Constructing Mutually Unbiased Bases in Dimension Six

The density matrix of a qudit may be reconstructed with optimal efficiency if the expectation values of a specific set of observables are known. In dimension six, the required observables only exist if it is possible to identify six mutually unbiased complex 6x6 Hadamard matrices. Prescribing a first Hadamard matrix, we construct all others mutually unbiased to it, using algebraic computations performed by a computer program. We repeat this calculation many times, sampling all known complex Hadamard matrices, and we never find more than two that are mutually unbiased. This result adds considerable support to the conjecture that no seven mutually unbiased bases exist in dimension six.Comment: As published version. Added discussion of the impact of numerical approximations and corrected the number of triples existing for non-affine families (cf Table 3

Dynamics-based centrality for general directed networks

Determining the relative importance of nodes in directed networks is important in, for example, ranking websites, publications, and sports teams, and for understanding signal flows in systems biology. A prevailing centrality measure in this respect is the PageRank. In this work, we focus on another class of centrality derived from the Laplacian of the network. We extend the Laplacian-based centrality, which has mainly been applied to strongly connected networks, to the case of general directed networks such that we can quantitatively compare arbitrary nodes. Toward this end, we adopt the idea used in the PageRank to introduce global connectivity between all the pairs of nodes with a certain strength. Numerical simulations are carried out on some networks. We also offer interpretations of the Laplacian-based centrality for general directed networks in terms of various dynamical and structural properties of networks. Importantly, the Laplacian-based centrality defined as the stationary density of the continuous-time random walk with random jumps is shown to be equivalent to the absorption probability of the random walk with sinks at each node but without random jumps. Similarly, the proposed centrality represents the importance of nodes in dynamics on the original network supplied with sinks but not with random jumps.Comment: 7 figure

Isomorphs in model molecular liquids

Isomorphs are curves in the phase diagram along which a number of static and dynamic quantities are invariant in reduced units. A liquid has good isomorphs if and only if it is strongly correlating, i.e., the equilibrium virial/potential energy fluctuations are more than 90% correlated in the NVT ensemble. This paper generalizes isomorphs to liquids composed of rigid molecules and study the isomorphs of two systems of small rigid molecules, the asymmetric dumbbell model and the Lewis-Wahnstrom OTP model. In particular, for both systems we find that the isochoric heat capacity, the excess entropy, the reduced molecular center-of-mass self part of the intermediate scattering function, the reduced molecular center-of-mass radial distribution function to a good approximation are invariant along an isomorph. In agreement with theory, we also find that an instantaneous change of temperature and density from an equilibrated state point to another isomorphic state point leads to no relaxation. The isomorphs of the Lewis-Wahnstrom OTP model were found to be more approximative than those of the asymmetric dumbbell model, which is consistent with the OTP model being less strongly correlating. For both models we find "master isomorphs", i.e., isomorphs have identical shape in the virial/potential energy phase diagram.Comment: 20 page

Perception of nonnative tonal contrasts by Mandarin-English and English-Mandarin sequential bilinguals

This study examined the role of acquisition order and crosslinguistic similarity in influencing transfer at the initial stage of perceptually acquiring a tonal third language (L3). Perception of tones in Yoruba and Thai was tested in adult sequential bilinguals representing three different first (L1) and second language (L2) backgrounds: L1 Mandarin-L2 English (MEBs), L1 English-L2 Mandarin (EMBs), and L1 English-L2 intonational/non-tonal (EIBs). MEBs outperformed EMBs and EIBs in discriminating L3 tonal contrasts in both languages, while EMBs showed a small advantage over EIBs on Yoruba. All groups showed better overall discrimination in Thai than Yoruba, but group differences were more robust in Yoruba. MEBs’ and EMBs’ poor discrimination of certain L3 contrasts was further reflected in the L3 tones being perceived as similar to the same Mandarin tone; however, EIBs, with no knowledge of Mandarin, showed many of the same similarity judgments. These findings thus suggest that L1 tonal experience has a particularly facilitative effect in L3 tone perception, but there is also a facilitative effect of L2 tonal experience. Further, crosslinguistic perceptual similarity between L1/L2 and L3 tones, as well as acoustic similarity between different L3 tones, play a significant role at this early stage of L3 tone acquisition.Published versio

