Semi-Global Exponential Stability of Augmented Primal-Dual Gradient Dynamics for Constrained Convex Optimization

Primal-dual gradient dynamics that find saddle points of a Lagrangian have been widely employed for handling constrained optimization problems. Building on existing methods, we extend the augmented primal-dual gradient dynamics (Aug-PDGD) to incorporate general convex and nonlinear inequality constraints, and we establish its semi-global exponential stability when the objective function is strongly convex. We also provide an example of a strongly convex quadratic program of which the Aug-PDGD fails to achieve global exponential stability. Numerical simulation also suggests that the exponential convergence rate could depend on the initial distance to the KKT point

A bracketing method for proton affinity measurements of dehydro-and didehydropyridines

Proton affinity (PA) is a fundamental property that is related to the structure and reactivity of a molecule. Currently, very few experimental PA values are available for organic radicals and none for biradicals. Equilibrium methods cannot be used for these measurements. The traditional bracketing method is based on monitoring reactions of different reference bases with known proton affinities with the protonated analyte for the occurrence of exothermic proton transfer to determine the upper and lower limits of proton affinity. However, the energy deposited into the precursor ions upon CAD when forming protonated radicals may cause endothermic proton transfer reactions occur albeit slowly. Their occurrence limits the accuracy of the measurement. The bracketing method was modified to allow distinction between exothermic and slightly endothermic proton transfer reactions. This method was used to measure the PA values for three dehydropyridine radicals and six didehydropyridine biradicals. The values were compared to those obtained using quantum chemical calculations

Monitoring Social Expectations in Second Life

Online virtual worlds such as Second Life provide a rich medium for unstructured human interaction in a shared simulated 3D environment. However, many human interactions take place in a structured social context where participants play particular roles and are subject to expectations governing their behaviour, and current virtual worlds do not provide any support for this type of interaction. There is therefore an opportunity to adapt the tools developed in the MAS community for structured social interactions between software agents (inspired by human society) and adapt these for use with the computer-mediated human communication provided by virtual worlds. This paper describes the application of one such tool for use with Second Life. A model checker for online monitoring of social expectations defined in temporal logic has been integrated with Second Life, allowing users to be notified when their expectations of others have been fulfilled or violated. Avatar actions in the virtual world are detected by a script, encoded as propositions and sent to the model checker, along with the social expectation rules to be monitored. Notifications of expectation fulfilment and violation are returned to the script to be displayed to the user. This utility of this tool is reliant on the ability of the Linden scripting language (LSL) to detect events of significance in the application domain, and a discussion is presented on how a range of monitored structured social scenarios could be realised despite the limitations of LSL