Relations, residuals, regular interiors, and relative regular equivalence

Given a relation α (a binary sociogram) and an a priori equivalence relation π, both on the same set of individuals, it is interesting to look for the largest equivalence πo that is contained in and is regular with respect to α. The equivalence relation πo is called the regular interior of π with respect to α. The computation of πo involves the left and right residuals, a concept that generalized group inverses to the algebra of relations. A polynomial-time procedure is presented (Theorem 11) and illustrated with examples. In particular, the regular interior gives meet in the lattice of regular equivalences: the regular meet of regular equivalences is the regular interior of their intersection. Finally, the concept of relative regular equivalence is defined and compared with regular equivalence.

Counter-terrorism, anti-extremism, armed conflict and human rights: using a Russian case study

This paper critically examines Russia’s compliance with human rights obligations and the rule of law in its ‘war on terror’. It seeks to draw wider parallels with respect for human rights in the framework of the fight against ‘new global terrorism’. Threats to due process, the discriminatory application of the forces of law and order specifically against perceived “non-traditional” Muslim communities, and a ratcheting up of fear of an Islamist threat can be traced following the war in Chechnya and the handling of the Dubrovka Theatre and Beslan school sieges. To what extent are there commonalities with UK complicity in the practice of extraordinary rendition, with atrocities perpetrated in Iraq and Afghanistan, and abuses in Abu Ghraib and Guantanamo? Are the impact of these reflected in domestic security policy and British minority ethnic community relations? [From the Author]