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Concept: Number


The CDC recommends that healthcare settings provide influenza patients with facemasks as a means of reducing transmission to staff and other patients, and a recent report suggested that surgical masks can capture influenza virus in large droplet spray. However, there is minimal data on influenza virus aerosol shedding, the infectiousness of exhaled aerosols, and none on the impact of facemasks on viral aerosol shedding from patients with seasonal influenza. We collected samples of exhaled particles (one with and one without a facemask) in two size fractions (“coarse”>5 µm, “fine"≤5 µm) from 37 volunteers within 5 days of seasonal influenza onset, measured viral copy number using quantitative RT-PCR, and tested the fine-particle fraction for culturable virus. Fine particles contained 8.8 (95% CI 4.1 to 19) fold more viral copies than did coarse particles. Surgical masks reduced viral copy numbers in the fine fraction by 2.8 fold (95% CI 1.5 to 5.2) and in the coarse fraction by 25 fold (95% CI 3.5 to 180). Overall, masks produced a 3.4 fold (95% CI 1.8 to 6.3) reduction in viral aerosol shedding. Correlations between nasopharyngeal swab and the aerosol fraction copy numbers were weak (r = 0.17, coarse; r = 0.29, fine fraction). Copy numbers in exhaled breath declined rapidly with day after onset of illness. Two subjects with the highest copy numbers gave culture positive fine particle samples. Surgical masks worn by patients reduce aerosols shedding of virus. The abundance of viral copies in fine particle aerosols and evidence for their infectiousness suggests an important role in seasonal influenza transmission. Monitoring exhaled virus aerosols will be important for validation of experimental transmission studies in humans.

Concepts: Influenza, Number, Part, Particulate, Aerosol, Particulates, Reassortment, Global dimming


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


Redox-based resistive switching random access memory (ReRAM) offers excellent properties to implement future non-volatile memory arrays. Recently, the capability of two-state ReRAMs to implement Boolean logic functionality gained wide interest. Here, we report on seven-states Tantalum Oxide Devices, which enable the realization of an intrinsic modular arithmetic using a ternary number system. Modular arithmetic, a fundamental system for operating on numbers within the limit of a modulus, is known to mathematicians since the days of Euclid and finds applications in diverse areas ranging from e-commerce to musical notations. We demonstrate that multistate devices not only reduce the storage area consumption drastically, but also enable novel in-memory operations, such as computing using high-radix number systems, which could not be implemented using two-state devices. The use of high radix number system reduces the computational complexity by reducing the number of needed digits. Thus the number of calculation operations in an addition and the number of logic devices can be reduced.

Concepts: Mathematics, Computer, Number, Computational complexity theory, Computer data storage, Numeral system, Boolean logic, Number theory


Numerical processing has been demonstrated to be closely associated with arithmetic skills, however, our knowledge on the development of the relevant cognitive mechanisms is limited. The present longitudinal study investigated the developmental trajectories of numerical processing in 42 children with age-adequate arithmetic development and 41 children with dyscalculia over a 2-year period from beginning of Grade 2, when children were 7; 6 years old, to beginning of Grade 4. A battery of numerical processing tasks (dot enumeration, non-symbolic and symbolic comparison of one- and two-digit numbers, physical comparison, number line estimation) was given five times during the study (beginning and middle of each school year). Efficiency of numerical processing was a very good indicator of development in numerical processing while within-task effects remained largely constant and showed low long-term stability before middle of Grade 3. Children with dyscalculia showed less efficient numerical processing reflected in specifically prolonged response times. Importantly, they showed consistently larger slopes for dot enumeration in the subitizing range, an untypically large compatibility effect when processing two-digit numbers, and they were consistently less accurate in placing numbers on a number line. Thus, we were able to identify parameters that can be used in future research to characterize numerical processing in typical and dyscalculic development. These parameters can also be helpful for identification of children who struggle in their numerical development.

Concepts: Time, Mathematics, Developmental psychology, Number, C, Educational years, Counting, Third grade


Finite simple groups are the building blocks of finite symmetry. The effort to classify them precipitated the discovery of new examples, including the monster, and six pariah groups which do not belong to any of the natural families, and are not involved in the monster. It also precipitated monstrous moonshine, which is an appearance of monster symmetry in number theory that catalysed developments in mathematics and physics. Forty years ago the pioneers of moonshine asked if there is anything similar for pariahs. Here we report on a solution to this problem that reveals the O'Nan pariah group as a source of hidden symmetry in quadratic forms and elliptic curves. Using this we prove congruences for class numbers, and Selmer groups and Tate-Shafarevich groups of elliptic curves. This demonstrates that pariah groups play a role in some of the deepest problems in mathematics, and represents an appearance of pariah groups in nature.Classifying groups is an important challenge in mathematics and has led to the identification of groups which do not belong to the main families. Here Duncan et al. introduce a type of moonshine which is a connection between these groups, number theory and potentially physics.

