Using the Chu construction for generalizing formal concept analysis

Abstract. The goal of this paper is to show a connection between FCA generalisations and the Chu construction on the category ChuCors, the category of formal contexts and Chu correspondences. All needed categorical properties like categorical product, tensor product and its bifunctor properties are presented and proved. Finally, the second order generalisation of FCA is represented by a category built up in terms of the Chu construction

Structure of the icosahedral Ti-Zr-Ni quasicrystal

The atomic structure of the icosahedral Ti-Zr-Ni quasicrystal is determined by invoking similarities to periodic crystalline phases, diffraction data and the results from ab initio calculations. The structure is modeled by decorations of the canonical cell tiling geometry. The initial decoration model is based on the structure of the Frank-Kasper phase W-TiZrNi, the 1/1 approximant structure of the quasicrystal. The decoration model is optimized using a new method of structural analysis combining a least-squares refinement of diffraction data with results from ab initio calculations. The resulting structural model of icosahedral Ti-Zr-Ni is interpreted as a simple decoration rule and structural details are discussed.Comment: 12 pages, 8 figure

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

Risk for Behavioral Problems Independent of Cognitive Functioning in Children Born at Low Gestational Ages

This study aimed to investigate cognitive and behavioral outcomes in relation to gestational age (GA) in school-aged children born preterm (PT). Results from the Wechsler Intelligence Scale for Children, 4th edition (WISC-IV), and the Child Behavior Checklist (CBCL) were analyzed in 51 children (mean age: 7.8 years [range: 7.0–8.7]) born PT (mean GA: 31 weeks [range: 23–35]; birth weight, mean: 1,637 g [range:404–2,962]) with the majority (96%) having no diagnosed cognitive, sensory, or motor impairments. The control group included 57 age-matched typically developing children (mean age: 7.9 years [range: 6.2–8.7]) born full-term (FT). Children born PT, extremelyPT (GA < 28) in particular, showed significantly lower cognitive performance and higher behavioral problem scores compared with children born FT. GA was found to predict aspects of both cognitive functioning and behavioral problems within the PT group, with lower GA being related to both poorer cognitive outcomes and elevated affective and attention-deficit/hyperactivity problems. Global cognitive functioning did not independently predict aspects of behavioral outcomes. Findings demonstrate that, even in children born PT without severe perinatal and/or postnatal complications and receiving active perinatal care, a short gestation is an evident risk factor for long-term negative effects on mental health independent of cognitive functioning. Additional findings suggest that both reduced growth and lower parental educational level may contribute to increased risk for poorer cognitive and behavioral functioning in children born PT