4 - POSITIVES AND NEGATIVES

Numerical estimation has been used to study how children mentally represent numbers for many years (e.g., Siegler & Opfer, 2003). However, these studies have always presented children with positive numbers and positive number lines. Children’s mental representation of negative numbers has never been addressed. The present study tested children in the 2nd, 4th, and 6th grades to assess their mental representations of both positive and negative numbers using a standard numerical estimation task. We replicated the shift from a logarithmic to linear representation for positive numbers (0–1,000 scale) in that 2nd graders represented positive numbers logarithmically, but 4th and 6th graders represented the numbers linearly. Furthermore, children’s representation of negative numbers paralleled their representations of positive numbers and showed the same shift from a logarithmic representation at Grade 2 to linear representations at Grades 4 and 6. This is the first study to provide data on children’s representation of negative numbers, and the implications of these findings are discussed.

Previous studies suggest that there is an association between positive numbers and space; however, there is less agreement for negative numbers. The main purpose of the present study was to investigate the nature of the processing and representation of negative numbers, and the association between negative numbers and space. Results of the two experiments show that low-level processing (perception) of negative numbers can induce spatial shifts of attention. Whether this is caused by their numerical value or absolute value depends on the numerical context and task requirements, indicating that there are both components and holistic processing, and representation for negative numbers. The representation is automatically associated with leftward space; the coding and representation of the mental number line is adaptable to the specific numerical context and task requirements. The mental number line, therefore, can extend to the left side of zero, thus supporting the context-dependent view.

The teaching of negative numbers is dealt with herein from the point of view of expanding the number classes from those containing only positive numbers to those that also include the negatives (and zero). The expansion involves generalizing the concept of “number” and making modifications in the definitions of the arithmetical operations. Each of these actions generates cognitive obstacles, both historically and pedagogically. In contrast to the historical situation, the concept of negative number is not problematic for the contemporary student because he/she encounters them with certain frequency in his/her daily life. The addition of negative numbers, especially in the case in which it becomes equivalent to subtraction in the natural numbers with the subtrahend greater than the minuend, is subject to a didactical obstacle, which can be overcome by using the number line as a visual/conceptual support. Also, the multiplication of two negative numbers, resulting in a positive number, constitutes a genuine epistemological obstacle due to the fact that the usual metaphors used to explain the negative numbers do not clarify this operation. The article thus proposes to consider double negatives as inverses of inverses and delineates a sequence of activities based on this metaphor to overcome the mentioned epistemological obstacle.

7 - Roots and Radicals

This research paper deals with using supervised machine learning algorithms to detect authenticity of bank notes. In this research we were successful in achieving very high accuracy (of the order of 99%) by applying some data preprocessing tricks and then running the processed data on supervised learning algorithms like SVM, Decision Trees, Logistic Regression, KNN. We then proceed to analyze the misclassified points. We examine the confusion matrix to find out which algorithms had more number of false positives and which algorithm had more number of False negatives. This research paper deals with using supervised machine learning algorithms to detect authenticity of bank notes. In this research we were successful in achieving very high accuracy (of the order of 99%) by applying some data preprocessing tricks and then running the processed data on supervised learning algorithms like SVM, Decision Trees, Logistic Regression, KNN. We then proceed to analyze the misclassified points. We examine the confusion matrix to find out which algorithms had more number of false positives and which algorithm had more number of False negatives.

