Determining the Dependence Structure of Multivariate Extremes

In multivariate extreme value analysis, the nature of the extremal dependence between variables should be considered when selecting appropriate statistical models. Interest often lies with determining which subsets of variables can take their largest values simultaneously, while the others are of smaller order. Our approach to this problem exploits hidden regular variation properties on a collection of non-standard cones and provides a new set of indices that reveal aspects of the extremal dependence structure not available through existing measures of dependence. We derive theoretical properties of these indices, demonstrate their value through a series of examples, and develop methods of inference that also estimate the proportion of extremal mass associated with each cone. We apply the methods to UK river flows, estimating the probabilities of different subsets of sites being large simultaneously

Tetrahydrobiopterin analogues with NO-dependent pulmonary vasodilator properties

Reduced NO levels due to the deficiency of tetrahydrobiopterin (BH4) contribute to impaired vasodilation in pulmonary hypertension Due to the chemically unstable nature of BH4 it was hypothesised that oxidatively stable analogues of BR, would be able to support NO synthesis to improve Endothelial dysfunction in pulmonary hypertension Two analogues of BH4 namely 6-hydroxymethyl pterin (HMP) and 6-acetyl 7 7-dimethyl 7 8-dihydropterin (ADDP) were evaluated for vasodilator activity on precontracted rat pulmonary artery rings ADDP was administered to pulmonary hypertensive rats followed by measurement of pulmonary vascular resistance in perfused lungs and eNOS expression by immunohistochemistry ADDP and HMP caused significant relaxation in vitro in rat pulmonary arteries depleted of BH4 with a maximum relaxation at 0 3 mu M (both P<005) Vasodilator activity of ADDP and HMP was completely abolished following preincubation with the NO synthase inhibitor L-NAME ADDP and HMP did not alter relaxation induced by carbachol or spermine NONOate BH4 Itself did not produce relaxation In rats receiving ADDP 141 mg/kg/day pulmonary vasodilation induced by calcium ionophore A23187 was augmented and eNOS immunoreactivity was increased In conclusion ADDP and HMP are two analogues of BH4 which can act as oxidatively stable alternatives to BH4 in causing NO-mediated vasorelaxation Chronic treatment with ADDP resulted in Improvement of NO-mediated pulmonary artery dilation and enhanced expression of eNOS in the pulmonary vascular endothelium Chemically stable analogue, of BH4 may be able to limit endothelial dysfunction in the pulmonary vasculatur

Experimental Realization of a One-way Quantum Computer Algorithm Solving Simon's Problem

We report an experimental demonstration of a one-way implementation of a quantum algorithm solving Simon's Problem - a black box period-finding problem which has an exponential gap between the classical and quantum runtime. Using an all-optical setup and modifying the bases of single-qubit measurements on a five-qubit cluster state, key representative functions of the logical two-qubit version's black box can be queried and solved. To the best of our knowledge, this work represents the first experimental realization of the quantum algorithm solving Simon's Problem. The experimental results are in excellent agreement with the theoretical model, demonstrating the successful performance of the algorithm. With a view to scaling up to larger numbers of qubits, we analyze the resource requirements for an n-qubit version. This work helps highlight how one-way quantum computing provides a practical route to experimentally investigating the quantum-classical gap in the query complexity model.Comment: 9 pages, 5 figure

Conditional Modelling of Spatio-Temporal Extremes for Red Sea Surface Temperatures

Recent extreme value theory literature has seen significant emphasis on the modelling of spatial extremes, with comparatively little consideration of spatio-temporal extensions. This neglects an important feature of extreme events: their evolution over time. Many existing models for the spatial case are limited by the number of locations they can handle; this impedes extension to space-time settings, where models for higher dimensions are required. Moreover, the spatio-temporal models that do exist are restrictive in terms of the range of extremal dependence types they can capture. Recently, conditional approaches for studying multivariate and spatial extremes have been proposed, which enjoy benefits in terms of computational efficiency and an ability to capture both asymptotic dependence and asymptotic independence. We extend this class of models to a spatio-temporal setting, conditioning on the occurrence of an extreme value at a single space-time location. We adopt a composite likelihood approach for inference, which combines information from full likelihoods across multiple space-time conditioning locations. We apply our model to Red Sea surface temperatures, show that it fits well using a range of diagnostic plots, and demonstrate how it can be used to assess the risk of coral bleaching attributed to high water temperatures over consecutive days

