Characterizing Operations Preserving Separability Measures via Linear Preserver Problems

We use classical results from the theory of linear preserver problems to characterize operators that send the set of pure states with Schmidt rank no greater than k back into itself, extending known results characterizing operators that send separable pure states to separable pure states. We also provide a new proof of an analogous statement in the multipartite setting. We use these results to develop a bipartite version of a classical result about the structure of maps that preserve rank-1 operators and then characterize the isometries for two families of norms that have recently been studied in quantum information theory. We see in particular that for k at least 2 the operator norms induced by states with Schmidt rank k are invariant only under local unitaries, the swap operator and the transpose map. However, in the k = 1 case there is an additional isometry: the partial transpose map.Comment: 16 pages, typos corrected, references added, proof of Theorem 4.3 simplified and clarifie

Obstructing extensions of the functor Spec to noncommutative rings

In this paper we study contravariant functors from the category of rings to the category of sets whose restriction to the full subcategory of commutative rings is isomorphic to the prime spectrum functor Spec. The main result reveals a common characteristic of these functors: every such functor assigns the empty set to M_n(C) for n >= 3. The proof relies, in part, on the Kochen-Specker Theorem of quantum mechanics. The analogous result for noncommutative extensions of the Gelfand spectrum functor for C*-algebras is also proved.Comment: 23 pages. To appear in Israel J. Math. Title was changed; introduction was rewritten; old Section 2 was removed to streamline the exposition; final section was rewritten to omit an error in the earlier proof of Theorem 1.

Structure of the mature Rous sarcoma virus lattice reveals a role for IP6 in the formation of the capsid hexamer

Inositol hexakisphosphate (IP6) is an assembly cofactor for HIV-1. We report here that IP6 is also used for assembly of Rous sarcoma virus (RSV), a retrovirus from a different genus. IP6 is ~100-fold more potent at promoting RSV mature capsid protein (CA) assembly than observed for HIV-1 and removal of IP6 in cells reduces infectivity by 100-fold. Here, visualized by cryo-electron tomography and subtomogram averaging, mature capsid-like particles show an IP6-like density in the CA hexamer, coordinated by rings of six lysines and six arginines. Phosphate and IP6 have opposing effects on CA in vitro assembly, inducing formation of T = 1 icosahedrons and tubes, respectively, implying that phosphate promotes pentamer and IP6 hexamer formation. Subtomogram averaging and classification optimized for analysis of pleomorphic retrovirus particles reveal that the heterogeneity of mature RSV CA polyhedrons results from an unexpected, intrinsic CA hexamer flexibility. In contrast, the CA pentamer forms rigid units organizing the local architecture. These different features of hexamers and pentamers determine the structural mechanism to form CA polyhedrons of variable shape in mature RSV particles

Fourier-Space Crystallography as Group Cohomology

We reformulate Fourier-space crystallography in the language of cohomology of groups. Once the problem is understood as a classification of linear functions on the lattice, restricted by a particular group relation, and identified by gauge transformation, the cohomological description becomes natural. We review Fourier-space crystallography and group cohomology, quote the fact that cohomology is dual to homology, and exhibit several results, previously established for special cases or by intricate calculation, that fall immediately out of the formalism. In particular, we prove that {\it two phase functions are gauge equivalent if and only if they agree on all their gauge-invariant integral linear combinations} and show how to find all these linear combinations systematically.Comment: plain tex, 14 pages (replaced 5/8/01 to include archive preprint number for reference 22

Continued Fractions and Fermionic Representations for Characters of M(p,p') minimal models

We present fermionic sum representations of the characters $\chi^{(p,p')}_{r,s}$ of the minimal $M(p,p')$ models for all relatively prime integers $p'>p$ for some allowed values of $r$ and $s$. Our starting point is binomial (q-binomial) identities derived from a truncation of the state counting equations of the XXZ spin ${1\over 2}$ chain of anisotropy $-\Delta=-\cos(\pi{p\over p'})$. We use the Takahashi-Suzuki method to express the allowed values of $r$ (and $s$) in terms of the continued fraction decomposition of $\{{p'\over p}\}$ (and ${p\over p'}$) where $\{x\}$ stands for the fractional part of $x.$ These values are, in fact, the dimensions of the hermitian irreducible representations of $SU_{q_{-}}(2)$ (and $SU_{q_{+}}(2)$) with $q_{-}=\exp (i \pi \{{p'\over p}\})$ (and $q_{+}=\exp ( i \pi {p\over p'})).$ We also establish the duality relation $M(p,p')\leftrightarrow M(p'-p,p')$ and discuss the action of the Andrews-Bailey transformation in the space of minimal models. Many new identities of the Rogers-Ramanujan type are presented.Comment: Several references, one further explicit result and several discussion remarks adde

