On cyclic branched coverings of prime knots

We prove that a prime knot K is not determined by its p-fold cyclic branched cover for at most two odd primes p. Moreover, we show that for a given odd prime p, the p-fold cyclic branched cover of a prime knot K is the p-fold cyclic branched cover of at most one more knot K' non equivalent to K. To prove the main theorem, a result concerning the symmetries of knots is also obtained. This latter result can be interpreted as a characterisation of the trivial knot.Comment: 28 pages, 2 figure

On abstract commensurators of groups

We prove that the abstract commensurator of a nonabelian free group, an infinite surface group, or more generally of a group that splits appropriately over a cyclic subgroup, is not finitely generated. This applies in particular to all torsion-free word-hyperbolic groups with infinite outer automorphism group and abelianization of rank at least 2. We also construct a finitely generated, torsion-free group which can be mapped onto Z and which has a finitely generated commensurator.Comment: 13 pages, no figur

The communication of Franciscan spirituality : appropriating Francis of Assisi's religious insights

It is generally understood that the spirituality of Francis of Assisi is a life-long journey of religious conversion, which begins with an experience of God's love and proceeds through an ongoing commitment to living each day authentically in accordance with gospel values. Through a deliberate and explicit use of Lonergan's transcendental method for enabling theology that is sound and meaningful, this study endeavors to receive the poverello 's own authentic communication of his spirituality by appreciating the historic context in which his messages were conceived, crafted and conveyed. Moreover, it indicates the merit of using this same carefully honed methodological approach to communicate Francis' numerous religious insights to our own contemporary culture in a manner that is both relevant and compelling

Using error correction to determine the noise model

Quantum error correcting codes have been shown to have the ability of making quantum information resilient against noise. Here we show that we can use quantum error correcting codes as diagnostics to characterise noise. The experiment is based on a three-bit quantum error correcting code carried out on a three-qubit nuclear magnetic resonance (NMR) quantum information processor. Utilizing both engineered and natural noise, the degree of correlations present in the noise affecting a two-qubit subsystem was determined. We measured a correlation factor of c=0.5+/-0.2 using the error correction protocol, and c=0.3+/-0.2 using a standard NMR technique based on coherence pathway selection. Although the error correction method demands precise control, the results demonstrate that the required precision is achievable in the liquid-state NMR setting.Comment: 10 pages, 3 figures. Added discussion section, improved figure

Collisions of particles in locally AdS spacetimes II Moduli of globally hyperbolic spaces

We investigate 3-dimensional globally hyperbolic AdS manifolds containing "particles", i.e., cone singularities of angles less than $2\pi$ along a time-like graph $\Gamma$. To each such space we associate a graph and a finite family of pairs of hyperbolic surfaces with cone singularities. We show that this data is sufficient to recover the space locally (i.e., in the neighborhood of a fixed metric). This is a partial extension of a result of Mess for non-singular globally hyperbolic AdS manifolds.Comment: 29 pages, 3 figures. v2: 41 pages, improved exposition. To appear, Comm. Math. Phys. arXiv admin note: text overlap with arXiv:0905.182

The resource theory of quantum reference frames: manipulations and monotones

Every restriction on quantum operations defines a resource theory, determining how quantum states that cannot be prepared under the restriction may be manipulated and used to circumvent the restriction. A superselection rule is a restriction that arises through the lack of a classical reference frame and the states that circumvent it (the resource) are quantum reference frames. We consider the resource theories that arise from three types of superselection rule, associated respectively with lacking: (i) a phase reference, (ii) a frame for chirality, and (iii) a frame for spatial orientation. Focussing on pure unipartite quantum states (and in some cases restricting our attention even further to subsets of these), we explore single-copy and asymptotic manipulations. In particular, we identify the necessary and sufficient conditions for a deterministic transformation between two resource states to be possible and, when these conditions are not met, the maximum probability with which the transformation can be achieved. We also determine when a particular transformation can be achieved reversibly in the limit of arbitrarily many copies and find the maximum rate of conversion. A comparison of the three resource theories demonstrates that the extent to which resources can be interconverted decreases as the strength of the restriction increases. Along the way, we introduce several measures of frameness and prove that these are monotonically nonincreasing under various classes of operations that are permitted by the superselection rule.Comment: 37 pages, 4 figures, Published Versio

HDQLIFE and neuro‐QoL physical function measures: Responsiveness in persons with huntington’s disease

