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

Evolution of hierarchical clustering in the CFHTLS-Wide since z~1

We present measurements of higher order clustering of galaxies from the latest release of the Canada-France-Hawaii-Telescope Legacy Survey (CFHTLS) Wide. We construct a volume-limited sample of galaxies that contains more than one million galaxies in the redshift range 0.2<z<1 distributed over the four independent fields of the CFHTLS. We use a counts in cells technique to measure the variance and the hierarchical moments S_n = /^(n-1) (3<n<5) as a function of redshift and angular scale.The robustness of our measurements if thoroughly tested, and the field-to-field scatter is in very good agreement with analytical predictions. At small scales, corresponding to the highly non-linear regime, we find a suggestion that the hierarchical moments increase with redshift. At large scales, corresponding to the weakly non-linear regime, measurements are fully consistent with perturbation theory predictions for standard LambdaCDM cosmology with a simple linear bias.Comment: 17 pages, 11 figures, submitted to MNRA

Stochasticity of Bias and Nonlocality of Galaxy Formation: Linear Scales

If one wants to represent the galaxy number density at some point in terms of only the mass density at the same point, there appears the stochasticity in such a relation, which is referred to as ``stochastic bias''. The stochasticity is there because the galaxy number density is not merely a local function of a mass density field, but it is a nonlocal functional, instead. Thus, the phenomenological stochasticity of the bias should be accounted for by nonlocal features of galaxy formation processes. Based on mathematical arguments, we show that there are simple relations between biasing and nonlocality on linear scales of density fluctuations, and that the stochasticity in Fourier space does not exist on linear scales under a certain condition, even if the galaxy formation itself is a complex nonlinear and nonlocal precess. The stochasticity in real space, however, arise from the scale-dependence of bias parameter, $b$. As examples, we derive the stochastic bias parameters of simple nonlocal models of galaxy formation, i.e., the local Lagrangian bias models, the cooperative model, and the peak model. We show that the stochasticity in real space is also weak, except on the scales of nonlocality of the galaxy formation. Therefore, we do not have to worry too much about the stochasticity on linear scales, especially in Fourier space, even if we do not know the details of galaxy formation process.Comment: 24 pages, latex, including 2 figures, ApJ, in pres

Cosmological Perturbation Theory Using the Schr\"odinger Equation

We introduce the theory of non-linear cosmological perturbations using the correspondence limit of the Schr\"odinger equation. The resulting formalism is equivalent to using the collisionless Boltzman (or Vlasov) equations which remain valid during the whole evolution, even after shell crossing. Other formulations of perturbation theory explicitly break down at shell crossing, e.g. Eulerean perturbation theory, which describes gravitational collapse in the fluid limit. This paper lays the groundwork by introducing the new formalism, calculating the perturbation theory kernels which form the basis of all subsequent calculations. We also establish the connection with conventional perturbation theories, by showing that third order tree level results, such as bispectrum, skewness, cumulant correlators, three-point function are exactly reproduced in the appropriate expansion of our results. We explicitly show that cumulants up to N=5 predicted by Eulerian perturbation theory for the dark matter field $\delta$ are exactly recovered in the corresponding limit. A logarithmic mapping of the field naturally arises in the Schr\"odinger context, which means that tree level perturbation theory translates into (possibly incomplete) loop corrections for the conventional perturbation theory. We show that the first loop correction for the variance is $\sigma^2 = \sigma_L^2+ (-1.14+n)\sigma_L^4$ for a field with spectral index $n$. This yields 1.86 and 0.86 for $n=-3,-2$ respectively, and to be compared with the exact loop order corrections 1.82, and 0.88. Thus our tree-level theory recovers the dominant part of first order loop corrections of the conventional theory, while including (partial) loop corrections to infinite order in terms of $\delta$.Comment: 5 pages, submitted to ApJ Letter

Hyperextended Cosmological Perturbation Theory: Predicting Non-linear Clustering Amplitudes

We consider the long-standing problem of predicting the hierarchical clustering amplitudes $S_p$ in the strongly non-linear regime of gravitational evolution. N-body results for the non-linear evolution of the bispectrum (the Fourier transform of the three-point density correlation function) suggest a physically motivated ansatz that yields the strongly non-linear behavior of the skewness, $S_3$, starting from leading-order perturbation theory. When generalized to higher-order ($p>3$) polyspectra or correlation functions, this ansatz leads to a good description of non-linear amplitudes in the strongly non-linear regime for both scale-free and cold dark matter models. Furthermore, these results allow us to provide a general fitting formula for the non-linear evolution of the bispectrum that interpolates between the weakly and strongly non-linear regimes, analogous to previous expressions for the power spectrum.Comment: 20 pages, 6 figures. Final version accepted by ApJ. Includes new paragraphs on factorizable hierarchical models and agreement of HEPT with the excursion set model for white-noise Gaussian fluctuation

