Analytical and numerical comparisons of two methods of estimation of additive × additive × additive interaction of QTL effects

This paper presents the analytical and numerical comparison of two methods of estimation of additive × additive × additive (aaa) interaction of QTL effects. The first method takes into account only the plant phenotype, while in the second we also included genotypic information from molecular marker observation. Analysis was made on 150 doubled haploid (DH) lines of barley derived from cross Steptoe × Morex and 145 DH lines from Harrington × TR306 cross. In total, 153 sets of observation was analyzed. In most cases, aaa interactions were found with an exert effect on QTL. Results also show that with molecular marker observations, obtained estimators had smaller absolute values than phenotypic estimators.

EXPRESS: Sometimes nothing is simply nothing: Automatic processing of empty sets

Previous work using the numerical comparison task has shown that an empty set, the nonsymbolic manifestation of zero, can be represented as the smallest quantity of the numerical magnitude system. In the present study, we examined whether an empty set can be represented as such under conditions of automatic processing in which deliberate processing of stimuli magnitudes is not required by the task. In Experiment 1, participants performed physical and numerical comparisons of empty sets (i.e., empty frames) and of other numerosities presented as framed arrays of 1 to 9 dots. The physical sizes of the frames varied within pairs. Both tasks revealed a size congruity effect (SCE) for comparisons of non-empty sets. In contrast, comparisons to empty sets produced an inverted SCE in the physical comparison task, while no SCE was found for comparisons to empty sets in the numerical comparison task. In Experiment 2, participants performed an area comparison task using the same stimuli as Experiment 1 to examine the effect of visual cues on the automatic processing of empty sets. The results replicated the findings of the physical comparison task in Experiment 1. Taken together, our findings indicate that empty sets are not perceived as “zero”, but rather as “nothing”, when processed automatically. Hence, the perceptual dominance of empty sets seems to play a more important role under conditions of automatic processing, making it harder to abstract the numerical meaning of zero from empty sets.

Testing the role of symbols in preschool numeracy: An experimental computer-based intervention study

Numeracy is of critical importance for scholastic success and modern-day living, but the precise mechanisms that drive its development are poorly understood. Here we used novel experimental training methods to begin to investigate the role of symbols in the development of numeracy in preschool-aged children. We assigned pre-school children in the U.S. and Italy (N = 215; Mean age = 49.15 months) to play one of five versions of a computer-based numerical comparison game for two weeks. The different versions of the game were equated on basic features of gameplay and demands but systematically varied in numerical content. Critically, some versions included non-symbolic numerical comparisons only, while others combined non-symbolic numerical comparison with symbolic aids of various types. Before and after training we assessed four components of early numeracy: counting proficiency, non-symbolic numerical comparison, one-to-one correspondence, and arithmetic set transformation. We found that overall children showed improvement in most of these components after completing these short trainings. However, children trained on numerical comparisons with symbolic aids made larger gains on assessments of one-to-one correspondence and arithmetic transformation compared to children whose training involved non-symbolic numerical comparison only. Further exploratory analyses suggested that, although there were no major differences between children trained with verbal symbols (e.g., verbal counting) and non-verbal visuo-spatial symbols (i.e., abacus counting), the gains in one-to-one correspondence may have been driven by abacus training, while the gains in non-verbal arithmetic transformations may have been driven by verbal training. These results provide initial evidence that the introduction of symbols may contribute to the emergence of numeracy by enhancing the capacity for thinking about exact equality and the numerical effects of set transformations. More broadly, this study provides an empirical basis to motivate further focused study of the processes by which children’s mastery of symbols influences children’s developing mastery of numeracy.

Experimental study of hygrothermal conditions in a wooden room for numerical comparisons

The use of hygroscopic materials indoors has a significant impact on the hygrothermal balance of a room air. It affects both the temperature and the relative humidity. Numerical tools still lack of accuracy in predicting these parameters and some discrepancies are observed between their predictions and experimental measurements. It may be caused by the model itself or by incorrect inputs data (materials properties, occupancy schedule, ventilation rate, etc…) Therefore, an experimental study has been carried out at the room scale under real climate to obtain an experimental dataset as a basis for numerical comparisons. The hygrothermal parameters of the room air have been measured for different loads while all the inputs (heat and moisture generation, air exchange and materials properties) have been properly quantified. This article presents the experimental setup and some of the experimental data obtained.

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.

Bayesian Sensitivity-Specificity and ROC Analysis for Finding Key Drivers

Finding key drivers in regression modeling via Bayesian Sensitivity-Specificity and Receiver Operating Characteristic is suggested, and clearly interpretable results are obtained. Numerical comparisons with other techniques show that this methodology can be useful in practical statistical modeling and analysis helping to researchers and managers in making meaningful decisions.

The Maximum k-Colorable Subgraph Problem and Related Problems

The maximum k-colorable subgraph (MkCS) problem is to find an induced k-colorable subgraph with maximum cardinality in a given graph. This paper is an in-depth analysis of the MkCS problem that considers various semidefinite programming relaxations, including their theoretical and numerical comparisons. To simplify these relaxations, we exploit the symmetry arising from permuting the colors, as well as the symmetry of the given graphs when applicable. We also show how to exploit invariance under permutations of the subsets for other partition problems and how to use the MkCS problem to derive bounds on the chromatic number of a graph. Our numerical results verify that the proposed relaxations provide strong bounds for the MkCS problem and that those outperform existing bounds for most of the test instances. Summary of Contribution: The maximum k-colorable subgraph (MkCS) problem is to find an induced k-colorable subgraph with maximum cardinality in a given graph. The MkCS problem has a number of applications, such as channel assignment in spectrum sharing networks (e.g., Wi-Fi or cellular), very-large-scale integration design, human genetic research, and so on. The MkCS problem is also related to several other optimization problems, including the graph partition problem and the max-k-cut problem. The two mentioned problems have applications in parallel computing, network partitioning, floor planning, and so on. This paper is an in-depth analysis of the MkCS problem that considers various semidefinite programming relaxations, including their theoretical and numerical comparisons. Further, our analysis relates the MkCS results with the stable set and the chromatic number problems. We provide extended numerical results that verify that the proposed bounding approaches provide strong bounds for the MkCS problem and that those outperform existing bounds for most of the test instances. Moreover, our lower bounds on the chromatic number of a graph are competitive with existing bounds in the literature.

Modified Hybrid Method with Four Stages for Second Order Ordinary Differential Equations

A modified explicit hybrid method with four stages is presented, with the first stage exactly integrating exp(wx), while the remaining stages exactly integrate sin(wx) and cos(wx). Special attention is paid to the phase properties of the method during the process of parameter selection. Numerical comparisons of the proposed and existing hybrid methods for several second-order problems show that the proposed method gives high accuracy in solving the Duffing equation and Kramarz’s system.