Large-scale control of invasive plants can benefit strongly from reliable assessment of spatial variation in plant invasibility. With this knowledge, limited management resources can be concentrated in areas of high invasion risk. We assessed the influence of spatial environments and proximity to roads on the invasibility of African mustard (Brassica tournefortii Gouan) over the 280,000-ha Barry M. Goldwater Range West in southwestern Arizona, USA. We used presence/absence data of B. tournefortii acquired from a vegetation classification project, in which lands were mapped to the level of vegetation subassociations. Logistic regression models suggested that spatial environments represented by the subassociations, not proximity to roads, represented the only factor significantly explaining B. tournefortii presence. We then used the best model to predict B. tournefortii invasibility in each subassociation. This prediction indicates management strategy should differ between the western part and the central to eastern part of the range. The western range is a large spatial continuum with intermediate to high invasion risk, vulnerable to an untethered spread of B. tournefortii. Controlling efforts should focus on preventing existing local populations from further expansion. The central and eastern ranges are a mosaic varying strongly in invasion risk. Control efforts can take advantage of natural invasion barriers and further reduce connectivity through removal of source populations connected with other high-risk locations via roads and other dispersal corridors. We suggest our approach as one effective way to combine vegetation classification and plant invasion assessment to manage complex landscapes over large ranges, especially when this approach is used through an iterative prediction–validation process to achieve adaptive management of invasive plants.

We present a new iterative model order reduction method for large-scale linear time-invariant dynamical systems, based on a combined singular value decomposition–adaptive-order rational Arnoldi (SVD-AORA) approach. This method is an extension of the SVD-rational Krylov method. It is based on two-sided projections: the SVD side depends on the observability Gramian by the resolution of the Lyapunov equation, and the Krylov side is generated by the adaptive-order rational Arnoldi based on moment matching. The use of the SVD provides stability for the reduced system, and the use of the AORA method provides numerical efficiency and a relative lower computation complexity. The reduced model obtained is asymptotically stable and minimizes the error ($H_{2}$ and $H_{\infty }$) between the original and the reduced system. Two examples are given to study the performance of the proposed approach.

This study investigates whether large-scale, day-long stress management workshops open to the general public can work as well as small, weekly groups run for referred clients. It is suggested that the self-referral route may enable some people who might otherwise have been ‘‘filtered out’’ from the traditional health services to get help for their stress-related problems. Analysis showed that the large-scale format was just as effective with a more distressed subgroup as was the small weekly format for formally referred clients, which suggests that the effectiveness of this approach is not only related to a restricted client group. It would appear that the low drop-out rate, the effectiveness of the workshops and the severity of problem handled within this format indicates potential value in this type of approach.