What Interval of Daily Pain Assessment Is Required to Reliably Diagnose Chronic Pain in Sickle Cell Disease? the Pisces Study

The objective of this study was to assess the ability of four peripheral bone measurement sites to predict low bone mineral density of the lumbar spine, femoral neck, and total hip as defined by the WHO classification, and to evaluate their role as a screening procedure for central dual-energy X-ray absorptiometry (DXA). One thousand three hundred white women patients aged 58.3+/-13.9 years were enrolled. Correlations between the peripheral and central sites were moderate, varying between 0.51 and 0.67. In receiver-operating characteristic (ROC) analysis, the areas under the curve for the peripheral sites revealed a few small, but significant, differences between sites. The optimal cut-point was derived from the ROC data for each site to assess its value as a screening parameter. These proved to be unsatisfactory, because the average number of false positives and false negatives were 18% and 24%, respectively. A proposal is made which entails two cut-points, one for an acceptable percentage of false negatives and the other for an acceptable number of false positives. Patients with t-scores between these cut-points would be referred for central DXA for classification. The result is a substantial decrease in the number of false negatives, i.e., patients who would be candidates for treatment. The contentious issue is what proportion of supplemental DXAs is considered logistically and economically acceptable for any of the peripheral site measurements to be useful.

Identification, Segmentation, and Image Property Study of Acute Infarcts in Diffusion-Weighted Images by Using a Probabilistic Neural Network and Adaptive Gaussian Mixture Model

Vortex cores in fluid mechanics are easy to visualize, yet difficult to detect numerically. Precise knowledge of these allows fluid dynamics researchers to study complex flow structures and allow for a better understanding of the turbulence transition process and the development and evolution of flow instabilities, to name but a few relevant areas. Various approaches such as the Q, delta, and swirling strength criterion have been proposed to visualize vortical flows, and these approaches can be used to detect vortex core locations. Using these methods can result in spuriously detected vortex cores and which can be balanced by a cutoff filter, making these methods lack robustness. To overcome this shortcoming, we propose a new approach using convolutional neural networks to detect flow structures directly from streamline plots, using the line integral convolution method. We show that our computer vision-based approach is able to reduce the number of false positives and negatives while removing the need for a cutoff. We validate our approach using the Taylor–Green vortex problem to generate input images for our network. We show that with an increasing number of images used for training, we are able to monotonically reduce the number of false positives and negatives. We then apply our trained network to a different flow problem where vortices are still reliably detected. Thus, our study presents a robust approach that allows for reliable vortex detection which is applicable to a wide range of flow scenarios.

After 2 years of working on a design research project looking at the development of student thinking about negative numbers in the context of a computer game, I arrived at a critical problem. The game was designed such that the principles of working with adding and subtracting positive and negative numbers were integrated into the game play so that students could only achieve best scores across the game levels by utilizing these principles to make decisions during play. In as little as two sessions of 30 min of play, almost all students were able to master the basic principles as demonstrated by their success across all four game levels. When it came to measuring learning gains on a traditional pencil and paper posttest, however, students showed significant but limited gains. It was hypothesized that the factor limiting posttest scores was that students’ learning had been encoded in such a way as to reflect the purposes and goals of the game and that this encoding didn’t readily transfer to a traditional worksheet filled with addition and subtraction problems. In order to test this hypothesis, we borrowed a theoretical framework to see if students’ game playing could be conceptualized as a form of “preparation for future learning.” The results give strong support for this conceptualization of transfer in supporting game-based learning and suggest interesting possibilities for bridging game-based learning activities with the reality of more traditional school-based models of assessment.

