8,968 research outputs found
Normal approximation for nonlinear statistics using a concentration inequality approach
Let be a general sampling statistic that can be written as a linear
statistic plus an error term. Uniform and non-uniform Berry--Esseen type bounds
for are obtained. The bounds are the best possible for many known
statistics. Applications to U-statistics, multisample U-statistics,
L-statistics, random sums and functions of nonlinear statistics are discussed.Comment: Published at http://dx.doi.org/10.3150/07-BEJ5164 in the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Normal approximation under local dependence
We establish both uniform and nonuniform error bounds of the Berry-Esseen
type in normal approximation under local dependence. These results are of an
order close to the best possible if not best possible. They are more general or
sharper than many existing ones in the literature. The proofs couple Stein's
method with the concentration inequality approach.Comment: Published by the Institute of Mathematical Statistics
(http://www.imstat.org) in the Annals of Probability
(http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/00911790400000045
Moderate deviations in Poisson approximation: a first attempt
Poisson approximation using Stein's method has been extensively studied in
the literature. The main focus has been on bounding the total variation
distance. This paper is a first attempt on moderate deviations in Poisson
approximation for right-tail probabilities of sums of dependent indicators. We
obtain results under certain general conditions for local dependence as well as
for size-bias coupling. These results are then applied to independent
indicators, 2-runs, and the matching problem.Comment: 21 page
Steady Bell state generation via magnon-photon coupling
We show that parity-time () symmetry can be spontaneously
broken in the recently reported energy level attraction of magnons and cavity
photons. In the -broken phase, magnon and photon form a
high-fidelity Bell state with maximum entanglement. This entanglement is steady
and robust against the perturbation of environment, in contrast to the general
wisdom that expects instability of the hybridized state when the symmetry is
broken. This anomaly is further understood by the compete of non-Hermitian
evolution and particle number conservation of the hybridized system. As a
comparison, neither -symmetry broken nor steady magnon-photon
entanglement is observed inside the normal level repulsion case. Our results
may open a novel window to utilize magnon-photon entanglement as a resource for
quantum technologies.Comment: 5 pages, 4 figure
Defect Modes in One-Dimensional Granular Crystals
We study the vibrational spectra of one-dimensional statically compressed
granular crystals (arrays of elastic particles in contact) containing defects.
We focus on the prototypical settings of one or two spherical defects
(particles of smaller radii) interspersed in a chain of larger uniform
spherical particles. We measure the near-linear frequency spectrum within the
spatial vicinity of the defects, and identify the frequencies of the localized
defect modes. We compare the experimentally determined frequencies with those
obtained by numerical eigen-analysis and by analytical expressions based on
few-site considerations. We also present a brief numerical and experimental
example of the nonlinear generalization of a single-defect localized mode
Age-associated Arterial Remodelling and Cardiovascular Diseases
Arterial remodelling is a major risk factor for a variety of age-related diseases and represents a potential target for therapeutic development. During ageing, the structural, mechanical and functional changes of arteries predispose individuals to the development of diseases related to vascular abnormalities in vital organs such as the brain, heart, eye and kidney. For example, aortic stiffness increases nonlinearly with advancing age – a few percent prior to 50 years of age but over 70% after 70 years of age. The elevated stiffness in large elastic arteries leads to increased transmission of high pressure to downstream smaller blood vessels, in turn affecting the microcirculation and end-organ functions. Meanwhile, the augmented remodelling of small arteries accelerates central arterial stiffening. This chapter is to provide an overview of age-associated changes in the arterial wall and their contributions to both central and peripheral vascular abnormalities associated with ageing. Therapeutics that specially target the different aspects of arterial remodelling are expected to be more effective than the traditional medications, particularly for the treatment and management of vascular ageing-related diseases.published_or_final_versio
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