Concepts: Mathematics, Physics, Group, Group theory, Number, Modular arithmetic, Number theory, Monstrous moonshine


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


One in five adults in the United States is functionally innumerate; they do not possess the mathematical competencies needed for many modern jobs. We administered functional numeracy measures used in studies of young adults' employability and wages to 180 thirteen-year-olds. The adolescents began the study in kindergarten and participated in multiple assessments of intelligence, working memory, mathematical cognition, achievement, and in-class attentive behavior. Their number system knowledge at the beginning of first grade was defined by measures that assessed knowledge of the systematic relations among Arabic numerals and skill at using this knowledge to solve arithmetic problems. Early number system knowledge predicted functional numeracy more than six years later (ß = 0.195, p = .0014) controlling for intelligence, working memory, in-class attentive behavior, mathematical achievement, demographic and other factors, but skill at using counting procedures to solve arithmetic problems did not. In all, we identified specific beginning of schooling numerical knowledge that contributes to individual differences in adolescents' functional numeracy and demonstrated that performance on mathematical achievement tests underestimates the importance of this early knowledge.

Concepts: Mathematics, United States, Learning, Number, Arithmetic, Problem solving, Numeral system, Mathematics education


Hybrid Open Access is an intermediate form of OA, where authors pay scholarly publishers to make articles freely accessible within journals, in which reading the content otherwise requires a subscription or pay-per-view. Major scholarly publishers have in recent years started providing the hybrid option for the vast majority of their journals. Since the uptake usually has been low per journal and scattered over thousands of journals, it has been very difficult to obtain an overview of how common hybrid articles are. This study, using the results of earlier studies as well as a variety of methods, measures the evolution of hybrid OA over time. The number of journals offering the hybrid option has increased from around 2,000 in 2009 to almost 10,000 in 2016. The number of individual articles has in the same period grown from an estimated 8,000 in 2009 to 45,000 in 2016. The growth in article numbers has clearly increased since 2014, after some major research funders in Europe started to introduce new centralized payment schemes for the article processing charges (APCs).

Concepts: Mathematics, Number, Payment, Hybrid, The UpTake, Grammatical number


Although the health effects of long term exposure to air pollution are well established, it is difficult to effectively communicate the health risks of this (largely invisible) risk factor to the public and policy makers. The purpose of this study is to develop a method that expresses the health effects of air pollution in an equivalent number of daily passively smoked cigarettes.

Concepts: Risk, Economics, Decision theory, Pollution, Number, Derivative, Finance


Purpose: We provide background information/education for national recommendations to include initial newborn screening dried bloodspot serial numbers in electronic birth registrations. Mutual data linking would provide quality checks for each data source, determinations of percentages of newborns screened, and identification of locations where screening is lacking.Methods: State newborn screening dried bloodspot programs were surveyed to determine the extent of newborn screening dried bloodspot and electronic birth registration linking and the states' level of interest in such linkages. These data were reviewed with federal and state policy makers and presented to the Secretary of Health and Human Services' Advisory Committee on Heritable Disorders in Newborns and Children for national policy recommendations.Results: Only 40% of state newborn screening dried bloodspot programs reported comparing births with screens. All states use serially numbered newborn screening dried bloodspot collection cards, and electronic birth registrations exist in almost all states. Newborn screening dried bloodspot serial number data fields currently exist in only 24% of state electronic birth registrations.Conclusion: The Secretary of Health and Human Services' Advisory Committee on Heritable Disorders in Newborns and Children recommends the universal use of the newborn screening dried bloodspot serial number in a standardized format as part of state birth registration; consideration of including the initial newborn screening dried bloodspot serial number as a required data field; and, once established, using these data linkages to monitor completeness of newborn screening and to validate demographic information in both systems.Genet Med 2013:15(3):229-233.

Concepts: Childbirth, Number, Newborn screening, Genealogy, Serial number, Birth certificate, Birth registration in Ancient Rome, Serial numbers