Photon pair generation using four-wave mixing in a microstructured fibre: theory versus experiment

We develop a theoretical analysis of four-wave mixing used to generate photon pairs useful for quantum information processing. The analysis applies to a single mode microstructured fibre pumped by an ultra-short coherent pulse in the normal dispersion region. Given the values of the optical propagation constant inside the fibre, we can estimate the created number of photon pairs per pulse, their central wavelength and their respective bandwidth. We use the experimental results from a picosecond source of correlated photon pairs using a micro-structured fibre to validate the model. The fibre is pumped in the normal dispersion regime at 708nm and phase matching is satisfied for widely spaced parametric wavelengths of 586nm and 894nm. We measure the number of photons per pulse using a loss-independent coincidence scheme and compare the results with the theoretical expectation. We show a good agreement between the theoretical expectations and the experimental results for various fibre lengths and pump powers.Comment: 23 pages, 9 figure

An All Optical Fibre Quantum Controlled-NOT Gate

We report the first experimental demonstration of an optical controlled-NOT gate constructed entirely in fibre. We operate the gate using two heralded optical fibre single photon sources and find an average logical fidelity of 90% and an average process fidelity of 0.83<F<0.91. On the basis of a simple model we are able to conclude that imperfections are primarily due to the photon sources, meaning that the gate itself works with very high fidelity.Comment: 4 pages, 4 figures, comments welcom

Experimental demonstration of a graph state quantum error-correction code

Scalable quantum computing and communication requires the protection of quantum information from the detrimental effects of decoherence and noise. Previous work tackling this problem has relied on the original circuit model for quantum computing. However, recently a family of entangled resources known as graph states has emerged as a versatile alternative for protecting quantum information. Depending on the graph's structure, errors can be detected and corrected in an efficient way using measurement-based techniques. In this article we report an experimental demonstration of error correction using a graph state code. We have used an all-optical setup to encode quantum information into photons representing a four-qubit graph state. We are able to reliably detect errors and correct against qubit loss. The graph we have realized is setup independent, thus it could be employed in other physical settings. Our results show that graph state codes are a promising approach for achieving scalable quantum information processing

Two-photon interference between disparate sources for quantum networking

Quantum networks involve entanglement sharing between multiple users. Ideally, any two users would be able to connect regardless of the type of photon source they employ, provided they fulfill the requirements for two-photon interference. From a theoretical perspective, photons coming from different origins can interfere with a perfect visibility, provided they are made indistinguishable in all degrees of freedom. Previous experimental demonstrations of such a scenario have been limited to photon wavelengths below 900 nm, unsuitable for long distance communication, and suffered from low interference visibility. We report two-photon interference using two disparate heralded single photon sources, which involve different nonlinear effects, operating in the telecom wavelength range. The measured visibility of the two-photon interference is 80+/-4%, which paves the way to hybrid universal quantum networks

High-dimensional modeling of spatial and spatio-temporal conditional extremes using INLA and the SPDE approach

The conditional extremes framework allows for event-based stochastic modeling of dependent extremes, and has recently been extended to spatial and spatio-temporal settings. After standardizing the marginal distributions and applying an appropriate linear normalization, certain non-stationary Gaussian processes can be used as asymptotically-motivated models for the process conditioned on threshold exceedances at a fixed reference location and time. In this work, we adopt a Bayesian perspective by implementing estimation through the integrated nested Laplace approximation (INLA), allowing for novel and flexible semi-parametric specifications of the Gaussian mean function. By using Gauss-Markov approximations of the Mat\'ern covariance function (known as the Stochastic Partial Differential Equation approach) at a latent stage of the model, likelihood-based inference becomes feasible even with thousands of observed locations. We explain how constraints on the spatial and spatio-temporal Gaussian processes, arising from the conditioning mechanism, can be implemented through the latent variable approach without losing the computationally convenient Markov property. We discuss tools for the comparison of models via their posterior distributions, and illustrate the flexibility of the approach with gridded Red Sea surface temperature data at over 6,000 observed locations. Posterior sampling is exploited to study the probability distribution of cluster functionals of spatial and spatio-temporal extreme episodes