The Nonlinear Redshift Space Power Spectrum: Omega from Redshift Surveys

We examine the anisotropies in the power spectrum by the mapping of real to redshift space. Using the Zel'dovich approximation, we obtain an analytic expression for the nonlinear redshift space power spectrum in the distant observer limit. For a given unbiased galaxy distribution in redshift space, the anisotropies in the power spectrum depend on the parameter $f(\Omega)\approx \Omega^{0.6}$, where $\Omega$ is the density parameter. We quantify these anisotropies by the ratio, $R$, of the quadrupole to monopole angular moments of the power spectrum. In contrast to linear theory, the Zel'dovich approximation predicts a decline in $R$ with decreasing scale. This departure from linear theory is due to nonlinear dynamics and not a result of incoherent random velocities. The rate of decline depends strongly on $\Omega$ and the initial power spectrum. However, we find a {\it universal} relation between the quantity $R/R_{lin}$ (where $R_{lin}$ the linear theory value of $R$) and the dimensionless variable $k/k_{nl}$, where $k_{nl}$ is a wavenumber determined by the scale of nonlinear structures. The universal relation is in good agreement with a large N-body simulation. This universal relation greatly extends the scales over which redshift distortions can be used as a probe of $\Omega$. A preliminary application to the 1.2 Jy IRAS yields $\Omega\sim 0.4$ if IRAS galaxies are unbiased.Comment: uuencoded compressed postscript. The preprint is also available at http://www.ast.cam.ac.uk/preprint/PrePrint.htm

The Velocity Field from Type Ia Supernovae Matches the Gravity Field from Galaxy Surveys

We compare the peculiar velocities of nearby SNe Ia with those predicted by the gravity fields of full sky galaxy catalogs. The method provides a powerful test of the gravitational instability paradigm and strong constraints on the density parameter beta = Omega^0.6/b. For 24 SNe Ia within 10,000 km/s we find the observed SNe Ia peculiar velocities are well modeled by the predictions derived from the 1.2 Jy IRAS survey and the Optical Redshift Survey (ORS). Our best $\beta$ is 0.4 from IRAS, and 0.3 from the ORS, with beta>0.7 and beta<0.15 ruled out at 95% confidence levels from the IRAS comparison. Bootstrap resampling tests show these results to be robust in the mean and in its error. The precision of this technique will improve as additional nearby SNe Ia are discovered and monitored.Comment: 16 pages (LaTex), 3 postscript figure

Relativistic Model of Detonation Transition from Neutron to Strange Matter

We study the conversion of neutron matter into strange matter as a detonation wave. The detonation is assumed to originate from a central region in a spherically symmetric background of neutrons with a varying radial density distribution. We present self-similar solutions for the propagation of detonation in static and collapsing backgrounds of neutron matter. The solutions are obtained in the framework of general relativistic hydrodynamics, and are relevant for the possible transition of neutron into strange stars. Conditions for the formation of either bare or crusted strange stars are discussed.Comment: 16 pages, 4 figures. Submitted to IJMP

TIME-VARIANT SPECTRAL ANALYSIS OF SURFACE EMG SIGNALS – EXEMPLARILY SHOWN FOR ARCHERY

To analyse the spectral density of electromyographic (EMG) signals Fourier transforms are commonly used. The prerequisite of this transform is that the analysed signal is stationary. Generally, this can not be assumed for the electromyograms of muscle contractions of human movement. A new method to analyse non-stationary biological signals is the time-variant spectral analysis. The aim of this paper is to use the timevariant spectral analysis in a realistic sport application to show connections of the athlete’s level and the spectral density of the EMG. Five top-level archers participated in the study. The results suggest, that a higher level of performance generally corresponds to lower median-frequencies and a smaller variability of the median-frequencies of the EMG-signals

The Probability Distribution of the Lya transmitted flux from a sample of SDSS quasars

We present a measurement of the probability distribution function (PDF) of the transmitted flux in the Lya forest from a sample of 3492 quasars included in the SDSS DR3 data release. Our intention is to investigate the sensitivity of the Lya flux PDF as measured from low resolution and low signal-to-noise data to a number of systematic errors such as uncertainties in the mean flux, continuum and noise estimate. The quasar continuum is described by the superposition of a power law and emission lines. We perform a power law continuum fitting on a spectrum-by-spectrum basis, and obtain an average continuum slope of 0.59 +/- 0.36 in the redshift range 2.5<z<3.5. Taking into account the variation in the continuum indices increases the mean flux by 3 and 7 per cent at z=3 and 2.4, respectively, as compared to the values inferred with a single (mean) continuum slope. We compare our measurements to the PDF obtained with mock lognormal spectra, whose statistical properties have been constrained to match the observed Lya flux PDF and power spectrum of high resolution data. Using our power law continuum fitting and the SDSS pipeline noise estimate yields a poor agreement between the observed and mock PDFs. Allowing for a break in the continuum slope and, more importantly, for residual scatter in the continuum level substantially improves the agreement. A decrease of 10-15 per cent in the mean quasar continuum with a typical rms variance at the 20 per cent level can account for the data, provided that the noise excess correction is no larger than 10 per cent.Comment: 16 pages. submitted to MNRA

Tight Bounds for Approximate Near Neighbor Searching for Time Series under the {F}r\'{e}chet Distance

We study the $c$-approximate near neighbor problem under the continuous Fr\'echet distance: Given a set of $n$ polygonal curves with $m$ vertices, a radius $\delta > 0$, and a parameter $k \leq m$, we want to preprocess the curves into a data structure that, given a query curve $q$ with $k$ vertices, either returns an input curve with Fr\'echet distance at most $c\cdot \delta$ to $q$, or returns that there exists no input curve with Fr\'echet distance at most $\delta$ to $q$. We focus on the case where the input and the queries are one-dimensional polygonal curves -- also called time series -- and we give a comprehensive analysis for this case. We obtain new upper bounds that provide different tradeoffs between approximation factor, preprocessing time, and query time. Our data structures improve upon the state of the art in several ways. We show that for any $0 < \varepsilon \leq 1$ an approximation factor of $(1+\varepsilon)$ can be achieved within the same asymptotic time bounds as the previously best result for $(2+\varepsilon)$. Moreover, we show that an approximation factor of $(2+\varepsilon)$ can be obtained by using preprocessing time and space $O(nm)$, which is linear in the input size, and query time in $O(\frac{1}{\varepsilon})^{k+2}$, where the previously best result used preprocessing time in $n \cdot O(\frac{m}{\varepsilon k})^k$ and query time in $O(1)^k$. We complement our upper bounds with matching conditional lower bounds based on the Orthogonal Vectors Hypothesis. Interestingly, some of our lower bounds already hold for any super-constant value of $k$. This is achieved by proving hardness of a one-sided sparse version of the Orthogonal Vectors problem as an intermediate problem, which we believe to be of independent interest