Counting (3+1) - Avoiding permutations

A poset is {\it (\3+\1)-free} if it contains no induced subposet isomorphic to the disjoint union of a 3-element chain and a 1-element chain. These posets are of interest because of their connection with interval orders and their appearance in the (\3+\1)-free Conjecture of Stanley and Stembridge. The dimension 2 posets $P$ are exactly the ones which have an associated permutation $\pi$ where $i\prec j$ in $P$ if and only if $i<j$ as integers and $i$ comes before $j$ in the one-line notation of $\pi$. So we say that a permutation $\pi$ is {\it (\3+\1)-free} or {\it (\3+\1)-avoiding} if its poset is (\3+\1)-free. This is equivalent to $\pi$ avoiding the permutations 2341 and 4123 in the language of pattern avoidance. We give a complete structural characterization of such permutations. This permits us to find their generating function.Comment: 17 page

Inflations of Geometric Grid Classes: Three Case Studies

We enumerate three specific permutation classes defined by two forbidden patterns of length four. The techniques involve inflations of geometric grid classes

Subclasses of the separable permutations

We prove that all subclasses of the separable permutations not containing Av(231) or a symmetry of this class have rational generating functions. Our principal tools are partial well-order, atomicity, and the theory of strongly rational permutation classes introduced here for the first time

Connecting Terminals and 2-Disjoint Connected Subgraphs

Given a graph $G=(V,E)$ and a set of terminal vertices $T$ we say that a superset $S$ of $T$ is $T$-connecting if $S$ induces a connected graph, and $S$ is minimal if no strict subset of $S$ is $T$-connecting. In this paper we prove that there are at most ${|V \setminus T| \choose |T|-2} \cdot 3^{\frac{|V \setminus T|}{3}}$ minimal $T$-connecting sets when $|T| \leq n/3$ and that these can be enumerated within a polynomial factor of this bound. This generalizes the algorithm for enumerating all induced paths between a pair of vertices, corresponding to the case $|T|=2$. We apply our enumeration algorithm to solve the {\sc 2-Disjoint Connected Subgraphs} problem in time $O^*(1.7804^n)$, improving on the recent $O^*(1.933^n)$ algorithm of Cygan et al. 2012 LATIN paper.Comment: 13 pages, 1 figur

Forces Sauces and Eggs for Soldiers: food, nostalgia, and the rehabilitation of the British military

This article identifies, and considers the political implications of, the association of the contemporary British military and British soldiers with nostalgia. This aspect of the discursive project of rehabilitating the British military post-Iraq has not hitherto been theorized. The article analyses a set of exemplifying texts, four military charity food brands (Eggs for Soldiers, Forces Sauces, Red Lion Foods, and Rare Tea Company Battle of Britain Tea) to ask how nostalgic rehabilitation of the British military unfolds at the intersections of militarization, commemoration, and post-2008 “conscience capitalism”. I outline how military charity food brands are a form of “conscience capitalism” through which the perpetuation of militarized logics are produced as a notionally apolitical social “cause”, rendered intelligible within the terms of existing commoditized discourses of post-2008 vintage nostalgia. I then ask what understandings of British soldiers and the British military are constituted within the discourse of nostalgic rehabilitation, and secondly what forms of commemoration are entailed. I argue that a nostalgic generalization of soldiers and the military nullifies the potential unruliness of individual soldiers and obscures the specifics of recent, controversial, wars. Secondly nostalgic civil–military engagement entails a commemorative logic in which forms of quasi-military service are brought into the most banal spaces of everyday civilian life

Patterns of democracy: Coalition governance and majoritarian modification in the United Kingdom, 2010–2015

The UK is often regarded as the archetype of Westminster democracy and as the empirical antithesis of the power-sharing coalitions of Western Europe. Yet, in recent years a different account has emerged that focuses on the subtler institutional dynamics which limit the executive. It is to this body of scholarship that this article responds, locating the recent chapter of coalition government within the wider context of the UK’s democratic evolution. To do so, the article draws Lijphart’s two-dimensional typology of democracies, developing a refined framework that enables systematic comparison over time. The article demonstrates that between over the course of the 2010-15 Parliament, the UK underwent another period of majoritarian modification, driven by factors including the long-term influence of the constitutional forces unleashed under Labour and the short-term impact of coalition management. The article makes several important contributions, salient in the UK and beyond. Theoretically, it offers a critical rejoinder to debates regarding the relationship between institutional design and democratic performance. Methodologically, it demonstrates that the tools of large-scale comparison can be effectively scaled-down to facilitate withincase analysis. Empirically, it provides a series of conclusions regarding the tenability of the UK’s extant democratic architecture under the weight of pressures to which it continues to be subject

Functional Analyses of the Three Simian Hemorrhagic Fever Virus Nonstructural Protein 1 Papain-Like Proteases

The N-terminal region of simian hemorrhagic fever virus (SHFV) nonstructural polyprotein 1a is predicted to encode three papain-like proteases (PLP1α, PLP1β, and PLP1γ). Catalytic residues and cleavage sites for each of the SHFV PLP1s were predicted by alignment of the SHFV PLP1 region sequences with each other as well as with those of other arteriviruses, and the predicted catalytic residues were shown to be proximal by homology modeling of the SHFV nsp1s on porcine respiratory and reproductive syndrome virus (PRRSV) nsp1 crystal structures. The functionality of the predicted catalytic Cys residues and cleavage sites was tested by analysis of the autoproteolytic products generated in in vitro transcription/translation reactions done with wild-type or mutant SHFV nsp1 constructs. Cleavage sites were also analyzed by mass spectroscopy analysis of selected immunoprecipitated cleavage products. The data showed that each of the three SHFV PLP1s is an active protease. Cys63 was identified as the catalytic Cys of SHFV PLP1α and is adjacent to an Ala instead of the canonical Tyr observed in other arterivirus PLP1s. SHFV PLP1γ is able to cleave at both downstream and upstream nsp1 junction sites. Although intermediate precursor polyproteins as well as alternative products generated by each of the SHFV PLP1s cleaving at sites within the N-terminal region of nsp1β were produced in the in vitro reactions, Western blotting of SHFV-infected, MA104 cell lysates with SHFV nsp1 protein-specific antibodies detected only the three mature nsp1 proteins

Governing Uncertainty in a Secular Age: Rationalities of Violence, Theodicy and Torture

This article explores the problem of governing uncertainty in a secular age by focusing on the theological notion of ‘theodicy’ as the underlying rationale for the use of torture in the so-called ‘war on terror’. With God’s departure from the world, the problem of uncertainty acquires new salience as human beings can no longer explain tragic events as part of a transcendent order and must find immanent causes for the ‘evils’ that surround them. Taking a cue from Max Weber, I discuss how the problem of theodicy – how to reconcile the existence of God with the presence of evil in the world – does not disappear in the secular age but is mobilized through a Foucauldian biopolitical logic. Secular theodicy governs uncertainty through the production of economies of knowledge that rationalize processes of criminalization and securitization of entire groups and justify the use of violence. This process is particularly striking when analysing the use of torture in the so-called ‘war on terror’. Through a comparison with medieval practices and focusing on the cases of Guantanamo and Abu Ghraib, the article shows how secular torture is the product of a biopolitical theodicy aimed at governing uncertainty through the construction of the tortured as immanent evils who threaten our ‘good life’ and ‘deserve’ their treatment. Secular theodicy turns torture into an extreme form of governmentality of uncertainty in which the disciplining of conduct becomes the construction of subjectivities based on essentialist, stereotypical and racist – and for these very reasons, reassuring – economies of knowledge