A picture of eight turtles: the child’s understanding of cardinality and numerosity

An essential part of understanding number words (e.g., eight) is understanding that all number words refer to the dimension of experience we call numerosity. Knowledge of this general principle may be separable from knowledge of individual number word meanings. That is, children may learn the meanings of at least a few individual number words before realizing that all number words refer to numerosity. Alternatively, knowledge of this general principle may form relatively early and proceed to guide and constrain the acquisition of individual number word meanings. The current article describes two experiments in which 116 children (2½- to 4-year-olds) were given a Word Extension task as well as a standard Give-N task. Results show that only children who understood the cardinality principle of counting successfully extended number words from one set to another based on numerosity—with evidence that a developing understanding of this concept emerges as children approach the cardinality principle induction. These findings support the view that children do not use a broad understanding of number words to initially connect number words to numerosity but rather make this connection around the time that they figure out the cardinality principle of counting

Learning to represent exact numbers

This article focuses on how young children acquire concepts for exact, cardinal numbers (e.g., three, seven, two hundred, etc.). I believe that exact numbers are a conceptual structure that was invented by people, and that most children acquire gradually, over a period of months or years during early childhood. This article reviews studies that explore children’s number knowledge at various points during this acquisition process. Most of these studies were done in my own lab, and assume the theoretical framework proposed by Carey (2009). In this framework, the counting list (‘one,’ ‘two,’ ‘three,’ etc.) and the counting routine (i.e., reciting the list and pointing to objects, one at a time) form a placeholder structure. Over time, the placeholder structure is gradually filled in with meaning to become a conceptual structure that allows the child to represent exact numbers (e.g., There are 24 children in my class, so I need to bring 24 cupcakes for the party.) A number system is a socially shared, structured set of symbols that pose a learning challenge for children. But once children have acquired a number system, it allows them to represent information (i.e., large, exact cardinal values) that they had no way of representing before

Analysis of the impact of sex and age on the variation in the prevalence of antinuclear autoantibodies in Polish population: a nationwide observational, cross-sectional study

The detection of antinuclear autoantibody (ANA) is dependent on many factors and varies between the populations. The aim of the study was first to assess the prevalence of ANA in the Polish adult population depending on age, sex and the cutoff threshold used for the results obtained. Second, we estimated the occurrence of individual types of ANA-staining patterns. We tested 1731 patient samples using commercially available IIFA using two cutoff thresholds of 1:100 and 1:160. We found ANA in 260 participants (15.0%), but the percentage of positive results strongly depended on the cutoff level. For a cutoff threshold 1:100, the positive population was 19.5% and for the 1:160 cutoff threshold, it was 11.7%. The most prevalent ANA-staining pattern was AC-2 Dense Fine speckled (50%), followed by AC-21 Reticular/AMA (14.38%) ANA more common in women (72%); 64% of ANA-positive patients were over 50 years of age. ANA prevalence in the Polish population is at a level observed in other highly developed countries and is more prevalent in women and elderly individuals. To reduce the number of positive results released, we suggest that Polish laboratories should set 1:160 as the cutoff threshold

On asymptotic approach to reliability improvement of multi-state systems with components quantitative and qualitative redundancy : series and parallel systems

The paper is composed of two parts, in this part after introducing the multi-state and the asymptotic approaches to system reliability evaluation the multi-state homogeneous series and parallel systems with reserve components are defined and their multi-state limit reliability functions are determined. In order to improve of the reliability of these systems the following methods are used: (i) a warm duplication of components, (ii) a cold duplication of components, (iii) a mixed duplication of components, (iv) improving the reliability of components by reducing their failure rate. Next, the effects of the systems’ reliability different improvements are compared

On asymptotic approach to reliability improvement of multi-state systems with components quantitative and qualitative redundancy : „m out of n” systems

The paper is composed of two parts, in this part the multi-state homogeneous „m out of n” systems with reserve components are defined and their multi-state limit reliability functions are determined. In order to improve of the reliability of these systems the following methods are used: (i) a warm duplication of components, (ii) a cold duplication of components, (iii) a mixed duplication of components, (iv) improving the reliability of components by reducing their failure rate. Next, the effects of the systems’ reliability different improvements are compared

Reliability and risk function improvement of bulk cargo transportation system

In the paper the basic notions of the ageing multistate systems reliability analysis are introduced. The multistate system reliability functions are defined and the mean values of the multistate system lifetimes in the reliability state subsets and in the particular reliability states are determined. The notion of the multistate system risk function and the moment of the system exceeding the critical reliability state are introduced. Further, in the developed reliability models, it is assumed that the system’s components have the multistate Weibull reliability functions with various parameters in their different reliability state subsets. Under this assumption, the proposed multistate system reliability models are applied in maritime transport to the reliability analysis of a bulk cargo transportation system and its reliability function, moreover other main characteristics are determined

Models of reliability and availability improvement of series and parallel systems related to their operation processes

Integrated general models of approximate approaches of complex multi-state series and parallel systems, linking their reliability and availability improvement models and their operation processes models caused changing reliability and safety structures and components reliability characteristics in different operations states, are constructed. These joint models are applied to determining improved reliability and availability characteristics of the considered multi-state series and parallel systems related to their varying in time operation processes. The conditional reliability characteristics of the multi-state systems with hot, cold single reservation of component and the conditional reliability characteristics of the multi-state systems with reduced rate of departure by a factor of system components are defined

Preliminary reliability, risk and availability analysis and evaluation of bulk cargo transportation system in variable operation conditions

In the paper, definitions and theoretical results on system operations process, multi-state system reliability, risk and availability modelling are illustrated by the example of their application to a bulk cargo transportation system operating in Gdynia Port Bulk Cargo Terminal. The bulk cargo transportation system is considered in varying in time operation conditions. The system reliability structure and its components reliability functions are changing in variable operation conditions. The system reliability structures are fixed with a high accuracy. Whereas, the input reliability characteristics of the bulk cargo transportation system components and the system operation process characteristics are not sufficiently exact because of the lack of statistical data. Anyway, the obtained evaluation may be a very useful example in simple and quick systems reliability characteristics evaluation, especially during the design and improving the transportation systems operating in ports