Analysis of the variability of auditory brainstem response components through linear regression

(ABR) is of fundamental importance to the investiga- tion of the auditory system behavior, though its in- terpretation has a subjective nature because of the manual process employed in its study and the clinical experience required for its analysis. When analyzing the ABR, clinicians are often interested in the identi- fication of ABR signal components referred to as Jewett waves. In particular, the detection and study of the time when these waves occur (i.e., the wave la- tency) is a practical tool for the diagnosis of disorders affecting the auditory system. In this context, the aim of this research is to compare ABR manual/visual analysis provided by different examiners. Methods: The ABR data were collected from 10 normal-hearing subjects (5 men and 5 women, from 20 to 52 years). A total of 160 data samples were analyzed and a pair- wise comparison between four distinct examiners was executed. We carried out a statistical study aiming to identify significant differences between assessments provided by the examiners. For this, we used Linear Regression in conjunction with Bootstrap, as a me- thod for evaluating the relation between the responses given by the examiners. Results: The analysis sug- gests agreement among examiners however reveals differences between assessments of the variability of the waves. We quantified the magnitude of the ob- tained wave latency differences and 18% of the inves- tigated waves presented substantial differences (large and moderate) and of these 3.79% were considered not acceptable for the clinical practice. Conclusions: Our results characterize the variability of the manual analysis of ABR data and the necessity of establishing unified standards and protocols for the analysis of these data. These results may also contribute to the validation and development of automatic systems that are employed in the early diagnosis of hearing loss.

A generalized collectively compact operator theory with an application to integral equations on unbounded domains

In this paper a generalization of collectively compact operator theory in Banach spaces is developed. A feature of the new theory is that the operators involved are no longer required to be compact in the norm topology. Instead it is required that the image of a bounded set under the operator family is sequentially compact in a weaker topology. As an application, the theory developed is used to establish solvability results for a class of systems of second kind integral equations on unbounded domains, this class including in particular systems of Wiener-Hopf integral equations with L1 convolutions kernels

Solvability and spectral properties of integral equations on the real line: I. Weighted spaces of continuous functions

We consider in this paper the solvability of linear integral equations on the real line, in operator form (λ−K)φ=ψ, where and K is an integral operator. We impose conditions on the kernel, k, of K which ensure that K is bounded as an operator on . Let Xa denote the weighted space as |s|→∞}. Our first result is that if, additionally, |k(s,t)|⩽κ(s−t), with and κ(s)=O(|s|−b) as |s|→∞, for some b>1, then the spectrum of K is the same on Xa as on X, for 0operators, , which ensure that, if λ≠0 and λφ=Kkφ has only the trivial solution in X, for all k∈W, then, for 0⩽a⩽b, (λ−K)φ=ψ has exactly one solution φ∈Xa for every k∈W and ψ∈Xa. These conditions ensure further that is bounded uniformly in k∈W, for 0⩽a⩽b. As a particular application we consider the case when the kernel takes the form k(s,t)=κ(s−t)z(t), with , , and κ(s)=O(|s|−b) as |s|→∞, for some b>1. As an example where kernels of this latter form occur we discuss a boundary integral equation formulation of an impedance boundary value problem for the Helmholtz equation in a half-plane.

An exact local conservation theorem for finite-amplitude disturbances to non-parallel shear flows, with remarks on Hamiltonian structure and on Arnol'd's stability theorems

