatial metaphors and the design of everyday things

People use space (e.g., left-right, up-down) to think about a variety of non-spatial concepts like time, number, similarity, and emotional valence. These spatial metaphors can be used to inform the design of user interfaces, which visualize many of these concepts in space. Traditionally, researchers have relied on patterns in language to discover habits of metaphorical thinking. However, advances in cognitive science have revealed that many spatial metaphors remain unspoken, shaping people's preferences, memories, and actions independent of language - and even in contradiction to language. Here we argue that cognitive science can impact our everyday lives by informing the design of physical and digital objects via the spatial metaphors in people's minds. We propose a simple principle for predicting which spatial metaphors organize people's non-spatial concepts based on the structure of their linguistic, cultural, and bodily experiences. By leveraging the latent metaphorical structure of people's minds, we can design objects and interfaces that help people think.

Young children interpret number gestures differently than nonsymbolic sets

Researchers have long been interested in the origins of humans' understanding of symbolic number, focusing primarily on how children learn the meanings of number words (e.g., "one", "two", etc.). However, recent evidence indicates that children learn the meanings of number gestures before learning number words. In the present set of experiments, we ask whether children's early knowledge of number gestures resembles their knowledge of nonsymbolic number. In four experiments, we show that preschool children (n = 139 in total; age M = 4.14 years, SD = 0.71, range = 2.75-6.20) do not view number gestures in the same the way that they view nonsymbolic representations of quantity (i.e., arrays of shapes), which opens the door for the possibility that young children view number gestures as symbolic, as adults and older children do. This article is protected by copyright. All rights reserved.

Number Concentration Measurements of Polystyrene Submicrometer Particles

The number of techniques to measure number concentrations and size distributions of submicrometer particles has recently increased. Submicrometer particle standards are needed to improve the accuracy and reproducibility of these techniques. The number concentrations of fluorescently labeled polystyrene submicrometer sphere suspensions with nominal 100 nm, 200 nm and 500 nm diameters were measured using seven different techniques. Diameter values were also measured where possible. The diameter values were found to agree within 20%, but the number concentration values differed by as much as a factor of two. Accuracy and reproducibility related with the different techniques are discussed with the goal of using number concentration standards for instrument calibration. Three of the techniques were used to determine SI-traceable number concentration values, and the three independent values were averaged to give consensus values. This consensus approach is proposed as a protocol for certifying SI-traceable number concentration standards.

Memory for linguistic features and the focus of attention: evidence from the dynamics of agreement inside DP

The amount of information that can be concurrently maintained in the focus of attention is strongly restricted (Broadbent, 1958). The goal of this study was to test whether this restriction was functionally significant for language comprehension. We examined the time course dynamics of processing determiner-head agreement in English demonstrative phrases. We found evidence that agreement processing was slowed when determiner and head were no longer adjacent, but separated by modifiers. We argue that some information is shunted nearly immediately from the focus of attention, necessitating its later retrieval. Plural, the marked feature value for number, exhibits better preservation in the focus of attention, however, than the unmarked value, singular.

A proposed modified SEIQR epidemic model to analyze the COVID-19 spreading in Saudi Arabia

The key aim of this paper is to construct a modified version of the SEIQR essential disease dynamics model for the COVID-19 emergence. The modified SEIQR pandemic model takes a groundbreaking approach to evaluate and monitor the COVID-19 epidemic. The complex studies presented in this paper are based on real-world data from Saudi Arabia. A reproduction number and a systematic stability analysis are included in the new version of SEIQR model dynamics. Using the Jacobian linearization process, we can obtain the domain of the solution and the state of equilibrium based on the modified SEIQR model. The equilibrium and its importance have been identified, and the disease-free stability of the equilibrium has been investigated. The reproduction number was calculated using internal metrics, and the global stability of the current model's equilibrium was demonstrated using Lyapunov's stability theorem. To see how well the SEIQR proposed model went, it was compared to real COVID-19 spread data in Saudi Arabia. According to the results, the new SEIQR proposed model is a good match for researching the spread of epidemics like COVID-19. In the end, we presented an optimal protocol to prevent the dissemination of COVID-19. Staying at home and transporting sick people as far as possible to a safe region is the most effective strategy to prevent COVID-19 spread. It is critical to offer infected people safe and effective treatment, as well as antibiotics and nutrients to non-affected people. To detect confirmed infections, we must provide more effective and reliable diagnostic methods. Furthermore, increasing understanding of how to recognize the disease, its symptoms, and how to confirm the infection.

Not Only High Number and Specific Comorbidities but Also Age Are Closely Related to Progression and Poor Prognosis in Patients With COVID-19

Background: Some patients with comorbidities and rapid disease progression have a poor prognosis.

Aim: We aimed to investigate the characteristics of comorbidities and their relationship with disease progression and outcomes of COVID-19 patients.

Methods: A total of 718 COVID-19 patients were divided into five clinical type groups and eight age-interval groups. The characteristics of comorbidities were compared between the different clinical type groups and between the different age-interval groups, and their relationships with disease progression and outcomes of COVID-19 patients were assessed.

