Space station dynamics

Structural dynamic characteristics and responses of the Space Station due to the natural and induced environment are discussed. Problems that are peculiar to the Space Station are also discussed. These factors lead to an overall acceleration environment that users may expect. This acceleration environment can be considered as a loading, as well as a disturbance environment

High moment partial sum processes of residuals in GARCH models and their applications

In this paper we construct high moment partial sum processes based on residuals of a GARCH model when the mean is known to be 0. We consider partial sums of $k$th powers of residuals, CUSUM processes and self-normalized partial sum processes. The $k$th power partial sum process converges to a Brownian process plus a correction term, where the correction term depends on the $k$th moment $\mu_k$ of the innovation sequence. If $\mu_k=0$, then the correction term is 0 and, thus, the $k$th power partial sum process converges weakly to the same Gaussian process as does the $k$th power partial sum of the i.i.d. innovations sequence. In particular, since $\mu_1=0$, this holds for the first moment partial sum process, but fails for the second moment partial sum process. We also consider the CUSUM and the self-normalized processes, that is, standardized by the residual sample variance. These behave as if the residuals were asymptotically i.i.d. We also study the joint distribution of the $k$th and $(k+1)$st self-normalized partial sum processes. Applications to change-point problems and goodness-of-fit are considered, in particular, CUSUM statistics for testing GARCH model structure change and the Jarque--Bera omnibus statistic for testing normality of the unobservable innovation distribution of a GARCH model. The use of residuals for constructing a kernel density function estimation of the innovation distribution is discussed.Comment: Published at http://dx.doi.org/10.1214/009053605000000534 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Change Point Testing for the Drift Parameters of a Periodic Mean Reversion Process

In this paper we investigate the problem of detecting a change in the drift parameters of a generalized Ornstein-Uhlenbeck process which is defined as the solution of $dX_t=(L(t)-\alpha X_t) dt + \sigma dB_t$, and which is observed in continuous time. We derive an explicit representation of the generalized likelihood ratio test statistic assuming that the mean reversion function $L(t)$ is a finite linear combination of known basis functions. In the case of a periodic mean reversion function, we determine the asymptotic distribution of the test statistic under the null hypothesis

Overfishing Trends and the Global Food Crisis

Fish are a vital source of nourishment, especially to people in the world's poorest nations. Widespread over?shing has led to a decline in catch globally; however, the links between over?shing and food security have not been well-understood. The authors of scientific article "Food security implications of globalmarine catch losses due to overfishing." assessed potential losses, globally and regionally, in ?sheries catch and revenue resulting from over?shing. They found a third to a half of commercial marine species had been over?shed during the past half-century, with billions in potential revenue lost. By placing country-level catch loss trends in the context of undernourishment levels in many of the world's poorest countries, the authors estimated that in 2000 the additional catch from sustainable ?shing could have helped 20 million people cover their food de?cit and avert undernourishment. This Pew Ocean Science Series report is a summary of the scientists' ?ndings

Wurdi Youang: an Australian Aboriginal stone arrangement with possible solar indications

Wurdi Youang is an egg-shaped Aboriginal stone arrangement in Victoria, Australia. Here we present a new survey of the site, and show that its major axis is aligned within a few degrees of east-west. We confirm a previous hypothesis that it contains alignments to the position on the horizon of the setting sun at the equinox and the solstices, and show that two independent sets of indicators are aligned in these directions. We show that these alignments are unlikely to have arisen by chance, and instead the builders of this stone arrangement appear to have deliberately aligned the site on astronomically significant positions.Comment: Accepted by Rock Art Researc

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Model of Image Artifacts from Dust Particles

A mathematical model of image artifacts produced by dust particles on lenses has been derived. Machine-vision systems often have to work with camera lenses that become dusty during use. Dust particles on the front surface of a lens produce image artifacts that can potentially affect the performance of a machine-vision algorithm. The present model satisfies a need for a means of synthesizing dust image artifacts for testing machine-vision algorithms for robustness (or the lack thereof) in the presence of dust on lenses. A dust particle can absorb light or scatter light out of some pixels, thereby giving rise to a dark dust artifact. It can also scatter light into other pixels, thereby giving rise to a bright dust artifact. For the sake of simplicity, this model deals only with dark dust artifacts. The model effectively represents dark dust artifacts as an attenuation image consisting of an array of diffuse darkened spots centered at image locations corresponding to the locations of dust particles. The dust artifacts are computationally incorporated into a given test image by simply multiplying the brightness value of each pixel by a transmission factor that incorporates the factor of attenuation, by dust particles, of the light incident on that pixel. With respect to computation of the attenuation and transmission factors, the model is based on a first-order geometric (ray)-optics treatment of the shadows cast by dust particles on the image detector. In this model, the light collected by a pixel is deemed to be confined to a pair of cones defined by the location of the pixel s image in object space, the entrance pupil of the lens, and the location of the pixel in the image plane (see Figure 1). For simplicity, it is assumed that the size of a dust particle is somewhat less than the diameter, at the front surface of the lens, of any collection cone containing all or part of that dust particle. Under this assumption, the shape of any individual dust particle artifact is the shape (typically, circular) of the aperture, and the contribution of the particle to the attenuation factor for a given pixel is the fraction of the cross-sectional area of the collection cone occupied by the particle. Assuming that dust particles do not overlap, the net transmission factor for a given pixel is calculated as one minus the sum of attenuation factors contributed by all dust particles affecting that pixel. In a test, the model was used to synthesize attenuation images for random distributions of dust particles on the front surface of a lens at various relative aperture (F-number) settings. As shown in Figure 2, the attenuation images resembled dust artifacts in real test images recorded while the lens was aimed at a white target