Calogero-Moser space and Kostka polynomials

We consider the canonical map from the Calogero-Moser space to symmetric powers of the affine line, sending conjugacy classes of pairs of n by n matrices to their eigenvalues. We show that the character of a natural C^*-action on the scheme-theoretic zero fiber of this map is given by Kostka polynomials.Comment: 12pp., LaTe

The new scottish parliament project : a content analysis of two broadsheet newspapers

The new Scottish Parliament project in Edinburgh is intended to be a unique symbol of devolution and national distinctiveness. However, the project suffered significant setbacks due to cost escalations and programme delays. Since the projects inception in 1997, the design, construction and management of the project have undergone intense scrutiny from media journalists. In particular, two ‘broadsheet’ newspapers, The Scotsman and The Herald have documented the legacy surrounding this unique project. A content analysis of sample headlines from both newspapers suggests that The Scotsman has predominantly employed emotive metaphors in reporting and that this tone tends to emphasise the problems encountered by the project team. The Herald has taken a less judgemental approach with the majority of its reports being less bias in nature. Only a handful of reports could be considered positive in promoting the project and this may have ramifications for the image of the construction industry

Worst-Case Scenarios for Greedy, Centrality-Based Network Protection Strategies

The task of allocating preventative resources to a computer network in order to protect against the spread of viruses is addressed. Virus spreading dynamics are described by a linearized SIS model and protection is framed by an optimization problem which maximizes the rate at which a virus in the network is contained given finite resources. One approach to problems of this type involve greedy heuristics which allocate all resources to the nodes with large centrality measures. We address the worst case performance of such greedy algorithms be constructing networks for which these greedy allocations are arbitrarily inefficient. An example application is presented in which such a worst case network might arise naturally and our results are verified numerically by leveraging recent results which allow the exact optimal solution to be computed via geometric programming

Traffic Optimization to Control Epidemic Outbreaks in Metapopulation Models

We propose a novel framework to study viral spreading processes in metapopulation models. Large subpopulations (i.e., cities) are connected via metalinks (i.e., roads) according to a metagraph structure (i.e., the traffic infrastructure). The problem of containing the propagation of an epidemic outbreak in a metapopulation model by controlling the traffic between subpopulations is considered. Controlling the spread of an epidemic outbreak can be written as a spectral condition involving the eigenvalues of a matrix that depends on the network structure and the parameters of the model. Based on this spectral condition, we propose a convex optimization framework to find cost-optimal approaches to traffic control in epidemic outbreaks