751 research outputs found
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 Tâ=â1 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
of the minimal models for all relatively prime
integers for some allowed values of and . Our starting point is
binomial (q-binomial) identities derived from a truncation of the state
counting equations of the XXZ spin chain of anisotropy
. We use the Takahashi-Suzuki method to express
the allowed values of (and ) in terms of the continued fraction
decomposition of (and ) where stands for
the fractional part of These values are, in fact, the dimensions of the
hermitian irreducible representations of (and )
with (and We also establish the duality relation 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 FarmersâParticipation in Biodiversity Policies
This article reports the major findings from an interdisciplinary research project that synthesises key insights into farmersâ 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 farmersâ 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 â as a situation determined by one or several influencing factors â 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)
lawbreakersâ identity, reflexivity, and self-understanding have become central
preoccupations. In this article I interrogate aspects of the methodological âundersideâ
(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
âgive women voiceâ 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
Poor youths and âpacificationâ:dilemmas between discourse and practice from the perspective of young people about policing in Rio de Janeiroâs favelas
Polynomial super-gl(n) algebras
We introduce a class of finite dimensional nonlinear superalgebras providing gradings of . Odd generators close by anticommutation on polynomials (of
degree ) in the generators. Specifically, we investigate `type I'
super- algebras, having odd generators transforming in a single
irreducible representation of together with its contragredient.
Admissible structure constants are discussed in terms of available
couplings, and various special cases and candidate superalgebras are identified
and exemplified via concrete oscillator constructions. For the case of the
-dimensional defining representation, with odd generators , and even generators , , a three
parameter family of quadratic super- algebras (deformations of
) is defined. In general, additional covariant Serre-type conditions
are imposed, in order that the Jacobi identities be fulfilled. For these
quadratic super- 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
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