Acquiring the cardinal knowledge of number words: A conceptual replication

Understanding the way in which counting represent numerosities was shown to be a long-lasting process. As shown in the Give-a-number task, acquiring the meanings of verbal number words goes through successive developmental stages in which children first learn the cardinal meanings of small number words one at a time before generalizing the cardinal principle they have induced from the first three number words to all number words within their counting range. This acquisition would take about a year, and would be completed by the age of 3 ½ years. The aim of the present study was to provide a conceptual replication of the developmental sequence described in Wynn’s study nearly 30 years ago using the Give-a-number task. A first cross-sectional study was conducted on 213 Belgian children aged between 39 and 74 months using the Give-a-number task to examine the developmental pattern and the influence of age on this acquisition. The time span of acquisition was examined in a second study in which 34 children were tested five times every months between the age of 36 to 52 months. Results showed that acquiring the cardinal meanings of number words spread out over a protracted period, far more extended than assumed by Wynn. Furthermore, children do not generalize all-at-once to large number words, the cardinal knowledge they learned on small number words. Rather, number words were found to be learned one at a time in a really progressive manner. Results were discussed with regard to their implications for the existing theories and in relation with other tasks assessing the acquisition of verbal number symbols.

A stopping layer concept to improve the spatial resolution of GEM neutron detector

In recent years, Gas Electron Multiplier (GEM) neutron detector has been developing towards high spatial resolution and high dynamic counting range. A novel concept of the Al stopping layer was proposed to enable the detector to achieve sub-millimeter (sub-mm) spatial resolution. The neutron conversion layer was coated with the Al stopping layer to limit the emission angle of ions into the drift region. The short track projection of ions was obtained on the signal readout board, and the detector would get good spatial resolution. The spatial resolutions of the GEM neutron detector with Al stopping layer were simulated and optimized based on Geant4GarfieldInterface. When Al stopping layer was 3.0 μm thick, drift region was 2 mm thick, strip pitch was 600 μm, and digital readout was employed. The spatial resolution of the detector was 0.76 mm, and the thermal neutron detection efficiency was about 0.01%. Thus, the GEM neutron detector with a simple detector structure and a fast readout mode was developed to obtain a high spatial resolution and high dynamic counting range. It could be used for the direct measurement of a high-flux neutron beam, such as Bragg transmission imaging, very small-angle scattering neutron detection and neutron beam diagnostic.

Photobleaching step analysis for robust determination of protein complex stoichiometries

The counting of discrete photobleaching steps in fluorescence microscopy is ideally suited to study protein complex stoichiometry in situ. The counting range of photobleaching step analysis has significantly improved with more sophisticated algorithms for step detection, albeit at an increasing computational cost and with the necessity for high data quality. Here, we address concerns regarding robustness, automation, and experimental validation, optimizing both data acquisition and analysis. To make full use of the potential of photobleaching step analysis, we evaluate various labelling strategies with respect to their molecular brightness, photostability, and photoblinking. The developed analysis algorithm focuses on automation and computational efficiency. Moreover, we validate the developed methods with experimental data acquired on DNA origami labeled with defined fluorophore numbers, demonstrating counting of up to 35 fluorophores. Finally, we show the power of the combination of optimized trace acquisition and automated data analysis by counting labeled nucleoporin 107 in nuclear pore complexes of intact U2OS cells. The successful in situ application promotes this framework as a new resource enabling cell biologists to robustly determine the stoichiometries of molecular assemblies at the single-molecule level in an automated fashion.

Number symbols are processed more automatically than nonsymbolic numerical magnitudes: Findings from a Symbolic-Nonsymbolic Stroop task

Are number symbols (e.g., 3) and numerically equivalent quantities (e.g., •••) processed similarly or distinctly? If symbols and quantities are processed similarly then processing one format should activate the processing of the other. To experimentally probe this prediction, we assessed the processing of symbols and quantities using a Stroop-like paradigm. Participants (NStudy1 = 80, NStudy2 = 63) compared adjacent arrays of symbols (e.g., 4444 vs 333) and were instructed to indicate the side containing either the greater quantity of symbols (nonsymbolic task) or the numerically larger symbol (symbolic task). The tasks included congruent trials, where the greater symbol and quantity appeared on the same side (e.g. 333 vs. 4444), incongruent trials, where the greater symbol and quantity appeared on opposite sides (e.g. 3333 vs. 444), and neutral trials, where the irrelevant dimension was the same across both sides (e.g. 3333 vs. 333 for nonsymbolic; 333 vs. 444 for symbolic). The numerical distance between stimuli was systematically varied, and quantities in the subitizing and counting range were analyzed together and independently. Participants were more efficient comparing symbols and ignoring quantities, than comparing quantities and ignoring symbols. Similarly, while both symbols and quantities influenced each other as the irrelevant dimension, symbols influenced the processing of quantities more than quantities influenced the processing of symbols, especially for quantities in the counting rage. Additionally, symbols were less influenced by numerical distance than quantities, when acting as the relevant and irrelevant dimension. These findings suggest that symbols are processed differently and more automatically than quantities.

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.