Results: Approximately 91.23% (655/718) of COVID-19 patients were younger than 60 years old. Approximately 64.76% (465/718) had one or more comorbidities, and common comorbidities included non-alcoholic fatty liver disease (NAFLD), hyperlipidaemia, hypertension, diabetes mellitus (DM), chronic hepatitis B (CHB), hyperuricaemia, and gout. COVID-19 patients with comorbidities were older, especially those with chronic obstructive pulmonary disease (COPD) and cardiovascular disease (CVD). Hypertension, DM, COPD, chronic kidney disease (CKD) and CVD were mainly found in severe COVID-19 patients. According to spearman correlation analysis the number of comorbidities was correlated positively with disease severity, the number of comorbidities and NAFLD were correlated positively with virus negative conversion time, hypertension, CKD and CVD were primarily associated with those who died, and the above-mentioned correlation existed independently of age. Risk factors included age, the number of comorbidities and hyperlipidaemia for disease severity, the number of comorbidities, hyperlipidaemia, NAFLD and COPD for the virus negative conversion time, and the number of comorbidities and CKD for prognosis. Number of comorbidities and age played a predictive role in disease progression and outcomes.

Conclusion: Not only high number and specific comorbidities but also age are closely related to progression and poor prognosis in patients with COVID-19. These findings provide a reference for clinicians to focus on not only the number and specific comorbidities but also age in COVID-19 patients to predict disease progression and prognosis.

Clinical Trial Registry: Chinese Clinical Trial Register ChiCTR2000034563.

Archerfish number discrimination

Debates have arisen as to whether non-human animals actually can learn abstract non-symbolic numerousness or whether they always rely on some continuous physical aspect of the stimuli, covarying with number. Here, we investigated archerfish (Toxotes jaculatrix) non-symbolic numerical discrimination with accurate control for covarying continuous physical stimulus attributes. Archerfish were trained to select one of two groups of black dots (Exp. 1: 3 vs 6 elements; Exp. 2: 2 vs 3 elements); these were controlled for several combinations of physical variables (elements' size, overall area, overall perimeter, density, and sparsity), ensuring that only numerical information was available. Generalization tests with novel numerical comparisons (2 vs 3, 5 vs 8, and 6 vs 9 in Exp. 1; 3 vs 4, 3 vs 6 in Exp. 2) revealed choice for the largest or smallest numerical group according to the relative number that was rewarded at training. None of the continuous physical variables, including spatial frequency, were affecting archerfish performance. Results provide evidence that archerfish spontaneously use abstract relative numerical information for both small and large numbers when only numerical cues are available.

Can a Single Representational Object Account for Different Number-Space Mappings?

Numbers are mapped onto space from birth on, as evidenced by a variety of interactions between the processing of numerical and spatial information. In particular, larger numbers are associated to larger spatial extents (number/spatial extent mapping) and to rightward spatial locations (number/location mapping), and smaller numbers are associated to smaller spatial extents and leftward spatial locations. These two main types of number/space mappings (number/spatial extent and number/location mappings) are usually assumed to reflect the fact that numbers are represented on an internal continuum: the mental number line. However, to date there is very little evidence that these two mappings actually reflect a single representational object. Across two experiments in adults, we investigated the interaction between number/location and number/spatial extent congruency effects, both when numbers were presented in a non-symbolic and in a symbolic format. We observed a significant interaction between the two mappings, but only in the context of an implicit numerical task. The results were unaffected by the format of presentation of numbers. We conclude that the number/location and the number/spatial extent mappings can stem from the activation of a single representational object, but only in specific experimental contexts.

Impact of Inadequate Number of Lymph Nodes Examined on Survival in Stage II Colon Cancer

Background

Inadequate number of lymph nodes examined was not uncommon. We aimed to assess the clinical role of inadequate number of lymph nodes examined in stage II colon cancer.

Methods

The cancer data used in our study were obtained from the SEER (Surveillance, Epidemiology and End Results) program. Using the chi-square test, all the variables obtained in our study were compared based on whether patients had enough (≥12) lymph nodes examined. Kaplan–Meier analysis was used for overall survival (OS) analysis, and log-rank test was applied to compare different N stages with the total number of lymph nodes examined. Multivariate analysis was carried out by creating a Cox proportional hazard model to assess the prognostic roles of different variables.

Results

In total, 80,296 stage II/III colon cancer patients were recruited for our study. N0 stage with <8 lymph nodes examined would present with a worse prognosis compared to N1 stage (5-year OS rates, 51.6% vs. 57.1%, p < 0.001). Multivariate analyses indicated that OS of N0 stage with <8 lymph nodes examined was similar to that of N1 stage after adjusting for other recognized prognostic factors [hazard ratios (HRs) = 1.051, 95% confidence intervals (CIs) = 1.014–1.090, p = 0.018].

Conclusions

N0 stage with less than eight lymph nodes examined in stage II colon cancer presented with no better OS compared to that of N1 stage. Stage II colon cancer with less than eight lymph nodes examined needed to be given greater emphasis in clinical practice.

Elevated intracranial pressure with craniosynostosis: a multivariate model of age, syndromic status, and number of involved cranial sutures

OBJECTIVE

Children with multiple prematurely fused cranial sutures and those undergoing surgical correction later in life appear to experience worse neurocognitive outcomes, but it is unclear whether higher intracranial pressure (ICP) is implicated in this process. The purpose of this study was to elucidate the effect of age at intervention and number of involved cranial sutures on ICP, as well as to assess which cranial suture closure may be more associated with elevated ICP.

METHODS

The prospective craniofacial database at the authors' institution was queried for patients undergoing initial corrective surgery for craniosynostosis in whom intraoperative measurement of ICP was obtained prior to craniectomy. Age, involved sutures, and syndromic status were analyzed in the context of measured ICP by using multiple linear regression.

