Mapping skills between symbols and quantities in preschoolers: The role of finger patterns.

Mapping skills between different codes to represent numerical information, such as number symbols (i.e., verbal number words and written digits) and non-symbolic quantities, are important in the development of the concept of number. The aim of the current study is to investigate children's mapping skills by incorporating another numerical code that emerges at early stages in development, finger patterns. Specifically, the study investigates (i) the order in which mapping skills develop and the association with young children's understanding of cardinality; and (ii) whether finger patterns are processed similarly to symbolic codes or rather as non-symbolic quantities. Preschool children (3-year-olds, N = 113, Mage = 40.8 months, SDage = 3.6 months; 4-year-olds, N = 103, Mage = 52.9 months, SDage = 3.4 months) both cardinality knowers and subset-knowers, were presented with twelve tasks that assessed the mappings between number words, Arabic digits, finger patterns, and quantities. The results showed that children's ability to map symbolic numbers precedes the understanding that such symbols reflect quantities, and that children recognize finger patterns above their cardinality knowledge, suggesting that finger patterns are symbolic in essence. RESEARCH HIGHLIGHTS: Children are more accurate in mapping between finger patterns and symbols (number words and Arabic digits) than in mapping finger patterns and quantities, indicating that fingers are processed holistically as symbolic codes. Children can map finger patterns to symbols above their corresponding cardinality level even in subset-knowers. Finger patterns may play a role in the process by which children learn to map symbols to quantities. Fingers patterns' use in the classroom context may be an adequate instructional and diagnostic tool.

Miscategorized subset-knowers: Five- and six-knowers can compare only the numbers they know.

Initial acquisition of the first symbolic numbers is measured with the Give a Number (GaN) task. According to the classic method, it is assumed that children who know only 1, 2, 3, or 4 in the GaN task, (termed separately one-, two-, three-, and four-knowers, or collectively subset-knowers) have only a limited conceptual understanding of numbers. On the other hand, it is assumed that children who know larger numbers understand the fundamental properties of numbers (termed cardinality-principle-knowers), even if they do not know all the numbers as measured with the GaN task, that are in their counting list (e.g., five- or six-knowers). We argue that this practice may not be well-established. To validate this categorization method, here, the performances of groups with different GaN performances were measured separately in a symbolic comparison task. It was found that similar to one to four-knowers, five-, six-, and so forth, knowers can compare only the numbers that they know in the GaN task. We conclude that five-, six-, and so forth, knowers are subset-knowers because their conceptual understanding of numbers is fundamentally limited. We argue that knowledge of the cardinality principle should be identified with stricter criteria compared to the current practice in the literature. RESEARCH HIGHLIGHTS: Children who know numbers larger than 4 in the Give a Number (GaN) task are usually assumed to have a fundamental conceptual understanding of numbers. We tested children who know numbers larger than 4 but who do not know all the numbers in their counting list to see whether they compare numbers more similar to children who know only small numbers in the GaN task or to children who have more firm number knowledge. Five-, six-, and so forth, knowers can compare only the numbers they know in the GaN task, similar to the performance of the one, two, three, and four-knowers. We argue that these children have a limited conceptual understanding of numbers and that previous works may have miscategorized them.

A Cardinality Estimator in Complex Database Systems Based on TreeLSTM.

Cardinality estimation is critical for database management systems (DBMSs) to execute query optimization tasks, which can guide the query optimizer in choosing the best execution plan. However, traditional cardinality estimation methods cannot provide accurate estimates because they cannot accurately capture the correlation between multiple tables. Several recent studies have revealed that learning-based cardinality estimation methods can address the shortcomings of traditional methods and provide more accurate estimates. However, the learning-based cardinality estimation methods still have large errors when an SQL query involves multiple tables or is very complex. To address this problem, we propose a sampling-based tree long short-term memory (TreeLSTM) neural network to model queries. The proposed model addresses the weakness of traditional methods when no sampled tuples match the predicates and considers the join relationship between multiple tables and the conjunction and disjunction operations between predicates. We construct subexpressions as trees using operator types between predicates and improve the performance and accuracy of cardinality estimation by capturing the join-crossing correlations between tables and the order dependencies between predicates. In addition, we construct a new loss function to overcome the drawback that Q-error cannot distinguish between large and small cardinalities. Extensive experimental results from real-world datasets show that our proposed model improves the estimation quality and outperforms traditional cardinality estimation methods and the other compared deep learning methods in three evaluation metrics: Q-error, MAE, and SMAPE.

