Flow Visualization with Quantified Spatial and Temporal Errors Using Edge Maps

Robust analysis of vector fields has been established as an important tool for deriving insights from the complex systems these fields model. Traditional analysis and visualization techniques rely primarily on computing streamlines through numerical integration. The inherent numerical errors of such approaches are usually ignored, leading to inconsistencies that cause unreliable visualizations and can ultimately prevent in-depth analysis. We propose a new representation for vector fields on surfaces that replaces numerical integration through triangles with maps from the triangle boundaries to themselves. This representation, called edge maps, permits a concise description of flow behaviors and is equivalent to computing all possible streamlines at a user defined error threshold. Independent of this error streamlines computed using edge maps are guaranteed to be consistent up to floating point precision, enabling the stable extraction of features such as the topological skeleton. Furthermore, our representation explicitly stores spatial and temporal errors which we use to produce more informative visualizations. This work describes the construction of edge maps, the error quantification, and a refinement procedure to adhere to a user defined error bound. Finally, we introduce new visualizations using the additional information provided by edge maps to indicate the uncertainty involved in computing streamlines and topological structures.

Post-conventional Political Cultures via Processes of Direct Democracy: Theoretical Considerations Based on Jurgen Habermas and Lawrence Kohlberg

In this article, it is proposed to differentiate political cultures in two dimensions. First, inspired by Habermas' distinction of the contents of discourse, a distinction is suggested between moral, ethical-political and pragmatic elements of political culture as well as of an element of culture of balancing interests. Second, inspired by Kohlberg's stage models for the development of the individual moral consciousness and for moral culture, a distinction is similarly suggested between two pre-conventional, two conventional and two post-conventional collective stages of political culture. It can be shown that from a normative point of view, only deliberations made in a post-conventional political culture can produce reasonable or at least fair results. Conceptual considerations indicate processes of direct democracy as the method for promoting post-conventional political cultures. The more liberty that the citizens have to formulate and trigger processes of direct democracy, the more one can expect from them to generate post-conventional political cultures.