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

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 $\tau$. 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 $\tau^{-\gamma}$ for the localization of the SV. Moreover the same exponent $\gamma$ characterizes the finite-$\tau$ 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 $n$ degrees of freedom; starting with a general Hamiltonian $H$, 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