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Concept: Real number


Human infants in the first year of life possess an intuitive sense of number. This preverbal number sense may serve as a developmental building block for the uniquely human capacity for mathematics. In support of this idea, several studies have demonstrated that nonverbal number sense is correlated with mathematical abilities in children and adults. However, there has been no direct evidence that infant numerical abilities are related to mathematical abilities later in childhood. Here, we provide evidence that preverbal number sense in infancy predicts mathematical abilities in preschool-aged children. Numerical preference scores at 6 months of age correlated with both standardized math test scores and nonsymbolic number comparison scores at 3.5 years of age, suggesting that preverbal number sense facilitates the acquisition of numerical symbols and mathematical abilities. This relationship held even after controlling for general intelligence, indicating that preverbal number sense imparts a unique contribution to mathematical ability. These results validate the many prior studies purporting to show number sense in infancy and support the hypothesis that mathematics is built upon an intuitive sense of number that predates language.

Concepts: Infant, Mathematics, Number, Real number, Set theory, Natural number, Infinity, Arithmetic


Direct-to-consumer trackers and devices have potential to enhance theory-based physical activity interventions by offering a simple and pleasant way to help participants self-monitor their behavior. A secondary benefit of these devices is the opportunity for investigators to objectively track adherence to physical activity goals across weeks or even months, rather than relying on self-report or a small number of accelerometry wear periods. The use of consumer trackers for continuous monitoring of adherence has considerable potential to enhance physical activity research, but few studies have been published in this rapidly developing area.

Concepts: Cancer, Obesity, Physical exercise, Overweight, Menstrual cycle, Real number, Intervention, The Opportunity


We present a case with outspoken spontaneous vestibular schwannoma shrinkage and review the related literature. The patient was initially diagnosed with a left-sided, intrameatal vestibular schwannoma, which subsequently grew into the cerebello-pontine angle (CPA), followed by total shrinkage of the CPA component without any intervention over a 12-year observation period. The literature on spontaneous tumor shrinkage was retrieved by searching the subject terms “vestibular schwannoma, conservative management” in PubMed/MEDLINE database, without a time limit. Of the published data, the articles on “shrinkage” or “negative growth” or “regression” or “involution” of the tumor were selected, and the contents on the rate, extent and mechanism of spontaneous tumor shrinkage were extracted and reviewed. The reported rate of spontaneous shrinkage of vestibular schwannoma is 5-10% of patients managed conservatively. Extreme shrinkage of the tumor may occur spontaneously.

Concepts: Time, Patient, Subject, Real number, Conservatism, Schwannoma, Limit superior and limit inferior, Spontaneous human combustion


A number of centrality measures are available to determine the relative importance of a node in a complex network, and betweenness is prominent among them. However, the existing centrality measures are not adequate in network percolation scenarios (such as during infection transmission in a social network of individuals, spreading of computer viruses on computer networks, or transmission of disease over a network of towns) because they do not account for the changing percolation states of individual nodes. We propose a new measure, percolation centrality, that quantifies relative impact of nodes based on their topological connectivity, as well as their percolation states. The measure can be extended to include random walk based definitions, and its computational complexity is shown to be of the same order as that of betweenness centrality. We demonstrate the usage of percolation centrality by applying it to a canonical network as well as simulated and real world scale-free and random networks.

Concepts: Algorithm, Real number, Graph theory, Networks, Computational complexity theory, Social network, Centrality, Network topology


Current accounts of spatial cognition and human-object interaction suggest that the representation of peripersonal space depends on an action-specific system that remaps its representation according to action requirements. Here we demonstrate that this mechanism is sensitive to knowledge about properties of objects. In two experiments we explored the interaction between physical distance and object attributes (functionality, desirability, graspability, etc.) through a reaching estimation task in which participants indicated if objects were near enough to be reached. Using both a real and a cutting-edge digital scenario, we demonstrate that perceived reaching distance is influenced by ease of grasp and the affective valence of an object. Objects with a positive affective valence tend to be perceived reachable at locations at which neutral or negative objects are perceived as non-reachable. In addition to this, reaction time to distant (non-reachable) positive objects suggests a bias to perceive positive objects as closer than negative and neutral objects (exp. 2). These results highlight the importance of the affective valence of objects in the action-specific mapping of the peripersonal/extrapersonal space system.

Concepts: Time, Psychology, Cognition, Mind, Space, Real number, Graph theory, Metaphysics


The present study examined the validity of psychometrically assessed positive and negative schizotypy in a study of 214 Spanish young adults using interview and questionnaire measures of impairment and psychopathology. Schizotypy provides a useful construct for understanding the etiology and development of schizophrenia and related disorders. Recent interview, laboratory, and experience sampling studies have supported the validity of psychometrically assessed positive and negative symptom dimensions. The present study expands on previous findings by examining the validity of these dimensions in a Spanish sample and employing a widely used interview measure of the schizophrenia prodrome. As hypothesized, the positive schizotypy dimension predicted CAARMS ultra high-risk or psychosis threshold status, and both dimensions uniquely predicted the presence of schizophrenia-spectrum personality disorders. Furthermore, positive schizotypy was associated with psychotic-like, paranoid, schizotypal, and mood symptoms, whereas negative schizotypy was associated with interview ratings of negative and schizoid symptoms. The schizotypy dimensions were also distinguished by their associations with self and other schemas. Positive schizotypy was associated with increased negative self and other schemas, whereas negative schizotypy was associated with decreased positive self and other schemas. The findings provide further construct validation of positive and negative schizotypy and support these dimensions as universal constructs.