Photobleaching step analysis for robust determination of protein complex stoichiometries

The composition of cellular structures on the nanoscale is a key determinant of macroscopic functions in cell biology and beyond. Different fluorescence single-molecule techniques have proven ideally suited for measuring protein copy numbers of cellular structures in intact biological samples. Of these, photobleaching step analysis poses minimal demands on the microscope and its counting range has significantly improved with more sophisticated algorithms for step detection, albeit at an increasing computational cost. Here, we present a comprehensive framework for photobleaching step analysis, optimizing both data acquisition and analysis. To make full use of the potential of photobleaching step analysis, we evaluate various labelling strategies with respect to their molecular brightness and photostability. The developed analysis algorithm focuses on automation and computational efficiency. Moreover, we benchmark the framework with experimental data acquired on DNA origami labeled with defined fluorophore numbers to demonstrate counting of up to 35 fluorophores. Finally, we show the power of the combination of optimized trace acquisition and automated data analysis for robust protein counting by counting labelled nucleoporin 107 in nuclear pore complexes of intact U2OS cells. The successful in situ application promotes this framework as a new resource enabling cell biologists to robustly determine the stoichiometries of molecular assemblies at the single-molecule level in an automated fashion.

INVESTIGASI KANDUNGAN RADIOISOTOP DALAM SAMPEL BATUAN DI MUARA SUNGAI SUMLILI KUPANG BARAT

Abstrak Masalah pokok yang dikaji di penelitian ini adalah pemetaan dan analisis aktivitas jenis kandungan radioisotop dalam sampel batuan di muara sungai Sumlili Kupang Barat. Tujuan penelitian meliputi : menentukanrange cacah dan aktivitas jenis massa (C) kandungan radioisotop dalam sampel pasir di muara sungai Sumlili Kupang Barat, mengestimasi tingkat kontaminasi radioisotop sesuai standar di sekitar muara sungai Sumlili, dan memetakan sebaran cacah radioisotop pada luasan daerah tertentu yang terjangkau survei di lapangan. Metode penelitian meliputi : observasi/survei, sampling, serta analisis dan interpretasi data. Kisaran cacah radiasi di lapangan, di laboratorium, dan nilai aktivitas jenis massa kandungan radioisotop dalam 52 sampel pasir dari lokasi penelitian dimuara sungai Sumili Kupang Barat secara berturut-turut adalah 19 cpm sampai dengan 60 cpm, 29 cpm sampai dengan 73 cpm, dan 0,107 x 10-5μCi/gram sampai dengan 0,269 x 10-5μCi/gram. Berdasarkan kontur dan kurva tiga dimensi radiasi cacah radioisotop dalam sampel pasir di lapangan dan di laboratorium serta kontur dan kurva tiga dimensi aktivitas jenis massa di muara sungai Sumlili Kupang Barat dapat diketahui bahwa sebaran kontaminasi radioisotop di muara sungai Sumlili Kupang Barat lebih tinggi ke arah barat dan cenderung menurun ke arah timur. Hasil perhitungan aktivitas jenis massa kandungan radioisotop dalam sampel pasir di muara sungai Sumlili Kupang Barat, termaksud dalam kontaminasi rendah untuk radiasi alpha (α) dan beta (β), namun daerah ini perlu diwaspadai karna terdapat beberapa titik di lapangan, cacah radiasi nuklir kandungan radioisotop dalam deposit mineral cukup tinggi melebihi standar IAEA. Kata kunci : Radioisotop, Aktivitas Jenis Massa, Daerah Kontaminasi. ABSTRACT The main problem studied in this study is mapping and analyzing the activity of the types of radioisotope content in rock samples at the mouth of the Sumlili river in West Kupang. The research objectives included: determining the counting range and mass type activity (C) radioisotope content in the sand samples at the Sumlili River mouth in West Kupang, estimating the level of radioisotope contamination according to the standards around the Sumlili river estuary, and mapping the distribution of radioisotope counts in the area covered by surveys in field. Research methods include: observation / survey, sampling, and analysis and interpretation of data. The range of radiation counts in the field, in the laboratory, and the value of the type of mass activity of radioisotope content in 52 sand samples from the study locations in the West Kupang Sumili River are 19 cpm to 60 cpm, 29 cpm to 73 cpm, and 0.107 x 10-5μCi / gram up to 0.269 x 10-5μCi / gram. Based on the three-dimensional contour and curve of radiation from radioisotope counts in sand samples in the field and in the laboratory and three-dimensional contours and curves the activity of mass types in the Sumlili estuary of West Kupang can be seen that the distribution of radioisotope contamination in the Sumlili estuary of West Kupang is higher west and tends to decline to the east. The results of the calculation of the type of mass activity of radioisotope content in sand samples at the mouth of the Sumlili River in West Kupang, are referred to in low contamination for alpha (α) and beta (β) radiation, but this area needs to be watched out for there are several points in the field, nuclear radiation in mineral deposits quite high exceeding IAEA standards. Keywords : Radioisotopes, Mass Type Activities, Contamination Areas.

Counting to Infinity: Does learning the syntax of the count list predict knowledge that numbers are infinite?

By around the age of 5½, many children in the US judge that numbers never end, and that it is always possible to add +1 to a set. These same children also generally perform well when asked to label the quantity of a set after 1 object is added (e.g., judging that a set labeled “five” should now be “six”). These findings suggest that children have implicit knowledge of the “successor function”: every natural number, n, has a successor, n+1. Here, we explored how children discover this recursive function, and whether it might be related to discovering productive morphological rules that govern language-specific counting routines (e.g., the rules in English that represent base 10 structure). We tested 4- and 5-year-old children’s knowledge of counting with three tasks, which we then related to (1) children’s belief that 1 can always be added to any number (the successor function), and (2) their belief that numbers never end (infinity). Children who exhibited knowledge of a productive counting rule were significantly more likely to believe that numbers are infinite (i.e., there is no largest number), though such counting knowledge wasn’t directly linked to knowledge of the successor function, per se. Also, our findings suggest that children as young as four years of age are able to implement rules defined over their verbal count list to generate number words beyond their spontaneous counting range, an insight which may support reasoning over their acquired verbal count sequence to infer that numbers never end.