- Full text PDF available (31)
- This year (2)
- Last 5 years (22)
- Last 10 years (32)
We present a conjecture, based on computational results, on the area minimizing way to enclose and separate two arbitrary volumes in the flat cubic three-torus T 3. For comparable small volumes, we prove that an area minimizing double bubble in T 3 is the standard double bubble from R 3 .
In this paper we present the Active Documents Paradigm (semantically annotated documents associated with a content commons that holds the corresponding background ontologies) and the Planetary system (as an active document player). We show that the current Planetary system gives a solid foundation and can be extended modularly to address most of the… (More)
Determining conclusively whether a new version of software creatively exceeds a previous version or a third party system is difficult, yet very important for scientific approaches in Computational Creativity research. We argue that software product and process need to be assessed simultaneously in assessing progress, and we introduce a diagrammatic… (More)
Wiki-like or crowdsourcing models of collaboration can provide a number of benefits to academic work. These techniques may engage expertise from different disciplines, and potentially increase productivity. This paper presents a model of massively distributed collaborative authorship of academic papers. This model, developed by a collective of thirty… (More)
This paper motivates the use of computational argumentation for evaluating 'concept blends' and other forms of combina-torial creativity. We exemplify our approach in the domain of computer icon design, where icons are understood as creative artefacts generated through concept blending. We present a semiotic system for representing icons, showing how they… (More)
(2010). eMath 3.0: building blocks for a social and semantic Web for online mathematics & elearning. Copyright and Moral Rights for the articles on this site are retained by the individual authors and/or other copyright owners. For more information on Open Research Online's data policy on reuse of materials please consult the policies page. Abstract In this… (More)
We model the mathematical process whereby new mathematical theories are invented. Here we explain the use of conceptual blending for this purpose, and show examples to illustrate the process in action. Our longer-term goal is to support machine and human mathematical creativity.
Creativity cannot exist in a vacuum; it develops through feedback, learning, reflection and social interaction with others. However, this perspective has been relatively under-investigated in computational creativity research , which typically examines systems that operate individually. We develop a thought experiment showing how structured dialogues can… (More)
We characterize the perimeter-minimizing double bubbles on all flat two-tori and, as corollaries, on the flat infinite cylinder and the flat infinite strip with free boundary. Specifically, we show that there are five distinct types of minimizers on flat two-tori, depending on the areas to be enclosed.