Concepts: Real number, Schizophrenia, Psychosis, Delusion, Schizoid personality disorder, Schizotypal personality disorder, Schizotypy, Prodrome


Transcranial direct current stimulation (tDCS) is an innovative method to explore the causal structure-function relationship of brain areas. We investigated the specificity of bilateral bi-cephalic tDCS with two active electrodes of the same polarity (e.g., cathodal on both hemispheres) applied to intraparietal cortices bilaterally using a combined between- and within-task approach. Regarding between-task specificity, we observed that bilateral bi-cephalic tDCS affected a numerical (mental addition) but not a control task (colour word Stroop), indicating a specific influence of tDCS on numerical but not on domain general cognitive processes associated with the bilateral IPS. In particular, the numerical effect of distractor distance was more pronounced under cathodal than under anodal stimulation. Moreover, with respect to within-task specificity we only found the numerical distractor distance effect in mental addition to be modulated by direct current stimulation, whereas the effect of target identity was not affected. This implies a differential influence of bilateral bi-cephalic tDCS on the recruitment of different processing components within the same task (number magnitude processing vs. recognition of familiarity). In sum, this first successful application of bilateral bi-cephalic tDCS with two active electrodes of the same polarity in numerical cognition research corroborates the specific proposition of the Triple Code Model that number magnitude information is represented bilaterally in the intraparietal cortices.

Concepts: Psychology, Cognitive psychology, Cognition, Perception, Mind, Real number, Transcranial direct current stimulation, International relations theory


Many real world systems are at risk of undergoing critical transitions, leading to sudden qualitative and sometimes irreversible regime shifts. The development of early warning signals is recognized as a major challenge. Recent progress builds on a mathematical framework in which a real-world system is described by a low-dimensional equation system with a small number of key variables, where the critical transition often corresponds to a bifurcation. Here we show that in high-dimensional systems, containing many variables, we frequently encounter an additional non-bifurcative saddle-type mechanism leading to critical transitions. This generic class of transitions has been missed in the search for early-warnings up to now. In fact, the saddle-type mechanism also applies to low-dimensional systems with saddle-dynamics. Near a saddle a system moves slowly and the state may be perceived as stable over substantial time periods. We develop an early warning sign for the saddle-type transition. We illustrate our results in two network models and epidemiological data. This work thus establishes a connection from critical transitions to networks and an early warning sign for a new type of critical transition. In complex models and big data we anticipate that saddle-transitions will be encountered frequently in the future.

Concepts: Real number, Warning sign


Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic number line task, which required mapping positive and negative numbers on a physical horizontal line, and has been shown to correlate with more advanced numerical abilities and mathematical achievement. We found that mathematicians were more accurate compared with nonmathematicians when mapping positive, but not negative numbers, which are considered numerical primitives and cultural artifacts, respectively. Moreover, performance on positive number mapping could predict whether one is a mathematician or not, and was mediated by more advanced mathematical skills. This finding might suggest a link between basic and advanced mathematical skills. However, when we included visuospatial skills, as measured by block design subtest, the mediation analysis revealed that the relation between the performance in the number line task and the group membership was explained by non-numerical visuospatial skills. These results demonstrate that relation between basic, even specific, numerical skills and advanced mathematical achievement can be artifactual and explained by visuospatial processing. (PsycINFO Database Record

Concepts: Mathematics, Number, Real number, Set theory, 0, Inequality, Numbers, Subtraction


Information routing is one of the main tasks in many complex networks with a communication function. Maps produced by embedding the networks in hyperbolic space can assist this task enabling the implementation of efficient navigation strategies. However, only static maps have been considered so far, while navigation in more realistic situations, where the network structure may vary in time, remains largely unexplored. Here, we analyze the navigability of real networks by using greedy routing in hyperbolic space, where the nodes are subject to a stochastic activation-inactivation dynamics. We find that such dynamics enhances navigability with respect to the static case. Interestingly, there exists an optimal intermediate activation value, which ensures the best trade-off between the increase in the number of successful paths and a limited growth of their length. Contrary to expectations, the enhanced navigability is robust even when the most connected nodes inactivate with very high probability. Finally, our results indicate that some real networks are ultranavigable and remain highly navigable even if the network structure is extremely unsteady. These findings have important implications for the design and evaluation of efficient routing protocols that account for the temporal nature of real complex networks.

Concepts: Mathematics, Real number, Metaphysics, Complex number, Computer network, Social network, RealNetworks, Hyperbolic space