Fair Numerical Algorithm of Coset Cardinality Spectrum for Distributed Arithmetic Coding.

As a typical symbol-wise solution of asymmetric Slepian-Wolf coding problem, Distributed Arithmetic Coding (DAC) non-linearly partitions source space into disjoint cosets with unequal sizes. The distribution of DAC coset cardinalities, named the Coset Cardinality Spectrum (CCS), plays an important role in both theoretical understanding and decoder design for DAC. In general, CCS cannot be calculated directly. Instead, a numerical algorithm is usually used to obtain an approximation. This paper first finds that the contemporary numerical algorithm of CCS is theoretically imperfect and does not finally converge to the real CCS. Further, to solve this problem, we refine the original numerical algorithm based on rigorous theoretical analyses. Experimental results verify that the refined numerical algorithm amends the drawbacks of the original version.

A New Quantum Private Protocol for Set Intersection Cardinality Based on a Quantum Homomorphic Encryption Scheme for Toffoli Gate.

Set Intersection Cardinality (SI-CA) computes the intersection cardinality of two parties' sets, which has many important and practical applications such as data mining and data analysis. However, in the face of big data sets, it is difficult for two parties to execute the SI-CA protocol repeatedly. In order to reduce the execution pressure, a Private Set Intersection Cardinality (PSI-CA) protocol based on a quantum homomorphic encryption scheme for the Toffoli gate is proposed. Two parties encode their private sets into two quantum sequences and encrypt their sequences by way of a quantum homomorphic encryption scheme. After receiving the encrypted results, the semi-honest third party (TP) can determine the equality of two quantum sequences with the Toffoli gate and decrypted keys. The simulation of the quantum homomorphic encryption scheme for the Toffoli gate on two quantum bits is given by the IBM Quantum Experience platform. The simulation results show that the scheme can also realize the corresponding function on two quantum sequences.

Record linkage based patient intersection cardinality for rare disease studies using Mainzelliste and secure multi-party computation.

BACKGROUND: The low number of patients suffering from any given rare diseases poses a difficult problem for medical research: With the exception of some specialized biobanks and disease registries, potential study participants' information are disjoint and distributed over many medical institutions. Whenever some of those facilities are in close proximity, a significant overlap of patients can reasonably be expected, further complicating statistical study feasibility assessments and data gathering. Due to the sensitive nature of medical records and identifying data, data transfer and joint computations are often forbidden by law or associated with prohibitive amounts of effort. To alleviate this problem and to support rare disease research, we developed the Mainzelliste Secure EpiLinker (MainSEL) record linkage framework, a secure Multi-Party Computation based application using trusted-third-party-less cryptographic protocols to perform privacy-preserving record linkage with high security guarantees. In this work, we extend MainSEL to allow the record linkage based calculation of the number of common patients between institutions. This allows privacy-preserving statistical feasibility estimations for further analyses and data consolidation. Additionally, we created easy to deploy software packages using microservice containerization and continuous deployment/continuous integration. We performed tests with medical researchers using MainSEL in real-world medical IT environments, using synthetic patient data. RESULTS: We show that MainSEL achieves practical runtimes, performing 10 000 comparisons in approximately 5 minutes. Our approach proved to be feasible in a wide range of network settings and use cases. The "lessons learned" from the real-world testing show the need to explicitly support and document the usage and deployment for both analysis pipeline integration and researcher driven ad-hoc analysis use cases, thus clarifying the wide applicability of our software. MainSEL is freely available under: https://github.com/medicalinformatics/MainSEL CONCLUSIONS: MainSEL performs well in real-world settings and is a useful tool not only for rare disease research, but medical research in general. It achieves practical runtimes, improved security guarantees compared to existing solutions, and is simple to deploy in strict clinical IT environments. Based on the "lessons learned" from the real-word testing, we hope to enable a wide range of medical researchers to meet their needs and requirements using modern privacy-preserving technologies.

Children's attention to numerical quantities relates to verbal number knowledge: An introduction to the Build-A-Train task.

