Numerical Quantities Research Articles

Investigating the Generation and Spread of Numerical Misinformation: A Combined Eye Movement Monitoring and Social Transmission Approach

Abstract Numerical facts play a prominent role in public discourse, but individuals often provide incorrect estimates of policy-relevant numerical quantities (e.g., the number of immigrants in the country). Across two studies, we examined the role of schemas in the creation of numerical misinformation, and how misinformation can spread via person-to-person communication. In our first study, we combined eye movement monitoring and behavioral methods to examine how schemas distorted what people remembered about policy-relevant numerical information. Then, in a second study, we examined the consequences of these memory distortions via the social transmission of numerical information, using the serial reproduction paradigm. We found that individuals misremembered numerical information in a manner consistent with their schemas, and that person-to-person transmission can exacerbate these memory errors. Our studies highlight the mechanisms supporting the generation and spread of numerical misinformation and demonstrate the utility of a multi-method approach in the study of misinformation.

Topological properties of Graphene using some novel neighborhood degree-based topological indices

Topological indices are numeric quantities that transform chemical structure to real number. Topological indices are used in QSAR/QSPR studies to correlate the bioactivity and physiochemical properties of molecule. In this paper, some newly designed neighborhood degree-based topological indices named as neighborhood Zagreb index ([Formula: see text]), neighborhood version of Forgotten topological index ([Formula: see text]), modified neighborhood version of Forgotten topological index ([Formula: see text]), neighborhood version of second Zagreb index ([Formula: see text]) and neighborhood version of hyper Zagreb index ([Formula: see text]) are obtained for Graphene and line graph of Graphene using subdivision idea. In addition, these indices are compared graphically with respect to their response for Graphene and line graph of subdivision of Graphene.

Parallel Reaction Monitoring-Mass Spectrometry (PRM-MS)-Based Targeted Proteomic Surrogates for Intrinsic Subtypes in Breast Cancer: Comparative Analysis with Immunohistochemical Phenotypes.

Advances in targeted medications have improved the survival rate of breast cancer patients with molecular marker-positive tumors. To date, immunohistochemistry (IHC) has remained as the standard method for quantifying the markers including HER2, ER, and PR. Nevertheless, IHC-based grading is subjective, because the results depend on trained individuals' eye rather than numerical quantities. Thus, alternative methods that can account for quantitative levels of markers are gaining popularity, including targeted proteomics by mass spectrometry (MS). However, technical limitations have impeded the application of MS-based protein quantification to pathological FFPE slides that contain low amounts of cross-linked proteins. To challenge this, we developed a parallel reaction monitoring-mass spectrometry (PRM-MS) method to measure the expression levels of breast cancer markers. After developing the method using cell lines, we performed PRM-MS using 51 individuals' FFPE samples. As a result, we obtained numerical measures of targets, quantifying 13 peptides of 4 markers in a single analysis per sample. The results correlated well with the IHC readings of experienced pathologists. Moreover, the results distinguished a gray zone in HER2 classification, which IHC alone failed to do. This proof-of-concept study demonstrates the application of targeted proteomics in pathologic slides, further supporting the applicability of MS-based approaches in precision medicine.

Valency-Based Topological Descriptors and Structural Property of the Generalized Sierpiński Networks

A molecular network can be characterized by several different ways, like a matrix, a polynomial, a drawing or a topological descriptor. A topological descriptor is a numeric quantity associated with a network or a graph that characterizes its whole structural properties. Analyzing and determining the topological indices and structural properties of a network or a graph have been a worthy studied topic in the field of chemistry, networks analysis, etc. In this paper, we consider several types of the generalized Sierpinski networks and investigate the explicit expressions of some well-known valency-based topological indices. Taking into account the other structural property of the generalized Sierpinski networks, the average degree is determined.