RESULTS

Fifty patients met the inclusion criteria. Age at procedure (p = 0.028, β = +0.060 mm Hg/month) and multiple-suture involvement (p = 0.010, β = +4.175 mm Hg if multisuture) were both significantly implicated in elevated ICP. The actual number of major sutures involved was significantly correlated to ICP (p = 0.001; β = +1.687 mm Hg/suture). Among patients with single-suture involvement, there was an overall significant difference of median ICP across the suture types (p = 0.008), with metopic having the lowest (12.5 mm Hg) and sagittal having the highest (16.0 mm Hg). Patients with multiple-suture involvement had significantly higher ICP (p = 0.003; 18.5 mm Hg). Patients with craniofacial syndromes were 79.3 times more likely to have multiple-suture involvement (p < 0.001). Corrective surgery for craniosynostosis demonstrated significant intraoperative reduction of elevated ICP (all p < 0.050).

CONCLUSIONS

Syndromic status, older age at intervention for craniosynostosis, and multiple premature fusion of cranial sutures were associated with significantly higher ICP.

How We See Area and Why It Matters

A large and growing literature examines how we see the visual quantities of number, area, and density. The literature rests on an untested assumption: that our perception of area is veridical. Here, we discuss a systematic distortion of perceived area and its implications for quantity perception more broadly.

A tail's tale: Biomechanical roles of dorsal thoracic spine of barnacle nauplii

Many marine invertebrates have complex life histories that begin with a planktonic larval stage. Similar to other plankton, these larval invertebrates often possess protruding body extensions, but their function beyond predator deterrence is not well-documented. For example, the planktonic nauplii of crustaceans have spines. Using the epibiotic pedunculate barnacle Octolasmis spp., we investigated how the dorsal thoracic spine affects swimming and fluid disturbance by comparing nauplii with their spines partially removed against those with intact spines. Our motion analysis showed that amputated Octolasmis spp. swam slower, in jerkier trajectories, and were less efficient per stroke cycle than those with intact spines. Amputees showed alterations in limb beat pattern: larger beat amplitude, increased phase lag, and reduced contralateral symmetry. These changes might partially help increase propulsive force generation and streamline the flow, but were insufficient to restore full function. Particle image velocimetry further showed that amputees had a larger relative area of influence, implying elevated risk by rheotactic predator. Body extensions and their interactions with limb motion play important biomechanical roles in shaping larval performance, which likely influences the evolution of form.

The Evolutionary History of Brains for Numbers

Humans and other animals share a number sense', an intuitive understanding of countable quantities. Having evolved independent from one another for hundreds of millions of years, the brains of these diverse species, including monkeys, crows, zebrafishes, bees, and squids, differ radically. However, in all vertebrates investigated, the pallium of the telencephalon has been implicated in number processing. This suggests that properties of the telencephalon make it ideally suited to host number representations that evolved by convergent evolution as a result of common selection pressures. In addition, promising candidate regions in the brains of invertebrates, such as insects, spiders, and cephalopods, can be identified, opening the possibility of even deeper commonalities for number sense.

Numerosities and Other Magnitudes in the Brains: A Comparative View

The ability to represent, discriminate, and perform arithmetic operations on discrete quantities (numerosities) has been documented in a variety of species of different taxonomic groups, both vertebrates and invertebrates. We do not know, however, to what extent similarity in behavioral data corresponds to basic similarity in underlying neural mechanisms. Here, we review evidence for magnitude representation, both discrete (countable) and continuous, following the sensory input path from primary sensory systems to associative pallial territories in the vertebrate brains. We also speculate on possible underlying mechanisms in invertebrate brains and on the role played by modeling with artificial neural networks. This may provide a general overview on the nervous system involvement in approximating quantity in different animal species, and a general theoretical framework to future comparative studies on the neurobiology of number cognition.

Neuronal Correlates of Small Animal Phobia in Human Subjects through fMRI: The Role of the Number and Proximity of Stimuli

Brain regions involved in small-animal phobia include subcortical and cortical areas. The present study explored the neuronal correlates of small-animal phobia through fMRI data to determine whether a manipulation of number and proximity parameters affects the neurobiology of the processing of feared stimuli. The participants were 40 individuals with phobia and 40 individuals without phobia (28.7% male and 71.3% female). They watched videos of real and virtual images of spiders, cockroaches and lizards in motion presented more or less nearby with one or three stimuli in the different conditions. The results suggested a differential brain activity between participants with and without phobia depending on the proximity and number of phobic stimuli. Proximity activated the motor response marked by the precentral gyrus and the cingulate gyrus. By contrast, the number of stimuli was associated with significant sensory activity in the postcentral gyrus and ventromedial prefrontal cortex. We also observed a greater activity in the occipital cortex when exploring the number compared to the proximity factor. Threatening stimuli presented nearby and those presented in greater numbers generated an intense phobic response, suggesting a different emotion regulation strategy. Based on these findings, exposure therapies might consider including proximity to the threat and number of stimuli as key factors in treatment.

Neural state space alignment for magnitude generalization in humans and recurrent networks

A prerequisite for intelligent behavior is to understand how stimuli are related and to generalize this knowledge across contexts. Generalization can be challenging when relational patterns are shared across contexts but exist on different physical scales. Here, we studied neural representations in humans and recurrent neural networks performing a magnitude comparison task, for which it was advantageous to generalize concepts of "more" or "less" between contexts. Using multivariate analysis of human brain signals and of neural network hidden unit activity, we observed that both systems developed parallel neural "number lines" for each context. In both model systems, these number state spaces were aligned in a way that explicitly facilitated generalization of relational concepts (more and less). These findings suggest a previously overlooked role for neural normalization in supporting transfer of a simple form of abstract relational knowledge (magnitude) in humans and machine learning systems.

