Political risk in light rail transit PPP projects

Since 2003 public-private partnerships (PPPs) have represented between 10 and 13.5% of the total investment in public services in the UK. The macro-economic and political benefits of PPPs were among the key drivers for central government's decision to promote this form of procurement to improve UK public services. Political support for a PPP project is critical and is frequently cited as the most important critical success factor. This paper investigates the significance of political support and reviews the treatment of political risk in a business case by the public sector project sponsor for major UK-based light rail transit PPP projects during their development stage. The investigation demonstrates that in the early project stages it is not traditional quantitative Monte Carlo risk analysis that is important; rather it is the identification and representation of political support within a business case together with an understanding of how this information is then used to inform critical project decisions

On Fusion Algebras and Modular Matrices

We consider the fusion algebras arising in e.g. Wess-Zumino-Witten conformal field theories, affine Kac-Moody algebras at positive integer level, and quantum groups at roots of unity. Using properties of the modular matrix $S$, we find small sets of primary fields (equivalently, sets of highest weights) which can be identified with the variables of a polynomial realization of the $A_r$ fusion algebra at level $k$. We prove that for many choices of rank $r$ and level $k$, the number of these variables is the minimum possible, and we conjecture that it is in fact minimal for most $r$ and $k$. We also find new, systematic sources of zeros in the modular matrix $S$. In addition, we obtain a formula relating the entries of $S$ at fixed points, to entries of $S$ at smaller ranks and levels. Finally, we identify the number fields generated over the rationals by the entries of $S$, and by the fusion (Verlinde) eigenvalues.Comment: 28 pages, plain Te

The W_N minimal model classification

We first rigourously establish, for any N, that the toroidal modular invariant partition functions for the (not necessarily unitary) W_N(p,q) minimal models biject onto a well-defined subset of those of the SU(N)xSU(N) Wess-Zumino-Witten theories at level (p-N,q-N). This permits considerable simplifications to the proof of the Cappelli-Itzykson-Zuber classification of Virasoro minimal models. More important, we obtain from this the complete classification of all modular invariants for the W_3(p,q) minimal models. All should be realised by rational conformal field theories. Previously, only those for the unitary models, i.e. W_3(p,p+1), were classified. For all N our correspondence yields for free an extensive list of W_N(p,q) modular invariants. The W_3 modular invariants, like the Virasoro minimal models, all factorise into SU(3) modular invariants, but this fails in general for larger N. We also classify the SU(3)xSU(3) modular invariants, and find there a new infinite series of exceptionals.Comment: 25 page

National and Regional Estimates of the Prevalence of Opiate and/or Crack Cocaine use 2008-09: A summary of key findings

<p>This report summarises the results of a follow-up study to a three year project to estimate the prevalence of ‘problem drug use’ (defined as use of opiates and/or crack cocaine) nationally (England only), regionally and locally. The follow-up was carried out two years after the final sweep of the original project, so could therefore be considered as ‘sweep 5’. An overview of the national and regional estimates are presented in this report, as are comparisons with the estimates produced by the third (2006-07) sweep of the study. Estimates for 2007-08 are not available as a study was not commissioned for that year.</p> <p>Information about the number of people who use illicit drugs such as heroin, other opiates or crack cocaine is key to formulating effective policies for tackling drug-related harm as these drugs are associated with the highest levels of harm. It also helps inform service provision at the local level and provides a context in which to understand the population impact of interventions to reduce drug-related harm.</p> <p>Direct enumeration of those engaged in a largely covert activity such as the use of class A drugs is difficult and standard household survey techniques tend to underestimate the extent of such activity. Indirect techniques making use of various data sources offer a more reliable way of calculating prevalence estimates for the use of opiates and/or crack cocaine. The estimates presented in this report are derived using two indirect measurement techniques: the capture-recapture method (CRC ); and the multiple indicator (MIM ) method. These methods are described in detail in Hay et al., 2006 and Hay et al., 2007a. Methodological developments throughout the course of the previous three sweeps are discussed elsewhere (Hay et al., 2007b, Hay et al., 2008). The individuals covered by this study were people aged 15 to 64 and resident in each DAT area, and known to be using heroin, methadone, other opiate drugs or crack cocaine.</p&gt