1,939 research outputs found
Modified scattering for the cubic Schr{\"o}dinger equation on product spaces: the nonresonant case
We consider the cubic nonlinear Schr{\"o}dinger equation on the spatial
domain , and we perturb it with a convolution
potential. Using recent techniques of Hani-Pausader-Tzvetkov-Visciglia, we
prove a modified scattering result and construct modified wave operators, under
generic assumptions on the potential. In particular, this enables us to prove
that the Sobolev norms of small solutions of this nonresonant cubic NLS are
asymptotically constant
Dynamics of Klein-Gordon on a compact surface near an homoclinic orbit
We consider the Klein-Gordon equation on a Riemannian surface which is
globally well-posed in the energy space. This equation has an homoclinic orbit
to the origin, and in this paper we study the dynamics close to it. Using a
strategy from Groves-Schneider, we show that there are many solutions which
stay close to this homocline during all times. We point out that the solutions
we construct are not small.Comment: To appear in DCDS-A. The last part has been removed, and gives a
separate publicatio
Statistical analysis of -nearest neighbor collaborative recommendation
Collaborative recommendation is an information-filtering technique that
attempts to present information items that are likely of interest to an
Internet user. Traditionally, collaborative systems deal with situations with
two types of variables, users and items. In its most common form, the problem
is framed as trying to estimate ratings for items that have not yet been
consumed by a user. Despite wide-ranging literature, little is known about the
statistical properties of recommendation systems. In fact, no clear
probabilistic model even exists which would allow us to precisely describe the
mathematical forces driving collaborative filtering. To provide an initial
contribution to this, we propose to set out a general sequential stochastic
model for collaborative recommendation. We offer an in-depth analysis of the
so-called cosine-type nearest neighbor collaborative method, which is one of
the most widely used algorithms in collaborative filtering, and analyze its
asymptotic performance as the number of users grows. We establish consistency
of the procedure under mild assumptions on the model. Rates of convergence and
examples are also provided.Comment: Published in at http://dx.doi.org/10.1214/09-AOS759 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Machining of complex-shaped parts with guidance curves
Nowadays, high-speed machining is usually used for production of hardened
material parts with complex shapes such as dies and molds. In such parts, tool
paths generated for bottom machining feature with the conventional parallel
plane strategy induced many feed rate reductions, especially when boundaries of
the feature have a lot of curvatures and are not parallel. Several machining
experiments on hardened material lead to the conclusion that a tool path
implying stable cutting conditions might guarantee a better part surface
integrity. To ensure this stability, the shape machined must be decomposed when
conventional strategies are not suitable. In this paper, an experimental
approach based on high-speed performance simulation is conducted on a master
bottom machining feature in order to highlight the influence of the curvatures
towards a suitable decomposition of machining area. The decomposition is
achieved through the construction of intermediate curves between the closed
boundaries of the feature. These intermediate curves are used as guidance curve
for the tool paths generation with an alternative machining strategy called
"guidance curve strategy". For the construction of intermediate curves, key
parameters reflecting the influence of their proximity with each closed
boundary and the influence of the curvatures of this latter are introduced.
Based on the results, a method for defining guidance curves in four steps is
proposed
Post-Reconstruction Deconvolution of PET Images by Total Generalized Variation Regularization
Improving the quality of positron emission tomography (PET) images, affected
by low resolution and high level of noise, is a challenging task in nuclear
medicine and radiotherapy. This work proposes a restoration method, achieved
after tomographic reconstruction of the images and targeting clinical
situations where raw data are often not accessible. Based on inverse problem
methods, our contribution introduces the recently developed total generalized
variation (TGV) norm to regularize PET image deconvolution. Moreover, we
stabilize this procedure with additional image constraints such as positivity
and photometry invariance. A criterion for updating and adjusting automatically
the regularization parameter in case of Poisson noise is also presented.
Experiments are conducted on both synthetic data and real patient images.Comment: First published in the Proceedings of the 23rd European Signal
Processing Conference (EUSIPCO-2015) in 2015, published by EURASI
Negative reflection of elastic guided waves in chaotic and random scattering media
The propagation of waves in complex media can be harnessed either by taming
the incident wave-field impinging on the medium or by forcing waves along
desired paths through its careful design. These two alternative strategies have
given rise to fascinating concepts such as time reversal or negative
refraction. Here, we show how these two processes are intimately linked through
the negative reflection phenomenon. A negative reflecting mirror converts a
wave of positive phase velocity into its negative counterpart and vice versa.
In this article, we experimentally demonstrate this phenomenon with elastic
waves in a 2D billiard and in a disordered plate by means of laser
interferometry. Despite the complexity of such configurations, the negatively
reflected wave field focuses back towards the initial source location, thereby
mimicking a phase conjugation operation while being a fully passive process.
The super-focusing capability of negative reflection is also highlighted in a
monochromatic regime. The negative reflection phenomenon is not restricted to
guided elastic waves since it can occur in zero-gap systems such as photonic
crystals, chiral metamaterials or graphene. Negative reflection can thus become
a tool of choice for the control of waves in all fields of wave physics.Comment: 9 pages, 6 figure
Resonant dynamics for the quintic nonlinear Schrödinger equation
International audienceWe consider the quintic nonlinear Schrödinger equation (NLS) on the circle. We prove that there exist solutions corresponding to an initial datum built on four Fourier modes which form a resonant set, which have a non trivial dynamic that involves periodic energy exchanges between the modes initially excited. It is noticeable that this nonlinear phenomena does not depend on the choice of the resonant set. The dynamical result is obtained by calculating a resonant normal form up to order 10 of the Hamiltonian of the quintic NLS and then by isolating an effective term of order 6. Notice that this phenomena can not occur in the cubic NLS case for which the amplitudes of the Fourier modes are almost actions, i.e. they are almost constant
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