6,682 research outputs found
Nondiffracting Accelerating Waves: Weber waves and parabolic momentum
Diffraction is one of the universal phenomena of physics, and a way to
overcome it has always represented a challenge for physicists. In order to
control diffraction, the study of structured waves has become decisive. Here,
we present a specific class of nondiffracting spatially accelerating solutions
of the Maxwell equations: the Weber waves. These nonparaxial waves propagate
along parabolic trajectories while approximately preserving their shape. They
are expressed in an analytic closed form and naturally separate in forward and
backward propagation. We show that the Weber waves are self-healing, can form
periodic breather waves and have a well-defined conserved quantity: the
parabolic momentum. We find that our Weber waves for moderate to large values
of the parabolic momenta can be described by a modulated Airy function. Because
the Weber waves are exact time-harmonic solutions of the wave equation, they
have implications for many linear wave systems in nature, ranging from
acoustic, electromagnetic and elastic waves to surface waves in fluids and
membranes.Comment: 10 pages, 4 figures, v2: minor typos correcte
Universal, Unsupervised (Rule-Based), Uncovered Sentiment Analysis
We present a novel unsupervised approach for multilingual sentiment analysis
driven by compositional syntax-based rules. On the one hand, we exploit some of
the main advantages of unsupervised algorithms: (1) the interpretability of
their output, in contrast with most supervised models, which behave as a black
box and (2) their robustness across different corpora and domains. On the other
hand, by introducing the concept of compositional operations and exploiting
syntactic information in the form of universal dependencies, we tackle one of
their main drawbacks: their rigidity on data that are structured differently
depending on the language concerned. Experiments show an improvement both over
existing unsupervised methods, and over state-of-the-art supervised models when
evaluating outside their corpus of origin. Experiments also show how the same
compositional operations can be shared across languages. The system is
available at http://www.grupolys.org/software/UUUSA/Comment: 19 pages, 5 Tables, 6 Figures. This is the authors version of a work
that was accepted for publication in Knowledge-Based System
One model, two languages: training bilingual parsers with harmonized treebanks
We introduce an approach to train lexicalized parsers using bilingual corpora
obtained by merging harmonized treebanks of different languages, producing
parsers that can analyze sentences in either of the learned languages, or even
sentences that mix both. We test the approach on the Universal Dependency
Treebanks, training with MaltParser and MaltOptimizer. The results show that
these bilingual parsers are more than competitive, as most combinations not
only preserve accuracy, but some even achieve significant improvements over the
corresponding monolingual parsers. Preliminary experiments also show the
approach to be promising on texts with code-switching and when more languages
are added.Comment: 7 pages, 4 tables, 1 figur
Exponential localization of singular vectors in spatiotemporal chaos
In a dynamical system the singular vector (SV) indicates which perturbation
will exhibit maximal growth after a time interval . We show that in
systems with spatiotemporal chaos the SV exponentially localizes in space.
Under a suitable transformation, the SV can be described in terms of the
Kardar-Parisi-Zhang equation with periodic noise. A scaling argument allows us
to deduce a universal power law for the localization of the
SV. Moreover the same exponent characterizes the finite-
deviation of the Lyapunov exponent in excellent agreement with simulations. Our
results may help improving existing forecasting techniques.Comment: 5 page
A new proof of the higher-order superintegrability of a noncentral oscillator with inversely quadratic nonlinearities
The superintegrability of a rational harmonic oscillator (non-central
harmonic oscillator with rational ratio of frequencies) with non-linear
"centrifugal" terms is studied. In the first part, the system is directly
studied in the Euclidean plane; the existence of higher-order
superintegrability (integrals of motion of higher order than 2 in the momenta)
is proved by introducing a deformation in the quadratic complex equation of the
linear system. The constants of motion of the nonlinear system are explicitly
obtained. In the second part, the inverse problem is analyzed in the general
case of degrees of freedom; starting with a general Hamiltonian , and
introducing appropriate conditions for obtaining superintegrability, the
particular "centrifugal" nonlinearities are obtained.Comment: 16 page
Class of perfect 1/f noise and the low-frequency cutoff paradox
The low-frequency cutoff paradox occurring in 1/f processes has been revisited in a recent Letter [M. Niemann, H. Kantz, and E. Barkai, Phys. Rev. Lett. 110, 140603 (2013)PRLTAO0031-900710.1103/PhysRevLett.110.140603]. A model of independent pulses exhibiting an integrable 1/fβ power spectrum with β>1 explains this paradox. In this paper we explore a complementary possibility based on the use of multiplicative models to generate integrable 1/fβ processes. Three distinct types of models are considered. One of the most used methods of generating 1/f processes based on correlated pulses is among these models. Consequently we find that, contrary to what is generally thought, the low-frequency cutoff is not necessary to avoid the postulated divergence in a wide variety of processes.Peer Reviewe
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