Nathan Carter

Chaotic attractors with discrete planar symmetries

Abstract Chaotic behavior is known to be compatible with symmetry and illustrations are constructed using functions equivariant with respect to the desired symmetries. Earlier investigations determined families of equivariant functions for a few of the discrete symmetry groups in the plane; those results are extended to all the discrete symmetry groups of the plane. This includes consideration of the all the frieze and two-dimensional crystallographic groups.

Proactive Encouragement of Interdisciplinary Research Teams in a Business School Environment: Strategy and Results.

This case study describes efforts to promote collaborative research across traditional boundaries in a business‐oriented university as part of an institutional transformation. We model this activity within the framework of social network analysis and use quantitative tools from that field to characterize resulting impacts.

Frieze and wallpaper chaotic attractors with a polar spin

Abstract Previous work has investigated chaotic attractors possessing discrete planar symmetries, including the common cyclic and dihedral symmetry groups in addition to the frieze and crystallographic symmetries. Such images are converted via a polar coordinate transformation, transforming frieze and crystallographic patterns into fascinating images. These results have cyclic and dihedral symmetry enhanced in intricate ways by the symmetry of the original images.

Generating random networks from a given distribution

Several variations are given for an algorithm that generates random networks approximately respecting the probabilities given by any likelihood function, such as from a p^* social network model. A novel use of the genetic algorithm is incorporated in these methods, which improves its applicability to the degenerate distributions that can arise with p^* models. Our approach includes a convenient way to find the high-probability items of an arbitrary network distribution function.

A Web-Based Toolkit for Mathematical Word Processing Applications with Semantics

Lurch is an open-source word processor that can check the steps in students’ mathematical proofs. Users write in a natural language, but mark portions of a document as meaningful, so the software can distinguish content for human readers from content it should analyze.