Ophthalmic Artery Chemosurgery for Less Advanced Intraocular Retinoblastoma: Five Year Review

BACKGROUND: Ophthalmic artery chemosurgery (OAC) for retinoblastoma was introduced by us 5 years ago for advanced intraocular retinoblastoma. Because the success was higher than with existing alternatives and systemic side effects limited we have now treated less advanced intraocular retinoblastoma (Reese-Ellsworth (RE) I-III and International Classification Retinoblastoma (ICRB) B and C). METHODOLOGY/PRINCIPAL FINDINGS: Retrospective review of 5 year experience in eyes with Reese Ellsworth (Table 1) I (7 eyes), II (6 eyes) or III (6 eyes) and/or International Classification (Table 2) B (19 eyes) and C (11 eyes) treated with OAC (melphalan with or without topotecan) introduced directly into the ophthalmic artery. Patient survival was 100%. Ocular event-free survival was 100% for Reese-Ellsworth Groups I, II and III (and 96% for ICRB B and C) at a median of 16 months follow-up. One ICRB Group C (Reese-Ellsworth Vb) eye could not be treated on the second attempt for technical reasons and was therefore enucleated. No patient required a port and only one patient required transfusion of blood products. The electroretinogram (ERG) was unchanged or improved in 14/19 eyes. CONCLUSIONS/SIGNIFICANCE: Ophthalmic artery chemosurgery for retinoblastoma that was Reese-Ellsworth I, II and III (or International Classification B or C) was associated with high success (100% of treatable eyes were retained) and limited toxicity with results that equal or exceed conventional therapy with less toxicity

SGAS 143845.1+145407: A Big, Cool Starburst at Redshift 0.816

We present the discovery and a detailed multi-wavelength study of a strongly-lensed luminous infrared galaxy at z=0.816. Unlike most known lensed galaxies discovered at optical or near-infrared wavelengths this lensed source is red, r-Ks = 3.9 [AB], which the data presented here demonstrate is due to ongoing dusty star formation. The overall lensing magnification (a factor of 17) facilitates observations from the blue optical through to 500micron, fully capturing both the stellar photospheric emission as well as the re-processed thermal dust emission. We also present optical and near-IR spectroscopy. These extensive data show that this lensed galaxy is in many ways typical of IR-detected sources at z~1, with both a total luminosity and size in accordance with other (albeit much less detailed) measurements in samples of galaxies observed in deep fields with the Spitzer telescope. Its far-infrared spectral energy distribution is well-fit by local templates that are an order of magnitude less luminous than the lensed galaxy; local templates of comparable luminosity are too hot to fit. Its size (D~7kpc) is much larger than local luminous infrared galaxies, but in line with sizes observed for such galaxies at z~1. The star formation appears uniform across this spatial scale. In this source, the luminosity of which is typical of sources that dominate the cosmic infrared background, we find that star formation is spatially extended and well organised, quite unlike the compact merger-driven starbursts which are typical for sources of this luminosity at z~0.Comment: 18 pages, 10 figure

An intervention framework for collaboration

This paper provides an intervention framework for collaboration to improve services. When collaboration is an intervention, its development and effectiveness depend on intervention logic. Intervention logic requires a precise conceptualization of collaboration. This conceptualization emphasizes its vital and unique components. It includes a developmental progression in which collaboration is contrasted with companion concepts. It also includes progress benchmarks, outcome measures, and logic models. These models depict relations among the benchmarks and outcomes, and they identify the mediating and moderating variables that account for collaboration's development and effectiveness. These models are designed to improve planning, evaluation, and their relations. This intervention framework for collaboration contrasts sharply with other conceptualizations and strategies. Although its aim is to unify and improve collaboration policy and practice, its inherent selectivity is an obvious limitation. [PUBLICATION ABSTRACT

