Angles in C*-algebras

In this work we characterise the C*-algebras $\mathcal{A}$ generated by projections with the property that every pair of projections in $\mathcal{A}$ has positive angle, as certain extensions of abelian algebras by algebras of compact operators. We show that this property is equivalent to a lattice theoretic property of projections and also to the property that the set of finite dimensional *-subalgebras of $\mathcal{A}$ is directed.

Multipliers of multidimensional Fourier algebras

Let $G$ be a locally compact $\sigma$-compact group. Motivated by an earlier notion for discrete groups due to Effros and Ruan, we introduce the multidimensional Fourier algebra $A^n(G)$ of $G$. We characterise the completely bounded multidimensional multipliers associated with $A^n(G)$ in several equivalent ways. In particular, we establish a completely isometric embedding of the space of all $n$-dimensional completely bounded multipliers into the space of all Schur multipliers on $G^{n+1}$ with respect to the (left) Haar measure. We show that in the case $G$ is amenable the space of completely bounded multidimensional multipliers coincides with the multidimensional Fourier-Stieltjes algebra of $G$ introduced by Ylinen. We extend some well-known results for abelian groups to the multidimensional setting.

1-amenability of A(X) for Banach spaces with 1-unconditional bases

The main result of the note is a characterization of 1-amenability of Banach algebras of approximable operators for a class of Banach spaces with 1-unconditional bases in terms of a new basis property. It is also shown that amenability and symmetric amenability are equivalent concepts for Banach algebras of approximable operators, and that a type of Banach space that was long suspected to lack property A has in fact the property. Some further ideas on the problem of whether or not amenability (in this setting) implies property A are discussed.

British Constructions with Constitutions:The Formal and Informal Nature of 'Island' Relations on Montserrat and Gibraltar

This article explores social, economic and political relations on two British Dependent Territories (BDTs) -- Montserrat and Gibraltar. This article notes that though BDTs are British colonial constructions, created, sustained and modelled upon and by Britain, they differ from Britain in that they have political constitutions. They also exhibit an ambiguous dependence and independence upon and with Britain. This article goes on to look at social and economic relations on Montserrat and Gibraltar before comparing and contrasting the political climates on each BDT. Throughout this article, it is suggested that there is a dynamic tension between formal and informal aspects to managing life. Finally, this article concludes with a discussion about the suitability of the split between Executive and Legislative Councils in these two BDTs.

Common Ingroups and Complex Identities: Routes to Reducing Bias in Multiple Category Contexts

We tested the hypothesis that evaluative bias in common ingroup contexts versus crossed categorization contexts can be associated with two distinct underlying processes. We reasoned that in common ingroup contexts, self-categorization, but not perceived complexity, would be positively related to intergroup bias. In contrast, in crossed categorization contexts, perceived complexity, but not self-categorization, would be negatively related to intergroup bias. In two studies, and in line with predictions, we found that while self-categorization and intergroup bias were related in common ingroup contexts, this was not the case in crossed categorization contexts. Moreover, we found that perceived category complexity, and not self-categorization, predicted bias in crossed categorization contexts. We discuss the implications of these findings for models of social categorization and intergroup bias.

Minimal Hilbert series for quadratic algebras and the Anick conjecture

We study the question on whether the famous Golod–Shafarevich estimate, which gives a lower bound for the Hilbert series of a (noncommutative) algebra, is attained. This question was considered by Anick in his 1983 paper ‘Generic algebras and CW-complexes’, Princeton Univ. Press, where he proved that the estimate is attained for the number of quadratic relations $d\leq n^2/4$
and $d\geq n^2/2$, and conjectured that it is the case for any number of quadratic relations. The particular point where the number of relations is equal to $n(n-1)/2$ was addressed by Vershik. He conjectured that a generic algebra with this number of relations is finite dimensional. We announce here the result that over any infinite field, the Anick conjecture holds for $d \geq 4(n2+n)/9$ and an arbitrary number of generators. We also discuss the result that confirms the Vershik conjecture over any field of characteristic 0, and a series of related
asymptotic results.

