Noise Corruption of Empirical Mode Decomposition and Its Effect on Instantaneous Frequency

Huang's Empirical Mode Decomposition (EMD) is an algorithm for analyzing nonstationary data that provides a localized time-frequency representation by decomposing the data into adaptively defined modes. EMD can be used to estimate a signal's instantaneous frequency (IF) but suffers from poor performance in the presence of noise. To produce a meaningful IF, each mode of the decomposition must be nearly monochromatic, a condition that is not guaranteed by the algorithm and fails to be met when the signal is corrupted by noise. In this work, the extraction of modes containing both signal and noise is identified as the cause of poor IF estimation. The specific mechanism by which such "transition" modes are extracted is detailed and builds on the observation of Flandrin and Goncalves that EMD acts in a filter bank manner when analyzing pure noise. The mechanism is shown to be dependent on spectral leak between modes and the phase of the underlying signal. These ideas are developed through the use of simple signals and are tested on a synthetic seismic waveform.Comment: 28 pages, 19 figures. High quality color figures available on Daniel Kaslovsky's website: http://amath.colorado.edu/student/kaslovsk

Non-Asymptotic Analysis of Tangent Space Perturbation

Constructing an efficient parameterization of a large, noisy data set of points lying close to a smooth manifold in high dimension remains a fundamental problem. One approach consists in recovering a local parameterization using the local tangent plane. Principal component analysis (PCA) is often the tool of choice, as it returns an optimal basis in the case of noise-free samples from a linear subspace. To process noisy data samples from a nonlinear manifold, PCA must be applied locally, at a scale small enough such that the manifold is approximately linear, but at a scale large enough such that structure may be discerned from noise. Using eigenspace perturbation theory and non-asymptotic random matrix theory, we study the stability of the subspace estimated by PCA as a function of scale, and bound (with high probability) the angle it forms with the true tangent space. By adaptively selecting the scale that minimizes this bound, our analysis reveals an appropriate scale for local tangent plane recovery. We also introduce a geometric uncertainty principle quantifying the limits of noise-curvature perturbation for stable recovery. With the purpose of providing perturbation bounds that can be used in practice, we propose plug-in estimates that make it possible to directly apply the theoretical results to real data sets.Comment: 53 pages. Revised manuscript with new content addressing application of results to real data set

The Energy-Momentum Tensor(s) in Classical Gauge Theories

We give an introduction to, and review of, the energy-momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space-time. For the canonical energy-momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy-momentum tensor. The relationship with the Einstein-Hilbert tensor following from the coupling to a gravitational field is also discussed.Comment: 34 pages; v2: Slightly expanded version with some improvements of presentation; Contribution to Mathematical Foundations of Quantum Field Theory, special issue in memory of Raymond Stora, Nucl. Phys.

Three-dimensional fluid motion in Faraday waves: creation of vorticity and generation of two-dimensional turbulence

We study the generation of 2D turbulence in Faraday waves by investigating the creation of spatially periodic vortices in this system. Measurements which couple a diffusing light imaging technique and particle tracking algorithms allow the simultaneous observation of the three-dimensional fluid motion and of the temporal changes in the wave field topography. Quasi-standing waves are found to coexist with a spatially extended fluid transport. More specifically, the destruction of regular patterns of oscillons coincides with the emergence of a complex fluid motion whose statistics are similar to that of two-dimensional turbulence. We reveal that a lattice of oscillons generates vorticity at the oscillon scale in the horizontal flow. The interaction of these vortices explain how 2D turbulence is fueled by almost standing waves. Remarkably, the curvature of Lagrangian trajectories reveals a "footprint" of the forcing scale vortices in fully developed turbulence. 2D Navier-Stokes turbulence should be considered a source of disorder in Faraday waves. These findings also provide a new paradigm for vorticity creation in 2D flows

TRADE THROUGH FDI: investing in services

The type of relationship between different modes of trading services across international borders is of great interest, not only for the academic literature but also for the formulation trade liberalization offers under the GATS. Even more than for trade in goods, it is thus important to know whether cross-border trade and trade through commercial presence abroad act as complements or substitutes in services. The most commonly used analytical tool in the empirical analysis of this question is the gravity model of trade. This paper offers a consistent theoretical foundation for the application of the gravity model to services and to commercial presence, using a composite demand model with offers testable hypothesis about the complementary or substitutive relationship between different modes of supply. It further links the results to policy variables like market regulations which may act directly or implicitly as barriers to trade. Our empirical test for the sample of OECD countries over the decade 1994- 2004 yields robust complementary effects in the short-run, which is reinforced in the long-run by an increased potential for cross-border imports based on previous FDI inflows. A detailed analysis by individual service sectors highlights business, communication and financial services as showing the largest potential for cross-border trade when market regulations are reduced and when commercial presence increases.FDI, imports, services, panel data, substitution and complementary effects

Few Graphene layer/Carbon-Nanotube composite Grown at CMOS-compatible Temperature

We investigate the growth of the recently demonstrated composite material composed of vertically aligned carbon nanotubes capped by few graphene layers. We show that the carbon nanotubes grow epitaxially under the few graphene layers. By using a catalyst and gaseous carbon precursor different from those used originally we establish that such unconventional growth mode is not specific to a precise choice of catalyst-precursor couple. Furthermore, the composite can be grown using catalyst and temperatures compatible with CMOS processing (T < 450\degree C).Comment: 4 pages, 4 figure

Exploiting Non-Linearities in GDP Growth for Forecasting and Anticipating Regime Changes

. . .