The cohomology of exotic 2-local finite groups

There exist spaces BSol(q) which are the classifying spaces of a family of 2-local finite groups based on certain fusion system over the Sylow 2-subgroups of Spin_7(q). In this paper we calculate the cohomology of BSol(q) as an algebra over the Steenrod algebra A_2. We also provide the calculation of the cohomology algebra over A_2 of the finite group of Lie type G_2(q).Comment: 13 page

Between a Rock and a Hard Place

The perception of the WTO is currently one of an organisation in crisis. Yet, appraisal varies regarding its extent and seriousness: Is it merely a rough time or are we standing on the edge of destruction? The article will trace developments inside as well as outside the WTO in order to assess the magnitude of the crisis. It will be argued that while certain developments inside the organisation, when seen in accumulation would already warrant serious attention, only together with developments taking place outside of the WTO, the two strands of developments unfold their full potential for the crisis. The overall situation renders the WTO in a difficult position, as it is currently unable to adapt to these challenges, while keeping calm and carrying on might similarly further the crisis. While States might improve and further develop their trade relations in bi- and plurilateral agreements, it is only the WTO that reflects and stands for the multilateral post (cold) war order

Robustness in sparse linear models: relative efficiency based on robust approximate message passing

Understanding efficiency in high dimensional linear models is a longstanding problem of interest. Classical work with smaller dimensional problems dating back to Huber and Bickel has illustrated the benefits of efficient loss functions. When the number of parameters $p$ is of the same order as the sample size $n$, $p \approx n$, an efficiency pattern different from the one of Huber was recently established. In this work, we consider the effects of model selection on the estimation efficiency of penalized methods. In particular, we explore whether sparsity, results in new efficiency patterns when $p > n$. In the interest of deriving the asymptotic mean squared error for regularized M-estimators, we use the powerful framework of approximate message passing. We propose a novel, robust and sparse approximate message passing algorithm (RAMP), that is adaptive to the error distribution. Our algorithm includes many non-quadratic and non-differentiable loss functions. We derive its asymptotic mean squared error and show its convergence, while allowing $p, n, s \to \infty$, with $n/p \in (0,1)$ and $n/s \in (1,\infty)$. We identify new patterns of relative efficiency regarding a number of penalized $M$ estimators, when $p$ is much larger than $n$. We show that the classical information bound is no longer reachable, even for light--tailed error distributions. We show that the penalized least absolute deviation estimator dominates the penalized least square estimator, in cases of heavy--tailed distributions. We observe this pattern for all choices of the number of non-zero parameters $s$, both $s \leq n$ and $s \approx n$. In non-penalized problems where $s =p \approx n$, the opposite regime holds. Therefore, we discover that the presence of model selection significantly changes the efficiency patterns.Comment: 49 pages, 10 figure

Issues Coupled With International Assignments

Last month we presented key findings relating to trends in the usage of new forms of international working and highlighted some of the managerial control issues facing international HR managers. This month, Jelena Petrovic from CReME, looks in more detail at the people and management issues associated with each type of international assignment. These new types of international assignments include short-term, international commuter and frequent flyer assignments. Short-term assignments are defined as an assignment with a specified duration, usually less than one year, where the family may accompany the employee. An international commuter is an employee who commutes from the home country to a place of work in another country, usually on a weekly or bi-weekly basis, while the family remains at home. A frequent flyer is an employee who undertakes frequent international business trips but does not relocate.Published in Croner’s “Managing Internationally Mobile Employees” Issue No5 and reproduced with their permission. www.croner.cch.co.u