Topological Characterization of the Crystallographic Structure of Titanium Difluoride and Copper (I) Oxide

Owing to their distinguished properties, titanium difluoride (TiF2) and the crystallographic structure of Cu2O have attracted a great deal of attention in the field of quantitative structure–property relationships (QSPRs) in recent years. A topological index of a diagram (G) is a numerical quantity identified with G which portrays the sub-atomic chart G. In 1972, Gutman and Trinajstić resented the first and second Zagreb topological files of atomic diagrams. In this paper, we determine a hyper-Zagreb list, a first multiple Zagreb file, a second different Zagreb record, and Zagreb polynomials for titanium difluoride (TiF2) and the crystallographic structure of Cu2O.

Molecular Properties of Symmetrical Networks Using Topological Polynomials

AbstractA numeric quantity that comprehend characteristics of molecular graph Γ of chemical compound is known as topological index. This number is, in fact, invariant with respect to symmetry properties of molecular graph Γ. Many researchers have established, after diverse studies, a parallel between the physico chemical properties like boiling point, stability, similarity, chirality and melting point of chemical species and corresponding chemical graph. These descriptors defined on chemical graphs are extremely helpful for researchers to conduct regression model like QSAR/QSPR and better understand the physical features, complexity of molecules, chemical and biological properties of underlying compound.In this paper, several structure descriptors of vital importance, namely, first, second, modified and augmented Zagreb indices, inverse and general Randic indices, symmetric division, harmonic, inverse sum and forgotten indices of Hex-derived Meshes (networks) of two kinds, namely, HDN1(n) and HDN2(n) are computed and recovered using general approach of topological polynomials.

Distributional regression forests for probabilistic precipitation forecasting in complex terrain

To obtain a probabilistic model for a dependent variable based on some set of explanatory variables, a distributional approach is often adopted where the parameters of the distribution are linked to regressors. In many classical models this only captures the location of the distribution but over the last decade there has been increasing interest in distributional regression approaches modeling all parameters including location, scale and shape. Notably, so-called nonhomogeneous Gaussian regression (NGR) models both mean and variance of a Gaussian response and is particularly popular in weather forecasting. Moreover, generalized additive models for location, scale and shape (GAMLSS) provide a framework where each distribution parameter is modeled separately capturing smooth linear or nonlinear effects. However, when variable selection is required and/or there are nonsmooth dependencies or interactions (especially unknown or of high-order), it is challenging to establish a good GAMLSS. A natural alternative in these situations would be the application of regression trees or random forests but, so far, no general distributional framework is available for these. Therefore, a framework for distributional regression trees and forests is proposed that blends regression trees and random forests with classical distributions from the GAMLSS framework as well as their censored or truncated counterparts. To illustrate these novel approaches in practice, they are employed to obtain probabilistic precipitation forecasts at numerous sites in a mountainous region (Tyrol, Austria) based on a large number of numerical weather prediction quantities. It is shown that the novel distributional regression forests automatically select variables and interactions, performing on par or often even better than GAMLSS specified either through prior meteorological knowledge or a computationally more demanding boosting approach.

Selecting data to clean for fact checking

We study the optimization problem of selecting numerical quantities to clean in order to fact-check claims based on such data. Oftentimes, such claims are technically correct, but they can still mislead for two reasons. First, data may contain uncertainty and errors. Second, data can be "fished" to advance particular positions. In practice, fact-checkers cannot afford to clean all data and must choose to clean what "matters the most" to checking a claim. We explore alternative definitions of what "matters the most": one is to ascertain claim qualities (by minimizing uncertainty in these measures), while an alternative is just to counter the claim (by maximizing the probability of finding a counterargument). We show whether the two objectives align with each other, with important implications on when fact-checkers should exercise care in selective data cleaning, to avoid potential bias introduced by their desire to counter claims. We develop efficient algorithms for solving the various variants of the optimization problem, showing significant improvements over naive solutions. The problem is particularly challenging because the objectives in the fact-checking context are complex, non-linear functions over data. We obtain results that generalize to a large class of functions, with potential applications beyond fact-checking.

Does mental number line training work? The effects of cognitive training on real-life mathematics, numeracy, and decision making.