Starting small: exploring the origins of successor function knowledge

Although most U. S. children can accurately count sets by 4 years of age, many fail to understand the structural analogy between counting and number - that adding 1 to a set corresponds to counting up 1 word in the count list. While children are theorized to establish this Structure Mapping coincident with learning how counting is used to generate sets, they initially have an item-based understanding of this relationship, and can infer that, e.g, adding 1 to "five" is "six", while failing to infer that, e.g., adding 1 to "twenty-five" is "twenty-six" despite being able to recite these numbers when counting aloud. The item-specific nature of children's successes in reasoning about the relationship between changes in cardinality and the count list raises the possibility that such a Structure Mapping emerges later in development, and that this ability does not initially depend on learning to count. We test this hypothesis in two experiments and find evidence that children can perform item-based addition operations before they become competent counters. Even after children learn to count, we find that their ability to perform addition operations remains item-based and restricted to very small numbers, rather than drawing on generalized knowledge of how the count list represents number. We discuss how these early item-based associations between number words and sets might play a role in constructing a generalized Structure Mapping between counting and quantity.

Primary Cognitive Categories Are Determined by Their Invariances

The world as we perceive it is structured into objects, actions and places that form parts of events. In this article, my aim is to explain why these categories are cognitively primary. From an empiricist and evolutionary standpoint, it is argued that the reduction of the complexity of sensory signals is based on the brain's capacity to identify various types of invariances that are evolutionarily relevant for the activities of the organism. The first aim of the article is to explain why places, object and actions are primary cognitive categories in our constructions of the external world. It is shown that the invariances that determine these categories have their separate characteristics and that they are, by and large, independent of each other. This separation is supported by what is known about the neural mechanisms. The second aim is to show that the category of events can be analyzed as being constituted of the primary categories. The category of numbers is briefly discussed. Some implications for computational models of the categories are also presented.

Numeral Systems Across Languages Support Efficient Communication: From Approximate Numerosity to Recursion

Languages differ qualitatively in their numeral systems. At one extreme, some languages have a small set of number terms, which denote approximate or inexact numerosities; at the other extreme, many languages have forms for exact numerosities over a very large range, through a recursively defined counting system. Why do numeral systems vary as they do? Here, we use computational analyses to explore the numeral systems of 30 languages that span this spectrum. We find that these numeral systems all reflect a functional need for efficient communication, mirroring existing arguments in other semantic domains such as color, kinship, and space. Our findings suggest that cross-language variation in numeral systems may be understood in terms of a shared functional need to communicate precisely while using minimal cognitive resources.

An innovative method for the selection of inhibitors of the viral spike-glycoprotein of the SARS-CoV

This paper has developed and described a detailed method for selecting inhibitors based on modified natural peptides for the SARS-CoV BJ01 spike-glycoprotein. The selection of inhibitors is carried out by increasing the affinity of the peptide to the active center of the protein. This paper also provides a step-by-step algorithm for analyzing the affinity of protein interactions and presents an analysis of energy interactions between the active center of a protein and the wild-type peptide interacting with it, taking into account modifications of the latter. A description of the software package that implements the presented algorithm is given on the website https://binomlabs.com/covid19.

Estimated Number of Acupuncture Practitioners in Mainland China in 2018: Multiperspectives

Background and Objective: Acupuncture and Oriental medicine are widespread, practiced in >183 countries and regions. As such, it has played an important role in the world health care system. However, there are no official statistics available on the number of acupuncture practitioners in China. The aim of this study is to calculate the number ranges of acupuncture practitioners in China in 2018. Materials and Methods: In total, 33.708 million was used as the total number of patient visits for acupuncture in 2018 in China. This number was calculated using the data released by the National Administration of Traditional Chinese Medicine (China), in which the average daily workload of all acupuncture practitioners in China was 134,832 patient visits. Acupuncture practitioners in China are part of Chinese Medicine doctors (CMDs) at the physician level, called "acupuncture doctors." This number 134,832 was divided by the workload of a single doctor of acupuncture, which was 19.4 or 7.0 patient visits per day. These numbers were from a survey by the authors. There are also the numbers 16.0 or 9.4 patient visits per day; these numbers were calculated from the salary level of acupuncture practitioners at 10,000 Yuan per month (providing the doctor's net income was 30% or 50% in his/her gross income). From these 2 sources, the authors then obtained 2 sets of ranges of acupuncture practitioners in China in 2018. There were 9,927 CMDs in 49 big hospitals, of which 619 were acupuncture practitioners; the ratio of acupuncture practitioners to the whole of all CMDs was 6.23%. Using this ratio multiplied by the whole number of CMDs in 2018, then the number of acupuncture practitioners in China in 2018 could be obtained as well. Results: Calculating based on the workload, the range of acupuncture practitioners in China in 2018 was from 6,950 to 19,262. Calculating based on the salary level, the range was 10,618 to 17,697. Calculating based on the ratio of the number of acupuncture practitioners to the whole population of CMDs, the number was 28,360. Conclusions: The reasonable range of acupuncture practitioners in China in 2018 was 10,618 to 17,697, with a median of 14,157. Considering that some acupuncture practitioners are also engaged in teaching, research, and management, the mentioned number is enlarged by 30% to produce 18,404, which would be reasonable. It was also concluded that the density of acupuncture practitioners was 1.31 per 100,000 residents.

