Unit cell of graphene on Ru(0001): a 25 x 25 supercell with 1250 carbon atoms

The structure of a single layer of graphene on Ru(0001) has been studied using surface x-ray diffraction. A surprising superstructure has been determined, whereby 25 x 25 graphene unit cells lie on 23 x 23 unit cells of Ru. Each supercell contains 2 x 2 crystallographically inequivalent subcells caused by corrugation. Strong intensity oscillations in the superstructure rods demonstrate that the Ru substrate is also significantly corrugated down to several monolayers, and that the bonding between graphene and Ru is strong and cannot be caused by van der Waals bonds. Charge transfer from the Ru substrate to the graphene expands and weakens the C-C bonds, which helps accommodate the in-plane tensile stress. The elucidation of this superstructure provides important information in the potential application of graphene as a template for nanocluster arrays.Comment: 9 pages, 3 figures, paper submitted to peer reviewed journa

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

Editor's Choice: Contemporary treatment of popliteal artery aneurysm in eight countries: A Report from the Vascunet collaboration of registries.

To access publisher's full text version of this article, please click on the hyperlink in Additional Links field or click on the hyperlink at the top of the page marked Files. This article is open access.To study contemporary popliteal artery aneurysm (PA) repair.Vascunet is a collaboration of population-based registries in 10 countries: eight had data on PA repair (Australia, Finland, Hungary, Iceland, New Zealand, Norway, Sweden, and Switzerland).From January 2009 until June 2012, 1,471 PA repairs were registered. There were 9.59 operations per million person years, varying from 3.4 in Hungary to 17.6 in Sweden. Median age was 70 years, ranging from 66 years in Switzerland and Iceland to 74 years in Australia and New Zealand; 95.6% were men and 44% were active smokers. Elective surgery dominated, comprising 72% of all cases, but only 26.2% in Hungary and 39.7% in Finland, (p < .0001). The proportion of endovascular PA repair was 22.2%, varying from 34.7% in Australia, to zero in Switzerland, Finland, and Iceland (p < .0001). Endovascular repair was performed in 12.2% of patients with acute thrombosis and 24.1% of elective cases (p < .0001). A vein graft was used in 87.2% of open repairs, a synthetic or composite graft in 12.7%. Follow-up was until discharge or 30 days. Amputation rate was 2.0% overall: 6.5% after acute thrombosis, 1.0% after endovascular, 1.8% after open repair, and 26.3% after hybrid repair (p < .0001). Mortality was 0.7% overall: 0.1% after elective repair, 1.6% after acute thrombosis, and 11.1% after rupture.Great variability between countries in incidence of operations, indications for surgery, and choice of surgical technique was found, possibly a result of surgical tradition rather than differences in case mix. Comparative studies with longer follow-up data are warranted

Exotic complex Hadamard matrices, and their equivalence

In this paper we use a design theoretical approach to construct new, previously unknown complex Hadamard matrices. Our methods generalize and extend the earlier results of de la Harpe--Jones and Munemasa--Watatani and offer a theoretical explanation for the existence of some sporadic examples of complex Hadamard matrices in the existing literature. As it is increasingly difficult to distinguish inequivalent matrices from each other, we propose a new invariant, the fingerprint of complex Hadamard matrices. As a side result, we refute a conjecture of Koukouvinos et al. on (n-8)x(n-8) minors of real Hadamard matrices.Comment: 10 pages. To appear in Cryptography and Communications: Discrete Structures, Boolean Functions and Sequence

Generalized Mutual Subspace Based Methods for Image Set Classification

Abstract. The subspace-based methods are effectively applied to classify sets of feature vectors by modeling them as subspaces. It is, however, difficult to appropriately determine the subspace dimensionality in advance for better performance. For alleviating such issue, we present a generalized mutual subspace method by introducing soft weighting across the basis vectors of the subspace. The bases are effectively combined via the soft weights to measure the subspace similarities (angles) without definitely setting the subspace dimensionality. By using the soft weighting, we consequently propose a novel mutual subspace-based method to construct the discriminative space which renders more discriminative subspace similarities. In the experiments on 3D object recognition using image sets, the proposed methods exhibit stably favorable performances compared to the other subspace-based methods.

Graphene on Ru(0001): A corrugated and chiral structure

We present a structural analysis of the graphene/Ru(0001) system obtained by surface x-ray diffraction. The data were fit using Fourier-series expanded displacement fields from an ideal bulk structure, plus the application of symmetry constraints. The shape of the observed superstructure rods proves a reconstruction of the substrate, induced by strong bonding of graphene to ruthenium. Both the graphene layer and the underlying substrate are corrugated, with peak-to-peak heights of (0.82 +/- 0.15) A and (0.19 +/- 0.02) A for the graphene and topmost Ru-atomic layer, respectively. The Ru-corrugation decays slowly over several monolayers into the bulk. The system also exhibits chirality, whereby in-plane rotations of up to 2.0 degrees in those regions of the superstructure where the graphene is weakly bound are driven by elastic energy minimization

The Meissner effect in a strongly underdoped cuprate above its critical temperature

The Meissner effect and the associated perfect "bulk" diamagnetism together with zero resistance and gap opening are characteristic features of the superconducting state. In the pseudogap state of cuprates unusual diamagnetic signals as well as anomalous proximity effects have been detected but a Meissner effect has never been observed. Here we have probed the local diamagnetic response in the normal state of an underdoped La1.94Sr0.06CuO4 layer (up to 46 nm thick, critical temperature Tc' < 5 K) which was brought into close contact with two nearly optimally doped La1.84Sr0.16CuO4 layers (Tc \approx 32 K). We show that the entire 'barrier' layer of thickness much larger than the typical c axis coherence lengths of cuprates exhibits a Meissner effect at temperatures well above Tc' but below Tc. The temperature dependence of the effective penetration depth and superfluid density in different layers indicates that superfluidity with long-range phase coherence is induced in the underdoped layer by the proximity to optimally doped layers; however, this induced order is very sensitive to thermal excitation.Comment: 7 pages, 7 figures + Erratu

Better Nonlinear Models from Noisy Data: Attractors with Maximum Likelihood

A new approach to nonlinear modelling is presented which, by incorporating the global behaviour of the model, lifts shortcomings of both least squares and total least squares parameter estimates. Although ubiquitous in practice, a least squares approach is fundamentally flawed in that it assumes independent, normally distributed (IND) forecast errors: nonlinear models will not yield IND errors even if the noise is IND. A new cost function is obtained via the maximum likelihood principle; superior results are illustrated both for small data sets and infinitely long data streams.Comment: RevTex, 11 pages, 4 figure