Which dimension of a set of objects is more salient to young children: number or size? The 'Build-A-Train' task was developed and used to examine whether children spontaneously use a number or physical size approach on an un-cued matching task. In the Build-A-Train task, an experimenter assembles a train using one to five blocks of a particular length and asks the child to build the same train. The child's blocks differ in length from the experimenter's blocks, causing the child to build a train that matches based on either the number of blocks or length of the train, as it is not possible to match on both. One hundred and nineteen children between 2 years 2 months and 6 years 0 months of age (M = 4.05, SD = 0.84) completed the Build-A-Train task, and the Give-a-Number task, a classic task used to assess children's conceptual knowledge of verbal number words. Across train lengths and verbal number knowledge levels, children used a number approach more than a size approach on the Build-A-Train task. However, children were especially likely to use a number approach over a size approach when they knew the verbal number word that corresponded to the quantity of blocks in the train, particularly for quantities smaller than four. Therefore, children's attention to number relates to their knowledge of verbal number words. The Build-A-Train task and findings from the current study set a foundation for future longitudinal research to investigate the causal relationship between children's acquisition of symbolic mathematical concepts and attention to number.

Indirect covariate balance and residual confounding: An applied comparison of propensity score matching and cardinality matching.

PURPOSE: Propensity score matching (PSM) is subject to limitations associated with limited degrees of freedom and covariate overlap. Cardinality matching (CM), an optimization algorithm, overcomes these limitations by matching directly on the marginal distribution of covariates. This study compared the performance of PSM and CM. METHODS: Comparative cohort study of new users of angiotensin-converting enzyme inhibitor (ACEI) and ß-blocker monotherapy identified from a large U.S. administrative claims database. One-to-one matching was conducted through PSM using nearest-neighbor matching (caliper = 0.15) and CM permitting a maximum standardized mean difference (SMD) of 0, 0.01, 0.05, and 0.10 between comparison groups. Matching covariates included 37 patient demographic and clinical characteristics. Observed covariates included patient demographics, and all observed prior conditions, drug exposures, and procedures. Residual confounding was assessed based on the expected absolute systematic error of negative control outcome experiments. PSM and CM were compared in terms of post-match patient retention, matching and observed covariate balance, and residual confounding within a 10%, 1%, 0.25% and 0.125% sample group. RESULTS: The eligible study population included 182 235 (ACEI: 129363; ß-blocker: 56872) patients. CM achieved superior patient retention and matching covariate balance in all analyses. After PSM, 1.6% and 28.2% of matching covariates were imbalanced in the 10% and 0.125% sample groups, respectively. No significant difference in observed covariate balance was observed between matching techniques. CM permitting a maximum SMD <0.05 was associated with improved residual bias as compared to PSM. CONCLUSION: We recommend CM with more stringent balance criteria as an alternative to PSM when matching on a set of clinically relevant covariates.

Associations among socioeconomic status and preschool-aged children's, number skills, and spatial skills: The role of executive function.

Extensive literature has documented socioeconomic status (SES) disparities in young children's standardized math achievement, which primarily reflect differences in basic number and arithmetic skills. In addition, growing evidence indicates that direct assessments of executive function (EF) both predict standardized math achievement and mediate SES differences in standardized math tests. However, early spatial skills and children's approximate number system (ANS) acuity, critical components of later math competence, have been largely absent in this past research. The current study examined SES associations with multiple direct assessments of early ANS, cardinality, and spatial skills, as well as standardized math achievement, in a socioeconomically diverse sample of 4-year-old children (N = 149). Structural equation modeling revealed SES effect sizes of .21 for geometric sensitivity skills, .23 for ANS acuity, .39 for cardinality skills, and .28 for standardized math achievement. Furthermore, relations between SES and children's spatial skills, ANS acuity, cardinality, and standardized math skills were mediated by a composite measure of children's EF skills. Implications of pervasive SES disparities across multiple domains of early math development, as well as the mitigating role of EF, are discussed.

Applied comparison of large-scale propensity score matching and cardinality matching for causal inference in observational research.

