For a set Ω an unordered relation on Ω is a family R of subsets of Ω . If R is such a relation we let G(R) be the group of all permutations on Ω that preserve R, that is g belongs to G(R) if and only if x ∈R implies x ∈R. We are interested in permutation groups which can be represented as G= G(R) for a suitable unordered relation R on Ω . When this is the case, we say that G is defined by the r...

The framework and the basic results of Wille on triadic concept analysis, including his Basic Theorem of Triadic Concept Analysis, are here generalized to n-dimensional formal contexts. Mathematics Subject Classifications (2000): Primary: 06A23; secondary: 62-07.

The flow in a rapidly rotating cylinder forced to precess through a nutation angle α is investigated numerically, keeping all parameters constants except α, and tuned to a triadic resonance at α = 1◦. When increasing α, the flow undergoes a sequence of well-characterized bifurcations associated with triadic resonance, involving heteroclinic and homoclinic cycles, for α up to about 4◦. For large...

The widely-used notion of triadic closure has been conceptualized and measured in a variety of ways, most famously the clustering coefficient. This paper proposes a measure of triadic closure in affiliation networks designed to control for the influence of bicliques. In order to avoid arbitrariness, the paper introduces a triadic framework for affiliation networks, within which a range of possi...

Are children as young as 2 years old able to interact in groups of three? The study applied the family triad model first introduced by Parke, Power, and Gottman (1979) to the case of peer interaction. In Experiment 1, the model was refined for use in studies of peer interaction and applied to an existing dataset of 16 triads of newly acquainted 24-month-olds. In Experiment 2, the triadic coding...

Services such as Wikipedia, Flickr, Technorati, Yahoo!, YouTube, del.icio.us appear in many web applications, employ the folksonomy as their social tagging mechanism, where users assign tags to resources and share it with each other within their community. As the number of the folksonomy-based systems is increased, some proper data mining approaches to folksonomies are necessary to better under...

Triadic distance models can be used to analyse proximity data defined on triples of objects. Three-way symmetry is a common assumption for triadic distance models. In the present study three-way symmetry is not assumed. Triadic distance models are presented for the analysis of asymmetric three-way proximity data that result in a simultaneous representation of symmetry and asymmetry in a low-dim...

Triadic distances t defined as functions of the Euclidean (dyadic) distances a1, a2, a3 between three points are studied. Special attention is paid to the contours of all points giving the same value of t when a3 is kept constant . These isocontours allow some general comments to be made about the suitability, or not, for practical investigations of certain definitions of triadic distance. We a...

In this paper, we examine the evolution of triadic motifs in a large-scale human communication network. We consider extant models of triadic evolution, emphasizing vertex-, dyadic-, triadicand higher-level processes in order to generate testable hypotheses of the predictors of both over time triangle survival and triangle emergence from lower-order motifs. We find that the stability and formati...