Integral homology of real isotropic and odd orthogonal Grassmannians

We obtain a combinatorial expression for the coefficients of the boundary map of real isotropic and odd orthogonal Grassmannians providing a natural generalization of the formulas already obtained for Lagrangian and maximal isotropic Grassmannians. The results are given in terms of the classification into four types of covering pairs among the Schubert cells when identified with signed $k$-Grassmannian permutations. It turns out that these coefficients only depend on the positions changed over each pair of permutations. As an application, we give an orientability criterion, exhibit a symmetry of these coefficients and, compute low-dimensional homology groups.Comment: 24 pages, 8 figures. We have improved the main result

C++ programming language for an abstract massively parallel SIMD architecture

The aim of this work is to define and implement an extended C++ language to support the SIMD programming paradigm. The C++ programming language has been extended to express all the potentiality of an abstract SIMD machine consisting of a central Control Processor and a N-dimensional toroidal array of Numeric Processors. Very few extensions have been added to the standard C++ with the goal of minimising the effort for the programmer in learning a new language and to keep very high the performance of the compiled code. The proposed language has been implemented as a porting of the GNU C++ Compiler on a SIMD supercomputer.Comment: 10 page

The EU’s new Global Strategy remains wedded to an old-fashioned conception of foreign policy

Federica Mogherini presented a draft ‘Global Strategy’ on 28 June, which is intended to guide the EU’s foreign and security policy. Luigi Lonardo argues that by stressing the need for unity among member states, the new strategy overlooks the risks that can occur from a centralised foreign policy. A more flexible approach to foreign policy would not only help to alleviate these risks, but would also be preferable on democratic grounds

The EU’s ‘diplomatic accident’ with Morocco shows the perils of judge-led foreign policy

Morocco announced at the end of February that it was suspending ties with the European Union. The statement was issued following a ruling by the European Court of Justice that an EU-Morocco trade deal was illegal on the basis that it included the territory of Western Sahara. Luigi Lonardo writes that while the ruling is currently being appealed, the incident illustrates some of the dangers of the EU’s judiciary playing an active role in reviewing diplomatic and foreign policy issues

Political turmoil in Morocco spills over into tensions with the Netherlands

Morocco recalled its Ambassador to the Netherlands following a row over the extradition of a former Moroccan MP who has been linked to protests in the country. Luigi Lonardo explains the background to the incident and assesses what it might mean for Morocco’s relationship with the European Union