A time-domain test for some types of nonlinearity

The bispectrum and third-order moment can be viewed as equivalent tools for testing for the presence of nonlinearity in stationary time series. This is because the bispectrum is the Fourier transform of the third-order moment. An advantage of the bispectrum is that its estimator comprises terms that are asymptotically independent at distinct bifrequencies under the null hypothesis of linearity. An advantage of the third-order moment is that its values in any subset of joint lags can be used in the test, whereas when using the bispectrum the entire (or truncated) third-order moment is required to construct the Fourier transform. In this paper, we propose a test for nonlinearity based upon the estimated third-order moment. We use the phase scrambling bootstrap method to give a nonparametric estimate of the variance of our test statistic under the null hypothesis. Using a simulation study, we demonstrate that the test obtains its target significance level, with large power, when compared to an existing standard parametric test that uses the bispectrum. Further we show how the proposed test can be used to identify the source of nonlinearity due to interactions at specific frequencies. We also investigate implications for heuristic diagnosis of nonstationarity.

Analysis of the free vibration of rectangular plates with central cut-outs using the discrete Ritz method

We present an analysis of the free vibration of plates with internal discontinuities due to central cut-outs. A numerical formulation for a basic L-shaped element which is divided into appropriate sub-domains that are dependent upon the location of the cut-out is used as the basic building element. Trial functions formed to satisfy certain boundary conditions are employed to define the transverse deflection of each sub-domain. Mathematical treatments in terms of the continuities in displacement, slope, moment, and higher derivatives between the adjacent sub-domains are enforced at the interconnecting edges. The energy functional results, from the proper assembly of the coupled strain and kinetic energy contributions of each sub-domain, are minimized via the Ritz procedure to extract the vibration frequencies and. mode shapes of the plates. The procedures are demonstrated by considering plates with central cut-outs that are subjected to two types of boundary conditions. (C) 2003 Elsevier Ltd. All rights reserved.

Resolving the organization of the New World monkey third visual complex: The dorsal extrastriate cortex of the marmoset (Callithrix jacchus)

We tested current hypotheses on the functional organization of the third visual complex, a particularly controversial region of the primate extrastriate cortex. In anatomical experiments, injections of retrograde tracers were placed in the dorsal cortex immediately rostral to the second visual area (V2) of New World monkeys (Callithrix jacchus), revealing the topography of interconnections between the third tier cortex and the primary visual area (V1). The data indicate the presence of a dorsomedial area (DM), which represents the entire upper and lower quadrants of the visual field, and which receives strong, topographically organized projections from the superficial layers of V1. The visuotopic organization and boundaries of DM were confirmed by electrophysiological recordings in the same animals and by architectural characteristics which were distinct from those found in ventral extrastriate cortex rostral to V2. There was no electrophysiological or histological evidence for a transitional area between V2 and DM. In particular, the central representation of the upper quadrant in DM was directly adjacent to the representation of the horizontal meridian that marks the rostral border of V2. The present results argue in favor of the hypothesis that the third visual complex in New World monkeys contains different areas in its dorsal and ventral components: area DM, near the dorsal midline, and a homolog of area 19 of other mammals, located more lateral and ventrally. The characteristics of DM suggest that it may correspond to visual area 6 (V6) of Old World monkeys. (C) 2005 Wiley-Liss, Inc.