Asymptotic equivalence between the unconditional maximum likelihood and the square-law nonlinearity symbol timing estimation

This paper provides a systematic approach to theproblem of nondata aided symbol-timing estimation for linearmodulations. The study is performed under the unconditionalmaximum likelihood framework where the carrier-frequencyerror is included as a nuisance parameter in the mathematicalderivation. The second-order moments of the received signal arefound to be the sufficient statistics for the problem at hand and theyallow the provision of a robust performance in the presence of acarrier-frequency error uncertainty. We particularly focus on theexploitation of the cyclostationary property of linear modulations.This enables us to derive simple and closed-form symbol-timingestimators which are found to be based on the well-known squaretiming recovery method by Oerder and Meyr. Finally, we generalizethe OM method to the case of linear modulations withoffset formats. In this case, the square-law nonlinearity is foundto provide not only the symbol-timing but also the carrier-phaseerror.

Unbreakable PT symmetry of solitons supported by inhomogeneous defocusing nonlinearity

Peer Reviewed

Rigorous derivation of a nonlinear diffusion equation as fast-reaction limit of a continuous coagulation-fragmentation model with diffusion

Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [CDF2], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters.

A geometric mechanism of diffusion: Rigorous verification in a priori unstable Hamiltonian systems

In this paper we consider a representative a priori unstable Hamiltonian system with 2+1/2 degrees of freedom, to which we apply the geometric mechanism for diffusion introduced in the paper Delshams et al., Mem.Amer.Math. Soc. 2006, and generalized in Delshams and Huguet, Nonlinearity 2009, and provide explicit, concrete and easily verifiable conditions for the existence of diffusing orbits. The simplification of the hypotheses allows us to perform explicitly the computations along the proof, which contribute to present in an easily understandable way the geometric mechanism of diffusion. In particular, we fully describe the construction of the scattering map and the combination of two types of dynamics on a normally hyperbolic invariant manifold.

Growth in a Cross-Section of Cities: Location, Increasing Returns or Random Growth?

This article analyzes empirically the main existing theories on income and population city growth: increasing returns to scale, locational fundamentals and random growth. To do this we implement a threshold nonlinearity test that extends standard linear growth regression models to a dataset on urban, climatological and macroeconomic variables on 1,175 U.S. cities. Our analysis reveals the existence of increasing returns when per-capita income levels are beyond $19; 264. Despite this, income growth is mostly explained by social and locational fundamentals. Population growth also exhibits two distinct equilibria determined by a threshold value of 116,300 inhabitants beyond which city population grows at a higher rate. Income and population growth do not go hand in hand, implying an optimal level of population beyond which income growth stagnates or deteriorates

Nonlinear models and small sample performance of the generalized method of moments

In this paper I explore the issue of nonlinearity (both in the datageneration process and in the functional form that establishes therelationship between the parameters and the data) regarding the poorperformance of the Generalized Method of Moments (GMM) in small samples.To this purpose I build a sequence of models starting with a simple linearmodel and enlarging it progressively until I approximate a standard (nonlinear)neoclassical growth model. I then use simulation techniques to find the smallsample distribution of the GMM estimators in each of the models.

Initialisation of Nonlinearities for PNL and Wiener systems Inversion

This paper proposes a very fast method for blindly initial- izing a nonlinear mapping which transforms a sum of random variables. The method provides a surprisingly good approximation even when the basic assumption is not fully satis¯ed. The method can been used success- fully for initializing nonlinearity in post-nonlinear mixtures or in Wiener system inversion, for improving algorithm speed and convergence.

General electromagnetic simulation tool to predict the microwave nonlinear response of planar, arbitrarily-shaped HTS structures

This work describes a simulation tool being developed at UPC to predict the microwave nonlinear behavior of planar superconducting structures with very few restrictions on the geometry of the planar layout. The software is intended to be applicable to most structures used in planar HTS circuits, including line, patch, and quasi-lumped microstrip resonators. The tool combines Method of Moments (MoM) algorithms for general electromagnetic simulation with Harmonic Balance algorithms to take into account the nonlinearities in the HTS material. The Method of Moments code is based on discretization of the Electric Field Integral Equation in Rao, Wilton and Glisson Basis Functions. The multilayer dyadic Green's function is used with Sommerfeld integral formulation. The Harmonic Balance algorithm has been adapted to this application where the nonlinearity is distributed and where compatibility with the MoM algorithm is required. Tests of the algorithm in TM010 disk resonators agree with closed-form equations for both the fundamental and third-order intermodulation currents. Simulations of hairpin resonators show good qualitative agreement with previously published results, but it is found that a finer meshing would be necessary to get correct quantitative results. Possible improvements are suggested.

Forecasting tourism demand to Catalonia: neural networks vs. time series models

The increasing interest aroused by more advanced forecasting techniques, together with the requirement for more accurate forecasts of tourismdemand at the destination level due to the constant growth of world tourism, has lead us to evaluate the forecasting performance of neural modelling relative to that of time seriesmethods at a regional level. Seasonality and volatility are important features of tourism data, which makes it a particularly favourable context in which to compare the forecasting performance of linear models to that of nonlinear alternative approaches. Pre-processed official statistical data of overnight stays and tourist arrivals fromall the different countries of origin to Catalonia from 2001 to 2009 is used in the study. When comparing the forecasting accuracy of the different techniques for different time horizons, autoregressive integrated moving average models outperform self-exciting threshold autoregressions and artificial neural network models, especially for shorter horizons. These results suggest that the there is a trade-off between the degree of pre-processing and the accuracy of the forecasts obtained with neural networks, which are more suitable in the presence of nonlinearity in the data. In spite of the significant differences between countries, which can be explained by different patterns of consumer behaviour,we also find that forecasts of tourist arrivals aremore accurate than forecasts of overnight stays.

Coherent patterns and self-induced diffraction of electrons on a thin nonlinear layer

Electron scattering on a thin layer where the potential depends self-consistently on the wave function has been studied. When the amplitude of the incident wave exceeds a certain threshold, a soliton-shaped brightening (darkening) appears on the layer causing diffraction of the wave. Thus the spontaneously formed transverse pattern can be viewed as a self-induced nonlinear quantum screen. Attractive or repulsive nonlinearities result in different phase shifts of the wave function on the screen, which give rise to quite different diffraction patterns. Among others, the nonlinearity can cause self-focusing of the incident wave into a beam, splitting in two "beams," single or double traces with suppressed reflection or transmission, etc.