BACKGROUND: Cardinality matching (CM), a novel matching technique, finds the largest matched sample meeting prespecified balance criteria thereby overcoming limitations of propensity score matching (PSM) associated with limited covariate overlap, which are especially pronounced in studies with small sample sizes. The current study proposes a framework for large-scale CM (LS-CM); and compares large-scale PSM (LS-PSM) and LS-CM in terms of post-match sample size, covariate balance and residual confounding at progressively smaller sample sizes. METHODS: Evaluation of LS-PSM and LS-CM within a comparative cohort study of new users of angiotensin-converting enzyme inhibitor (ACEI) and thiazide or thiazide-like diuretic monotherapy identified from a U.S. insurance claims database. Candidate covariates included patient demographics, and all observed prior conditions, drug exposures and procedures. Propensity scores were calculated using LASSO regression, and candidate covariates with non-zero beta coefficients in the propensity model were defined as matching covariates for use in LS-CM. One-to-one matching was performed using progressively tighter parameter settings. Covariate balance was assessed using standardized mean differences. Hazard ratios for negative control outcomes perceived as unassociated with treatment (i.e., true hazard ratio of 1) were estimated using unconditional Cox models. Residual confounding was assessed using the expected systematic error of the empirical null distribution of negative control effect estimates compared to the ground truth. To simulate diverse research conditions, analyses were repeated within 10 %, 1 and 0.5 % subsample groups with increasingly limited covariate overlap. RESULTS: A total of 172,117 patients (ACEI: 129,078; thiazide: 43,039) met the study criteria. As compared to LS-PSM, LS-CM was associated with increased sample retention. Although LS-PSM achieved balance across all matching covariates within the full study population, substantial matching covariate imbalance was observed within the 1 and 0.5 % subsample groups. Meanwhile, LS-CM achieved matching covariate balance across all analyses. LS-PSM was associated with better candidate covariate balance within the full study population. Otherwise, both matching techniques achieved comparable candidate covariate balance and expected systematic error. CONCLUSIONS: LS-CM found the largest matched sample meeting prespecified balance criteria while achieving comparable candidate covariate balance and residual confounding. We recommend LS-CM as an alternative to LS-PSM in studies with small sample sizes or limited covariate overlap.

A robust optimization model for tactical capacity planning in an outpatient setting.

Tactical capacity planning is a key element of planning and control decisions in healthcare settings, focusing on the medium-term allocation of a clinic's resources to appointments of different types. One of the most scarce resources in healthcare is physician time. Due to uncertainty in demand for appointments, it is difficult to provide an exact match between the planned physician availability and appointment requests. Our study uses cardinality-constrained robust optimization to develop tactical capacity plans which are robust against uncertainty, providing a feasible allocation of capacity for all realizations of demand to the extent allowed by the budget of uncertainty. The outpatient setting we consider sees first-visit patients and re-visit patients, and both patient types have access time targets. We experimentally evaluate our robust model and its practical implications under different levels of conservatism. We show that we can guarantee 100% feasibility of the robust tactical capacity plan while not being fully conservative, which will lead to the clinic saving money while being able to meet demand despite uncertainty. We also show how the robust model helps us to identify the critical time periods leading to worst case physician peak load, which could be valuable to decision-makers. Throughout the experiments, we find that the step of translating available data into an uncertainty set can influence the true conservatism of a solution.

Give yourself a hand: The role of gesture and working memory in preschoolers' numerical knowledge.

Hand gestures can be beneficial in math contexts to reduce the user's cognitive load by supporting domain-general abilities such as working memory. Although prior work has shown a strong relation between young children's early math performance and their general cognitive abilities, it is important to consider how children's working memory ability may relate to their use of spontaneous gesture as well as their math-specific abilities. The current study examined how preschool-aged children's gesture use and working memory relate to their performance on an age-appropriate math task. Head Start preschoolers (N = 81) were videotaped while completing a modified version of the Give-N task to measure their cardinality understanding. Children also completed a forward word span task and a computerized Corsi Block task to assess their working memory. The results showed that children's spontaneous gesture use and working memory were related to their performance on the cardinality task. However, children's gestures were not significantly related to working memory after controlling for age. Findings suggest that young children from low-income backgrounds use gestures during math contexts in similar ways to preschoolers from higher-income backgrounds.

Robust Measurement-Driven Cardinality Balance Multi-Target Multi-Bernoulli Filter.

