General properties of cosmological models with an Isotropic Singularity

Much of the published work regarding the Isotropic Singularity is performed under the assumption that the matter source for the cosmological model is a barotropic perfect fluid, or even a perfect fluid with a $\gamma$-law equation of state. There are, however, some general properties of cosmological models which admit an Isotropic Singularity, irrespective of the matter source. In particular, we show that the Isotropic Singularity is a point-like singularity and that vacuum space-times cannot admit an Isotropic Singularity. The relationships between the Isotropic Singularity, and the energy conditions, and the Hubble parameter is explored. A review of work by the authors, regarding the Isotropic Singularity, is presented.Comment: 18 pages, 1 figur

Genetic Locus and Structural Characterization of the Biochemical Defect in the O-Antigenic Polysaccharide of the Symbiotically Deficient \u3cem\u3eRhizobium etli\u3c/em\u3e Mutant, CE166

The O-antigen polysaccharide (OPS) of Rhizobium etli CE3 lipopolysaccharide (LPS) is linked to the core oligosaccharide via an N-acetylquinovosaminosyl (QuiNAc) residue. A mutant of CE3, CE166, produces LPS with reduced amounts of OPS, and a suppressed mutant, CE166α, produces LPS with nearly normal OPS levels. Both mutants are deficient in QuiNAc production. Characterization of OPS from CE166 and CE166α showed that QuiNAc was replaced by its 4-keto derivative, 2-acetamido-2,6-dideoxyhexosyl-4-ulose. The identity of this residue was determined by NMR and mass spectrometry, and by gas chromatography-mass spectrometry analysis of its 2-acetamido-4-deutero-2,6-dideoxyhexosyl derivatives produced by reduction of the 4-keto group using borodeuteride. Mass spectrometric and methylation analyses showed that the 2-acetamido-2,6-dideoxyhexosyl-4-ulosyl residue was 3-linked and attached to the core-region external Kdo III residue of the LPS, the same position as that of QuiNAc in the CE3 LPS. DNA sequencing revealed that the transposon insertion in strain CE166 was located in an open reading frame whose predicted translation product, LpsQ, falls within a large family of predicted open reading frames, which includes biochemically characterized members that are sugar epimerases and/or reductases. A hypothesis to be tested in future work is that lpsQ encodes UDP-2-acetamido-2,6-dideoxyhexosyl-4-ulose reductase, the second step in the synthesis of UDP-QuiNAc from UDP-GlcNAc

Local and global statistical distances are equivalent on pure states

The statistical distance between pure quantum states is obtained by finding a measurement that is optimal in a sense defined by Wootters. As such, one may expect that the statistical distance will turn out to be different if the set of possible measurements is restricted in some way. It nonetheless turns out that if the restriction is to local operations and classical communication (LOCC) on any multipartite system, then the statistical distance is the same as it is without restriction, being equal to the angle between the states in Hilbert space.Comment: 5 pages, comments welcom

Minimum orbit dimension for local unitary action on n-qubit pure states

The group of local unitary transformations partitions the space of n-qubit quantum states into orbits, each of which is a differentiable manifold of some dimension. We prove that all orbits of the n-qubit quantum state space have dimension greater than or equal to 3n/2 for n even and greater than or equal to (3n + 1)/2 for n odd. This lower bound on orbit dimension is sharp, since n-qubit states composed of products of singlets achieve these lowest orbit dimensions.Comment: 19 page

Optimizing local protocols implementing nonlocal quantum gates

We present a method of optimizing recently designed protocols for implementing an arbitrary nonlocal unitary gate acting on a bipartite system. These protocols use only local operations and classical communication with the assistance of entanglement, and are deterministic while also being "one-shot", in that they use only one copy of an entangled resource state. The optimization is in the sense of minimizing the amount of entanglement used, and it is often the case that less entanglement is needed than with an alternative protocol using two-way teleportation.Comment: 11 pages, 1 figure. This is a companion paper to arXiv:1001.546

