3,881 research outputs found
Bayesian modelling of skewness and kurtosis with two-piece scale and shape distributions
We formalise and generalise the definition of the family of univariate double
two--piece distributions, obtained by using a density--based transformation of
unimodal symmetric continuous distributions with a shape parameter. The
resulting distributions contain five interpretable parameters that control the
mode, as well as the scale and shape in each direction. Four-parameter
subfamilies of this class of distributions that capture different types of
asymmetry are discussed. We propose interpretable scale and location-invariant
benchmark priors and derive conditions for the propriety of the corresponding
posterior distribution. The prior structures used allow for meaningful
comparisons through Bayes factors within flexible families of distributions.
These distributions are applied to data from finance, internet traffic and
medicine, comparing them with appropriate competitors
Hyperbolic Metamaterial Resonator-Antenna Scheme for Large, Broadband Emission Enhancement and Single Photon Collection
We model the broadband enhancement of single-photon emission from color
centres in silicon carbide nanocrystals coupled to a planar hyperbolic
metamaterial, HMM resonator. The design is based on positioning the single
photon emitters within the HMM resonator, made of a dielectric index-matched
with silicon-carbide material. The broadband response results from the
successive resonance peaks of the lossy Fabry Perot structure modes arising
within the high-index HMM cavity. To capture this broadband enhancement in the
single photon emitters spontaneous emission, we placed a simple gold based
cylindrical antenna on top of the HMM resonator. We analyzed the performance of
this HMM coupled antenna structure in terms of the Purcell enhancement, quantum
efficiency, collection efficiency and overall collected photon rate. For
perpendicular dipole orientation relative to the interface, the HMM coupled
antenna resonator leads to a significantly large spontaneous emission
enhancement with Purcell factor of the order of 250 along with a very high
average total collected photon rate, CPR of about 30 over a broad emission
spectrum, 700 nm to 1000 nm. The peak CPR increases to about 80 at 900 nm,
corresponding to the emission of silicon-carbide quantum emitters. This is a
state of the art improvement considering the previous computational designs
have reported a maximum average CPR of 25 across the nitrogen-vacancy centre
emission spectrum, 600 nm to 800 nm with the highest value being about 40 at
650 nm
On Describing Multivariate Skewness: A Directional Approach
Most multivariate measures of skewness in the literature measure the overall skewness of a distribution. While these measures are perfectly adequate for testing the hypothesis of distributional symmetry, their relevance for describing skewed distributions is less obvious. In this article, we consider the problem of characterising the skewness of multivariate distributions. We define directional skewness as the skewness along a direction and analyse parametric classes of skewed distributions using measures based on directional skewness. The analysis brings further insight into the classes, allowing for a more informed selection of particular classes for particular applications. In the context of Bayesian linear regression under skewed error we use the concept of directional skewness twice. First in the elicitation of a prior on the parameters of the error distribution, and then in the analysis of the skewness of the posterior distribution of the regression residuals.Bayesian methods, Multivariate distribution, Multivariate regression, Prior elicitation, Skewness.
Tracking emission rate dynamics of nitrogen vacancy centers in nanodiamonds
Spontaneous emission from crystal centers is in uenced by both the photonic local density of states and non- radiative processes. Here we monitor the spontaneous emission of single nitrogen vacancy (NV) centers as their host diamond is reduced in size from a large monolithic crystal to a nanocrystal by successive cycles of oxidation. The size reduction induces a quenching of the NV radiative emission. New non-radiative channels lead to a decrease of the uorescence intensity and the excited state lifetime. In one case we observe the onset of blinking which may provide a route to understand these additional non-radiative decay channels
The Josephson plasmon as a Bogoliubov quasiparticle
We study the Josephson effect in alkali atomic gases within the two-mode
approximation and show that there is a correspondence between the Bogoliubov
description and the harmonic limit of the phase representation. We demonstrate
that the quanta of the Josephson plasmon can be identified with the Bogoliubov
excitations of the two-site Bose fluid. We thus establish a mapping between the
Bogoliubov approximation for the many-body theory and the linearized pendulum
Hamiltonian.Comment: 9 pages, LaTeX, submitted to J. Phys.
Quantum state of two trapped Bose-Einstein condensates with a Josephson coupling
We consider the precise quantum state of two trapped, coupled Bose Einstein
condensates in the two-mode approximation. We seek a representation of the
state in terms of a Wigner-like distribution on the two-mode Bloch sphere. The
problem is solved using a self-consistent rotation of the unknown state to the
south pole of the sphere. The two-mode Hamiltonian is projected onto the
harmonic oscillator phase plane, where it can be solved by standard techniques.
Our results show how the number of atoms in each trap and the squeezing in the
number difference depend on the physical parameters. Considering negative
scattering lengths, we show that there is a regime of squeezing in the relative
phase of the condensates which occurs for weaker interactions than the
superposition states found by Cirac et al% (quant-ph/9706034, 13 June 1997).
The phase squeezing is also apparent in mildly asymmetric trap configurations.Comment: 26 pages, 11 figure
Efficient FPT algorithms for (strict) compatibility of unrooted phylogenetic trees
In phylogenetics, a central problem is to infer the evolutionary
relationships between a set of species ; these relationships are often
depicted via a phylogenetic tree -- a tree having its leaves univocally labeled
by elements of and without degree-2 nodes -- called the "species tree". One
common approach for reconstructing a species tree consists in first
constructing several phylogenetic trees from primary data (e.g. DNA sequences
originating from some species in ), and then constructing a single
phylogenetic tree maximizing the "concordance" with the input trees. The
so-obtained tree is our estimation of the species tree and, when the input
trees are defined on overlapping -- but not identical -- sets of labels, is
called "supertree". In this paper, we focus on two problems that are central
when combining phylogenetic trees into a supertree: the compatibility and the
strict compatibility problems for unrooted phylogenetic trees. These problems
are strongly related, respectively, to the notions of "containing as a minor"
and "containing as a topological minor" in the graph community. Both problems
are known to be fixed-parameter tractable in the number of input trees , by
using their expressibility in Monadic Second Order Logic and a reduction to
graphs of bounded treewidth. Motivated by the fact that the dependency on
of these algorithms is prohibitively large, we give the first explicit dynamic
programming algorithms for solving these problems, both running in time
, where is the total size of the input.Comment: 18 pages, 1 figur
Torsional-flexural buckling of unevenly battened columns under eccentrical compressive loading
In this paper, an analytical model is developed to determine the torsional-flexural buckling load of a channel column braced by unevenly distributed batten plates. Solutions of the critical-buckling loads were derived for three boundary cases using the energy method in which the rotating angle between the adjacent battens was presented in the form of a piecewise cubic Hermite interpolation (PCHI) for unequally spaced battens. The validity of the PCHI method was numerically verified by the classic analytical approach for evenly battened
columns and a finite-element analysis for unevenly battened ones, respectively. Parameter studies were then performed to examine the effects of loading eccentricities on the torsional-flexural buckling capacity of both evenly and unevenly battened columns. Design parameters taken into account were the ratios of pure torsional buckling load to pure flexural–buckling load, the number and position of battens, and the ratio of the relative extent of the eccentricity. Numerical results were summarized into a series of relative curves indicating the combination of the buckling load and corresponding moments for various buckling ratios.National Natural Science Foundation of China (NSFC) under grant number (No.) 51175442 and Sichuan International Cooperation Research Project under grant No. 2014HH002
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