Episodic memory and learning in patients with chronic schizophrenia

This study explored the pattern of memory functioning in 58 patients with chronic schizophrenia and compared their performance with 53 normal controls. Multiple domains of memory were assessed, including verbal and nonverbal memory span, verbal and non-verbal paired associate learning, verbal and visual long-term memory, spatial and non-spatial conditional associative learning, recognition memory and memory for temporal order. Consistent with previous studies, substantial deficits in long-term memory were observed, with relative preservation of memory span. Memory for temporal order and recognition memory was intact, although significant deficits were observed on the conditional associative learning tasks. There was no evidence of lateralized memory impairment. In these respects, the pattern of memory impairment in schizophrenia is more similar in nature to that found in patients with memory dysfunction following mesiotemporal lobe lesions, rather than that associated with focal frontal lobe damage. (C) 1999 Elsevier Science B.V. All rights reserved.

Logics for belief functions on MV-algebras

In this paper we present a generalization of belief functions over fuzzy events. In particular we focus on belief functions defined in the algebraic framework of finite MV-algebras of fuzzy sets. We introduce a fuzzy modal logic to formalize reasoning with belief functions on many-valued events. We prove, among other results, that several different notions of belief functions can be characterized in a quite uniform way, just by slightly modifying the complete axiomatization of one of the modal logics involved in the definition of our formalism. © 2012 Elsevier Inc. All rights reserved.

K-Theory of Azumaya Algebras over Schemes

Let X be a connected, noetherian scheme and A{script} be a sheaf of Azumaya algebras on X, which is a locally free O{script}-module of rank a. We show that the kernel and cokernel of K(X) ? K(A{script}) are torsion groups with exponent a for some m and any i = 0, when X is regular or X is of dimension d with an ample sheaf (in this case m = d + 1). As a consequence, K(X, Z/m) ? K(A{script}, Z/m), for any m relatively prime to a. © 2013 Copyright Taylor and Francis Group, LLC.

Deconstructing Victim and offender Identities in Discourses on Child Sexual Abuse: Hierarchies, Blame and the Good/Evil Dialectic

Contemporary social and political constructions of victimhood and offending behaviour lie at the heart of regulatory policies on child sexual abuse. Legislation is named after specific child victims of high profile cases, and a burgeoning range of pre-emptive measures are enacted to protect an amorphous class of ‘all potential victims’ from the risk sex offenders are seen as posing. Such policies are also heavily premised on the omnipresent predatory stranger. These constructed identities, however, are at odds with the actual identities of victims and offenders of such crimes. Drawing on a range of literatures, the core task of this article is to confront some of the complexities and tensions surrounding constructions of the victim/offender dyad within the specific context of sexual offending against children. In particular, the article argues that discourses on ‘blame’ – and the polarised notions of ‘innocence’ and ‘guilt’ – inform respective hierarchies of victimhood and offending concerning ‘legitimate’ victim and offender status. Based on these insights, the article argues for the need to move beyond such monochromatic understandings of victims and offenders of sexual crime and to reframe the politics of risk accordingly.

Sovereignty, Article 4(2) TEU and the Respect of National Identities: Swinging the Balance of Power in Favour of the Member States?

The question of whether and to what extent sovereignty has been transferred to the European Union (EU) from its Member States remains a central debate within the EU and is interlinked with issues such as Kompetenz-Kompetenz, direct effect and primacy. Central to any claim to sovereignty is the principle of primacy, which requires that Member States uphold EU law over national law where there is a conflict. However, limitations to primacy can traditionally be found in national jurisprudence and the Maastricht Treaty introduced a possible EU limitation with the requirement that the EU respect national identities of Member States. The Lisbon Treaty provided only minimal further support to the principle of primacy whilst simultaneously developing the provision on national identities, now found within Article 4(2) TEU. There are indications from the literature, national constitutional courts and the Court of Justice of the EU that the provision is gathering strength as a legal tool and is likely to have a wider scope than the text might indicate. In its new role, Article 4(2) TEU bolsters the Member States’ claim to sovereignty and the possibility to uphold aspects crucial to them in conflict with EU law and the principle of primacy. Consequently, it is central to the relationship between the constitutional courts of the Member States and the CJEU, and where the final elements of control remain in ‘hard cases’. However, it does so as part of EU law, thereby facilitating the evasion of direct fundamental conflicts and reflecting the concept of constitutional pluralism.

