Understanding Estimations of Magnitudes: An fMRI Investigation

The current study examined whether discrete numerical estimation is based on the same cognitive process as estimation of continuous magnitudes such as weight and time. While the verbal estimation of numerical quantities has a contingent unit of measurement (e.g., how many cookies fit in a cookie jar? _X_ cookies), estimation of time and weight does not (e.g., how much time does it take to fill a bath with water? _X_ minutes/hours/seconds). Therefore, estimation of the latter categories has another level of difficulty, requiring extensive involvement of cognitive control. During a functional magnetic resonance imaging (fMRI) scan, 18 students performed estimations with three estimation categories: number, time, and weight. Estimations elicited activity in multiple brain regions, mainly: (1) visual regions including bilateral lingual gyrus), (2) parietal regions including the left angular gyrus and right supramarginal gyrus, and (3) the frontal regions (cingulate gyrus and the inferior frontal cortex). Continuous magnitude estimations (mostly time) produced different frontal activity than discrete numerical estimations did, demonstrating different profiles of brain activations between discrete numerical estimations and estimations of continuous magnitudes. The activity level in the right middle and inferior frontal gyrus correlated with the tendency to give extreme responses, signifying the importance of the right prefrontal lobe in estimations.

Numerical and Experimental Study of Five-Layer Non-Symmetrical Paperboard Panel Stiffness

This paper concerns the analysis of five-layer corrugated paperboard subjected to a four-point bending test. The segment of paperboard was tested to determine the bending stiffness. The investigations were conducted experimentally and numerically. The non-damaging tests of bending were carried out in an elastic range of samples. The detailed layers of paperboard were modelled as an orthotropic material. The simulation of flexure was based on a finite element method using Ansys® software. Several material properties and thicknesses of papers in the samples were taken into account to analyse the influence on general stiffness. Two different discrete models based on two geometries of paperboard were considered in this study to validate the experimental stiffness. The present analysis shows the possibility of numerical modelling to achieve a good correlation with experimental results. Moreover, the results of numerical estimations indicate that modelling of the perfect structure gives a lower bending stiffness and some corrections of geometry should be implemented. The discrepancy in stiffness between both methods ranged from 3.04 to 32.88% depending on the analysed variant.

Shaping the Way from the Unknown to the Known: The Role of Convex Hull Shape in Numerical Comparisons

Various studies have shown that numerical processing is modulated by non-numerical physical properties. One such physical property is the convex hull – the smallest convex polygon surrounding all items in an array. The convex hull is usually discussed only in terms of its area. However, our group has shown that observers use the convex hull shape, as defined according to the number of vertices of the convex hull, to make numerical estimations (Katzin et al., 2020). Yet, it is still unknown if and how the convex hull shape affects comparison tasks, and how it interacts with its counterpart, convex hull area. Here we re-examine the data collected by Katzin and colleagues (2019). Using image processing, we extracted the information on the convex hull shape and showed that the shape affects latency and accuracy of numerical comparisons. We found that both the convex hull shape and other physical properties (i.e., convex hull area, average diameter, density, total circumference, and total surface area) have distinct effects on performance. Finally, the convex hull shape effect was found in counting and estimation ranges, however its effect decreased with numerosities above the counting range. Our results indicate that the interplay between convex hull shape and other physical properties, including convex hull area and numerosity, plays an important role in numerical decisions. We suggest that the convex hull shape should be controlled for when designing non-symbolic numerical tasks.

Appraisal of linear load effect on non-linear distortion coefficient from rectifier

Object and purpose of research. The object of research is the rectifier (transducer) OPED-12,5-115 (О – single phase; P – direct current; Е – natural air cooling; D – on diodes with an example of document record; 12.5 – current rating; 115 – voltage rating). Materials and methods. Methods of power electronics and harmonic analysis are applied. Main results. Ways of appraisal and restriction for the harmonic coefficient (non-linear distortion coefficient from transducer) are worked out taking account of an active load of higher frequencies generator (400 Hz). Conclusion. Numerical estimations for the attenuation coefficient of harmonics 3, 5 and 7 are obtained using basic values Xd and Xq of generator АТО-20.