The multi-target tracking filter under the Bayesian framework has strict requirements on the prior information of the target, such as detection probability density, clutter density, and target initial position information. This paper proposes a novel robust measurement-driven cardinality balance multi-target multi-Bernoulli filter (RMD-CBMeMBer) for solving the multiple targets tracking problem when the detection probability density is unknown, the background clutter density is unknown, and the target's prior position information is lacking. In RMD-CBMeMBer filtering, the target state is first extended, so that the extended target state includes detection probability, kernel state, and indicators of target and clutter. Secondly, the detection probability is modeled as a Beta distribution, and the clutter is modeled as a clutter generator that is independent of each other and obeys the Poisson distribution. Then, the detection probability, kernel state, and clutter density are jointly estimated through filtering. In addition, the correlation function (CF) is proposed for creating new Bernoulli component (BC) by using the measurement information at the previous moment. Numerical experiments have verified that the RMD-CBMeMBer filter can solve the multi-target tracking problem under the condition of unknown target detection probability, unknown background clutter density and inadequate prior position information of the target. It can effectively estimate the target detection probability and the clutter density.

Improved set-size labeling mediates the effect of a counting intervention on children's understanding of cardinality.

How does improving children's ability to label set sizes without counting affect the development of understanding of the cardinality principle? It may accelerate development by facilitating subsequent alignment and comparison of the cardinal label for a given set and the last word counted when counting that set (Mix et al., 2012). Alternatively, it may delay development by decreasing the need for a comprehensive abstract principle to understand and label exact numerosities (Piantadosi et al., 2012). In this study, preschoolers (N = 106, Mage  = 4;8) were randomly assigned to one of three conditions: (a) count-and-label, wherein children spent 6 weeks both counting and labeling sets arranged in canonical patterns like pips on a die; (b) label-first,wherein children spent the first 3 weeks learning to label the set sizes without counting before spending 3 weeks identical to the count-and-label condition; (c) print referencing control. Both counting conditions improved understanding of cardinality through increases in children's ability to label set sizes without counting. In addition to this indirect effect, there was a direct effect of the count-and-label condition on progress toward understanding of cardinality. Results highlight the roles of set labeling and equifinality in the development of children's understanding of number concepts.

Cardinality Leap for Open-Ended Evolution: Theoretical Consideration and Demonstration by Hash Chemistry.

Open-ended evolution requires unbounded possibilities that evolving entities can explore. The cardinality of a set of those possibilities thus has a significant implication for the open-endedness of evolution. I propose that facilitating formation of higher-order entities is a generalizable, effective way to cause a cardinality leap in the set of possibilities that promotes open-endedness. I demonstrate this idea with a simple, proof-of-concept toy model called Hash Chemistry that uses a hash function as a fitness evaluator of evolving entities of any size or order. Simulation results showed that the cumulative number of unique replicating entities that appeared in evolution increased almost linearly along time without an apparent bound, demonstrating the effectiveness of the proposed cardinality leap. It was also observed that the number of individual entities involved in a single replication event gradually increased over time, indicating evolutionary appearance of higher-order entities. Moreover, these behaviors were not observed in control experiments in which fitness evaluators were replaced by random number generators. This strongly suggests that the dynamics observed in Hash Chemistry were indeed evolutionary behaviors driven by selection and adaptation taking place at multiple scales.

Spatial order relates to the exact numerical magnitude of digits in young children.

Spatial representation of numbers has been repeatedly associated with the development of numerical and mathematical skills. However, few studies have explored the contribution of spatial mapping to exact number representation in young children. Here we designed a novel task that allows a detailed analysis of direction, ordinality, and accuracy of spatial mapping. Preschool children, who were classified as competent counters (cardinal principle knowers), placed triplets of sequentially presented digits on the visual line. The ability to correctly order triplets tended to decrease with the larger digits. When triplets were correctly ordered, the direction of spatial mapping was predominantly oriented from left to right and the positioning of the target digits was characterized by a pattern of underestimation with no evidence of logarithmic compression. Crucially, only ordinality was associated with performance in a digit comparison task. Our results suggest that the spatial (ordinal) arrangement of digits is a powerful source of information that young children can use to construct the representation of exact numbers. Therefore, digits may acquire numerical meaning based on their spatial order on the number line.

Preschoolers' selective sustained attention and numeracy skills and knowledge.

