Correlation dimension: A pivotal statistic for non-constrained realizations of composite hypotheses in surrogate data analysis

Currently surrogate data analysis can be used to determine if data is consistent with various linear systems, or something else (a nonlinear system). In this paper we propose an extension of these methods in an attempt to make more specific classifications within the class of nonlinear systems.

In the method of surrogate data one estimates the probability distribution of values of a test statistic for a set of experimental data under the assumption that the data is consistent with a given hypothesis. If the probability distribution of the test statistic is different for different dynamical systems consistent with the hypothesis, one must ensure that the surrogate generation technique generates surrogate data that are a good approximation to the data. This is often achieved with a careful choice of surrogate generation method and for noise driven linear surrogates such methods are commonly used.

This paper argues that, in many cases (particularly for nonlinear hypotheses), it is easier to select a test statistic for which the probability distribution of test statistic values is the same for all systems consistent with the hypothesis. For most linear hypotheses one can use a reliable estimator of a dynamic invariant of the underlying class of processes. For more complex, nonlinear hypothesis it requires suitable restatement (or cautious statement) of the hypothesis. Using such statistics one can build nonlinear models of the data and apply the methods of surrogate data to determine if the data is consistent with a simulation from a broad class of models. These ideas are illustrated with estimates of probability distribution functions for correlation dimension estimates of experimental and artificial data, and linear and nonlinear hypotheses.     

Energy Dispersive X-Ray Spectrometry by Microcalorimetry for the SEM

 Analytical X-ray spectrometry for electron beam instruments has advanced significantly with the development of the microcalorimeter energy dispersive X-ray spectrometer (μcal EDS). The μcal EDS operates by measuring the temperature rise when a single photon is absorbed in a metal target. A cryoelectronic circuit with electrothermal feedback and a superconducting transition edge sensor serves as the thermometer. Spectral resolution approaching 4.5 eV for high energy photons (6000 eV) and 2 eV for low energy photons below 2000 eV has been demonstrated in energy dispersive operation across a photon energy range from 250 eV to 8 keV. Spectra of a variety of materials demonstrate the power of the μcal EDS to solve practical problems while operating on a scanning electron microscope platform.     

Properties and examples of FCR-algebras

An algebra A over a field k is FCR if every finite dimensional representation of A is completely reducible and the intersection of the kernels of these representations is zero. We give a useful characterization of FCR-algebras and apply this to C ^*-algebras and to localizations. Moreover, we show that “small” products and sums of FCR-algebras are again FCR. Received: 25 October 2000     

Nonlinear polariton effects in the phenanthrene crystal

Two-photon fluorescence excitation (TPE) and second harmonic generation (SHG) spectra of the origin region of the 3500 Å system of the phenanthrene crystal at 2 K are presented and compared for both melt-grown and sublimed crystals. The dependence of the upper Davydov component position on the photon polarization and propagation direction reported previously is confirmed for both TPE and SHG- This behavior is considered to be a manifestation of phase matching to the upper branch of the b-polariton dispersion curve and is intrinsic to the two-photon process for transitions which are allowed in both one- and two-photon absorption. Both TPE and SHG are understood as resulting from the fundamental process of polariton fusion. The appearance of the dipole-forbidden lower Davydov component in these spectra is commented on in terms of misalignment and excitation of a longitudinal exciton.     

Non-photochemical hole burning and impurity site relaxation processes in organic glasses

Laser-induced holes in the inhomogeneously broadened absorption spectra of aromatic hydrocarbons in frozen glasses are reported. The holes are shown to be of non-photochemical origin. Mechanisms for excited state site interconversion based on a metastable distribution of sites in asymmetric double well potentials are presented. Methods of eliminating non-photochemical holes and of distinguishing between photochemical and non-photochemical holes are described.     

Tonal masking and frequency selectivity for the monaural and binaural hearing systems

A series of masking experiments was performed with the aim of comparing frequency selectivity for the monaural and binaural systems. The masking stimulus used in this study combined a sinusoid, which was gated simultaneously with the signal, with a continuous broadband noise. Signal frequency was fixed at 500 Hz. In one condition, the tonal masker and noise were interaurally in phase and the signal was phase reversed. In a second condition, noise, tonal masker, and signal were presented to one ear alone. Signal thresholds were obtained as a function of masker frequency for these two conditions. After making an appropriate selection of noise levels, masking functions for the monaural and binaural system conditions were found to agree closely except for a region about their tips where the binaural condition was more detectable. Two possible interpretations of these results are discussed. Either the monaural and binaural systems contain filters each which have similarly shaped skirts, or the frequency selectivity observed under both diotic and dichotic conditions (for large frequency separations of masker and signal) reflect the operation of a common peripheral filter.     

Investigation of a Unified Chaotic System and Its Synchronization by Simulations*

We investigate a unified chaotic system and its synchronization including feedback synchronization and adaptive synchronization by numerical simulations. We propose a new dynamical quantity denoted by K, which connects adaptive synchronization and feedback synchronization, to analyze synchronization schemes. We find that K can estimate the smallest coupling strength for a unified chaotic system whether it is complete feedback or one-sided feedback. Based on the previous work, we also give a new dynamical method to compute the leading Lyapunov exponent.     

Formulae for null curves deriving from elliptic curves

Any elliptic curve can be realised in the tangent bundle of the complex projective line as a double cover branched at four distinct points on the zero section. Such a curve generates, via classical osculation duality, a null curve in C³${\mathbb{C}}^3$ and thus an algebraic minimal surface in R³${\mathbb{R}}^3$. We derive simple formulae for the coordinate functions of such a null curve.     

Nil subsets of graded algebras

We prove that if is a Noetherian -graded algebra, then the Jacobson radical of is nilpotent under mild hypotheses on . We also consider affine PI-algebras graded by torsion groups. Finally we prove a Nullstellensatz-type theorem for enveloping algebras of Lie color algebras.