A note on behaviour at an isotropic singularity

The behaviour of Jacobi fields along a time-like geodesic running into an isotropic singularity is studied. It is shown that the Jacobi fields are crushed to zero length at a rate which is the same in every direction orthogonal to the geodesic. We show by means of a counter-example that this crushing effect depends crucially on a technicality of the definition of isotropic singularities, and not just on the uniform degeneracy of the metric at the singularity.Comment: 13 pp. plain latex. To appear in Classical and Quantum Gravit

Brain-Blood Partition Coefficient and Cerebral Blood Flow in Canines Using Calibrated Short TR Recovery (CaSTRR) Correction Method.

The brain-blood partition coefficient (BBPC) is necessary for quantifying cerebral blood flow (CBF) when using tracer based techniques like arterial spin labeling (ASL). A recent improvement to traditional MRI measurements of BBPC, called calibrated short TR recovery (CaSTRR), has demonstrated a significant reduction in acquisition time for BBPC maps in mice. In this study CaSTRR is applied to a cohort of healthy canines (n = 17, age = 5.0 - 8.0 years) using a protocol suited for application in humans at 3T. The imaging protocol included CaSTRR for BBPC maps, pseudo-continuous ASL for CBF maps, and high resolution anatomical images. The standard CaSTRR method of normalizing BBPC to gadolinium-doped deuterium oxide phantoms was also compared to normalization using hematocrit (Hct) as a proxy value for blood water content. The results show that CaSTRR is able to produce high quality BBPC maps with a 4 min acquisition time. The BBPC maps demonstrate significantly higher BBPC in gray matter (0.83 ± 0.05 mL/g) than in white matter (0.78 ± 0.04 mL/g, p = 0.006). Maps of CBF acquired with pCASL demonstrate a negative correlation between gray matter perfusion and age (p = 0.003). Voxel-wise correction for BBPC is also shown to improve contrast to noise ratio between gray and white matter in CBF maps. A novel aspect of the study was to show that that BBPC measurements can be calculated based on the known Hct of the blood sample placed in scanner. We found a strong correlation (R 2 = 0.81 in gray matter, R 2 = 0.59 in white matter) established between BBPC maps normalized to the doped phantoms and BBPC maps normalized using Hct. This obviates the need for doped water phantoms which simplifies both the acquisition protocol and the post-processing methods. Together this suggests that CaSTRR represents a feasible, rapid method to account for BBPC variability when quantifying CBF. As canines have been used widely for aging and Alzheimer's disease studies, the CaSTRR method established in the animals may further improve CBF measurements and advance our understanding of cerebrovascular changes in aging and neurodegeneration

Calculating the transfer function of noise removal by principal component analysis and application to AzTEC observations

Instruments using arrays of many bolometers have become increasingly common in the past decade. The maps produced by such instruments typically include the filtering effects of the instrument as well as those from subsequent steps performed in the reduction of the data. Therefore interpretation of the maps is dependent upon accurately calculating the transfer function of the chosen reduction technique on the signal of interest. Many of these instruments use non-linear and iterative techniques to reduce their data because such methods can offer improved signal-to-noise over those that are purely linear, particularly for signals at scales comparable to that subtended by the array. We discuss a general approach for measuring the transfer function of principal component analysis (PCA) on point sources that are small compared to the spatial extent seen by any single bolometer within the array. The results are applied to previously released AzTEC catalogues of the COSMOS, Lockman Hole, Subaru XMM-Newton Deep Field, GOODS-North and GOODS-South fields. Source flux density and noise estimates increase by roughly +10 per cent for fields observed while AzTEC was installed at the Atacama Submillimeter Telescope Experiment and +15-25 per cent while AzTEC was installed at the James Clerk Maxwell Telescope. Detection significance is, on average, unaffected by the revised technique. The revised photometry technique will be used in subsequent AzTEC releases.Comment: 14 pages, 4 figure