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.     

Fermion–Antifermion Condensate Contribution to the Anomalous Magnetic Moment of a Fundamental Dirac Fermion

We consider the contribution offermion–antifermion condensates to the anomalousmagnetic moment of a fermion in a vacuum in which suchcondensates exist. The real part of the condensatecontribution to the anomalous magnetic moment is shown to bezero. A nonzero imaginary part is obtained below thekinematic threshold for intermediatefermion–antifermion pairs. The calculation isshown to be gauge-parameter independent provided a single fermion masscharacterizes both the fermion propagator andcondensate-sensitive contributions, suggestive of adynamically generated fermion mass. The nonzeroimaginary part is then argued to correspond to the kinematicproduction of the intermediatestate Goldstone bosonsanticipated from a chiral-noninvariant vacuum. Finally,speculations are presented concerning the applicability of these results to quark electromagneticproperties.     

The memory of thin polymer films generated by spin coating

The European Physical Journal E - The interstitial tumor microenvironment is composed of heterogeneously organized collagen-rich porous networks as well as channel-like structures and interfaces...     

Assessment of Hydrocarbon Electron‐Impact Ionization Cross Section Measurements for Magnetic Fusion

Partial ionization cross section experiments have been carried out recently at the University of Innsbruck for three types of hydrocarbons, i.e. acetylene, ethylene and propene. Cross section data fits are generated and compared to the compilation of earlier experimental data summarized in the online database HYDKIN [www.hydkin.de]. New data fits are brought into a suitable form to be incorporated into the database. In order to illuminate underlying dissociation mechanisms the energy dependence of branching ratios above energies of 20 –30 eV is reviewed in light of the present results (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A characterization of the scattered acoustic intensity field in the resonance region for simple spheres

The properties of the scattered acoustic vector fields generated by simple spheres illuminated by monotonic continuous wave (CW) plane waves are investigated. Analytical solutions are derived from general acoustic pressure scattering models and analyzed for wave numbers in the resonance region. Of particular interest is the understanding of the characteristics of the scattered acoustic vector field in the near-to-far-field transition region. The separable active and reactive components of the acoustic intensity are used to investigate the structural features of the scattered field components. Numerical results are presented for the near and transition regions for a rigid sphere. A method of mapping nulls in the scattered intensity field components is described. The analysis is then extended to include a simple fluid-filled boundary and finally the evacuated thin-walled shell. Near field acoustic intensity field structures are compared against mechanical material properties of vacuous shells. The ability to extract scattered field features is illustrated with measurements obtained from a recent in-air experiment using an anechoic chamber and acoustic vector sensor probes to measure the scattered acoustic vector field from rigid spheres.     

Anomalous NMR relaxation in cartilage matrix components and native cartilage: fractional-order models

We present a fractional-order extension of the Bloch equations to describe anomalous NMR relaxation phenomena (T(1) and T(2)). The model has solutions in the form of Mittag-Leffler and stretched exponential functions that generalize conventional exponential relaxation. Such functions have been shown by others to be useful for describing dielectric and viscoelastic relaxation in complex, heterogeneous materials. Here, we apply these fractional-order T(1) and T(2) relaxation models to experiments performed at 9.4 and 11.7 Tesla on type I collagen gels, chondroitin sulfate mixtures, and to bovine nasal cartilage (BNC), a largely isotropic and homogeneous form of cartilage. The results show that the fractional-order analysis captures important features of NMR relaxation that are typically described by multi-exponential decay models. We find that the T(2) relaxation of BNC can be described in a unique way by a single fractional-order parameter (α), in contrast to the lack of uniqueness of multi-exponential fits in the realistic setting of a finite signal-to-noise ratio. No anomalous behavior of T(1) was observed in BNC. In the single-component gels, for T(2) measurements, increasing the concentration of the largest components of cartilage matrix, collagen and chondroitin sulfate, results in a decrease in α, reflecting a more restricted aqueous environment. The quality of the curve fits obtained using Mittag-Leffler and stretched exponential functions are in some cases superior to those obtained using mono- and bi-exponential models. In both gels and BNC, α appears to account for micro-structural complexity in the setting of an altered distribution of relaxation times. This work suggests the utility of fractional-order models to describe T(2) NMR relaxation processes in biological tissues.     

Probing the independence of formant control using altered auditory feedback

Two auditory feedback perturbation experiments were conducted to examine the nature of control of the first two formants in vowels. In the first experiment, talkers heard their auditory feedback with either F1 or F2 shifted in frequency. Talkers altered production of the perturbed formant by changing its frequency in the opposite direction to the perturbation but did not produce a correlated alteration of the unperturbed formant. Thus, the motor control system is capable of fine-grained independent control of F1 and F2. In the second experiment, a large meta-analysis was conducted on data from talkers who received feedback where both F1 and F2 had been perturbed. A moderate correlation was found between individual compensations in F1 and F2 suggesting that the control of F1 and F2 is processed in a common manner at some level. While a wide range of individual compensation magnitudes were observed, no significant correlations were found between individuals' compensations and vowel space differences. Similarly, no significant correlations were found between individuals' compensations and variability in normal vowel production. Further, when receiving normal auditory feedback, most of the population exhibited no significant correlation between the natural variation in production of F1 and F2.     

Bending insensitivity of fiber Bragg gratings in suspended-core optical fibers

This Letter presents simulation and experimental results that explore bending insensitivity of fiber Bragg gratings in suspended-core optical fibers. The implementation of thin silica bridge in the fibers enhances index contrast of the fiber core and reduces bending-induced strain transfer to the fiber core. This fiber design lead to a reduction of over 7 times in strain-induced fiber Bragg grating resonant peak shifts in the suspended-core fiber compared with that in standard telecommunication fiber, and an 0.14 dB bending loss at a bending radius of 6.35 mm.     

Modification of terminating species and band alignment at the interface between alumina films and metal single crystals

Thin epitaxial alumina films were grown on Cu(111), Cu–9 at.%Al(111), Ni(111) and NiAl(110) single crystals. The alumina films grew in such a manner that hexagonal or pseudo-hexagonal oxygen lattices were parallel to the surface of the substrates. Photoelectron spectra were obtained either with synchrotron or Al K-alpha radiation. We measured Al 2p spectra and determined the atomic species that terminated the interface between the alumina films and the substrates. The influence of Al in the substrates on the species that terminated the interface has been discussed based on thermodynamics. From valence band spectra, p-type Schottky barrier height (energy difference between the Fermi level of the metallic substrates and the valence band maximum of the alumina films, band offset) was determined. Differences in interface terminating species resulted in variations in p-type Schottky barrier height, or band alignment.