Confidence Bands for Isotonic Median Curves using Sign-Tests

Suppose that one observes independent random variables (X1, Y1), (X2, Y2), …, (Xn, Yn) in R2 with unknown distributions, except that Median(Yi | Xi = M(x) for some unknown isotonic function M. We describe an explicit algorithm for the computation of confidence bands for the median function M whose running time is of order O(n2). The bands rely on multiscale sign tests and are shown to have desirable asymptotic properties.

Extraction of spin periods of space debris from optical light curves

The population of space debris increased drastically during the last years. These objects have become a great threat for active satellites. Because the relative velocities between space debris and satellites are high, space debris objects may destroy active satellites through collisions. Furthermore, collisions involving massive objects produce large number of fragments leading to significant growth of the space debris population. The long term evolution of the debris population is essentially driven by so-called catastrophic collisions. An effective remediation measure in order to stabilize the population in Low Earth Orbit (LEO) is therefore the removal of large, massive space debris. To remove these objects, not only precise orbits, but also more detailed information about their attitude states will be required. One important property of an object targeted for removal is its spin period, spin axis orientation and their change over time. Rotating objects will produce periodic brightness variations with frequencies which are related to the spin periods. Such a brightness variation over time is called a light curve. Collecting, but also processing light curves is challenging due to several reasons. Light curves may be undersampled, low frequency components due to phase angle and atmospheric extinction changes may be present, and beat frequencies may occur when the rotation period is close to a multiple of the sampling period. Depending on the method which is used to extract the frequencies, also method-specific properties have to be taken into account. The astronomical Institute of the University of Bern (AIUB) light curve database will be introduced, which contains more than 1,300 light curves acquired over more than seven years. We will discuss properties and reliability of different time series analysis methods tested and currently used by AIUB for the light curve processing. Extracted frequencies and reconstructed phases for some interesting targets, e.g. GLONASS satellites, for which also SLR data were available for the period confirmation, will be presented. Finally we will present the reconstructed phase and its evolution over time of a High-Area-to-Mass-Ratio (HAMR) object, which AIUB observed for several years.

Photometric monitoring of non-resolved space debris and databases of optical light curves.

The population of space debris increased drastically during the last years. Collisions involving massive objects may produce large number of fragments leading to significantly growth of the space debris population. An effective remediation measure in order to stabilize the population in LEO, is therefore the removal of large, massive space debris. To remove these objects, not only precise orbits, but also more detailed information about their attitude states will be required. One important property of an object targeted for removal is its spin period and spin axis orientation. If we observe a rotating object, the observer sees different surface areas of the object which leads to changes in the measured intensity. Rotating objects will produce periodic brightness vari ations with frequencies which are related to the spin periods. Photometric monitoring is the real tool for remote diagnostics of the satellite rotation around its center of mass. This information is also useful, for example, in case of contingency. Moreover, it is also important to take into account the orientation of non-spherical body (e.g. space debris) in the numerical integration of its motion when a close approach with the another spacecr aft is predicted. We introduce the two databases of light curves: the AIUB data base, which contains about a thousand light curves of LEO, MEO and high-altitude debris objects (including a few functional objects) obtained over more than seven years, and the data base of the Astronomical Observatory of Odessa University (Ukraine), which contains the results of more than 10 years of photometric monitoring of functioning satellites and large space debris objects in low Earth orbit. AIUB used its 1m ZIMLAT telescope for all light curves. For tracking low-orbit satellites, the Astronomical Observatory of Odessa used the KT-50 telescope, which has an alt-azimuth mount and allows tracking objects moving at a high angular velocity. The diameter of the KT-50 main mirror is 0.5 m, and the focal length is 3 m. The Odessa's Atlas of light curves includes almost 5,5 thousand light curves for ~500 correlated objects from a time period of 2005-2014. The processing of light curves and the determination of the rotation period in the inertial frame is challenging. Extracted frequencies and reconstructed phases for some interesting targets, e.g. GLONASS satellites, for which also SLR data were available for confirmation, will be presented. The rotation of the Envisat satellite after its sudden failure will be analyzed. The deceleration of its rotation rate within 3 years is studied together with the attempt to determine the orientation of the rotation axis.

