2,015 research outputs found
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
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
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
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
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
The narrative potential of the British Birth Cohort Studies
This paper draws attention to the narrative potential of longitudinal studies such as the British Birth Cohort Studies (BBCS), and explores the possibility of creating narrative case histories and conducting narrative analysis based on information available from the studies. The BBCS have historically adopted a quantitative research design and used structured interviews and questionnaires to collect data from large samples of individuals born in specific years. However, the longitudinal nature of these studies means that they follow the same sample of individuals from birth through childhood into adult life, and this leads to the creation of data that can be understood as a quantitative auto/biography
Maximal Sharing in the Lambda Calculus with letrec
Increasing sharing in programs is desirable to compactify the code, and to
avoid duplication of reduction work at run-time, thereby speeding up execution.
We show how a maximal degree of sharing can be obtained for programs expressed
as terms in the lambda calculus with letrec. We introduce a notion of `maximal
compactness' for lambda-letrec-terms among all terms with the same infinite
unfolding. Instead of defined purely syntactically, this notion is based on a
graph semantics. lambda-letrec-terms are interpreted as first-order term graphs
so that unfolding equivalence between terms is preserved and reflected through
bisimilarity of the term graph interpretations. Compactness of the term graphs
can then be compared via functional bisimulation.
We describe practical and efficient methods for the following two problems:
transforming a lambda-letrec-term into a maximally compact form; and deciding
whether two lambda-letrec-terms are unfolding-equivalent. The transformation of
a lambda-letrec-term into maximally compact form proceeds in three
steps:
(i) translate L into its term graph ; (ii) compute the maximally
shared form of as its bisimulation collapse ; (iii) read back a
lambda-letrec-term from the term graph with the property . This guarantees that and have the same unfolding, and that
exhibits maximal sharing.
The procedure for deciding whether two given lambda-letrec-terms and
are unfolding-equivalent computes their term graph interpretations and , and checks whether these term graphs are bisimilar.
For illustration, we also provide a readily usable implementation.Comment: 18 pages, plus 19 pages appendi
Experimental sheep BSE prions generate the vCJD phenotype when serially passaged in transgenic mice expressing human prion protein
The epizootic prion disease of cattle, bovine spongiform encephalopathy (BSE), causes variant Creutzfeldt-Jakob disease (vCJD) in humans following dietary exposure. While it is assumed that all cases of vCJD attributed to a dietary aetiology are related to cattle BSE, sheep and goats are susceptible to experimental oral challenge with cattle BSE prions and farmed animals in the UK were undoubtedly exposed to BSE-contaminated meat and bone meal during the late 1980s and early 1990s. Although no natural field cases of sheep BSE have been identified, it cannot be excluded that some BSE-infected sheep might have entered the European human food chain. Evaluation of the zoonotic potential of sheep BSE prions has been addressed by examining the transmission properties of experimental brain isolates in transgenic mice that express human prion protein, however to-date there have been relatively few studies. Here we report that serial passage of experimental sheep BSE prions in transgenic mice expressing human prion protein with methionine at residue 129 produces the vCJD phenotype that mirrors that seen when the same mice are challenged with vCJD prions from patient brain. These findings are congruent with those reported previously by another laboratory, and thereby strongly reinforce the view that sheep BSE prions could have acted as a causal agent of vCJD within Europe
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