We developed and validated intervention aimed at enhancing numeracy (the ability to understand and use the concept of probability and statistical information) and decision making. One hundred and twenty-two participants were randomly assigned to a Mental Number Line Training condition (MNLT) or an Arithmetic Training Active Control condition (ATAC). Response mode (a slider anchored within the current response range vs. a numerical keyboard) was the only, and essential, difference between experimental conditions. After MNLT, participants developed a more precise mapping of numbers onto the mental number line. However, the results regarding the transfer of this effect to performance in other cognitive tasks were mixed. We observed the transfer to an ability to quickly estimate the sum of numerical quantities (measured by the precision of estimates for the total price of everyday products), but we did not find evidence that MNLT, as compared to the control condition, improved performance on numerical competencies measures or decision-making tasks. Interestingly, we found that both MNLT and ATAC resulted in higher subjective numeracy as well as normatively better financial decisions, and valuation of risky prospects. Developing more exact symbolic-number mapping may be a promising direction of future research on improving decision making skills. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

On Some New Neighborhood Degree-Based Indices for Some Oxide and Silicate Networks

Topological indices are numeric quantities that describes the topology of molecular structure in mathematical chemistry. An important area of applied mathematics is the chemical reaction network theory. Real-world problems can be modeled using this theory. Due to its worldwide applications, chemical networks have attracted researchers since their foundation. In this report, some silicate and oxide networks are studied, and exact expressions of some newly-developed neighborhood degree-based topological indices named as the neighborhood Zagreb index ( M N ), the neighborhood version of the forgotten topological index ( F N ), the modified neighborhood version of the forgotten topological index ( F N ∗ ), the neighborhood version of the second Zagreb index ( M 2 ∗ ), and neighborhood version of the hyper Zagreb index ( H M N ) are obtained for the aforementioned networks. In addition, a comparison among all the indices is shown graphically.

Applying machine learning to predict future adherence to physical activity programs

BackgroundIdentifying individuals who are unlikely to adhere to a physical exercise regime has potential to improve physical activity interventions. The aim of this paper is to develop and test adherence prediction models using objectively measured physical activity data in the Mobile Phone-Based Physical Activity Education program (mPED) trial. To the best of our knowledge, this is the first to apply Machine Learning methods to predict exercise relapse using accelerometer-recorded physical activity data.MethodsWe use logistic regression and support vector machine methods to design two versions of a Discontinuation Prediction Score (DiPS), which uses objectively measured past data (e.g., steps and goal achievement) to provide a numerical quantity indicating the likelihood of exercise relapse in the upcoming week. The respective prediction accuracy of these two versions of DiPS are compared, and then numerical simulation is performed to explore the potential of using DiPS to selectively allocate financial incentives to participants to encourage them to increase physical activity.Resultswe had access to a physical activity trial data that were continuously collected every 60 sec every day for 9 months in 210 participants. By using the first 15 weeks of data as training and test on weeks 16–30, we show that both versions of DiPS have a test AUC of 0.9 with high sensitivity and specificity in predicting the probability of exercise adherence. Simulation results assuming different intervention regimes suggest the potential benefit of using DiPS as a score to allocate resources in physical activity intervention programs in reducing costs over other allocation schemes.ConclusionsDiPS is capable of making accurate and robust predictions for future weeks. The most predictive features are steps and physical activity intensity. Furthermore, the use of DiPS scores can be a promising approach to determine when or if to provide just-in-time messages and step goal adjustments to improve compliance. Further studies on the use of DiPS in the design of physical activity promotion programs are warranted.Trial registrationClinicalTrials.gov NCT01280812 Registered on January 21, 2011.

Attentional amplification of neural codes for number independent of other quantities along the dorsal visual stream.

Humans and other animals base important decisions on estimates of number, and intraparietal cortex is thought to provide a crucial substrate of this ability. However, it remains debated whether an independent neuronal processing mechanism underlies this 'number sense', or whether number is instead judged indirectly on the basis of other quantitative features. We performed high-resolution 7 Tesla fMRI while adult human volunteers attended either to the numerosity or an orthogonal dimension (average item size) of visual dot arrays. Along the dorsal visual stream, numerosity explained a significant amount of variance in activation patterns, above and beyond non-numerical dimensions. Its representation was selectively amplified and progressively enhanced across the hierarchy when task relevant. Our results reveal a sensory extraction mechanism yielding information on numerosity separable from other dimensions already at early visual stages and suggest that later regions along the dorsal stream are most important for explicit manipulation of numerical quantity.