Understanding development requires assessing the relevant environment: Examples from mathematics learning

Although almost everyone agrees that the environment shapes children's learning, surprisingly few studies assess in detail the specific environments that shape children's learning of specific content. The present article briefly reviews examples of how such environmental assessments have improved understanding of child development in diverse areas, and examines in depth the contributions of analyses of one type of environment to one type of learning: how biased distributions of problems in mathematics textbooks influence children's learning of fraction arithmetic. We find extensive parallels between types of problems that are rarely presented in US textbooks and problems where children in the US encounter greater difficulty than might be expected from the apparent difficulty of the procedures involved. We also consider how some children master fraction arithmetic despite also learning the textbook distributions. Finally, we present findings from a recent intervention that indicates how children's fraction learning can be improved.

A left visual advantage for quantity processing in neonates

Forty-eight newborn infants were tested in one of three multimodal stimulus conditions, in which auditory quantities were presented alongside visual object arrays in two test trials. These tests varied with respect to which side (either left or right) numerically matched the auditory number. The infants looked longer to the test trials in which the left side of the visual display exhibited a quantity that matched the presented auditory quantity. This study provides the first evidence for an untrained, innate bias for humans to preferentially process quantity information presented in the left field of vision.

Optimal number of harvested lymph nodes for curatively resected gallbladder adenocarcinoma based on a Bayesian network model

BACKGROUND AND OBJECTIVES

To identify the optimal range and the minimum number of lymph nodes (LNs) to be examined to maximize survival time of patients with curatively resected gallbladder adenocarcinoma (GBAC).

METHODS

Data were collected from the surveillance, epidemiology, and end results database on patients with GBAC who underwent curative resection between 2004 and 2015. A Bayesian network (BN) model was constructed to identify the optimal range of harvested LNs. Model accuracy was evaluated using the confusion matrix and receiver operating characteristic (ROC) curve.

RESULTS

A total of 1268 patients were enrolled in this study. Accuracy of the BN model was 72.82%, and the area under the curve of the ROC for the testing dataset was 78.49%. We found that at least seven LNs should be harvested to maximize survival time, and that the optimal count of harvested LNs was in the range of 7 to 10 overall, with an optimal range of 10 to 11 for N+ patients, 7 to 10 for stage T1-T2 patients, and 7 to 11 for stage T3-T4 patients.

CONCLUSIONS

According to a BN model, at least seven LNs should be retrieved for GBAC with curative resection, with an overall optimal range of 7 to 10 harvested LNs.

Basic quantitative morphological methods applied to the central nervous system

Generating numbers has become an almost inevitable task associated with studies of the morphology of the nervous system. Numbers serve a desire for clarity and objectivity in the presentation of results and are a prerequisite for the statistical evaluation of experimental outcomes. Clarity, objectivity, and statistics make demands on the quality of the numbers that are not met by many methods. This review provides a refresher of problems associated with generating numbers that describe the nervous system in terms of the volumes, surfaces, lengths, and numbers of its components. An important aim is to provide comprehensible descriptions of the methods that address these problems. Collectively known as design‐based stereology, these methods share two features critical to their application. First, they are firmly based in mathematics and its proofs. Second and critically underemphasized, an understanding of their mathematical background is not necessary for their informed and productive application. Understanding and applying estimators of volume, surface, length or number does not require more of an organizational mastermind than an immunohistochemical protocol. And when it comes to calculations, square roots are the gravest challenges to overcome. Sampling strategies that are combined with stereological probes are efficient and allow a rational assessment if the numbers that have been generated are “good enough.” Much may be unfamiliar, but very little is difficult. These methods can no longer be scapegoats for discrepant results but faithfully produce numbers on the material that is assessed. They also faithfully reflect problems that associated with the histological material and the anatomically informed decisions needed to generate numbers that are not only valid in theory. It is within reach to generate practically useful numbers that must integrate with qualitative knowledge to understand the function of neural systems.

What is the ideal number of biopsy cores per lesion in targeted prostate biopsy?

Background

The number of cores to be obtained in targeted biopsy (TB) is important. This study aimed to evaluate the TB outcomes in suspicious prostate lesions classified according to the Prostate Imaging Reporting and Data System (PI-RADS) and to determine the ideal number of biopsy cores per lesion.

Methods

This retrospective study included patients who underwent multiparametric magnetic resonance imaging–guided fusion prostate biopsy owing to increased serum prostate-specific antigen (PSA) levels and suspicious digital rectal examination outcomes in our institute. Patients with PI-RADS <3 lesions, PSA levels >10 ng/ml, and a prior diagnosis of prostate cancer (PCa) (active surveillance) were excluded from the study. The number of biopsy cores to be obtained from each lesion was determined by the clinician.

Results

The study included a total of 418 patients and 684 lesions. Among PI-RADS 3 lesions, clinically significant PCa (sPCa) detection rate was similar in the lesions from which 2 and 3 cores were obtained (9.1% and 10.0%, respectively), whereas it was relatively higher in the lesions from which 4 biopsy cores were obtained (18.5%). Among PI-RADS 4 lesions, sPCa detection rate was similar in the lesions from which 3 and 4 cores were obtained (35.6% and 32.3%, respectively), whereas it was relatively lower in the lesions from which 2 biopsy cores were obtained (17.9%). Among PI-RADS 5 lesions, however, sPCa detection rate was similar in the lesions from which 2, 3, or 4 cores were obtained (47.6%, 46.0%, 48.9%, respectively).

