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Concept: Natural 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


We examine the temporal evolution of digital communication activity relating to the American anti-capitalist movement Occupy Wall Street. Using a high-volume sample from the microblogging site Twitter, we investigate changes in Occupy participant engagement, interests, and social connectivity over a fifteen month period starting three months prior to the movement’s first protest action. The results of this analysis indicate that, on Twitter, the Occupy movement tended to elicit participation from a set of highly interconnected users with pre-existing interests in domestic politics and foreign social movements. These users, while highly vocal in the months immediately following the birth of the movement, appear to have lost interest in Occupy related communication over the remainder of the study period.

Concepts: Sociology, Natural number, Integer, Remainder, Social movement, Twitter, ASCII, Activism


We report the enantiospecific total synthesis of (+)-tubingensin A. Our synthesis features an aryne cyclization to efficiently introduce the vicinal quaternary stereocenters of the natural product and proceeds in only 9 steps (longest linear sequence) from known compounds.

Concepts: Total synthesis, Paclitaxel total synthesis, Natural number, Isomorphism, Integer, Partially ordered set, Ordinal number, Well-order


Given a set of points on the plane and an assignment of values to them, an optimal linear partition is a division of the set into two subsets which are separated by a straight line and maximally contrast with each other in the values assigned to their points. We present a method for inspecting and rating all linear partitions of a finite set, and a package of three functions in the R language for executing the computations. One function is for finding the optimal linear partitions and corresponding separating lines, another for graphically representing the results, and a third for testing how well the data comply with the linear separability condition. We illustrate the method on possible data from a psychophysical experiment (concerning the size-weight illusion) and compare its performance with that of linear discriminant analysis and multiple logistic regression, adapted to dividing linearly a set of points on the plane.

Concepts: Logistic regression, Set theory, Natural number, Linear equation, Line, Empty set, Bijection, Basic concepts in set theory


We report a detailed binding study addressing both the thermodynamics and kinetics of binding of a large set of guest molecules - with widely varying properties - to a water-soluble metal-organic M4L6 host. The effects of different guest properties upon binding strength and kinetics are elucidated by a systematic analysis of the binding data through principal component analysis, thus allowing for structure-property relationships to be determined. These insights allowed us to design more complex encapsulation sequences, in which multiple guests, added simultaneously, are bound and released by the host in a time-dependent manner, thus allowing multiple states of the system to be accessed sequentially. Moreover, by inclusion of the pH-sensitive guest pyridine we were able to further extend our control over binding by creating a reversible pH-controlled three-guest sequential binding cycle.

Concepts: Series, Mathematical analysis, Sequence, Principal component analysis, Natural number, Set, Real analysis, Limit of a sequence


Tissues are complex milieus consisting of numerous cell types. Several recent methods have attempted to enumerate cell subsets from transcriptomes. However, the available methods have used limited sources for training and give only a partial portrayal of the full cellular landscape. Here we present xCell, a novel gene signature-based method, and use it to infer 64 immune and stromal cell types. We harmonized 1822 pure human cell type transcriptomes from various sources and employed a curve fitting approach for linear comparison of cell types and introduced a novel spillover compensation technique for separating them. Using extensive in silico analyses and comparison to cytometry immunophenotyping, we show that xCell outperforms other methods. xCell is available at .

Concepts: Cell, Cellular differentiation, Cell type, Natural number


Despite recent discoveries of germline and somatic mutations in melanoma, naevus count remains the most important risk factor for melanoma. Counting naevi on the whole body is time consuming. In order to identify patients at risk for melanoma, many studies have used naevus count on selected body sites as a proxy for total body naevus count.

Concepts: Natural selection, Statistics, Natural number, Dysplastic nevus, Ordinal number


In this paper, the stability problem is studied for a class of stochastic neural networks (NNs) with local impulsive effects. The impulsive effects considered can be not only nonidentical in different dimensions of the system state but also various at distinct impulsive instants. Hence, the impulses here can encompass several typical impulses in NNs. The aim of this paper is to derive stability criteria such that stochastic NNs with local impulsive effects are exponentially stable in mean square. By means of the mathematical induction method, several easy-to-check conditions are obtained to ensure the mean square stability of NNs. Three examples are given to show the effectiveness of the proposed stability criterion.

Concepts: Effect, Dimension, Arithmetic mean, Natural number, Neural network, Cauchy distribution, Mathematical logic, Mathematical proof


The genetic architecture of common traits, including the number, frequency, and effect sizes of inherited variants that contribute to individual risk, has been long debated. Genome-wide association studies have identified scores of common variants associated with type 2 diabetes, but in aggregate, these explain only a fraction of the heritability of this disease. Here, to test the hypothesis that lower-frequency variants explain much of the remainder, the GoT2D and T2D-GENES consortia performed whole-genome sequencing in 2,657 European individuals with and without diabetes, and exome sequencing in 12,940 individuals from five ancestry groups. To increase statistical power, we expanded the sample size via genotyping and imputation in a further 111,548 subjects. Variants associated with type 2 diabetes after sequencing were overwhelmingly common and most fell within regions previously identified by genome-wide association studies. Comprehensive enumeration of sequence variation is necessary to identify functional alleles that provide important clues to disease pathophysiology, but large-scale sequencing does not support the idea that lower-frequency variants have a major role in predisposition to type 2 diabetes.

Concepts: Scientific method, Genetics, Sample size, Diabetes mellitus type 2, Statistical significance, Natural number, Effect size, Statistical power


In humans, the ability to reason about mathematical quantities depends on a frontoparietal network that includes the intraparietal sulcus (IPS). How do nature and nurture give rise to the neurobiology of numerical cognition? We asked how visual experience shapes the neural basis of numerical thinking by studying numerical cognition in congenitally blind individuals. Blind (n = 17) and blindfolded sighted (n = 19) participants solved math equations that varied in difficulty (e.g., 27 - 12 = x vs. 7 - 2 = x), and performed a control sentence comprehension task while undergoing fMRI. Whole-cortex analyses revealed that in both blind and sighted participants, the IPS and dorsolateral prefrontal cortices were more active during the math task than the language task, and activity in the IPS increased parametrically with equation difficulty. Thus, the classic frontoparietal number network is preserved in the total absence of visual experience. However, surprisingly, blind but not sighted individuals additionally recruited a subset of early visual areas during symbolic math calculation. The functional profile of these “visual” regions was identical to that of the IPS in blind but not sighted individuals. Furthermore, in blindness, number-responsive visual cortices exhibited increased functional connectivity with prefrontal and IPS regions that process numbers. We conclude that the frontoparietal number network develops independently of visual experience. In blindness, this number network colonizes parts of deafferented visual cortex. These results suggest that human cortex is highly functionally flexible early in life, and point to frontoparietal input as a mechanism of cross-modal plasticity in blindness.

Concepts: Brain, Mathematics, Cognitive science, Cerebrum, Visual perception, Number, Set theory, Natural number