Disturbances of arbitrary amplitude are superposed on a basic flow which is assumed to be steady and either (a) two-dimensional, homogeneous, and incompressible (rotating or non-rotating) or (b) stably stratified and quasi-geostrophic. Flow over shallow topography is allowed in either case. The basic flow, as well as the disturbance, is assumed to be subject neither to external forcing nor to dissipative processes like viscosity. An exact, local ‘wave-activity conservation theorem’ is derived in which the density A and flux F are second-order ‘wave properties’ or ‘disturbance properties’, meaning that they are O(a2) in magnitude as disturbance amplitude a [rightward arrow] 0, and that they are evaluable correct to O(a2) from linear theory, to O(a3) from second-order theory, and so on to higher orders in a. For a disturbance in the form of a single, slowly varying, non-stationary Rossby wavetrain, $\overline{F}/\overline{A}$ reduces approximately to the Rossby-wave group velocity, where (${}^{-}$) is an appropriate averaging operator. F and A have the formal appearance of Eulerian quantities, but generally involve a multivalued function the correct branch of which requires a certain amount of Lagrangian information for its determination. It is shown that, in a certain sense, the construction of conservable, quasi-Eulerian wave properties like A is unique and that the multivaluedness is inescapable in general. The connection with the concepts of pseudoenergy (quasi-energy), pseudomomentum (quasi-momentum), and ‘Eliassen-Palm wave activity’ is noted. The relationship of this and similar conservation theorems to dynamical fundamentals and to Arnol'd's nonlinear stability theorems is discussed in the light of recent advances in Hamiltonian dynamics. These show where such conservation theorems come from and how to construct them in other cases. An elementary proof of the Hamiltonian structure of two-dimensional Eulerian vortex dynamics is put on record, with explicit attention to the boundary conditions. The connection between Arnol'd's second stability theorem and the suppression of shear and self-tuning resonant instabilities by boundary constraints is discussed, and a finite-amplitude counterpart to Rayleigh's inflection-point theorem noted

First order k-th moment finite element analysis of nonlinear operator equations with stochastic data

We develop and analyze a class of efficient Galerkin approximation methods for uncertainty quantification of nonlinear operator equations. The algorithms are based on sparse Galerkin discretizations of tensorized linearizations at nominal parameters. Specifically, we consider abstract, nonlinear, parametric operator equations J(\alpha ,u)=0 for random input \alpha (\omega ) with almost sure realizations in a neighborhood of a nominal input parameter \alpha _0. Under some structural assumptions on the parameter dependence, we prove existence and uniqueness of a random solution, u(\omega ) = S(\alpha (\omega )). We derive a multilinear, tensorized operator equation for the deterministic computation of k-th order statistical moments of the random solution's fluctuations u(\omega ) - S(\alpha _0). We introduce and analyse sparse tensor Galerkin discretization schemes for the efficient, deterministic computation of the k-th statistical moment equation. We prove a shift theorem for the k-point correlation equation in anisotropic smoothness scales and deduce that sparse tensor Galerkin discretizations of this equation converge in accuracy vs. complexity which equals, up to logarithmic terms, that of the Galerkin discretization of a single instance of the mean field problem. We illustrate the abstract theory for nonstationary diffusion problems in random domains.

Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex

In this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d >= 2. Optimal error estimates are established in the case of Sobolev regularity and illustrated on several numerical examples. The proof is based on the collapsed coordinate transform and the expansion into various polynomial bases involving Jacobi polynomials and their antiderivatives. The results of the present paper generalize corresponding estimates for cubes in Rd from [P. Houston, C. Schwab, E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002), no. 6, 2133-2163].

Synthesis of novel hyperbranched polymers featuring oxazoline linear units and their application in fast-drying solvent-borne coating formulations

Novel acid-terminated hyperbranched polymers (HBPs) containing adipic acid and oxazoline monomers derived from oleic and linoleic acid have been synthesized via a bulk polymerization procedure. Branching was achieved as a consequence of an acid-catalyzed opening of the oxazoline ring to produce a trifunctional monomer in situ which delivered branching levels of >45% as determined by 1H and 13C NMR spectroscopy. The HBPs were soluble in common solvents, such as CHCl3, acetone, tetrahydrofuran, dimethylformamide, and dimethyl sulfoxide and were further functionalized by addition of citronellol to afford white-spirit soluble materials that could be used in coating formulations. During end group modification, a reduction in branching levels of the HBPs (down to 12–24%) was observed, predominantly on account of oxazoline ring reformation and trans-esterification processes under the reaction conditions used. In comparison to commercial alkyd resin paint coatings, formulations of the citronellol-functionalized hyperbranched materials blended with a commercial alkyd resin exhibited dramatic decreases of the blend viscosity when the HBP content was increased. The curing characteristics of the HBP/alkyd blend formulations were studied by dynamic mechanical analysis which revealed that the new coatings cured more quickly and produced tougher materials than otherwise identical coatings prepared from only the commercial alkyd resins.

