Quantitative Concept Analysis

Formal Concept Analysis (FCA) begins from a context, given as a binary relation between some objects and some attributes, and derives a lattice of concepts, where each concept is given as a set of objects and a set of attributes, such that the first set consists of all objects that satisfy all attributes in the second, and vice versa. Many applications, though, provide contexts with quantitative information, telling not just whether an object satisfies an attribute, but also quantifying this satisfaction. Contexts in this form arise as rating matrices in recommender systems, as occurrence matrices in text analysis, as pixel intensity matrices in digital image processing, etc. Such applications have attracted a lot of attention, and several numeric extensions of FCA have been proposed. We propose the framework of proximity sets (proxets), which subsume partially ordered sets (posets) as well as metric spaces. One feature of this approach is that it extracts from quantified contexts quantified concepts, and thus allows full use of the available information. Another feature is that the categorical approach allows analyzing any universal properties that the classical FCA and the new versions may have, and thus provides structural guidance for aligning and combining the approaches.Comment: 16 pages, 3 figures, ICFCA 201

Quantitative research

This article describes the basic tenets of quantitative research. The concepts of dependent and independent variables are addressed and the concept of measurement and its associated issues, such as error, reliability and validity, are explored. Experiments and surveys – the principal research designs in quantitative research – are described and key features explained. The importance of the double-blind randomised controlled trial is emphasised, alongside the importance of longitudinal surveys, as opposed to cross-sectional surveys. Essential features of data storage are covered, with an emphasis on safe, anonymous storage. Finally, the article explores the analysis of quantitative data, considering what may be analysed and the main uses of statistics in analysis

A Quali-quantitative evaluation approach to pedodiversity by multivariate analysis: introduction to the concept of "pedocharacter"

A model has been developed for the interpretation of the complexity of pedological systems; this is referred to as “pedocharacter”. The main aim of the model was to reduce the variables able to define soils and their relationships with the environment through the following quali-quantitative approach: i) definition of a fair number of qualitative characters; and ii) development of an analytic function, defined as “Land Relevance of the Factor”

Analysis of students’ quantitative literacy in human coordination system concept

This study aimed to measure and analyze students’ quantitative literacy (QL) in human coordination system concept. It involved 76 participants (16-17 years old) from the second grade of senior high school at two national schools in Subang, West Java, Indonesia. These participants consisted of 39 males and 37 female students. Their QL was assessed by four essay tests to examine their QL indicators including interpretation, representation, calculation, and analysis through coordination system in human issue. Their answers were analyzed by a QL rubric according to Association of American Colleges and University (AACU) assessment. QL achievement for each indicator was categorized into four levels. The analysis result showed that students’ interpretation, representation, calculation, and analysis were at level 3, 2, 3, and 1, respectively. Based on data analysis, students’ achievement in calculation, interpretation, and representation were categorized as the milestone (mediocre). Meanwhile, their analysis skill was classified as a benchmark or the lowest QL level

Charge separation: From the topology of molecular electronic transitions to the dye/semiconductor interfacial energetics and kinetics

Charge separation properties, that is the ability of a chromophore, or a chromophore/semiconductor interface, to separate charges upon light absorption, are crucial characteristics for an efficient photovoltaic device. Starting from this concept, we devote the first part of this book chapter to the topological analysis of molecular electronic transitions induced by photon capture. Such analysis can be either qualitative or quantitative, and is presented here in the framework of the reduced density matrix theory applied to single-reference, multiconfigurational excited states. The qualitative strategies are separated into density-based and wave function-based approaches, while the quantitative methods reported here for analysing the photoinduced charge transfer nature are either fragment-based, global or statistical. In the second part of this chapter we extend the analysis to dye-sensitized metal oxide surface models, discussing interfacial charge separation, energetics and electron injection kinetics from the dye excited state to the semiconductor conduction band states

Measuring electron energy distribution by current fluctuations

A recent concept of local noise sensor is extended to measure the energy resolved electronic energy distribution $f(\varepsilon)$ at a given location inside a non-equilibrium normal metal interconnect. A quantitative analysis of $f(\varepsilon)$ is complicated because of a nonlinear differential resistance of the noise sensor, represented by a diffusive InAs nanowire. Nevertheless, by comparing the non-equilibrium results with reference equilibrium measurements, we conclude that $f(\varepsilon)$ is indistinguishable from the Fermi distribution