Topological Characterization of Nanosheet Covered by C3 and C6

A topological index of a graph is a single numeric quantity which relates the chemical structure with its underlying physical and chemical properties. Topological indices of a nanosheet can help us to understand the properties of the material better. This study deals with computation of degree-dependent topological indices like the Randic index, first Zagreb index, second Zagreb index, geometric arithmetic index, atom bond connectivity index, sum connectivity index and hyper Zagreb index of nanosheet covered by C3 and C6. Furthermore, M-polynomial of the nanosheet is also computed, which provides an alternate way to express the topological indices.

People overestimate verbal quantities of nutrients on nutrition labels

Nutrition labels provide information about nutrient quantities in food, thus offering consumers a tool to make healthy eating choices. These labels are often presented with verbal quantity information (e.g., ‘low’). However, little is known about how consumers actually interpret this information. We investigated whether participants’ translations of verbal quantities fit standard guidelines, and whether nutrient valence and individual differences predicted interpretational variability. In Experiment 1, participants (N = 82) gave numerical percentages for five verbal quantities, selected a verbal expression that best described eight numerical quantities, and estimated the amount conveyed by quantities of both formats on a visual analogue scale (all quantities and nutrients manipulated within-subject). In Experiment 2, participants (N = 801) translated five verbal quantities into numerical percentages. Participants interpreted quantities with great variability (SDs for given estimates ranging from 12 to 30%). About 50% of participants substantially overestimated the numerical value of verbal quantities as compared to food labelling guideline ranges. Participants’ estimates were greater for minerals than fat in Experiment 2. The magnitude of estimations persisted across participants with different individual characteristics. Thus, consumers misinterpret verbal labels by overestimating the quantities they describe. It could be beneficial to refine guideline ranges for nutrient values to better match people’s intuitive interpretation of verbal quantities.

Degree based topological invariants of splitting graph

Topological invariants are the graph theoretical tools to the theoretical chemists, that correlates the molecular structure with several chemical reactivity, physical properties or biological activity numerically. A function having a set of networks(graph, molecular structure) as its domain and a set of real numbers as its range is referred as a topological invariant(index). Topological invariants are numerical quantity of a network that are invariant under graph isomorphism. Topological invariants such as Zagreb index, Randić index and multiplicative Zagreb indices are used to predict the bioactiviy of chemical compounds in QSAR/QSPR study. In this paper, we compute the general expression of certain degree based topological invariants such as second Zagreb index, F-index, Hyper-Zagreb index, Symmetric division degree index, irregularity of Splitting graph. And also we obtain upper bound for first and second multiplicative Zagreb indices of Splitting graph of a graph H, (S′(H)).

Digitizing gauge fields: Lattice Monte Carlo results for future quantum computers

In the near-future noisy intermediate-scale quantum (NISQ) era of quantum computing technology, applications of quantum computing will be limited to calculations of very modest scales in terms of the number of qubits used. The need to represent numeric quantities using limited resources leads to digitization errors which must be taken into account. As a first step towards quantum simulations of realistic high-energy physics problems, we explore classically the effects of digitizing elements of the $\mathrm{SU}(2)$ gauge group to a finite set. We consider several methods for digitizing the group, finding the best performance from an action-preserving projection onto a mesh. Working in (3+1) dimensions, we find that using $\sim 7$ (qu)bits to represent each $\mathrm{SU}(2)$ gauge link induces a digitization error on the order of $10\%$ in short-distance observables and $2\%$ in long-distance observables. Promisingly, our results indicate that each $\mathrm{SU}(2)$ gauge link can be represented by $\mathcal{O}(10)$ (qu)bits, from which we estimate that a $16^3$ $\mathrm{SU}(2)$ lattice could be simulated with no more than $\mathcal{O}(10^5)$ (qu)bits. Our results on digitization are also of interest as a form of lossy compression that could be used in high-performance classical computing to alleviate communications bottlenecks.

