94,873 research outputs found
GEE analysis of clustered binary data with diverging number of covariates
Clustered binary data with a large number of covariates have become
increasingly common in many scientific disciplines. This paper develops an
asymptotic theory for generalized estimating equations (GEE) analysis of
clustered binary data when the number of covariates grows to infinity with the
number of clusters. In this "large , diverging " framework, we provide
appropriate regularity conditions and establish the existence, consistency and
asymptotic normality of the GEE estimator. Furthermore, we prove that the
sandwich variance formula remains valid. Even when the working correlation
matrix is misspecified, the use of the sandwich variance formula leads to an
asymptotically valid confidence interval and Wald test for an estimable linear
combination of the unknown parameters. The accuracy of the asymptotic
approximation is examined via numerical simulations. We also discuss the
"diverging " asymptotic theory for general GEE. The results in this paper
extend the recent elegant work of Xie and Yang [Ann. Statist. 31 (2003)
310--347] and Balan and Schiopu-Kratina [Ann. Statist. 32 (2005) 522--541] in
the "fixed " setting.Comment: Published in at http://dx.doi.org/10.1214/10-AOS846 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Efficient entanglement concentration for arbitrary less-entangled N-atom state
A recent paper (Phys. Rev. A 86, 034305 (2012)) proposed an entanglement
concentration protocol (ECP) for less-entangled -atom GHZ state with the
help of the photonic Faraday rotation. It is shown that the maximally entangled
atom state can be distilled from two pairs of less-entangled atom states. In
this paper, we put forward an improved ECP for arbitrary less-entangled N-atom
GHZ state with only one pair of less-entangled atom state, one auxiliary atom
and one auxiliary photon. Moreover, our ECP can be used repeatedly to obtain a
higher success probability. If consider the practical operation and imperfect
detection, our protocol is more efficient. This ECP may be useful in current
quantum information processing.Comment: 10 page, 5 figur
Efficient single-photon entanglement concentration for quantum communications
We present two protocols for the single-photon entanglement concentration.
With the help of the 50:50 beam splitter, variable beam splitter and an
auxiliary photon, we can concentrate a less-entangled single-photon state into
a maximally single-photon entangled state with some probability. The first
protocol is implemented with linear optics and the second protocol is
implemented with the cross-Kerr nonlinearity. Our two protocols do not need two
pairs of entangled states shared by the two parties, which makes our protocols
more economic. Especially, in the second protocol, with the help of the
cross-Kerr nonlinearity, the sophisticated single photon detector is not
required. Moreover, the second protocol can be reused to get higher success
probability. All these advantages may make our protocols useful in the
long-distance quantum communication.Comment: 9 pages, 3 figure
Gradient Sliding for Composite Optimization
We consider in this paper a class of composite optimization problems whose
objective function is given by the summation of a general smooth and nonsmooth
component, together with a relatively simple nonsmooth term. We present a new
class of first-order methods, namely the gradient sliding algorithms, which can
skip the computation of the gradient for the smooth component from time to
time. As a consequence, these algorithms require only gradient evaluations for the smooth component in order
to find an -solution for the composite problem, while still
maintaining the optimal bound on the total number of
subgradient evaluations for the nonsmooth component. We then present a
stochastic counterpart for these algorithms and establish similar complexity
bounds for solving an important class of stochastic composite optimization
problems. Moreover, if the smooth component in the composite function is
strongly convex, the developed gradient sliding algorithms can significantly
reduce the number of graduate and subgradient evaluations for the smooth and
nonsmooth component to and , respectively. Finally, we generalize these algorithms to the
case when the smooth component is replaced by a nonsmooth one possessing a
certain bi-linear saddle point structure
Blow-up solutions for -supercritical gKdV equations with exactly blow-up points
In this paper we consider the slightly -supercritical gKdV equations
, with the nonlinearity
and . In the previous work of the
author we know that there exists an stable self-similar blow-up dynamics for
slightly -supercritical gKdV equations. Such solution can be viewed as
solutions with single blow-up point. In this paper we will prove the existence
of solutions with multiple blow-up points, and give a description of the
