Redshift distortions of galaxy correlation functions

To examine how peculiar velocities can affect the 2-, 3-, and 4-point redshift correlation functions, we evaluate volume-average correlations for configurations that emphasize and minimize redshift distortions for four different volume-limited samples from each of the CfA, SSRS, and IRAS redshift catalogs. We find a characteristic distortion for the 2-point correlation, \xibar_2: the slope $\gamma$ is flatter and the correlation length is larger in redshift space than in real space; that is, redshift distortions ``move'' correlations from small to large scales. At the largest scales (up to 12 \Mpc), the extra power in the redshift distribution is compatible with $\Omega^{4/7}/b \approx 1$. We estimate $\Omega^{4/7}/b$ to be $0.53 \pm 0.15$, $1.10 \pm 0.16$ and $0.84 \pm 0.45$ for the CfA, SSRS and IRAS catalogs. Higher order correlations \xibar_3 and \xibar_4 suffer similar redshift distortions, but in such a way that, within the accuracy of our analysis, the normalized amplitudes $S_3$ and $S_4$ are insensitive to this effect. The hierarchical amplitudes $S_3$ and $S_4$ are constant as a function of scale between 1--12 \Mpc and have similar values in all samples and catalogues, $S_3 \approx 2$ and $S_4 \approx 6$, despite the fact that \xibar_2, \xibar_3, and \xibar_4 differ from one sample to another by large factors (up to a factor of 4 in \xibar_2, 8 for \xibar_3, and 12 for \xibar_4). The agreement between the independent estimations of $S_3$ and $S_4$Comment: 20 pages (12 figues available on request), LaTeX, FERMILAB-Pub-93-097-

Void Statistics and Hierarchical Scaling in the Halo Model

We study scaling behaviour of statistics of voids in the context of the halo model of nonlinear large-scale structure. The halo model allows us to understand why the observed galaxy void probability obeys hierarchical scaling, even though the premise from which the scaling is derived is not satisfied. We argue that the commonly observed negative binomial scaling is not fundamental, but merely the result of the specific values of bias and number density for typical galaxies. The model implies quantitative relations between void statistics measured for two populations of galaxies, such as SDSS red and blue galaxies, and their number density and bias.Comment: 11 pages, 11 figures, accepted for publication in MNRA

Cosmological structure formation from soft topological defects

Some models have extremely low-mass pseudo-Goldstone bosons that can lead to vacuum phase transitions at late times, after the decoupling of the microwave background.. This can generate structure formation at redshifts z greater than or approx 10 on mass scales as large as M approx 10 to the 18th solar masses. Such low energy transitions can lead to large but phenomenologically acceptable density inhomogeneities in soft topological defects (e.g., domain walls) with minimal variations in the microwave anisotropy, as small as delta Y/T less than or approx 10 to the minus 6 power. This mechanism is independent of the existence of hot, cold, or baryonic dark matter. It is a novel alternative to both cosmic string and to inflationary quantum fluctuations as the origin of structure in the Universe

Gaussianizing the non-Gaussian lensing convergence field I: the performance of the Gaussianization

Motivated by recent works of Neyrinck et al. 2009 and Scherrer et al. 2010, we proposed a Gaussianization transform to Gaussianize the non-Gaussian lensing convergence field $\kappa$. It performs a local monotonic transformation $\kappa\rightarrow y$ pixel by pixel to make the unsmoothed one-point probability distribution function of the new variable $y$ Gaussian. We tested whether the whole $y$ field is Gaussian against N-body simulations. (1) We found that the proposed Gaussianization suppresses the non-Gaussianity by orders of magnitude, in measures of the skewness, the kurtosis, the 5th- and 6th-order cumulants of the $y$ field smoothed over various angular scales relative to that of the corresponding smoothed $\kappa$ field. The residual non-Gaussianities are often consistent with zero within the statistical errors. (2) The Gaussianization significantly suppresses the bispectrum. Furthermore, the residual scatters around zero, depending on the configuration in the Fourier space. (3) The Gaussianization works with even better performance for the 2D fields of the matter density projected over \sim 300 \mpch distance interval centered at $z\in(0,2)$, which can be reconstructed from the weak lensing tomography. (4) We identified imperfectness and complexities of the proposed Gaussianization. We noticed weak residual non-Gaussianity in the $y$ field. We verified the widely used logarithmic transformation as a good approximation to the Gaussianization transformation. However, we also found noticeable deviations.Comment: 13 pages, 15 figures, accepted by PR

Visual control of flight speed in Drosophila melanogaster

Flight control in insects depends on self-induced image motion (optic flow), which the visual system must process to generate appropriate corrective steering maneuvers. Classic experiments in tethered insects applied rigorous system identification techniques for the analysis of turning reactions in the presence of rotating pattern stimuli delivered in open-loop. However, the functional relevance of these measurements for visual free-flight control remains equivocal due to the largely unknown effects of the highly constrained experimental conditions. To perform a systems analysis of the visual flight speed response under free-flight conditions, we implemented a `one-parameter open-loop' paradigm using `TrackFly' in a wind tunnel equipped with real-time tracking and virtual reality display technology. Upwind flying flies were stimulated with sine gratings of varying temporal and spatial frequencies, and the resulting speed responses were measured from the resulting flight speed reactions. To control flight speed, the visual system of the fruit fly extracts linear pattern velocity robustly over a broad range of spatio–temporal frequencies. The speed signal is used for a proportional control of flight speed within locomotor limits. The extraction of pattern velocity over a broad spatio–temporal frequency range may require more sophisticated motion processing mechanisms than those identified in flies so far. In Drosophila, the neuromotor pathways underlying flight speed control may be suitably explored by applying advanced genetic techniques, for which our data can serve as a baseline. Finally, the high-level control principles identified in the fly can be meaningfully transferred into a robotic context, such as for the robust and efficient control of autonomous flying micro air vehicles