Granularity matters in mathematics. For example, in introductory textbooks intermediate proof steps are often skipped, when this seems appropriate. Such a situation is given in the elementary proof in basic set theory reproduced in Figure 1. Whereas most of the proof steps consist of the application of exactly one mathematical fact (a definition or a lemma), the step from assertion 9 to asserti...

Wayfinding in road networks is a hierarchical process. It involves a sequence of tasks, starting with route planning, continuing with the extraction of wayfinding instructions, and leading to the actual driving. From one task level to the next, the relevant road network becomes more detailed. How does the wayfinding process change? Building on a previous, informal hierarchical highway navigatio...

Temporal and spatial phenomena can be seen at a more or less precise granularity, depending on the kind of perceivable details. As a consequence, the relationship between two objects may differ depending on the granularity considered. When merging representations of different granularity, this may raise problems. This paper presents general rules of granularity conversion in relation algebras. ...

Both similarity-based and popularity-based document ranking functions have been successfully applied to information retrieval (IR) in general. However, the dimension of semantic granularity also should be considered for effective retrieval. In this paper, we propose a semantic granularity based IR model which takes into account the three dimensions, namely similarity, popularity, and semantic g...

Reverse Engineering is the process of reconstructing high-level design information from program code 3]. Reverse engineering in traditional engineering disciplines is an extraneous activity but in the eld of software engineering it is an integral part of software maintenance. A maintainer needs to understand the code in terms of which part of the code is implementing which of the domain functio...

This paper looks at granularity issues in machine translation evaluation. We start with work by (White, 2001) who examined the correlation between intelligibility and fidelity at the document level. His work showed that intelligibility and fidelity do not correlate well at the document level. These dissimilarities lead to our investigation of evaluation granularity. In particular, we revisit th...

To analyze the complex and heterogenous real-time embedded systems, recent works have proposed interface techniques between real-time calculus (RTC) and timed automata (TA), in order to take advantage of the strengths of each technique for analyzing various components. But the time to analyze a state-based component modeled by TA may be prohibitively high, due to the state space explosion probl...