Quantum Nonlocality without Entanglement

We exhibit an orthogonal set of product states of two three-state particles that nevertheless cannot be reliably distinguished by a pair of separated observers ignorant of which of the states has been presented to them, even if the observers are allowed any sequence of local operations and classical communication between the separate observers. It is proved that there is a finite gap between the mutual information obtainable by a joint measurement on these states and a measurement in which only local actions are permitted. This result implies the existence of separable superoperators that cannot be implemented locally. A set of states are found involving three two-state particles which also appear to be nonmeasurable locally. These and other multipartite states are classified according to the entropy and entanglement costs of preparing and measuring them by local operations.Comment: 27 pages, Latex, 6 ps figures. To be submitted to Phys. Rev. A. Version 2: 30 pages, many small revisions and extensions, author added. Version 3: Proof in Appendix D corrected, many small changes; final version for Phys. Rev. A Version 4: Report of Popescu conjecture modifie

Long-Term Functionality of Rural Water Services in Developing Countries: A System Dynamics Approach to Understanding the Dynamic Interaction of Causal Factors

Research has shown that sustainability of rural water infrastructure in developing countries is largely affected by the dynamic and systemic interactions of technical, social, financial, institutional, and environmental factors that can lead to premature water system failure. This research employs systems dynamic modeling, which uses feedback mechanisms to understand how these factors interact dynamically to influence long-term rural water system functionality. To do this, the research first identified and aggregated key factors from literature, then asked water sector experts to indicate the polarity and strength between factors through Delphi and cross impact survey questionnaires, and finally used system dynamics modeling to identify and prioritize feedback mechanisms. The resulting model identified 101 feedback mechanisms that were dominated primarily by three and four-factor loops that contained some combination of the factors: Water System Functionality, Community, Financial, Government, Management, and Technology. These feedback mechanisms were then scored and prioritized, with the most dominant feedback mechanism identified as Water System Functionality – Community – Finance – Management. This research offers insight into the dynamic interaction of factors impacting sustainability of rural water infrastructure through the identification of these feedback mechanisms and makes a compelling case for future research to longitudinally investigate the interaction of these factors in various contexts

The Grism Lens-amplified Survey from Space (GLASS). X. Sub-kiloparsec Resolution Gas-phase Metallicity Maps at Cosmic Noon behind the Hubble Frontier Fields Cluster MACS1149.6+2223

We combine deep Hubble Space Telescope grism spectroscopy with a new Bayesian method to derive maps of gas-phase metallicity for 10 star-forming galaxies at high redshift ($1.2\lesssim z\lesssim 2.3$). Exploiting lensing magnification by the foreground cluster MACS1149.6+2223, we reach sub-kiloparsec spatial resolution and push the limit of stellar mass associated with such high-z spatially resolved measurements below ${10}^{8}\,{M}_{\odot }$ for the first time. Our maps exhibit diverse morphologies, indicative of various effects such as efficient radial mixing from tidal torques, rapid accretion of low-metallicity gas, and other physical processes that can affect the gas and metallicity distributions in individual galaxies. Based upon an exhaustive sample of all existing sub-kiloparesec resolution metallicity gradient measurements at high z, we find that predictions given by analytical chemical evolution models assuming a relatively extended star-formation profile in the early disk-formation phase can explain the majority of observed metallicity gradients, without involving galactic feedback or radial outflows. We observe a tentative correlation between stellar mass and metallicity gradients, consistent with the "downsizing" galaxy formation picture that more massive galaxies are more evolved into a later phase of disk growth, where they experience more coherent mass assembly at all radii and thus show shallower metallicity gradients. In addition to the spatially resolved analysis, we compile a sample of homogeneously cross-calibrated integrated metallicity measurements spanning three orders of magnitude in stellar mass at z ~ 1.8. We use this sample to study the mass–metallicity relation (MZR) and find that the slope of the observed MZR can rule out the momentum-driven wind model at a 3σ confidence level