Relativistic cosmological perturbation scheme on a general background: scalar perturbations for irrotational dust

In standard perturbation approaches and N-body simulations, inhomogeneities are described to evolve on a predefined background cosmology, commonly taken as the homogeneous-isotropic solutions of Einstein's field equations (Friedmann-Lema\^itre-Robertson-Walker (FLRW) cosmologies). In order to make physical sense, this background cosmology must provide a reasonable description of the effective, i.e. spatially averaged, evolution of structure inhomogeneities also in the nonlinear regime. Guided by the insights that (i) the average over an inhomogeneous distribution of matter and geometry is in general not given by a homogeneous solution of general relativity, and that (ii) the class of FLRW cosmologies is not only locally but also globally gravitationally unstable in relevant cases, we here develop a perturbation approach that describes the evolution of inhomogeneities on a general background being defined by the spatially averaged evolution equations. This physical background interacts with the formation of structures. We derive and discuss the resulting perturbation scheme for the matter model `irrotational dust' in the Lagrangian picture, restricting our attention to scalar perturbations.Comment: 18 pages. Matches published version in CQ

Factors Affecting European Farmers’Participation in Biodiversity Policies

This article reports the major findings from an interdisciplinary research project that synthesises key insights into farmers’ willingness and ability to co-operate with biodiversity policies. The results of the study are based on an assessment of about 160 publications and research reports from six EU member states and from international comparative research.We developed a conceptual framework to systematically review the existent literature relevant for our purposes. This framework provides a common structure for analysing farmers’ perspectives regarding the introduction into farming practices of measures relevant to biodiversity. The analysis is coupled and contrasted with a survey of experts. The results presented above suggest that it is important to view support for practices oriented towards biodiversity protection not in a static sense – as a situation determined by one or several influencing factors – but rather as a process marked by interaction. Financial compensation and incentives function as a necessary, though clearly not sufficient condition in this process

Sociological stalking? Methods, ethics and power in longitudinal criminological research

Scholarship on criminal careers and desistance from crime employing longitudinal methodologies has paid scant attention to sociological and anthropological debates regarding epistemology, reflexivity and researcher positionality. This is surprising in light of a recent phenomenological turn in desistance research wherein (former) lawbreakers’ identity, reflexivity, and self-understanding have become central preoccupations. In this article I interrogate aspects of the methodological ‘underside’ (Gelsthorpe, 2007) of qualitative longitudinal research with criminalised women through an examination of the surveillant position of the researcher. Focusing on methods, ethics and power, I examine some contradictions of feminist concerns to ‘give women voice’ in research involving re-tracing an over-surveilled and highly stigmatised population. I reflect on the effects of researcher positionality through a conceptualisation of re-tracing methods as, at worst, a form of sociological stalking

Polynomial super-gl(n) algebras

We introduce a class of finite dimensional nonlinear superalgebras $L = L_{\bar{0}} + L_{\bar{1}}$ providing gradings of $L_{\bar{0}} = gl(n) \simeq sl(n) + gl(1)$. Odd generators close by anticommutation on polynomials (of degree $>1$) in the $gl(n)$ generators. Specifically, we investigate `type I' super-$gl(n)$ algebras, having odd generators transforming in a single irreducible representation of $gl(n)$ together with its contragredient. Admissible structure constants are discussed in terms of available $gl(n)$ couplings, and various special cases and candidate superalgebras are identified and exemplified via concrete oscillator constructions. For the case of the $n$-dimensional defining representation, with odd generators $Q_{a}, \bar{Q}{}^{b}$, and even generators ${E^{a}}_{b}$, $a,b = 1,...,n$, a three parameter family of quadratic super-$gl(n)$ algebras (deformations of $sl(n/1)$) is defined. In general, additional covariant Serre-type conditions are imposed, in order that the Jacobi identities be fulfilled. For these quadratic super-$gl(n)$ algebras, the construction of Kac modules, and conditions for atypicality, are briefly considered. Applications in quantum field theory, including Hamiltonian lattice QCD and space-time supersymmetry, are discussed.Comment: 31 pages, LaTeX, including minor corrections to equation (3) and reference [60