Applying the expanding photosphere and standardized candle methods to Type II-Plateau supernovae at cosmologically significant redshifts: the distance to SN 2013eq

Based on optical imaging and spectroscopy of the Type II-Plateau SN 2013eq, we present a comparative study of commonly used distance determination methods based on Type II supernovae. The occurrence of SN 2013eq in the Hubble flow (z = 0.041 +/- 0.001) prompted us to investigate the implications of the difference between "angular" and "luminosity" distances within the framework of the expanding photosphere method (EPM) that relies upon a relation between flux and angular size to yield a distance. Following a re-derivation of the basic equations of the EPM for SNe at non-negligible redshifts, we conclude that the EPM results in an angular distance. The observed flux should be converted into the SN rest frame and the angular size, theta, has to be corrected by a factor of (1+z)^2. Alternatively, the EPM angular distance can be converted to a luminosity distance by implementing a modification of the angular size. For SN 2013eq, we find EPM luminosity distances of D_L = 151 +/- 18 Mpc and D_L = 164 +/- 20 Mpc by making use of different sets of dilution factors taken from the literature. Application of the standardized candle method for Type II-P SNe results in an independent luminosity distance estimate (D_L = 168 +/- 16 Mpc) that is consistent with the EPM estimate.Comment: 12 pages, 4 figures, accepted by A&

The topological structure of scaling limits of large planar maps

We discuss scaling limits of large bipartite planar maps. If p is a fixed integer strictly greater than 1, we consider a random planar map M(n) which is uniformly distributed over the set of all 2p-angulations with n faces. Then, at least along a suitable subsequence, the metric space M(n) equipped with the graph distance rescaled by the factor n to the power -1/4 converges in distribution as n tends to infinity towards a limiting random compact metric space, in the sense of the Gromov-Hausdorff distance. We prove that the topology of the limiting space is uniquely determined independently of p, and that this space can be obtained as the quotient of the Continuum Random Tree for an equivalence relation which is defined from Brownian labels attached to the vertices. We also verify that the Hausdorff dimension of the limit is almost surely equal to 4.Comment: 45 pages Second version with minor modification

Pairing effects on the collectivity of quadrupole states around 32Mg

The first 2+ states in N=20 isotones including neutron-rich nuclei 32Mg and 30Ne are studied by the Hartree-Fock-Bogoliubov plus quasiparticle random phase approximation method based on the Green's function approach. The residual interaction between the quasiparticles is consistently derived from the hamiltonian density of Skyrme interactions with explicit velocity dependence. The B(E2) transition probabilities and the excitation energies of the first 2+ states are well described within a single framework. We conclude that pairing effects account largely for the anomalously large B(E2) value and the very low excitation energy in 32Mg.Comment: 14 pages, 9 figure

Quantum Algorithms for Matrix Products over Semirings

In this paper we construct quantum algorithms for matrix products over several algebraic structures called semirings, including the (max,min)-matrix product, the distance matrix product and the Boolean matrix product. In particular, we obtain the following results. We construct a quantum algorithm computing the product of two n x n matrices over the (max,min) semiring with time complexity O(n^{2.473}). In comparison, the best known classical algorithm for the same problem, by Duan and Pettie, has complexity O(n^{2.687}). As an application, we obtain a O(n^{2.473})-time quantum algorithm for computing the all-pairs bottleneck paths of a graph with n vertices, while classically the best upper bound for this task is O(n^{2.687}), again by Duan and Pettie. We construct a quantum algorithm computing the L most significant bits of each entry of the distance product of two n x n matrices in time O(2^{0.64L} n^{2.46}). In comparison, prior to the present work, the best known classical algorithm for the same problem, by Vassilevska and Williams and Yuster, had complexity O(2^{L}n^{2.69}). Our techniques lead to further improvements for classical algorithms as well, reducing the classical complexity to O(2^{0.96L}n^{2.69}), which gives a sublinear dependency on 2^L. The above two algorithms are the first quantum algorithms that perform better than the $\tilde O(n^{5/2})$-time straightforward quantum algorithm based on quantum search for matrix multiplication over these semirings. We also consider the Boolean semiring, and construct a quantum algorithm computing the product of two n x n Boolean matrices that outperforms the best known classical algorithms for sparse matrices. For instance, if the input matrices have O(n^{1.686...}) non-zero entries, then our algorithm has time complexity O(n^{2.277}), while the best classical algorithm has complexity O(n^{2.373}).Comment: 19 page

The state of workplace union reps organisation in Britain today

This article provides a brief evaluation of the state of workplace union reps’ organization in Britain as we approach the second decade of the 2000s. It documents the severe weakening of workplace union organization over the last 25 years, which is reflected in the declining number of reps, reduced bargaining power and the problem of bureaucratization. But it also provides evidence of the continuing resilience, and even combativity in certain areas of employment, of workplace union reps organization, and considers the future potential for a revival of fortunes

Development and preliminary validation of a tool measuring concordance and belief about performing pressure-relieving activities for pressure ulcer prevention in spinal cord injury

Objective: To develop and examine the reliability, and validity of a questionnaire measuring concordance for performing pressure-relief for pressure ulcer (PrU) prevention in people with Spinal Cord Injury (SCI). Methods: Phase I included item development, content and face validity testing. In phase II, the questionnaire was evaluated for preliminary acceptability, reliability and validity among 48 wheelchair users with SCI. Results: Thirty-seven items were initially explored. Item and factor analysis resulted in a final 26-item questionnaire with four factors reflecting concordance, perceived benefits, perceived negative consequences, and personal practical barriers to performing pressure-relief activities. The internal consistency reliability for four domains were very good (Cronbach's α = .75-.89). Pearson correlation coefficient on a test-retest of the same subjects yielded significant correlations in concordance (r = .91, p = .005), perceived benefit (r = .71, p < .04), perceived negative consequences (r = .98, p < .0001), personal barriers (r = .93, p= .002). Participants with higher levels of concordance reported a greater amount of pressure-relieving performed. Individuals viewing PrU as a threatening illness were associated with higher scores of concordance and tended to report a greater amount of pressure-relieving performance which provides evidence of criterion related validity. Conclusion: The new questionnaire demonstrated good preliminary reliability and validity in people with SCI. Further evaluation is necessary to confirm these findings using larger samples with follow-up data for predictive validity. Such a questionnaire could be used by clinicians to identify high risk of patients and to design individualised education programme for PrU prevention

Exponential Separation of Quantum and Classical Online Space Complexity

Although quantum algorithms realizing an exponential time speed-up over the best known classical algorithms exist, no quantum algorithm is known performing computation using less space resources than classical algorithms. In this paper, we study, for the first time explicitly, space-bounded quantum algorithms for computational problems where the input is given not as a whole, but bit by bit. We show that there exist such problems that a quantum computer can solve using exponentially less work space than a classical computer. More precisely, we introduce a very natural and simple model of a space-bounded quantum online machine and prove an exponential separation of classical and quantum online space complexity, in the bounded-error setting and for a total language. The language we consider is inspired by a communication problem (the set intersection function) that Buhrman, Cleve and Wigderson used to show an almost quadratic separation of quantum and classical bounded-error communication complexity. We prove that, in the framework of online space complexity, the separation becomes exponential.Comment: 13 pages. v3: minor change