The politicization of indigenous identities in Peru

Until now, scholars have argued that, unlike other Latin American countries with sizable indigenous populations, indigenous politics are largely unimportant in Peru because indigenous-based parties or national-level movements are absent. Rather than focusing solely on the emergence of indigenous parties or movements, which ignores the larger consequence of individuals' indigenous identifications for electoral politics, we argue that it is more important to examine the emergence of indigenous political divisions and their effects on indigenous representation. Using data from the World Values Survey across the presidential elections of 1995, 2001, and 2006, we show that, as indigenous identity has become more carefully defined, indigenous voting divisions have emerged in Peru, and concomitantly, parties have begun to recognize and respond to these divisions.

Ideals of A(G) and bimodules over maximal abelian selfadjoint algebras

This paper is concerned with weak⁎ closed masa-bimodules generated by A(G)-invariant subspaces of VN(G). An annihilator formula is established, which is used to characterise the weak⁎ closed subspaces of B(L2(G)) which are invariant under both Schur multipliers and a canonical action of M(G) on B(L2(G)) via completely bounded maps. We study the special cases of extremal ideals with a given null set and, for a large class of groups, we establish a link between relative spectral synthesis and relative operator synthesis.

“A quiet still voice that just touches”: music’s relevance for adults living with life-threatening cancer diagnoses.

Purpose
Music has historically aided health and loss-adaptation, however, cancer patients’ experience of music for self-care is not well understood. This study examines adult cancer patients’ views about music’s role before and after diagnosis.
Methods
Constructivist approach, with grounded theory informed design using convenience, snowball and theoretical sampling. Patients from Australian metropolitan cancer and hospice settings completed demographic questionnaires and participated in semi-structured interviews. Qualitative inter-rater reliability was applied.
Results
Fifty-two patients reported comparable time spent experiencing music pre-post diagnosis. Music may remain incidental; however, many patients adapt music usage to ameliorate cancer’s aversive effects. Patients often draw from their musical lives and explore unfamiliar music to: remain connected with pre-illness identities; strengthen capacity for enduring treatment, ongoing survival (even when knowing “you’re going to die”), or facing death; reframe upended worlds; and live enriched lives. Patients can ascribe human or physical properties to music when describing its transformative effects. Familiar lyrics maybe reinterpreted, and patients’ intensified emotional reactions to music can reflect their threatened mortality. Sometimes music becomes inaccessible, elusive, and/or intensifies distress and is avoided. Families’, friends’ and professionals’ recognition of patients’ altered musical lives and music-based suggestions can extend patients’ use of music for self-care.
Conclusion
Health professionals can support patients by inquiring about their music behaviours and recognising that altered music usage may signify vulnerability. Although commonly recommended, hospital concerts and music broadcasts need sensitive delivery. Patients’ preferred music should be available in diagnostic, treatment and palliative settings because it can promote endurance and life enrichment.

On the complexity of solving polytree-shaped limited memory influence diagrams with binary variables

Influence diagrams are intuitive and concise representations of structured decision problems. When the problem is non-Markovian, an optimal strategy can be exponentially large in the size of the diagram. We can avoid the inherent intractability by constraining the size of admissible strategies, giving rise to limited memory influence diagrams. A valuable question is then how small do strategies need to be to enable efficient optimal planning. Arguably, the smallest strategies one can conceive simply prescribe an action for each time step, without considering past decisions or observations. Previous work has shown that finding such optimal strategies even for polytree-shaped diagrams with ternary variables and a single value node is NP-hard, but the case of binary variables was left open. In this paper we address such a case, by first noting that optimal strategies can be obtained in polynomial time for polytree-shaped diagrams with binary variables and a single value node. We then show that the same problem is NP-hard if the diagram has multiple value nodes. These two results close the fixed-parameter complexity analysis of optimal strategy selection in influence diagrams parametrized by the shape of the diagram, the number of value nodes and the maximum variable cardinality.