Graph Transformations and Game Theory: A Generative Mechanism for Network Formation

Many systems can be described in terms of networks with characteristic structural properties. To better understand the formation and the dynamics of complex networks one can develop generative models. We propose here a generative model (named dynamic spatial game) that combines graph transformations and game theory. The idea is that a complex network is obtained by a sequence of node-based transformations determined by the interactions of nodes present in the network. We model the node-based transformations by using graph grammars and the interactions between the nodes by using game theory. We illustrate dynamic spatial games on a couple of examples: the role of cooperation in tissue formation and tumor development and the emergence of patterns during the formation of ecological networks

Graph Grammars, Insertion Lie Algebras, and Quantum Field Theory

Graph grammars extend the theory of formal languages in order to model distributed parallelism in theoretical computer science. We show here that to certain classes of context-free and context-sensitive graph grammars one can associate a Lie algebra, whose structure is reminiscent of the insertion Lie algebras of quantum field theory. We also show that the Feynman graphs of quantum field theories are graph languages generated by a theory dependent graph grammar.Comment: 19 pages, LaTeX, 3 jpeg figure

Exploiting lattice structures in shape grammar implementations

The ability to work with ambiguity and compute new designs based on both defined and emergent shapes are unique advantages of shape grammars. Realizing these benefits in design practice requires the implementation of general purpose shape grammar interpreters that support: (a) the detection of arbitrary subshapes in arbitrary shapes and (b) the application of shape rules that use these subshapes to create new shapes. The complexity of currently available interpreters results from their combination of shape computation (for subshape detection and the application of rules) with computational geometry (for the geometric operations need to generate new shapes). This paper proposes a shape grammar implementation method for three-dimensional circular arcs represented as rational quadratic Bézier curves based on lattice theory that reduces this complexity by separating steps in a shape computation process from the geometrical operations associated with specific grammars and shapes. The method is demonstrated through application to two well-known shape grammars: Stiny's triangles grammar and Jowers and Earl's trefoil grammar. A prototype computer implementation of an interpreter kernel has been built and its application to both grammars is presented. The use of Bézier curves in three dimensions opens the possibility to extend shape grammar implementations to cover the wider range of applications that are needed before practical implementations for use in real life product design and development processes become feasible

Modeling Graph Languages with Grammars Extracted via Tree Decompositions

Work on probabilistic models of natural language tends to focus on strings and trees, but there is increasing interest in more general graph-shaped structures since they seem to be better suited for representing natural language semantics, ontologies, or other varieties of knowledge structures. However, while there are relatively simple approaches to defining generative models over strings and trees, it has proven more challenging for more general graphs. This paper describes a natural generalization of the n-gram to graphs, making use of Hyperedge Replacement Grammars to define generative models of graph languages.9 page(s

LFG without C-structures

We explore the use of two dependency parsers, Malt and MST, in a Lexical Functional Grammar parsing pipeline. We compare this to the traditional LFG parsing pipeline which uses constituency parsers. We train the dependency parsers not on classical LFG f-structures but rather on modified dependency-tree versions of these in which all words in the input sentence are represented and multiple heads are removed. For the purposes of comparison, we also modify the existing CFG-based LFG parsing pipeline so that these "LFG-inspired" dependency trees are produced. We find that the differences in parsing accuracy over the various parsing architectures is small

Computer-aided exploration of architectural design spaces: a digital sketchbook

Het ontwerpproces van architecten vormt vaak geen lineair pad van ontwerpopgave tot eindresultaat, maar wordt veeleer gekenmerkt door exploratie of het doorzoeken van meerdere alternatieven in een (conceptuele) ontwerpruimte. Dit proces wordt in de praktijk vaak ondersteund door manueel schetsen, waarbij de ontwerpers schetsboek kan gelezen worden als een reeks exploraties. Dit soort interactie met de ontwerpruimte wordt in veel mindere mate ondersteund door hedendaagse computerondersteunde ontwerpsystemen. De metafoor van een digitaal schetsboek, waarbij menselijke exploratie wordt versterkt door de (reken)kracht van een computer, is het centrale onderzoeksthema van dit proefschrift. Hoewel het opzet van een ontwerpruimte op het eerste gezicht schatplichtig lijkt aan het onderzoeksveld van de artificiële intelligentie (AI), wordt het ontwerpen hier ruimer geïnterpreteerd dan het oplossen van problemen. Als onderzoeksmethodologie worden vormengrammatica’s ingezet, die enerzijds nauw aanleunen bij de AI en een formeel raamwerk bieden voor de exploratie van ontwerpruimtes, maar tegelijkertijd ook weerstand bieden tegen de AI en een vorm van visueel denken en ambiguïteit toelaten. De twee bijhorende onderzoeksvragen zijn hoe deze vormengrammatica’s digitaal kunnen worden gerepresenteerd, en op welke manier de ontwerper-computer interactie kan gebeuren. De resultaten van deze twee onderzoeksvragen vormen de basis van een nieuw hulpmiddel voor architecten: het digitaal schetsboek