This brief report addresses preschoolers' selective sustained attention (SSA) and early numeracy skills and knowledge. Past research indicates that children's attention and early numeracy are positively associated, yet some concerns have emerged about the age appropriateness of tools used to measure preschoolers' SSA. This study used a new measure-the Track-It Task-that demonstrates strong psychometric properties. In total, 31 at-risk preschoolers (Mage = 46.6 months) participated and were assessed on SSA, nonsymbolic quantity discrimination, and symbolic quantitative skills and knowledge. The ability to sustain attention in the face of distractions was positively correlated with preschoolers' verbal counting and one-to-one correspondence, Arabic numeral recognition, and cardinal principle knowledge. SSA was not significantly associated with child age or performance on a memory task. This study provides preliminary evidence that SSA may facilitate the process whereby young children become reliable counters and learn that the symbol system of numbers represents specific quantities.

Improved Multitarget Tracking in Clutter Using Bearings-Only Measurements.

Multitarget tracking in clutter using bearings-only measurements is a challenging problem. In this paper, a performance improved nonlinear filter is proposed on the basis of the Random Finite Set (RFS) theory and is named as Gaussian mixture measurements-based cardinality probability hypothesis density (GMMbCPHD) filter. The GMMbCPHD filter enables to address two main issues: measurement-origin-uncertainty and measurement nonlinearity, which constitutes the key problems in bearings-only multitarget tracking in clutter. For the measurement-origin-uncertainty issue, the proposed filter estimates the intensity of RFS of multiple targets as well as propagates the posterior cardinality distribution. For the measurement-origin-nonlinearity issue, the GMMbCPHD approximates the measurement likelihood function using a Gaussian mixture rather than a single Gaussian distribution as used in extended Kalman filter (EKF). The superiority of the proposed GMMbCPHD are validated by comparing with several state-of-the-art algorithms via intensive simulation studies.

A systematic analysis of scoring functions in rigid-body protein docking: The delicate balance between the predictive rate improvement and the risk of overtraining.

Protein-protein interactions play fundamental roles in biological processes including signaling, metabolism, and trafficking. While the structure of a protein complex reveals crucial details about the interaction, it is often difficult to acquire this information experimentally. As the number of interactions discovered increases faster than they can be characterized, protein-protein docking calculations may be able to reduce this disparity by providing models of the interacting proteins. Rigid-body docking is a widely used docking approach, and is often capable of generating a pool of models within which a near-native structure can be found. These models need to be scored in order to select the acceptable ones from the set of poses. Recently, more than 100 scoring functions from the CCharPPI server were evaluated for this task using decoy structures generated with SwarmDock. Here, we extend this analysis to identify the predictive success rates of the scoring functions on decoys from three rigid-body docking programs, ZDOCK, FTDock, and SDOCK, allowing us to assess the transferability of the functions. We also apply set-theoretic measure to test whether the scoring functions are capable of identifying near-native poses within different subsets of the benchmark. This information can provide guides for the use of the most efficient scoring function for each docking method, as well as instruct future scoring functions development efforts. Proteins 2017; 85:1287-1297. © 2017 Wiley Periodicals, Inc.

Numerical morphology supports early number word learning: Evidence from a comparison of young Mandarin and English learners.

Previous studies showed that children learning a language with an obligatory singular/plural distinction (Russian and English) learn the meaning of the number word for one earlier than children learning Japanese, a language without obligatory number morphology (Barner, Libenson, Cheung, & Takasaki, 2009; Sarnecka, Kamenskaya, Yamana, Ogura, & Yudovina, 2007). This can be explained by differences in number morphology, but it can also be explained by many other differences between the languages and the environments of the children who were compared. The present study tests the hypothesis that the morphological singular/plural distinction supports the early acquisition of the meaning of the number word for one by comparing young English learners to age and SES matched young Mandarin Chinese learners. Mandarin does not have obligatory number morphology but is more similar to English than Japanese in many crucial respects. Corpus analyses show that, compared to English learners, Mandarin learners hear number words more frequently, are more likely to hear number words followed by a noun, and are more likely to hear number words in contexts where they denote a cardinal value. Two tasks show that, despite these advantages, Mandarin learners learn the meaning of the number word for one three to six months later than do English learners. These results provide the strongest evidence to date that prior knowledge of the numerical meaning of the distinction between singular and plural supports the acquisition of the meaning of the number word for one.