11,387 research outputs found
Groupoid normalisers of tensor products: infinite von Neumann algebras
The groupoid normalisers of a unital inclusion of von Neumann
algebras consist of the set of partial isometries
with and . Given two unital inclusions
of von Neumann algebras, we examine groupoid normalisers for
the tensor product inclusion $B_1\ \overline{\otimes}\ B_2\subseteq M_1\
\overline{\otimes}\ M_2$
\mathcal{GN}_{M_1\,\overline{\otimes}\,M_2}(B_1\ \overline{\otimes}\
B_2)''=\mathcal{GN}_{M_1}(B_1)''\ \overline{\otimes}\ \mathcal{GN}_{M_2}(B_2)''
when one inclusion has a discrete relative commutant equal to
the centre of (no assumption is made on the second inclusion). This
result also holds when one inclusion is a generator masa in a free group
factor. We also examine when a unitary
normalising a tensor product of irreducible
subfactors factorises as (for some unitary $w\in B_1\
\overline{\otimes}\ B_2v_i\in\mathcal{N}_{M_i}(B_i)M_iB_i_1B_1M_1, B_2M_2$) as
those with a trivial fundamental group.Comment: 22 page
Normalizers of Irreducible Subfactors
We consider normalizers of an irreducible inclusion of
factors. In the infinite index setting an inclusion
can be strict, forcing us to also investigate the semigroup
of one-sided normalizers. We relate these normalizers of in to
projections in the basic construction and show that every trace one projection
in the relative commutant is of the form for some
unitary with . This enables us to identify the
normalizers and the algebras they generate in several situations. In particular
each normalizer of a tensor product of irreducible subfactors is a tensor
product of normalizers modulo a unitary. We also examine normalizers of
irreducible subfactors arising from subgroup--group inclusions .
Here the normalizers are the normalizing group elements modulo a unitary from
. We are also able to identify the finite trace -bimodules in
as double cosets which are also finite unions of left cosets.Comment: 33 Page
Responding to accents after experiencing interactive or mediated speech
Very little known is about how speakers learn
about and/or respond to speech experienced
without the possibility for interaction. This paper
reports an experiment which considers the effects
of two kinds of exposure to speech (interactive or
non-interactive mediated) on Scottish English
speakers’ responses to another accent (Southern
British English), for two processing tasks,
phonological awareness and speech production.
Only marginal group effects are found according to
exposure type. The main findings show a
difference between subjects according to exposure
type before exposure, and individual shifts in
responses to speech according to exposure type
Dissecting the Genetic Basis of Variation in Drosophila Sleep Using a Multiparental QTL Mapping Resource
There is considerable variation in sleep duration, timing and quality in human populations, and sleep dysregulation has been implicated as a risk factor for a range of health problems. Human sleep traits are known to be regulated by genetic factors, but also by an array of environmental and social factors. These uncontrolled, non-genetic effects complicate powerful identification of the loci contributing to sleep directly in humans. The model system, Drosophila melanogaster, exhibits a behavior that shows the hallmarks of mammalian sleep, and here we use a multitiered approach, encompassing high-resolution QTL mapping, expression QTL data, and functional validation with RNAi to investigate the genetic basis of sleep under highly controlled environmental conditions. We measured a battery of sleep phenotypes in >750 genotypes derived from a multiparental mapping panel and identified several, modest-effect QTL contributing to natural variation for sleep. Merging sleep QTL data with a large head transcriptome eQTL mapping dataset from the same population allowed us to refine the list of plausible candidate causative sleep loci. This set includes genes with previously characterized effects on sleep and circadian rhythms, in addition to novel candidates. Finally, we employed adult, nervous system-specific RNAi on the Dopa decarboxylase, dyschronic, and timeless genes, finding significant effects on sleep phenotypes for all three. The genes we resolve are strong candidates to harbor causative, regulatory variation contributing to sleep
Dissecting the Genetic Basis of Variation in Drosophila Sleep Using a Multiparental QTL Mapping Resource
This work is licensed under a Creative Commons Attribution 4.0 International License.There is considerable variation in sleep duration, timing and quality in human populations, and sleep dysregulation has been implicated as a risk factor for a range of health problems. Human sleep traits are known to be regulated by genetic factors, but also by an array of environmental and social factors. These uncontrolled, non-genetic effects complicate powerful identification of the loci contributing to sleep directly in humans. The model system, Drosophila melanogaster, exhibits a behavior that shows the hallmarks of mammalian sleep, and here we use a multitiered approach, encompassing high-resolution QTL mapping, expression QTL data, and functional validation with RNAi to investigate the genetic basis of sleep under highly controlled environmental conditions. We measured a battery of sleep phenotypes in >750 genotypes derived from a multiparental mapping panel and identified several, modest-effect QTL contributing to natural variation for sleep. Merging sleep QTL data with a large head transcriptome eQTL mapping dataset from the same population allowed us to refine the list of plausible candidate causative sleep loci. This set includes genes with previously characterized effects on sleep and circadian rhythms, in addition to novel candidates. Finally, we employed adult, nervous system-specific RNAi on the Dopa decarboxylase, dyschronic, and timeless genes, finding significant effects on sleep phenotypes for all three. The genes we resolve are strong candidates to harbor causative, regulatory variation contributing to sleep
Kadison-Kastler stable factors
A conjecture of Kadison and Kastler from 1972 asks whether sufficiently close operator algebras in a natural uniform sense must be small unitary perturbations of one another. For n≥3 and a free, ergodic, probability measure-preserving action of SL<sub>n</sub>(Z) on a standard nonatomic probability space (X,μ), write M=(L<sup>∞</sup>(X,μ)⋊SL<sub>n</sub>(Z))⊗¯¯¯R, where R is the hyperfinite II1-factor. We show that whenever M is represented as a von Neumann algebra on some Hilbert space H and N⊆B(H) is sufficiently close to M, then there is a unitary u on H close to the identity operator with uMu∗=N. This provides the first nonamenable class of von Neumann algebras satisfying Kadison and Kastler’s conjecture.
We also obtain stability results for crossed products L<sup>∞</sup>(X,μ)⋊Γ whenever the comparison map from the bounded to usual group cohomology vanishes in degree 2 for the module L<sup>2</sup>(X,μ). In this case, any von Neumann algebra sufficiently close to such a crossed product is necessarily isomorphic to it. In particular, this result applies when Γ is a free group
A remark on the similarity and perturbation problems
In this note we show that Kadison's similarity problem for C*-algebras is
equivalent to a problem in perturbation theory: must close C*-algebras have
close commutants?Comment: 6 Pages, minor typos fixed. C. R. Acad. Sci. Canada, to appea
Toward autonomous architecture: The convergence of digital design, robotics, and the built environment
The way we design, construct, and inhabit buildings is changing—moving toward greater integration of robotic and autonomous systems that challenge our preconceived notions of how buildings are made, what they are, or what they should be
Antioxidant activity of β-lactoglobulin and its modified derivatives
Both native ss-lactoglobulin and its modified derivatives (Figure 1) exhibited antioxidant activity when assessed by the FRAP assay (which measures total reducing power of the sample). A positive correlation was observed between antioxidant activity and protein concentration in all samples. Compared to the native protein, the concentration dependence of the antioxidant activity was significantly greater when ss-lactoglobulin was modified with the Maillard reaction (p=0.000) and Enzyme hydrolysis (p=0.022)....<br /
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