Nonlinear time-series analysis revisited

In 1980 and 1981, two pioneering papers laid the foundation for what became known as nonlinear time-series analysis: the analysis of observed data---typically univariate---via dynamical systems theory. Based on the concept of state-space reconstruction, this set of methods allows us to compute characteristic quantities such as Lyapunov exponents and fractal dimensions, to predict the future course of the time series, and even to reconstruct the equations of motion in some cases. In practice, however, there are a number of issues that restrict the power of this approach: whether the signal accurately and thoroughly samples the dynamics, for instance, and whether it contains noise. Moreover, the numerical algorithms that we use to instantiate these ideas are not perfect; they involve approximations, scale parameters, and finite-precision arithmetic, among other things. Even so, nonlinear time-series analysis has been used to great advantage on thousands of real and synthetic data sets from a wide variety of systems ranging from roulette wheels to lasers to the human heart. Even in cases where the data do not meet the mathematical or algorithmic requirements to assure full topological conjugacy, the results of nonlinear time-series analysis can be helpful in understanding, characterizing, and predicting dynamical systems

Comment on the choice of time in a two-component formulation of the Wheeler--DeWitt equation

The two-component formalism in quantum cosmology is revisited with a particular emphasis on the identification of time. Its relation with the appearance of imaginary eigenvalues is established. It is explicitly shown how a good choice of the global time prevents this peculiarity.Comment: 8 pages; version accepted for publication in Int. J. Mod. Phys.

The Time Series Consumption Function Revisited

macroeconomics, consumption, life-cycle hypothesis, consumer spending, income

Low-temperature electron dephasing time in AuPd revisited

Ever since the first discoveries of the quantum-interference transport in mesoscopic systems, the electron dephasing times, $\tau_\phi$, in the concentrated AuPd alloys have been extensively measured. The samples were made from different sources with different compositions, prepared by different deposition methods, and various geometries (1D narrow wires, 2D thin films, and 3D thickfilms) were studied. Surprisingly, the low-temperature behavior of $\tau_\phi$ inferred by different groups over two decades reveals a systematic correlation with the level of disorder of the sample. At low temperatures, where $\tau_\phi$ is (nearly) independent of temperature, a scaling $\tau_\phi^{\rm max} \propto D^{-\alpha}$ is found, where $tau_\phi^{\rm max}$ is the maximum value of $\tau_\phi$ measured in the experiment, $D$ is the electron diffusion constant, and the exponent $\alpha$ is close to or slightly larger than 1. We address this nontrivial scaling behavior and suggest that the most possible origin for this unusual dephasing is due to dynamical structure defects, while other theoretical explanations may not be totally ruled out.Comment: to appear in Physica E, Proceedings for the International Seminar and Workshop "Quantum Coherence, Noise, and Decoherence in Nanostructures", 15-26 May 2006, Dresde

Time delays for 11 gravitationally lensed quasars revisited

We test the robustness of published time delays for 11 lensed quasars by using two techniques to measure time shifts in their light curves. We chose to use two fundamentally different techniques to determine time delays in gravitationally lensed quasars: a method based on fitting a numerical model and another one derived from the minimum dispersion method introduced by Pelt and collaborators. To analyse our sample in a homogeneous way and avoid bias caused by the choice of the method used, we apply both methods to 11 different lensed systems for which delays have been published: JVAS B0218+357, SBS 0909+523, RX J0911+0551, FBQS J0951+2635, HE 1104-1805, PG 1115+080, JVAS B1422+231, SBS 1520+530, CLASS B1600+434, CLASS B1608+656, and HE 2149-2745 Time delays for three double lenses, JVAS B0218+357, HE 1104-1805, and CLASS B1600+434, as well as the quadruply lensed quasar CLASS B1608+656 are confirmed within the error bars. We correct the delay for SBS 1520+530. For PG 1115+080 and RX J0911+0551, the existence of a second solution on top of the published delay is revealed. The time delays in four systems, SBS 0909+523, FBQS J0951+2635, JVAS B1422+231, and HE 2149-2745 prove to be less reliable than previously claimed. If we wish to derive an estimate of H_0 based on time delays in gravitationally lensed quasars, we need to obtain more robust light curves for most of these systems in order to achieve a higher accuracy and robustness on the time delays