4,951 research outputs found
Asymptotic constant-factor approximation algorithm for the Traveling Salesperson Problem for Dubins' vehicle
This article proposes the first known algorithm that achieves a
constant-factor approximation of the minimum length tour for a Dubins' vehicle
through points on the plane. By Dubins' vehicle, we mean a vehicle
constrained to move at constant speed along paths with bounded curvature
without reversing direction. For this version of the classic Traveling
Salesperson Problem, our algorithm closes the gap between previously
established lower and upper bounds; the achievable performance is of order
A new Sobolev gradient method for direct minimization of the Gross-Pitaevskii energy with rotation
In this paper we improve traditional steepest descent methods for the direct
minimization of the Gross-Pitaevskii (GP) energy with rotation at two levels.
We first define a new inner product to equip the Sobolev space and derive
the corresponding gradient. Secondly, for the treatment of the mass
conservation constraint, we use a projection method that avoids more
complicated approaches based on modified energy functionals or traditional
normalization methods. The descent method with these two new ingredients is
studied theoretically in a Hilbert space setting and we give a proof of the
global existence and convergence in the asymptotic limit to a minimizer of the
GP energy. The new method is implemented in both finite difference and finite
element two-dimensional settings and used to compute various complex
configurations with vortices of rotating Bose-Einstein condensates. The new
Sobolev gradient method shows better numerical performances compared to
classical or gradient methods, especially when high rotation rates
are considered.Comment: to appear in SIAM J Sci Computin
A residual-based bootstrap test for panel cointegration
We address the issue of panel cointegration testing in dependent panels, showing by simulations that tests based on the stationary bootstrap deliver good size and power performances even with small time and cross-section sample sizes and allowing for a break at a known date. They can thus be an empirically important alternative to asymptotic methods based on the estimation of common factors. Potential extensions include test for cointegration allowing for a break in the cointegrating coefficients at an unknown date.Panel Cointegration, Stationary Bootstrap, Commmon Factors.
A constructive and unifying framework for zero-bit watermarking
In the watermark detection scenario, also known as zero-bit watermarking, a
watermark, carrying no hidden message, is inserted in content. The watermark
detector checks for the presence of this particular weak signal in content. The
article looks at this problem from a classical detection theory point of view,
but with side information enabled at the embedding side. This means that the
watermark signal is a function of the host content. Our study is twofold. The
first step is to design the best embedding function for a given detection
function, and the best detection function for a given embedding function. This
yields two conditions, which are mixed into one `fundamental' partial
differential equation. It appears that many famous watermarking schemes are
indeed solution to this `fundamental' equation. This study thus gives birth to
a constructive framework unifying solutions, so far perceived as very
different.Comment: submitted to IEEE Trans. on Information Forensics and Securit
A note on an Adaptive Goodness-of-Fit test with Finite Sample Validity for Random Design Regression Models
Given an i.i.d. sample from the random
design regression model with , in this paper we consider the problem of testing the (simple) null
hypothesis , against the alternative for a fixed , where denotes the marginal distribution of the
design variable . The procedure proposed is an adaptation to the regression
setting of a multiple testing technique introduced by Fromont and Laurent
(2005), and it amounts to consider a suitable collection of unbiased estimators
of the --distance ,
rejecting the null hypothesis when at least one of them is greater than its
quantile, with calibrated to obtain a level--
test. To build these estimators, we will use the warped wavelet basis
introduced by Picard and Kerkyacharian (2004). We do not assume that the errors
are normally distributed, and we do not assume that and are
independent but, mainly for technical reasons, we will assume, as in most part
of the current literature in learning theory, that is uniformly
bounded (almost everywhere). We show that our test is adaptive over a
particular collection of approximation spaces linked to the classical Besov
spaces
A Robbins-Monro procedure for estimation in semiparametric regression models
This paper is devoted to the parametric estimation of a shift together with
the nonparametric estimation of a regression function in a semiparametric
regression model. We implement a very efficient and easy to handle
Robbins-Monro procedure. On the one hand, we propose a stochastic algorithm
similar to that of Robbins-Monro in order to estimate the shift parameter. A
preliminary evaluation of the regression function is not necessary to estimate
the shift parameter. On the other hand, we make use of a recursive
Nadaraya-Watson estimator for the estimation of the regression function. This
kernel estimator takes into account the previous estimation of the shift
parameter. We establish the almost sure convergence for both Robbins-Monro and
Nadaraya--Watson estimators. The asymptotic normality of our estimates is also
provided. Finally, we illustrate our semiparametric estimation procedure on
simulated and real data.Comment: Published in at http://dx.doi.org/10.1214/12-AOS969 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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