Deformation pathway and defect generation in crystals: a combined group theory and graph theory description

The generation and motion of crystalline defects during plastic deformation are critical processes that determine the mechanical properties of a crystal. The types of defect generated are not only related to the symmetry of a crystal but also associated with the symmetry-breaking process during deformation. Proposed here is a new mathematical framework to capture the intrinsic coupling between crystal symmetry and deformation-induced symmetry breaking. Using a combination of group theory and graph theory, a general approach is demonstrated for the systematic determination of the types of crystalline defect induced by plastic deformation, through the construction of a crystal deformation group and a deformation pathway graph. The types of defect generated in the deformation of a face-centered cubic crystal are analyzed through the deformation pathway graph and compared with experimental observations.

Graph query algebra and visual proximity rules for biological pathway exploration

We present the design and validation of an example-based pathway graph query algebra and visual proximity rules to address challenging large biological pathway exploration tasks. Our pathway graph query algebra interprets relationship queries given by selected examples to find a match for, extract identical parts between, or trace a path from any pathway components. To support the relationship query, users can composite pathway visualizations through visual proximity rules that use proximity to infer users’ intentions in the exploration process. By allowing selection of one or more objects from multiple on-screen grouped graphs as query inputs and using the query outputs as next-query inputs, pathway graph query algebra and visual proximity rules achieve intuitiveness, concurrence, and dynamics for pathway exploration.