Retrieval characteristics of non-linear sea surface temperature from the Advanced Very High Resolution Radiometer

Criteria are proposed for evaluating sea surface temperature (SST) retrieved from satellite infra-red imagery: bias should be small on regional scales; sensitivity to atmospheric humidity should be small; and sensitivity of retrieved SST to surface temperature should be close to 1 K K−1. Their application is illustrated for non-linear sea surface temperature (NLSST) estimates. 233929 observations from the Advanced Very High Resolution Radiometer (AVHRR) on Metop-A are matched with in situ data and numerical weather prediction (NWP) fields. NLSST coefficients derived from these matches have regional biases from −0.5 to +0.3 K. Using radiative transfer modelling we find that a 10% increase in humidity alone can change the retrieved NLSST by between −0.5 K and +0.1 K. A 1 K increase in SST changes NLSST by <0.5 K in extreme cases. The validity of estimates of sensitivity by radiative transfer modelling is confirmed empirically.

Further investigations of the quartz optically stimulated luminescence components using linear modulation

The optically stimulated luminescence (OSL) from quartz is known to be the sum of several components with different rates of charge loss, originating from different trap types. The OSL components are clearly distinguished using the linear modulation (LM OSL) technique. A variety of pre-treatment and measurement conditions have been used on sedimentary samples in conjunction with linearly modulated optical stimulation to study in detail the behaviour of the OSL components of quartz. Single aliquots of different quartz samples have been found to contain typically five or six common LM OSL components when stimulated at View the MathML source. The components have been parameterised in terms of thermal stability (i.e. E and s), photoionisation cross-section energy dependence and dose response. The results of studies concerning applications of component-resolved LM OSL measurements on quartz are also presented. These include the detection of partial bleaching in young samples, use of ‘stepped wavelength’ stimulation to observe OSL from single components and attempts to extend the age range of quartz OSL dating.

Linear vs. log-linear unit-root specification: an application of mis-specification encompassing

The objective of this paper is to apply the mis-specification (M-S) encompassing perspective to the problem of choosing between linear and log-linear unit-root models. A simple M-S encompassing test, based on an auxiliary regression stemming from the conditional second moment, is proposed and its empirical size and power are investigated using Monte Carlo simulations. It is shown that by focusing on the conditional process the sampling distributions of the relevant statistics are well behaved under both the null and alternative hypotheses. The proposed M-S encompassing test is illustrated using US total disposable income quarterly data.

Spectral asymmetry of the massless Dirac operator on a 3-torus

Consider the massless Dirac operator on a 3-torus equipped with Euclidean metric and standard spin structure. It is known that the eigenvalues can be calculated explicitly: the spectrum is symmetric about zero and zero itself is a double eigenvalue. The aim of the paper is to develop a perturbation theory for the eigenvalue with smallest modulus with respect to perturbations of the metric. Here the application of perturbation techniques is hindered by the fact that eigenvalues of the massless Dirac operator have even multiplicity, which is a consequence of this operator commuting with the antilinear operator of charge conjugation (a peculiar feature of dimension 3). We derive an asymptotic formula for the eigenvalue with smallest modulus for arbitrary perturbations of the metric and present two particular families of Riemannian metrics for which the eigenvalue with smallest modulus can be evaluated explicitly. We also establish a relation between our asymptotic formula and the eta invariant.

Conditional mean functions of non-linear models of US output

We compare a number of models of post War US output growth in terms of the degree and pattern of non-linearity they impart to the conditional mean, where we condition on either the previous period's growth rate, or the previous two periods' growth rates. The conditional means are estimated non-parametrically using a nearest-neighbour technique on data simulated from the models. In this way, we condense the complex, dynamic, responses that may be present in to graphical displays of the implied conditional mean.

A comparison of tests of non-linear cointegration with an application to the predictability of US interest rates using the term structure

We test whether there are nonlinearities in the response of short- and long-term interest rates to the spread in interest rates, and assess the out-of-sample predictability of interest rates using linear and nonlinear models. We find strong evidence of nonlinearities in the response of interest rates to the spread. Nonlinearities are shown to result in more accurate short-horizon forecasts, especially of the spread.

Forecasting economic and financial time series with non-linear models

In this paper we discuss the current state-of-the-art in estimating, evaluating, and selecting among non-linear forecasting models for economic and financial time series. We review theoretical and empirical issues, including predictive density, interval and point evaluation and model selection, loss functions, data-mining, and aggregation. In addition, we argue that although the evidence in favor of constructing forecasts using non-linear models is rather sparse, there is reason to be optimistic. However, much remains to be done. Finally, we outline a variety of topics for future research, and discuss a number of areas which have received considerable attention in the recent literature, but where many questions remain.