A new complexity measure for time series analysis and classification

Complexity measures are used in a number of applications including extraction of information from data such as ecological time series, detection of non-random structure in biomedical signals, testing of random number generators, language recognition and authorship attribution etc. Different complexity measures proposed in the literature like Shannon entropy, Relative entropy, Lempel-Ziv, Kolmogrov and Algorithmic complexity are mostly ineffective in analyzing short sequences that are further corrupted with noise. To address this problem, we propose a new complexity measure ETC and define it as the “Effort To Compress” the input sequence by a lossless compression algorithm. Here, we employ the lossless compression algorithm known as Non-Sequential Recursive Pair Substitution (NSRPS) and define ETC as the number of iterations needed for NSRPS to transform the input sequence to a constant sequence. We demonstrate the utility of ETC in two applications. ETC is shown to have better correlation with Lyapunov exponent than Shannon entropy even with relatively short and noisy time series. The measure also has a greater rate of success in automatic identification and classification of short noisy sequences, compared to entropy and a popular measure based on Lempel-Ziv compression (implemented by Gzip).     

Comparison of adjoint‐based and feature‐based grid adaptation for functional outputs

Adjoint‐based and feature‐based grid adaptive strategies are compared for their robustness and effectiveness in improving the accuracy of functional outputs such as lift and drag coefficients. The output‐based adjoint approach strives to improve the adjoint error estimates that relate the local residual errors to the global error in an output function via adjoint variables as weight functions. A conservative adaptive indicator that takes into account the residual errors in both the primal (flow) and dual (adjoint) solutions is implemented for the adjoint approach. The physics‐based feature approach strives to identify and resolve significant features of the flow to improve functional accuracy. Adaptive indicators that represent expansions and compressions in the flow direction and gradients normal to the flow direction are implemented for the feature approach. The adaptive approaches are compared for functional outputs of three‐dimensional arbitrary Mach number flow simulations on mixed‐element unstructured meshes. Grid adaptation is performed with h‐refinement and results are presented for inviscid, laminar and turbulent flows. Copyright © 2006 John Wiley & Sons, Ltd.     

First results of investigation of radiation from positrons in a crystalline undulator

Radiation emitted by positrons moving in a periodically deformed crystal has been experimentally observed for the first time. Radiation spectra have been measured in a wide energy range. Experimental evidence has been obtained for an undulator peak in a radiation spectrum, which is qualitatively consistent with calculations. Crystalline undulators ensure an equivalent magnetic field of 1000 T and a period in the submillimeter range and can therefore be used to generate x-ray and gamma radiation that is a hundred times harder than radiation in usual undulators.     

Application of a momentum method to some rarefied gas flow problems

Zusammenfassung Eine Kombination der Lees-Methode und des Mott-Smith Ansatzes wird auf zwei Probleme der Couette-Strömung zwischen zwei Zylindern angewandt. Es werden Ausdrücke hergeleitet für das Moment im Fall, dass ein Zylinder rotiert, und für den Wärmefluss im Fall, dass beide Zylinder stationär sind, aber verschiedene Temperatur haben; diese Ausdrücke sind für alle Werte der Knudsenzahl gültig.     

Relativistic calculations of the spectroscopic properties of low-lying states of ICI

Relativistic quantum calculations which include spin-orbit interactions and correlations were carried out for the low-lying states of ICl. Spectroscopic properties (R₃, ω_e, T_e) were calculated for these states. Based on the energies and wave functions both the absorption and emission spectra of ICl in the region below 45000 cm⁻¹ were interpreted. These calculations confirm the predissociation of the B0⁺ state and the existence of a second minimum (B′0⁺) in the 0⁺(II) state. Properties of the 0⁻(I)(³Π_0⁻) state which is yet to be observed were also predicted. The calculated properties for the 2(I)(³Π₂) state are in very good agreement with the properties obtained by the very recent characterization of the A′ state by optical three-photon resonance. The continuous and diffuse absorption spectra of ICl in the region below 45000 cm⁻¹ were interpreted and assigned to the appropriate electronic transitions.     

Synthesis of 3-substituted coumarins via sequential pericyclic transformations of δ-aryloxymethylacrylic acids and enophiles

A new procedure for the synthesis of 3-functionally substituted coumarins via sequential Claisen and ene reactions of δ-aryloxymethylacrylic acids and anophiles has been developed.