Frameworks, Symmetry and Rigidity

Symmetry equations are obtained for the rigidity matrix of a bar-joint framework in R^d. These form the basis for a short proof of the Fowler-Guest symmetry group generalisation of the Calladine-Maxwell counting rules. Similar symmetry equations are obtained for the Jacobian of diverse framework systems, including constrained point-line systems that appear in CAD, body-pin frameworks, hybrid systems of distance constrained objects and infinite bar-joint frameworks. This leads to generalised forms of the Fowler-Guest character formula together with counting rules in terms of counts of symmetry-fixed elements. Necessary conditions for isostaticity are obtained for asymmetric frameworks, both when symmetries are present in subframeworks and when symmetries occur in partition-derived frameworks.Comment: 5 Figures. Replaces Dec. 2008 version. To appear in IJCG

Radically solvable graphs

A 2-dimensional framework is a straight line realisation of a graph in the Euclidean plane. It is radically solvable if the set of vertex coordinates is contained in a radical extension of the field of rationals extended by the squared edge lengths. We show that the radical solvability of a generic framework depends only on its underlying graph and characterise which planar graphs give rise to radically solvable generic frameworks. We conjecture that our characterisation extends to all graphs

Rigidity of Frameworks Supported on Surfaces

A theorem of Laman gives a combinatorial characterisation of the graphs that admit a realisation as a minimally rigid generic bar-joint framework in \bR^2. A more general theory is developed for frameworks in \bR^3 whose vertices are constrained to move on a two-dimensional smooth submanifold \M. Furthermore, when \M is a union of concentric spheres, or a union of parallel planes or a union of concentric cylinders, necessary and sufficient combinatorial conditions are obtained for the minimal rigidity of generic frameworks.Comment: Final version, 28 pages, with new figure

SimDialog: A visual game dialog editor

SimDialog is a visual editor for dialog in computer games. This paper presents the design of SimDialog, illustrating how script writers and non-programmers can easily create dialog for video games with complex branching structures and dynamic response characteristics. The system creates dialog as a directed graph. This allows for play using the dialog with a state-based cause and effect system that controls selection of non-player character responses and can provide a basic scoring mechanism for games

How to adapt broad-band gravitational-wave searches for r-modes

Up to now there has been no search for gravitational waves from the r-modes of neutron stars in spite of the theoretical interest in the subject. Several oddities of r-modes must be addressed to obtain an observational result: The gravitational radiation field is dominated by the mass current (gravitomagnetic) quadrupole rather than the usual mass quadrupole, and the consequent difference in polarization affects detection statistics and parameter estimation. To astrophysically interpret a detection or upper limit it is necessary to convert the wave amplitude to an r-mode amplitude. Also, it is helpful to know indirect limits on gravitational-wave emission to gauge the interest of various searches. Here I address these issues, thereby providing the ingredients to adapt broad-band searches for continuous gravitational waves to obtain r-mode results. I also show that searches of existing data can already have interesting sensitivities to r-modes.Comment: 8 pages, no figure

Consultation and consequences: A view on the services experienced by some young people and six families

Reports the views of some young people and 6 families on services received from social care professionals. Summarises the main themes that emerged and emphasises the issue of professional reliability as articulated in these 2 small, but in depth, studies. The views of both sets of interviewees contributed to the creation of a course for front line managers drawing from user and worker consultations. Draws on the interviews to shed light on various aspects of professional relationships with services users and what they said they wanted. Discussion sets this in the context of policy agenda