Normalizers of Irreducible Subfactors

We consider normalizers of an irreducible inclusion $N\subseteq M$ of $\mathrm{II}_1$ factors. In the infinite index setting an inclusion $uNu^*\subseteq N$ can be strict, forcing us to also investigate the semigroup of one-sided normalizers. We relate these normalizers of $N$ in $M$ to projections in the basic construction and show that every trace one projection in the relative commutant $N'\cap$ is of the form $u^*e_Nu$ for some unitary $u\in M$ with $uNu^*\subseteq N$. 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 $H\subseteq G$. Here the normalizers are the normalizing group elements modulo a unitary from $L(H)$. We are also able to identify the finite trace $L(H)$-bimodules in $\ell^2(G)$ as double cosets which are also finite unions of left cosets.Comment: 33 Page

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

Efficient Environment Guided Approach for Exploration of Complex Environments

Remote inspection of a complex environment is a difficult, time consuming task for human operators to perform. The need to manually avoid obstacles whilst considering other performance factors i.e. time taken, joint effort and information gained represents significant challenges to continuous operation. This paper proposes an autonomous robotic solution for exploration of an unknown, complex environment using a high DoF robot arm with an eye in hand depth sensor. The main contribution of this work is a new strategy to find the next best view by evaluating frontier regions of the map to maximise coverage, in contrast to many current approaches which densely sample joint or workspace configurations of the robot. Multiple utility functions were evaluated that showed different behaviours. Our results indicated that the presented algorithm can explore an arbitrary environment efficiently while optimising various performance criteria based on the utility function chosen, application constraints and the desires of the user

Cross-accent intelligibility of speech in noise: Long-term familiarity and short-term familiarization

Listeners must cope with a great deal of variability in the speech signal, and thus theories of speech perception must also account for variability, which comes from a number of sources, including variation between accents. It is well-known that there is a processing cost when listening to speech in an accent other than one’s own, but recent work has suggested that this cost is reduced when listening to a familiar accent widely represented in the media, and/or when short amounts of exposure to an accent are provided. Little is known, however, about how these factors (long-term familiarity and short-term familiarization with an accent) interact. The current study tested this interaction by playing listeners difficult-to-segment sentences in noise, before and after a familiarization period where the same sentences were heard in the clear, allowing us to manipulate short-term familiarization. Listeners were speakers of either Glasgow English or Standard Southern British English, and they listened to speech in either their own or the other accent, thereby allowing us to manipulate long-term familiarity. Results suggest that both long-term familiarity and short-term familiarization mitigate the perceptual processing costs of listening to an accent that is not one’s own, but seem not to compensate for them entirely, even when the accent is widely heard in the media

Clustering in 18O - absolute determination of branching ratios via high-resolution particle spectroscopy

The determination of absolute branching ratios for high-energy states in light nuclei is an important and useful tool for probing the underlying nuclear structure of individual resonances: for example, in establishing the tendency of an excited state towards α -cluster structure. Difficulty arises in measuring these branching ratios due to similarities in available decay channels, such as ( 18 O, n ) and ( 18 O, 2 n ), as well as differences in geometric efficiencies due to population of bound excited levels in daughter nuclei. Methods are presented using Monte Carlo techniques to overcome these issues

Distribution and Environmental Tolerances of Aquatic Macroinvertebrate Families in the Agricultural Zone of Southwestern Australia

The agricultural zone of southwestern Australia is an extensively modified landscape. Ninety percent of the perennial native vegetation has been cleared and replaced by annual cereal crops and pasture. Consequently, groundwater has risen and much of the region is affected by dryland salinity. River geomorphology and water quality have been severely impacted by land clearing, anthropogenic patterns of land use, and secondary salinization. The objectives of this study were to determine patterns of distribution of aquatic macroinvertebrates in the region, and to identify environmental variables influencing these patterns. Aquatic macroinvertebrates were sampled at 176 river sites during spring 1997 and a range of environmental data were collected at each site. Eighty-one families were collected, with the fauna being dominated by insects. At the family level, macroinvertebrate communities were homogeneous and depauperate, and consisted of families that tolerated a broad range of environmental conditions. The fauna was particularly resilient to high salinities, with some families tolerating salinities orders of magnitude greater than previously reported for lotic waters. The most significant environmental factors influencing the distribution of aquatic invertebrates were rainfall, salinity, land use, and instream habitat

Behaving Optimistically: How the (Un)Desirability of an Outcome Can Bias People’s Preparations for It

Past research on the desirability bias and on bracing for bad news has focused on the potential influence of outcome desirability on people’s stated expectations. The present studies examined its influence on behavior—that is, what is done in anticipation of, or preparation for, an uncertain outcome. In five studies, the desirability of possible outcomes for an event, which was uncertain and uncontrollable by the participant, was manipulated, and preparation behavior was measured. Study 1 used a hypothetical‐events paradigm. Studies 2 and 3 involved a computer activity in which behavior was tracked on a trial‐by‐trial basis. In Studies 4 and 5, the uncertain event was the ending of a videotaped basketball game. Rather than exhibiting bracing or a reluctance to tempt fate, participants tended to behave in a manner consistent with an optimistic desirability bias. In a subset of studies, predictions and likelihood judgments were also solicited; the differential effects of outcome desirability on these measures are discussed. Copyright © 2015 John Wiley & Sons, Ltd.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135587/1/bdm1918_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/135587/2/bdm1918.pd

Groupoid normalizers of tensor products

We consider an inclusion B [subset of or equal to] M of finite von Neumann algebras satisfying B′∩M [subset of or equal to] B. A partial isometry vset membership, variantM is called a groupoid normalizer if vBv*,v*Bv[subset of or equal to] B. Given two such inclusions B<sub>i</sub> [subset of or equal to] M<sub>i</sub>, i=1,2, we find approximations to the groupoid normalizers of [formula] in [formula], from which we deduce that the von Neumann algebra generated by the groupoid normalizers of the tensor product is equal to the tensor product of the von Neumann algebras generated by the groupoid normalizers. Examples are given to show that this can fail without the hypothesis [formula], i=1,2. We also prove a parallel result where the groupoid normalizers are replaced by the intertwiners, those partial isometries vset membership, variantM satisfying vBv*[subset of or equal to] B and v*v,vv*[set membership, variant] B