Conclusion

The results indicated that the ideal number of cores to be obtained from each suspicious lesion in TB depends on the characteristics of the lesions. Accordingly, while obtaining 2–3 biopsy cores could be adequate in PI-RADS 4 and 5 lesions, which have a serious risk of cancer, a minimum of 4 biopsy cores should be obtained from PI-RADS 3 lesions to ensure accurate histopathological results.

Clinical trial number (ClinicalTrials.gov)NCT03936296.

Why do we need to regulate autophagy (and how can we do it)? A cartoon depiction

In a recent issue of this journal I attempted to explain the purpose of macroautophagy/autophagy to a non-specialist audience through the use of cartoons. In the present article, I am continuing this approach by considering the topic of autophagy regulation-why does the cell need to modulate the autophagic response, and what are the basic morphological mechanisms that can be used to attain different levels of autophagy activity?

Ontogenetic Origins of Human Integer Representations

Do children learn number words by associating them with perceptual magnitudes? Recent studies argue that approximate numerical magnitudes play a foundational role in the development of integer concepts. Against this, we argue that approximate number representations fail both empirically and in principle to provide the content required of integer concepts. Instead, we suggest that children's understanding of integer concepts proceeds in two phases. In the first phase, children learn small exact number word meanings by associating words with small sets. In the second phase, children learn the meanings of larger number words by mastering the logic of exact counting algorithms, which implement the successor function and Hume's principle (that one-to-one correspondence guarantees exact equality). In neither phase do approximate number representations play a foundational role.

An Insect's Sense of Number

Recent studies revealed numerosity judgments in bees, which include the concept of zero, subtraction and addition, and matching symbols to numbers. Despite their distant origins, bees and vertebrates share similarities in their numeric competences, thus suggesting that numerosity is evolutionary conserved and can be implemented in miniature brains without neocortex.

The Attractions of Agreement: Why Person Is Different

This paper establishes the generalization that whenever agreement with the finite verb is controlled by a constituent that is not in a Spec–Head relation with the inflectional head of the clause, this agreement cannot affect person. A syntactic representation for person inside the noun phrase and on the clausal spine is proposed which, in conjunction with the workings of agreement and concord, accommodates this empirical generalization and derives Baker’s Structural Condition on Person Agreement. The proposal also provides an explanation for the φ-feature agreement facts of specificational copular sentences. The paper places its findings on person vs. number agreement in the context of recent psycho- and neuro-linguistic investigation of number/person dissociation.

Symbolic representation of numerosity by honeybees ( Apis mellifera): matching characters to small quantities

The assignment of a symbolic representation to a specific numerosity is a fundamental requirement for humans solving complex mathematical calculations used in diverse applications such as algebra, accounting, physics and everyday commerce. Here we show that honeybees are able to learn to match a sign to a numerosity, or a numerosity to a sign, and subsequently transfer this knowledge to novel numerosity stimuli changed in colour properties, shape and configuration. While honeybees learned the associations between two quantities (two; three) and two signs (N-shape; inverted T-shape), they failed at reversing their specific task of sign-to-numerosity matching to numerosity-to-sign matching and vice versa (i.e. a honeybee that learned to match a sign to a number of elements was not able to invert this learning to match the numerosity of elements to a sign). Thus, while bees could learn the association between a symbol and numerosity, it was linked to the specific task and bees could not spontaneously extrapolate the association to a novel, reversed task. Our study therefore reveals that the basic requirement for numerical symbolic representation can be fulfilled by an insect brain, suggesting that the absence of its spontaneous emergence in animals is not due to cognitive limitation.

Plural Conjuncts and Syncretism Facilitate Gender Agreement in Serbo-Croatian:Experimental Evidence

The literature on agreement in South Slavic generalizes that conjunct agreement in gender is only possible when all conjuncts are plural (e.g., Bošković, 2009). Marušič et al. (2015) and Arsenijević and Mitić (2016a,b) attest a significant level of patterns contradicting this claim in elicited production experiments. They weaken the earlier generalization to a facilitating role of plural number for conjunct agreement in gender. However, the stimuli in the two respective experiments involve syncretism between the members of conjunction. The syncretism removes the possibility - at Phonological Form at least - that by agreeing with one conjunct, the verb disagrees with the other. It is hence expected to result in a similar surface effect as the facilitation by plurals, which makes it a potential confound variable. We report and discuss the results of an experiment aimed to test both the effect of syncretism and the reality of the facilitating effects of plural number. The results of the experiment yield positive answers to both questions: syncretism is a facilitating factor, but plural number nevertheless has its facilitating effect too - as confirmed by the stimuli without syncretism. Since syncretism is a phenomenon in which phonological information plays a central role, our findings support syntactic models of agreement which extend to the interface with phonology. Moreover, our results reveal a double similarity of conjunct agreement with agreement attraction, in both showing a (stronger) attraction effect of plural number compared to singular, and in being sensitive to syncretism (cf. Badecker and Kuminiak, 2007; Malko and Slioussar, 2013; i.e., Bader and Meng, 2002; Hartsuiker et al., 2003; Slioussar, 2018).