BackgroundHuntington’s disease (HD) is a neurological disorder that causes severe motor symptoms that adversely impact health‐related quality of life. Patient‐reported physical function outcome measures in HD have shown cross‐sectional evidence of validity, but responsiveness has not yet been assessed.ObjectivesThis study evaluates the responsiveness of the Huntington Disease Health‐Related Quality of Life (HDQLIFE) and the Quality of Life in Neurological Disorders (Neuro‐QoL) physical function measures in persons with HD.MethodsA total of 347 participants completed baseline and at least 1 follow‐up (12‐month and 24‐month) measure (HDQLIFE Chorea, HDQLIFE Swallowing Difficulties, HDQLIFE Speech Difficulties, Neuro‐QoL Upper Extremity Function, and/or Neuro‐QoL Lower Extremity Function). Of the participants that completed the baseline assessment, 338 (90.9%) completed the 12‐month assessment, and 293 (78.8%) completed the 24‐month assessment. Standardized response means and general linear models evaluated whether the physical function measures were responsive to self‐reported and clinician‐rated change over time.ResultsSmall to moderate effect sizes for the standardized response means supported 12‐month and 24‐month responsiveness of the HDQLIFE and Neuro‐QoL measures for those with either self‐reported or clinician‐rated declines in function. General linear models supported 12‐month and 24‐month responsiveness for all HRQOL measures relative to self‐reported declines in health, but generally only 24‐month responsiveness was supported relative to clinician‐rated declines in function.ConclusionsLongitudinal analyses indicate that the HDQLIFE and the Neuro‐QoL physical function measures are sensitive to change over time in individuals with HD. Thus, these scales exhibit evidence of responsiveness and may be useful outcome measures in future clinical trials. © 2019 International Parkinson and Movement Disorder SocietyPeer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/154235/1/mds27908_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/154235/2/mds27908.pd

A specious unlinking strategy

We show that the following unlinking strategy does not always yield an optimal sequence of crossing changes: first split the link with the minimal number of crossing changes, and then unknot the resulting components

Gene family structure, expression and functional analysis of HD-Zip III genes in angiosperm and gymnosperm forest trees

BACKGROUND: Class III Homeodomain Leucine Zipper (HD-Zip III) proteins have been implicated in the regulation of cambium identity, as well as primary and secondary vascular differentiation and patterning in herbaceous plants. They have been proposed to regulate wood formation but relatively little evidence is available to validate such a role. We characterised and compared HD-Zip III gene family in an angiosperm tree, Populus spp. (poplar), and the gymnosperm Picea glauca (white spruce), representing two highly evolutionarily divergent groups. RESULTS: Full-length cDNA sequences were isolated from poplar and white spruce. Phylogenetic reconstruction indicated that some of the gymnosperm sequences were derived from lineages that diverged earlier than angiosperm sequences, and seem to have been lost in angiosperm lineages. Transcript accumulation profiles were assessed by RT-qPCR on tissue panels from both species and in poplar trees in response to an inhibitor of polar auxin transport. The overall transcript profiles HD-Zip III complexes in white spruce and poplar exhibited substantial differences, reflecting their evolutionary history. Furthermore, two poplar sequences homologous to HD-Zip III genes involved in xylem development in Arabidopsis and Zinnia were over-expressed in poplar plants. PtaHB1 over-expression produced noticeable effects on petiole and primary shoot fibre development, suggesting that PtaHB1 is involved in primary xylem development. We also obtained evidence indicating that expression of PtaHB1 affected the transcriptome by altering the accumulation of 48 distinct transcripts, many of which are predicted to be involved in growth and cell wall synthesis. Most of them were down-regulated, as was the case for several of the poplar HD-Zip III sequences. No visible physiological effect of over-expression was observed on PtaHB7 transgenic trees, suggesting that PtaHB1 and PtaHB7 likely have distinct roles in tree development, which is in agreement with the functions that have been assigned to close homologs in herbaceous plants. CONCLUSIONS: This study provides an overview of HD-zip III genes related to woody plant development and identifies sequences putatively involved in secondary vascular growth in angiosperms and in gymnosperms. These gene sequences are candidate regulators of wood formation and could be a source of molecular markers for tree breeding related to wood properties

Using LES to Study Reacting Flows and Instabilities in Annular Combustion Chambers

Great prominence is put on the design of aeronautical gas turbines due to increasingly stringent regulations and the need to tackle rising fuel prices. This drive towards innovation has resulted sometimes in new concepts being prone to combustion instabilities. In the particular field of annular combustion chambers, these instabilities often take the form of azimuthal modes. To predict these modes, one must compute the full combustion chamber, which remained out of reach until very recently and the development of massively parallel computers. Since one of the most limiting factors in performing Large Eddy Simulation (LES) of real combustors is estimating the adequate grid, the effects of mesh resolution are investigated by computing full annular LES of a realistic helicopter combustion chamber on three grids, respectively made of 38, 93 and 336 million elements. Results are compared in terms of mean and fluctuating fields. LES captures self-established azimuthal modes. The presence and structure of the modes is discussed. This study therefore highlights the potential of LES for studying combustion instabilities in annular gas turbine combustors