Evaluation of Simplified Physics-Based Building Energy Model for the Purpose of Automatic Fault Detection

Buildings are complex systems with dynamic loading and ever-changing usage. Additionally, there is a need to reduce unnecessary energy consumption while increasing occupant health in buildings via implementation of manual fault detection with available building design programs. However, a common problem with the current lineup of programs is that they require extensive inputs for material properties and usage loads; this results in spending extensive amounts of time performing model calibration and having to adjust multiple values (sometimes hundreds) to bring a model in alignment with actual building use. However, a simplified physics-based model (SPBM) can achieve a level of modeling accuracy sufficient for automatic fault detection with as few as ten automatically calibrated unknown parameters. Obviously, other simplified building energy models exist; however, these often rely on ignoring important details, such as humidity, CO2, and per-hour performance, or implement averaged numerical estimations. Due to the limitations of current modeling programs, some development has begun on rule-based and component-based fault detection by several companies and researchers. While component-based fault detection is effective, it relies on accurate sensor readings and does not account for actual building performance. A suitable rigorous physics-based model has not been developed for the purpose of fault detection. Therefore, by comparing the accuracy of an automatically calibrated SPBM with real-world building performance and high-fidelity building energy models will provide baseline knowledge about if such a model can even achieve a high enough level of fidelity to reliably represent the complexity of a building.

MANIFESTATION OF AN EXCITED ELECTRON IN e⁺e¯ → γγ REACTION

The differential cross section and some polarization observables have been calculated for the e⁺e¯ → γγ reaction taking into account the contribution of the excited electron. The spin correlation coefficients were calculated for the case when both beams are polarized. We consider two approaches for the excited electron contribution: the eу → γγ contact interaction and the exchange of the excited electron in t- and u-channels. Numerical estimations are given for the excited electron contribution to the differential cross section and spin correlation coefficients for vari-ous values of the electron beam energy and excited electron mass.

Developmental trajectories of number line estimations in math anxiety: evidence from bounded and unbounded number line estimation

In the number line estimation task, participants are instructed to place a number, spatially, on a number line. In the present study, 2nd, 3rd and 5th grade children (n = 94) participated in bounded and unbounded number line estimation tasks, half with low math anxiety (LMA) and half with high MA (HMA). The spatial theory views MA as resulting from weakness in spatial abilities, subsequent to deficits in basic numerical abilities. Accordingly, due to number space associations, weakness in estimations are expected in HMA individuals. Accordingly, young children with HMA show non-mature numerical estimations compared to participants with LMA. Specifically, HMA participants showed higher logarithmic tendency than LMA peers, and showed indications for usage of 2 reference points rather than 3 reference points in number line estimations (bounded and unbounded). However, for older HMA children, estimations were normalized and group differences were eliminated. Finally, we found that estimations (linear fits and errors) in the bounded but not the unbounded tasks, predicted usage of advance memory-based strategies in simple addition operations. These results indicated that bounded and unbounded number line estimations are dissociable in 1) developmental trajectories, 2) in relation to MA and 3) in relation to math performances.

Модель графаноподобных соединений h-AB-C: аналитические оценки

In analogy with graphane and fluorographene the model for the compounds h-AB – C, where А and В atoms occupy the sites of the flat hexagonal lattice and С atoms, connected with А and В atoms, are placed by the opposite sides of the АВ-list is proposed. Numerical estimations are fulfilled for the h-A3B5 – C4 compounds, where А, В and С are the atoms from the same row of the Periodic Table. Analytical results are obtained for the electronic spectrum, quantum capacitance, local defect states, force constants and characteristics phonon friquences.

Personalized Key Drivers for Individual Responses in Regression Modeling

Identification of personalized key drivers is useful to managers in finding a special set of tools for each customer for a better contingency to a higher satisfaction and loyalty and for diminishing risk and uncertainty of decision making. Finding the most attractive attributes of a product for a buyer, or the main helpful features of a medicine for a patient, can be considered via identifying the key drivers in regression modeling. The problem of predictor importance is usually considered on the aggregate level for a set of all respondents. This article shows how to identify a specific set of key drivers for each individual respondent. Two techniques are proposed: the orthonormal matrices used for the relative importance by Gibson and R. Johnson, and the cooperative game theory by Shapley value of predictors in regression. Numerical estimations show that a specific set of key drivers can be found for each respondent or customer, that can be valuable for managerial decisions in marketing research and other areas of practical statistical modeling.