Processing Differences Between Person and Number: A Theoretical Interpretation

The literature on processing of person and number agreement contains some apparently contradictory results. On the one hand, some ERP studies do not find a qualitative difference between person and number when an agreeing verb does not match the features of its subject, the controller of the agreement relation (Silva-Pereyra and Carreiras, 2007; Zawiszewski et al., 2016). On the other hand, an ERP study reported in Mancini et al. (2011b) did find a qualitative difference between agreement violations in person and agreement violations in number, a result further corroborated by an fMRI study reported in Mancini et al. (2017). At the same time, there is also a trend on which the literature appears to agree: on the whole the response to agreement violations in person is stronger than the response to number agreement violations. In this paper we argue that the constellation of reported results can be accounted for by adopting a theory of person and number features that has the following two core properties: (i) pronouns are specified for both person and number, but regular NPs are specified for number only and do not carry any person specification; (ii) all of first, second and third person are characterized by one or more person features, whereas, in contrast, one of the numbers (singular) corresponds to the absence of number features.

Relation between the number of board-certified gynecologic oncologists per hospital and survival of cervical cancer

AIMS

In cancer therapy, choice of treatment method has a tremendous influence on patient prognosis. We aimed to evaluate the impact of the number of Gynecologic Oncology (GO) Specialists on treatment outcomes of cervical cancer patients.

METHODS

We used data for 5-year treatment outcomes obtained from the annual treatment reports of the Gynecologic Oncology Committee of Japan Society of Obstetrics and Gynecology (JSOG). We compared this to data posted on the Japanese Society of Gynecologic Oncology (JSGO) website regarding the enrollment of GO Specialists at each hospital.

RESULTS

The 5-year survival ratio of cervical cancer patients treated in hospitals with 2-or-more GO Specialists was 79.0% (2010/2543). This was significantly higher than 75.4% (974/1292) for facilities with 0 or 1 specialist (P = 0.011); however, the number of GO Specialists was not an independent prognostic factor (P = 0.77, adjusted HR: 1.13 [0.38-2.03]). The 5-year survival ratio significantly increased in medical facilities whose number of GO Specialists increased from 0 to 1 or more, or from 1 to 2 or more (P = 0.045).

CONCLUSION

This study demonstrates a causal relationship between the numbers of GO Specialists and treatment outcomes of cervical cancer patients for the first time. Our study suggests that although JSGO board-certified gynecologic oncologists do clearly contribute to improving treatment outcome, the number of specialists was not an independent factor for improving the prognosis of the patients. Thus, it was not clear whether simply increasing the number of GO Specialists, beyond two, will lead to any significant improvement in cervical cancer patient prognosis.

Electrophysiological markers of poor versus superior math abilities in healthy individuals

Interindividual differences in the numerical ability of healthy adults have been previously demonstrated, mainly with tasks involving mental number line or size representation. However, electrophysiological correlates of superior versus poor arithmetic ability (in the healthy population) have been scarcely investigated. We correlated electric potentials with math performance in 13 skilled and 13 poor calculators selected from a sample of 41 graduate students on the basis of their poor or superior math abilities assessed through a timed test. EEG was recorded from 128 channels while participants solved 352 arithmetical operations (additions, subtractions, multiplications, divisions) and decided whether the provided solution was correct or incorrect. Overall skilled individuals correctly solved a higher number of operations than poor calculators and had faster response times. Consistently, the latency of fronto-central P300 component of event-related potentials (ERPs) peaked earlier in the skilled than poor group. The P300 was larger in amplitude to correct than incorrect solutions, but just in the skilled group, with a tendency found in poor calculators. Spearman's ρ correlation coefficient analyses showed that the larger P300 response was to correct arithmetic solutions, the better the performance; conversely, the larger the P300 amplitude was to incorrect solutions, the worse the performance. The results suggest that poor calculators had a less clear representation of arithmetic solutions and difficulty in quickly accessing it. This study provides a standard method for directly investigating math abilities throughout ERP recordings that could be useful for assessing acalculia/dyscalculia in the clinical population (children, elderly, brain-damaged patients).

Development of a Possible General Magnitude System for Number and Space

There is strong evidence for a link between numerical and spatial processing. However, whether this association is based on a common general magnitude system is far from conclusive and the impact of development is not yet known. Hence, the present study aimed to investigate the association between discrete non-symbolic number processing (comparison of dot arrays) and continuous spatial processing (comparison of angle sizes) in children between the third and sixth grade (N = 367). Present findings suggest that the processing of comparisons of number of dots or angle are related to each other, but with angle processing developing earlier and being more easily comparable than discrete number representations for children of this age range. Accordingly, results favor the existence of a more complex underlying magnitude system consisting of dissociated but closely interacting representations for continuous and discrete magnitudes.

Computing Value from Quality and Quantity in Human Decision-Making

How organisms learn the value of single stimuli through experience is well described. In many decisions, however, value estimates are computed “on the fly” by combining multiple stimulus attributes. The neural basis of this computation is poorly understood. Here we explore a common scenario in which decision-makers must combine information about quality and quantity to determine the best option. Using fMRI, we examined the neural representation of quality, quantity, and their integration into an integrated subjective value signal in humans of both genders. We found that activity within inferior frontal gyrus (IFG) correlated with offer quality, while activity in the intraparietal sulcus (IPS) specifically correlated with offer quantity. Several brain regions, including the anterior cingulate cortex (ACC), were sensitive to an interaction of quality and quantity. However, the ACC was uniquely activated by quality, quantity, and their interaction, suggesting that this region provides a substrate for flexible computation of value from both quality and quantity. Furthermore, ACC signals across subjects correlated with the strength of quality and quantity signals in IFG and IPS, respectively. ACC tracking of subjective value also correlated with choice predictability. Finally, activity in the ACC was elevated for choice trials, suggesting that ACC provides a nexus for the computation of subjective value in multiattribute decision-making.