formation of the singularity near the blow-up time.Comment: 35 Pages. Minor revisio
Self-Folding Metasheets: The Optimal Pattern of Strain of Miura-Ori Folded State
Self-folding origami has emerged as a tool to make functional objects in
material science. The common idea is to pattern a sheet with creases and
activate them to have the object fold spontaneously into a desired
configuration. This article shows that collinear quadrilateral metasheets are
able to fold into the Miura-Ori configuration, if we only impose strain on part
of their creases. In this study, we define and determine the optimal pattern of
strain (OPS) on a collinear quadrilateral metasheet, that is the pattern of
minimum "functional" creases with which the self-folding metasheet can fold
into Miura-Ori state stably. By comparing the energy evolution along the
folding pathway of each possible folded state under OPS, we conclude that the
energy predominance of the desired Miura-Ori pathway during the initial period
of time accounts for why the OPS works. Furthermore, we measure the projected
force of the OPS on the intial flat metasheet and give insights on how to
determine the OPS using only local information of the initial flat state.Comment: 12 pages, 11 figure
Measurement of arbitrary two-photon entanglement state with the photonic Faraday rotation
We propose an efficient protocol for measuring the concurrence of arbitrary
two-photon pure entangled state with the help of the photonic Faraday rotation.
In the protocol, the concurrence of the photonic entangled state can be
conversed into the total success probability for picking up the odd-parity
photonic state. For completing the measurement task, we require some auxiliary
three-level atoms, which are trapped in the low-quality cavities. Our protocol
can be well realized under current experimental conditions. Moreover, under
practical imperfect atom state detection and photonic Faraday rotation
conditions, our protocol can also work well. Based on these features, our
protocol may be useful in current quantum information processing.Comment: 15 pages, 2 figure
Bundle-Level Type Methods Uniformly Optimal for Smooth and Nonsmooth Convex Optimization
The main goal of this paper is to develop uniformly optimal first-order
methods for convex programming (CP). By uniform optimality we mean that the
first-order methods themselves do not require the input of any problem
parameters, but can still achieve the best possible iteration complexity
bounds. By incorporating a multi-step acceleration scheme into the well-known
bundle-level method, we develop an accelerated bundle-level (ABL) method, and
show that it can achieve the optimal complexity for solving a general class of
black-box CP problems without requiring the input of any smoothness
information, such as, whether the problem is smooth, nonsmooth or weakly
smooth, as well as the specific values of Lipschitz constant and smoothness
level. We then develop a more practical, restricted memory version of this
method, namely the accelerated prox-level (APL) method. We investigate the
generalization of the APL method for solving certain composite CP problems and
an important class of saddle-point problems recently studied by Nesterov
[Mathematical Programming, 103 (2005), pp 127-152]. We present promising
numerical results for these new bundle-level methods applied to solve certain
classes of semidefinite programming (SDP) and stochastic programming (SP)
problems.Comment: A combination of the previous two papers submitted to Mathematical
Programming, i.e., "Bundle-type methods uniformly optimal for smooth and
nonsmooth convex optimization" (December 2010) and "Level methods uniformly
optimal for composite and structured nonsmooth convex optimization (April
2011
On continuation properties after blow-up time for -critical gKdV equations
In this paper, we consider a blow-up solution to the -critical
gKdV equation , with finite blow-up time
. We expect to construct a natural extension of after the
blow-up time. To do this, we consider the solution to the
saturated -critical gKdV equation with the same initial data, where and . A
standard argument shows that is always global in time and for
all , converges to in as
. We prove in this paper that for all ,
converges to some as , in a certain
sense. This limiting function is a weak solution to the unperturbed
-critical gKdV, hence can be viewed as a natural extension of after
the blow-up time.Comment: 24 pages, minor revisio
A note about Domination and monotonicity in disordered systems
In this note we establish several inequalities and monotonicity properties
for the free energy of directed polymers under certain stochastic orders: the
usual stochastic order, the Laplace transform order and the convex order. For
the latter our results cover also many classical disordered systems
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