Abstract: Evolving entities in space and time generate complex networks whose structural properties require the development of formal models. The research presented in this paper introduces a graph-based model whose objective is to retain the semantics of these networks. Entities are related at a given time, through space according to the locations they occupy, and across time according to some dependency relations. We propose an approach that characterises these different properties using several graphs, and where emerging properties are analysed at the local and global levels. This allows for a manipulation of these spatial, spatio-temporal and temporal graphs using neighbourhood, descendant and ancestor operations at the local level. Global properties are studied according to the way two given entities in one of these graphs are related according to the possible routes between them. The principles of the modelling approach are illustrated by a case study of the propagation of brambles.
Abstract: Motivation: Modules in biology appeared quickly as an accurate way for summarizing complex living systems by simple ones. Therefore, finding an appropriate relationship between modules extracted from a biological graph and protein complexes remains a crucial task. Recent studies successfully proposed various descriptions of protein interaction networks. These approaches succeed in showing modules within the network and how the modules interact. However, describing the interactions within the modules, i.e. intra-modular interactions, remains little analyzed despite its interest for understanding module functions.
Results: We overcome this weakness by adding a complementary description to the already successful approaches: a hierarchical decomposition named homogeneous decomposition. This decomposition represents a natural refinement of previous analyses and details interactions within a module. We propose to illustrate these improvements by three practical cases. Among them, we decompose the yeast protein interaction network and show reachable biological insights that might be extracted from a complex large-scale network.
Abstract: We present a novel approach to modelling the evolution of spatial entities over time by using bigraphs. We use the links in a bi-graph to represent the sharing of a common ancestor and the places in a bigraph to represent spatial nesting as usual. We provide bigraphical reaction rules that are able to model situations such as two crowds of people merging together while still keeping track of the resulting crowd's historical links.