Background: The Consumer Price Index (CPI) is the main indicator for determining the prices level of a certain economy. The above-mentioned rate refers to the average prices on an indicated period and it is calculated mainly on goods consumed basis by selected families through weighting criteria and therefore, identifying the inflation damages on waged workers as well as their life standards thus, providing precise information on their earnings improvement or compensating their previous or equivalent buying empowerment. The application of rates is based on statistics models whereby; the temporary series is identified as observation of different periods that relevant variable values stand to foresee the future hypothesis confirmation. Objective: To Estimate the Consumer Price Index in Mozambique using Time Series Models. Methods: The following study based on monthly CPI data of Mozambique dating January 2011 to July 2020 out of 115 observed analyses. The data was processed through free open codes Gretl and 4.02-R Version Statistic Packages. The data hereby used was provided by the Mozambican National Statistics Institute (INE). The study applied the Box and Jenkins approach claiming that each temporary series value is based on its previous values due to the temporarily correlation between the series values that generally exist. The method consists of adjusting the Auto-regressive integrated Moving Average Method (ARIMA) to a data group under four interactive stages cycles Results: From 103 observations taken into account, the highest registered index was 158,25 corresponding to December 2016. On the other hand, it is notable that 101,62 is the smallest rate corresponding to January 2011period. The 114,68 medium rate breaks apart the price series in half resulting 50% of rates below such price and consequently, the remaining 50% above the same price. The similar parameter indicates all distribution format ends. Positive numbers indicate the widest end on the right while the negative numbers indicate the widest end on the left. Consequently, the positive asymmetry (1, 5217) indicates that the distribution has a wide end on the right. For kurtosis, the series is platykurtic since its result is less than 3 (2,6904 <3). Conclusion: The CPI in Mozambique showed an increasing trend in the period analyzed, between January 2011 and July 2020, with a sharp rise in 2016 returning to the original level and the normal growth trend of the series. In the estimation stage, it was possible to adequately select (02) two ARIMA models (p,d,q) that presented good fit to the data, and among them, the model selected as the most appropriate for predictions according to performance measures, was ARIMA (0.1.0) with constant, because it presented lower values of absolute mean percentage error (AMPS) and mean quadratic error (REQM). According to the selected model, the previsions for the period from August 2020 to July 2021 indicate a slight growth in consumer price index.

Causal inference is a statistical approach that aims to understand and quantify the causal relationship between variables, allowing us to determine the impact of one variable on another while accounting for potential confounding factors. In this study, we chose the Infant Health and Development Program (IHDP) dataset to test whether high-quality early childhood education and medical care will enhance their cognitive and academic ability. We use some common and classic algorithms to achieve this study by calculating the CATE (Conditional Average Treatment Effect) of the dataset; if the result is a negative number, that means early treatment doesn’t improve children’s further ability; if the result is a positive number, that means treatment improves it. After fitting the targeted models, BART(Bayesian Additive Regression Trees) and Metalearners, into this dataset, we found out that all the models will get positive CATE, which means that these early treatments positively affect children’s future development. Also, we can judge which model gives us a more accurate result according to the standard variance of TE(treatment effect). The result of this study will provide us with an insightful idea about whether we should give children some treatments regarding education and medical care and which model is more suitable for this casual inference test.

In mathematics science, subtraction is rather simple computation of arithmetic. However, no matter what advanced computer in the world, and no matter what backward calculator (such as abacus in China etc.) in people’s hand, to get difference of subtraction is always a NP problem in all the time. Such as capacities of numbers Minuend and Subtrahend, symbols (±) of number value (positive number or negative number), precise computing (PC), computing precision (CP), perturbation motion (PM) in computing of numbers, etc. This paper makes an algorithm of novel subtraction with AI-VCR computation in computer, and gives solutions of avoiding the difference’s overflowing, insufficient valid figures, etc.

The present study extends recently‐acquired knowledge about the affective aspects of negotiations by examining the effects of defining negotiation outcomes in affective terms rather than numeric terms. Using a 2 x 2 experimental design, the researchers represented the negotiation outcomes in four different ways: happy faces, unhappy faces, positive numbers, and negative numbers. The results indicate that representing outcomes in affective terms leads to longer negotiation times and higher impasse rates. In addition, participants whose outcomes were represented as happy faces reported the highest levels of emotional involvement, the lowest levels of cooperation and trust, and most frequently experienced negative emotions. Emotional involvement and negative emotions also helped explain differences in negotiation time and individual outcomes over and above the effects of the experimental manipulations. The implications of these results for negotiation research are discussed.

We use example of the Davey-Stewartson hierarchy to show that in addition to the standard equations given by Lax operator and evolutions of times with positive numbers, one can consider time evolutions with negative numbers and the same Lax operator. We derive corresponding Lax pairs and integrable equations.