Certain polynomials and related topological indices for the series of benzenoid graphs

A topological index of a molecular structure is a numerical quantity that differentiates between a base molecular structure and its branching pattern and helps in understanding the physical, chemical and biological properties of molecular structures. In this article, we quantify four counting polynomials and their related topological indices for the series of a concealed non-Kekulean benzenoid graph. Moreover, we device a new method to calculate the PI and Sd indices with the help of Theta and Omega polynomials.

Where words meet numbers: Comprehension of measurement unit terms in posterior cortical atrophy

Units of measurement (e.g., metre, week, gram) are critically important concepts in everyday life. Little is known about how knowledge of units is represented in the brain or how this relates to other forms of semantic knowledge. As unit terms are intimately connected with numerical quantity, we might expect knowledge for these concepts to be supported by parietally-mediated representations of space, time and magnitude. We investigated knowledge for measurement units in patients with posterior cortical atrophy (PCA), who display profound impairments of spatial and numerical cognition associated with occipital and parietal lobe atrophy. Relative to healthy controls, PCA patients displayed impairments for a range of unit-based knowledge, including the ability to specify the dimension which a unit refers to (e.g., grams measure mass), to select the appropriate units to measure everyday quantities (e.g., grams for sugar) and to determine the relative magnitudes of different unit terms (e.g., gram is smaller than kilogram). In most cases, their performance was also significantly poorer than a patient control group diagnosed with typical Alzheimer's disease. Our results suggest that impairment to systems that code numerical and spatial magnitudes has an effect on non-numerical verbal knowledge for measurement units. Units of measurement appear to lie at the intersection of the brain's verbal and numerical semantic systems, making them a critical class of concepts in which to investigate how magnitude-based codes contribute to verbal semantic representation.

The progressive 6-year-old conserver: Numerical saliency and sensitivity as core mechanisms of numerical abstraction in a Piaget-like estimation task

In Piaget’s theory of number development, children do not possess a true concept of number until they are able to reason on numerical quantity regardless of changes in other nonnumerical magnitudes, such as length. Recent studies have echoed this result by arguing that abstracting number from nonnumerical dimensions of magnitude is a developmental milestone and a strong predictor of mathematics achievement. However, the mechanisms supporting such abstraction remain largely underspecified. We aimed to study how identification of the numerical equivalence in a Piaget-like estimation task by 6-year-old children is affected by (a) the degree of interference between number and nonnumerical magnitudes and (b) children’s spontaneous orientation to numerosity. Six-year-old children first performed a card sorting task assessing their spontaneous orientation towards numerosity, spacing, or item size in a set of dots. Then, they completed a Piaget-like same/different numerical estimation task using two rows of dots in which the length ratio between the two rows varied systematically. Children were less likely to accept the numerical equivalence in the Piaget-like estimation task (a) as the difference in spacing between the dots increased and (b) as the children were more spontaneously oriented towards spacing over number in the card sorting task. Our results suggest that abstracting number depends on its saliency, which varies both as a function of the context (i.e., length ratio between the two rows) and of individual differences in children’s sensitivity to the numerical aspects of their environment. These factors could be at the root of the observed development of performance in the seminal number-conservation task, which appears as a progressive abstraction of number rather than a conceptual shift, as Piaget hypothesized.

Deflected trajectory of a single fluid-driven crack under anisotropic in-situ stress

Deflected crack trajectories are detected in hydraulic fracturing. There are numerous physical quantities impacting the deflection of a fluid-driven crack. A 2D model of the elasto-hydrodynamics system is established to predict the crack trajectory and to investigate the coupling effects of anisotropic in-situ stress, fluid viscosity, fluid injection rate and crack inclination on the crack deflection. The displacement discontinuity method (DDM) and the finite difference method (FDM) are used to solve the nonlinear problem. The concept of deflection region is defined to quantify the crack deflection. Results show that the size of the deflection region is dominated by the inclination angle. Increase of the magnitude and the difference of in-situ stresses promotes crack deflection. The combined effects of fluid viscosity and fluid injection rate are divided into three stages: significant prevention stage, significant promotion stage and insignificant prevention stage. This study provides the method for crack trajectory prediction and crack deflection control.