(Table 2) Stratigraphic position of midpoints of reddish and beige layers of lithologic cycles in the Loulja-A Section and their astronomical ages after tuning to the ETP and Summer Insolation Curves of the La2004 solution

An integrated high-resolution stratigraphy and orbital tuning is presented for the Loulja sections located in the Bou Regreg area on the Atlantic side of Morocco. The sections constitute the upward continuation of the upper Messinian Ain el Beida section and contain a well-exposed, continuous record of the interval straddling the Miocene-Pliocene (M-P) boundary. The older Loulja-A section, which covers the interval from ~5.59 to 5.12 Ma, reveals a dominantly precession-controlled color cyclicity that allows for a straightforward orbital tuning of the boundary interval and for detailed cyclostratigraphic correlations to the Mediterranean; the high-resolution and high-quality benthic isotope record allows us to trace the dominantly obliquity-controlled glacial history. Our results reveal that the M-P boundary coincides with a minor, partly precession-related shift to lighter "interglacial" values in d18O. This shift and hence the M-P boundary may not correlate with isotope stage TG5, as previously thought, but with an extra (weak) obliquity-controlled cycle between TG7 and TG5. Consequently, the M-P boundary and basal Pliocene flooding of the Mediterranean following the Messinian salinity crisis are not associated with a major deglaciation and glacio-eustatic sea level rise, indicating that other factors, such as tectonics, must have played a fundamental role. On the other hand, the onset of the Upper Evaporites in the Mediterranean marked by hyposaline conditions coincides with the major deglaciation step between marine isotope stage TG12 and TG11, suggesting that the associated sea level rise is at least partly responsible for the apparent onset of intermittently restricted marine conditions following the main desiccation phase. Finally, the Loulja-A section would represent an excellent auxiliary boundary stratotype for the M-P boundary as formally defined at the base of the Trubi marls in the Eraclea Minoa section on Sicily.

Compaction curves and sediment characteristics of ODP Leg 165 and Leg 130 sites

Compaction curves for 11 samples from the mixed sediments and calcareous chalk with clay from the Caribbean Sites 999 and 1001 are discussed with reference to compaction curves for calcareous ooze and chalk of the Ontong Java Plateau (Leg 130). The burial history is discussed from preconsolidation data and present burial conditions and suggests a removal of ~400 m of sediment at the hiatus 166 meters below seafloor (mbsf) at Site 1001. This interpretation predicts a previous burial to >500 mbsf for depth intervals containing microstylolites, which corresponds to observations at Sites 999 and 807 (Ontong Java Plateau). Thus, data from three sites from two widely separate regions indicate that microstylolites in carbonates form at minimum burial depths deeper than 500 m. No direct link between formation of microstylolites and cementation was found, suggesting that dissolution and precipitation are not necessarily related. Porosity rebound during core retrieval could not be detected for soft sediments, whereas a porosity rebound of ~2% was deduced for deeper, cemented intervals. Comparing the compaction curves, two distinct rates of porosity loss are noted: (1) samples dominated by clay (>45% insoluble residue) compact at a higher rate than samples dominated by fine-grained carbonate and (2) fine-grained carbonate supported samples (with <45% insoluble residue) compact at the same rate irrespective of the content of nonsupporting microfossils or pore-filling clay.

LORENZ: Stata module to estimate and display Lorenz curves and concentration curves

Lorenz estimates Lorenz and concentration curves from individual-level data and, optionally, displays the results in a graph. Relative as well as generalized, absolute, unnormalized, or custom-normalized Lorenz or concentration curves are supported, and tools for computing contrasts between different subpopulations or outcome variables are provided. Variance estimation for complex samples is fully supported.

Estimating Lorenz and concentration curves in Stata

Lorenz and concentration curves are widely used tools in inequality research. In this paper I present a new Stata command called -lorenz- that estimates Lorenz and concentration curves from individual-level data and, optionally, displays the results in a graph. The -lorenz- command supports relative as well as generalized, absolute, unnormalized, or custom-normalized Lorenz or concentration curves, and provides tools for computing contrasts between different subpopulations or outcome variables. Variance estimation for complex samples is fully supported.