Tom Hanika

Individuality in Social Networks

We consider individuality in bi-modal social networks, a facet that has not been considered before in the mathematical analysis of social networks. We use methods from formal concept analysis to develop a natural definition for individuality, and provide experimental evidence that this yields a meaningful approach for additional insights into the nature of social networks.

Social event network analysis: structure, preferences, and reality

This paper focuses on the analysis of socio-spatial data, i. e., user-performance relations at a distributed event. We consider the data as a bimodal network (i. e., model it as a bipartite graph), and investigate its structural characteristics towards a social network. We focus on plans of the participants (expressed by preferences) and their fulfilment, and propose measures for matching preference and reality. We specifically analyse behavioural patterns w.r.t. distinct user and performance groups. We utilise real-world data collected at the Lange Nacht der Musik (Long Night of Music) 2013 in Munich.

„Ich denke, es ist wichtig zu verstehen, warum die Netzwerkanalyse jetzt populär und besonders interessant für die Forschung geworden ist.“

In diesem Interview befragen zwei Soziologen einen Mathematiker und einen Informatiker zu den Grundlagen der Netzwerkanalyse. Das Interview ist durch Reflexionen und Gedankenexperimente aufgelockert und fuhrt das Thema der digitalen Bewertungsinfrastrukturen so aus einer experimentellen Perspektive ein. Der Schwerpunkt liegt auf der (oftmals unsichtbaren) Arbeit, die hinter Netzwerkinfrastrukturen steht. Es wird uber die lange Forschungstradition der Netzwerkanalyse gesprochen, disziplinare und interdisziplinare Herausforderungen werden diskutiert, zudem wird ein Einblick gegeben in aktuelle Forschungen zum Thema der Wissensverarbeitung, mit denen sich die befragten Personen beschaftigen. Berichtet wird etwa von Waldbranden auf Indonesien, die mit Daten von Twitter in einem UN-Projekt fur die lokale Regierung aufbereitet werden, und von mathematischer Auseinandersetzung mit Individualitat, die sich auch auf soziologische Grundbegriffe bezieht. In diesem Beitrag werden zudem Dokumente und wissenschaftliche Praktiken analysiert; im Sinne der Science and Technology Studies wird sich der „Science in Action“ und ihrer Unsicherheiten angenahert.

Towards Collaborative Conceptual Exploration

In domains with high knowledge distribution a natural objective is to create principle foundations for collaborative interactive learning environments. We present a first mathematical characterization of a collaborative learning group, a consortium, based on closure systems of attribute sets and the well-known attribute exploration algorithm from formal concept analysis. To this end, we introduce (weak) local experts for subdomains of a given knowledge domain. These entities are able to refute and potentially accept a given (implicational) query for some closure system that is a restriction of the whole domain. On this we build up a consortial expert and show first insights about the ability of such an expert to answer queries. Furthermore, we depict techniques on how to cope with falsely accepted implications and on combining counterexamples. Using notions from combinatorial design theory we further expand those insights as far as providing first results on the decidability problem if a given consortium is able to explore some target domain. Applications in conceptual knowledge acquisition as well as in collaborative interactive ontology learning are at hand.

On the Usability of Probably Approximately Correct Implication Bases

We revisit the notion of probably approximately correct implication bases from the literature and present a first formulation in the language of formal concept analysis, with the goal to investigate whether such bases represent a suitable substitute for exact implication bases in practical use cases. To this end, we quantitatively examine the behavior of probably approximately correct implication bases on artificial and real-world data sets and compare their precision and recall with respect to their corresponding exact implication bases. Using a small example, we also provide evidence suggesting that implications from probably approximately correct bases can still represent meaningful knowledge from a given data set.