SIGNIFICANCE STATEMENT Would you prefer three apples or two oranges? Many choices we make each day require us to weigh up the quality and quantity of different outcomes. Using fMRI, we show that option quality is selectively represented in the inferior frontal gyrus, while option quantity correlates with areas of the intraparietal sulcus that have previously been associated with numerical processing. We show that information about the two is integrated into a value signal in the anterior cingulate cortex, and the fidelity of this integration predicts choice predictability. Our results demonstrate how on-the-fly value estimates are computed from multiple attributes in human value-based decision-making.

Evolution of cognitive and neural solutions enabling numerosity judgements: lessons from primates and corvids

Brains that are capable of representing numerosity, the number of items in a set, have arisen repeatedly and independently in different animal taxa. This review compares the cognitive and physiological mechanisms found in a nonhuman primate, the rhesus macaque, and a corvid songbird, the carrion crow, in order to elucidate the evolutionary adaptations underlying numerical competence. Monkeys and corvids are known for their advanced cognitive competence, despite them both having independently and distinctly evolved endbrains that resulted from a long history of parallel evolution. In both species, numerosity is represented as an analogue magnitude by an approximate number system that obeys the Weber-Fechner Law. In addition, the activity of numerosity-selective neurons in the fronto-parietal association cortex of monkeys and the telencephalic associative area nidopallium caudolaterale of crows mirrors the animals' performance. In both species' brains, neuronal activity is tuned to a preferred numerosity, encodes the numerical value in an approximate fashion, and is best represented on a logarithmic scale. Collectively, the data show an impressive correspondence of the cognitive and neuronal mechanisms for numerosity representations across monkeys and crows. This suggests that remotely related vertebrates with distinctly developed endbrains adopted similar physiological solutions to common computational problems in numerosity processing.This article is part of a discussion meeting issue 'The origins of numerical abilities'.

Is There Really an Evolved Capacity for Number?

Humans and other species have biologically endowed abilities for discriminating quantities. A widely accepted view sees such abilities as an evolved capacity specific for number and arithmetic. This view, however, is based on an implicit teleological rationale, builds on inaccurate conceptions of biological evolution, downplays human data from non-industrialized cultures, overinterprets results from trained animals, and is enabled by loose terminology that facilitates teleological argumentation. A distinction between quantical (e.g., quantity discrimination) and numerical (exact, symbolic) cognition is needed: quantical cognition provides biologically evolved preconditions for numerical cognition but it does not scale up to number and arithmetic, which require cultural mediation. The argument has implications for debates about the origins of other special capacities - geometry, music, art, and language.

An Introduction to the Approximate Number System

What are young children's first intuitions about numbers and what role do these play in their later understanding of mathematics? Traditionally, number has been viewed as a culturally derived breakthrough occurring relatively recently in human history that requires years of education to master. Contrary to this view, research in cognitive development indicates that our minds come equipped with a rich and flexible sense of number-the Approximate Number System (ANS). Recently, several major challenges have been mounted to the existence of the ANS and its value as a domain-specific system for representing number. In this article, we review five questions related to the ANS (what, who, why, where, and how) to argue that the ANS is defined by key behavioral and neural signatures, operates independently from nonnumeric dimensions such as time and space, and is used for a variety of functions (including formal mathematics) throughout life. We identify research questions that help elucidate the nature of the ANS and the role it plays in shaping children's earliest understanding of the world around them.

Neurons in the Endbrain of Numerically Naive Crows Spontaneously Encode Visual Numerosity

Endowed with an elaborate cerebral cortex, humans and other primates can assess the number of items in a set, or numerosity, from birth on [1] and without being trained [2]. Whether spontaneous numerosity extraction is a unique feat of the mammalian cerebral cortex [3-7] or rather an adaptive property that can be found in differently designed and independently evolved neural substrates, such as the avian enbrain [8], is unknown. To address this question, we recorded single-cell activity from the nidopallium caudolaterale (NCL), a high-level avian association brain area [9-11], of numerically naive crows. We found that a proportion of NCL neurons were spontaneously responsive to numerosity and tuned to the number of items, even though the crows were never trained to assess numerical quantity. Our data show that numerosity-selective neuronal responses are spontaneously present in the distinct endbrains of diverge vertebrate taxa. This seemingly hard-wired property of the avian endbrain to extract numerical quantity explains how birds in the wild, or right after hatching, can exploit numerical cues when making foraging or social decisions. It suggests that endbrain circuitries that evolved based on convergent evolution, such as the avian endbrain, give rise to the same numerosity code.

Cognitive Development Is a Reconstruction Process that May Follow Different Pathways: The Case of Number

Some cognitive functions shared by humans and certain animals were acquired early in the course of phylogeny and, in humans, are operational in their primitive form shortly after birth. This is the case for the quantification of discrete objects. The further phylogenetic evolution of the human brain allows such functions to be reconstructed in a much more sophisticated way during child development. Certain functional characteristics of the brain (plasticity, multiple cognitive processes involved in the same response, interactions, and substitution relationships between those processes) provide degrees of freedom that open up the possibility of different pathways of reconstruction. The within- and between-individual variability of these developmental pathways offers an original window on the dynamics of development. Here, I will illustrate this theoretical approach to cognitive development-which can be called "reconstructivist" and "pluralistic"-using children's construction of number as an example.