Nonlinear projective filtering I: Background in chaos theory

We derive a locally projective noise reduction scheme for nonlinear time series using concepts from deterministic dynamical systems, or chaos theory. We will demonstrate its effectiveness with an example with known deterministic dynamics and discuss methods for the verification of the results in the case of an unknown deterministic system.Comment: 4 pages, PS figures, needs nolta.st

Nonlinear projective filtering I: Application to real time series

We discuss applications of nonlinear filtering of time series by locally linear phase space projections. Noise can be reduced whenever the error due to the manifold approximation is smaller than the noise in the system. Examples include the real time extraction of the fetal electrocardiogram from abdominal recordings.Comment: 4 pages, PS figures, needs nolta.st

Non-homogeneous polygonal Markov fields in the plane: graphical representations and geometry of higher order correlations

We consider polygonal Markov fields originally introduced by Arak and Surgailis (1989). Our attention is focused on fields with nodes of order two, which can be regarded as continuum ensembles of non-intersecting contours in the plane, sharing a number of features with the two-dimensional Ising model. We introduce non-homogeneous version of polygonal fields in anisotropic enviroment. For these fields we provide a class of new graphical constructions and random dynamics. These include a generalised dynamic representation, generalised and defective disagreement loop dynamics as well as a generalised contour birth and death dynamics. Next, we use these constructions as tools to obtain new exact results on the geometry of higher order correlations of polygonal Markov fields in their consistent regime.Comment: 54 page

Direct measurement of diurnal polar motion by ring laser gyroscopes

We report the first direct measurements of the very small effect of forced diurnal polar motion, successfully observed on three of our large ring lasers, which now measure the instantaneous direction of Earth's rotation axis to a precision of 1 part in 10^8 when averaged over a time interval of several hours. Ring laser gyroscopes provide a new viable technique for directly and continuously measuring the position of the instantaneous rotation axis of the Earth and the amplitudes of the Oppolzer modes. In contrast, the space geodetic techniques (VLBI, SLR, GPS, etc.) contain no information about the position of the instantaneous axis of rotation of the Earth, but are sensitive to the complete transformation matrix between the Earth-fixed and inertial reference frame. Further improvements of gyroscopes will provide a powerful new tool for studying the Earth's interior.Comment: 5 pages, 4 figures, agu2001.cl

Nonlinear projective filtering in a data stream

We introduce a modified algorithm to perform nonlinear filtering of a time series by locally linear phase space projections. Unlike previous implementations, the algorithm can be used not only for a posteriori processing but includes the possibility to perform real time filtering in a data stream. The data base that represents the phase space structure generated by the data is updated dynamically. This also allows filtering of non-stationary signals and dynamic parameter adjustment. We discuss exemplary applications, including the real time extraction of the fetal electrocardiogram from abdominal recordings.Comment: 8 page

White dwarf masses in cataclysmic variables

The white dwarf (WD) mass distribution of cataclysmic variables (CVs) has recently been found to dramatically disagree with the predictions of the standard CV formation model. The high mean WD mass among CVs is not imprinted in the currently observed sample of CV progenitors and cannot be attributed to selection effects. Two possibilities have been put forward: either the WD grows in mass during CV evolution, or in a significant fraction of cases, CV formation is preceded by a (short) phase of thermal time-scale mass transfer (TTMT) in which the WD gains a sufficient amount of mass. We investigate if either of these two scenarios can bring theoretical predictions and observations into agreement. We employed binary population synthesis models to simulate the present intrinsic CV population. We incorporated aspects specific to CV evolution such as an appropriate mass-radius relation of the donor star and a more detailed prescription for the critical mass ratio for dynamically unstable mass transfer. We also implemented a previously suggested wind from the surface of the WD during TTMT and tested the idea of WD mass growth during the CV phase by arbitrarily changing the accretion efficiency. We compare the model predictions with the characteristics of CVs derived from observed samples. We find that mass growth of the WDs in CVs fails to reproduce the observed WD mass distribution. In the case of TTMT, we are able to produce a large number of massive WDs if we assume significant mass loss from the surface of the WD during the TTMT phase. However, the model still produces too many CVs with helium WDs. Moreover, the donor stars are evolved in many of these post-TTMT CVs, which contradicts the observations. We conclude that in our current framework of CV evolution neither TTMT nor WD mass growth can fully explain either the observed WD mass or the period distribution in CVs.Comment: 15 pages, 7 figures, 1 table, accepted for publication in A&A. Replaced and added a reference, corrected typo

The ultra-compact binary candidate KUV 23182+1007 is a bright quasar

KUV 23182+1007 was identified as a blue object in the Kiso UV Survey in the 1980s. Classification-dispersion spectroscopy showed a featureless continuum except for a strong emission line in the region of He II 4686 A. This is a hallmark of the rare AM CVn class of cataclysmic variable star, so we have obtained a high-S/N blue spectrum of this object to check its classification. Instead, the spectrum shows a strong quasar-like emission line centred on 4662 A. Comparison with the SDSS quasar template spectra confirms that KUV 23182+1007 is a quasar with a redshift of z = 0.665.Comment: 4 pages, 2 figures, to appear in IBVS. Data are available from http://www.astro.keele.ac.uk/~jkt