Biased-estimations of the Variance and Skewness

Nonlinear combinations of direct observables are often used to estimate quantities of theoretical interest. Without sufficient caution, this could lead to biased estimations. An example of great interest is the skewness $S_3$ of the galaxy distribution, defined as the ratio of the third moment \xibar_3 and the variance squared \xibar_2^2. Suppose one is given unbiased estimators for \xibar_3 and \xibar_2^2 respectively, taking a ratio of the two does not necessarily result in an unbiased estimator of $S_3$. Exactly such an estimation-bias affects most existing measurements of $S_3$. Furthermore, common estimators for \xibar_3 and \xibar_2 suffer also from this kind of estimation-bias themselves: for \xibar_2, it is equivalent to what is commonly known as the integral constraint. We present a unifying treatment allowing all these estimation-biases to be calculated analytically. They are in general negative, and decrease in significance as the survey volume increases, for a given smoothing scale. We present a re-analysis of some existing measurements of the variance and skewness and show that most of the well-known systematic discrepancies between surveys with similar selection criteria, but different sizes, can be attributed to the volume-dependent estimation-biases. This affects the inference of the galaxy-bias(es) from these surveys. Our methodology can be adapted to measurements of analogous quantities in quasar spectra and weak-lensing maps. We suggest methods to reduce the above estimation-biases, and point out other examples in LSS studies which might suffer from the same type of a nonlinear-estimation-bias.Comment: 28 pages of text, 9 ps figures, submitted to Ap

Statistical Tests for CHDM and \LambdaCDM Cosmologies

We apply several statistical estimators to high-resolution N-body simulations of two currently viable cosmological models: a mixed dark matter model, having $\Omega_\nu=0.2$ contributed by two massive neutrinos (C+2\nuDM), and a Cold Dark Matter model with Cosmological Constant (\LambdaCDM) with $\Omega_0=0.3$ and h=0.7. Our aim is to compare simulated galaxy samples with the Perseus-Pisces redshift survey (PPS). We consider the n-point correlation functions (n=2-4), the N-count probability functions P_N, including the void probability function P_0, and the underdensity probability function U_\epsilon (where \epsilon fixes the underdensity threshold in percentage of the average). We find that P_0 (for which PPS and CfA2 data agree) and P_1 distinguish efficiently between the models, while U_\epsilon is only marginally discriminatory. On the contrary, the reduced skewness and kurtosis are, respectively, S_3\simeq 2.2 and S_4\simeq 6-7 in all cases, quite independent of the scale, in agreement with hierarchical scaling predictions and estimates based on redshift surveys. Among our results, we emphasize the remarkable agreement between PPS data and C+2\nuDM in all the tests performed. In contrast, the above \LambdaCDM model has serious difficulties in reproducing observational data if galaxies and matter overdensities are related in a simple way.Comment: 12 pages, 10 figures, LaTeX (aaspp4 macro), in press on ApJ, Vol. 479, April 199

Looking back and beyond the 2017 diagnostic criteria for hypermobile Ehlers-Danlos syndrome: A retrospective cross-sectional study from an Italian reference center

The most common conditions with symptomatic joint hypermobility are hypermobile Ehlers-Danlos syndrome (hEDS) and hypermobility spectrum disorders (HSD). Diagnosing these overlapping connective tissue disorders remains challenging due to the lack of established causes and reliable diagnostic tests. hEDS is diagnosed applying the 2017 diagnostic criteria, and patients with symptomatic joint hypermobility but not fulfilling these criteria are labeled as HSD, which is not officially recognized by all healthcare systems. The 2017 criteria were introduced to improve diagnostic specificity but have faced criticism for being too stringent and failing to adequately capture the multisystemic involvement of hEDS. Herein, we retrospectively evaluated 327 patients from 213 families with a prior diagnosis of hypermobility type EDS or joint hypermobility syndrome based on Villefranche and Brighton criteria, to assess the effectiveness of the 2017 criteria in distinguishing between hEDS and HSD and document the frequencies of extra-articular manifestations. Based on our findings, we propose that the 2017 criteria should be made less stringent to include a greater number of patients who are currently encompassed within the HSD category. This will lead to improved diagnostic accuracy and enhanced patient care by properly capturing the diverse range of symptoms and manifestations present within the hEDS/HSD spectrum

Cell count moments in the halo model

We study cell count moments up to fifth order of the distributions of haloes, of halo substructures as a proxy for galaxies, and of mass in the context of the halo model and compare theoretical predictions to the results of numerical simulations. On scales larger than the size of the largest cluster, we present a simple point cluster model in which results depend only on cluster-cluster correlations and on the distribution of the number of objects within a cluster, or cluster occupancy. The point cluster model leads to expressions for moments of galaxy counts in which the volume-averaged moments on large scales approach those of the halo distribution and on smaller scales exhibit hierarchical clustering with amplitudes Sk determined by moments of the occupancy distribution. In this limit, the halo model predictions are purely combinatoric, and have no dependence on halo profile, concentration parameter or potential asphericity. The full halo model introduces only two additional effects: on large scales, haloes of different mass have different clustering strengths, introducing relative bias parameters; and on the smallest scales, halo structure is resolved and details of the halo profile become important, introducing shape-dependent form factors. Because of differences between discrete and continuous statistics, the hierarchical amplitudes for galaxies and for mass behave differently on small scales even if galaxy number is exactly proportional to mass, a difference that is not necessarily well described in terms of bia

Enhanced sensing and conversion of ultrasonic Rayleigh waves by elastic metasurfaces

Recent years have heralded the introduction of metasurfaces that advantageously combine the vision of sub-wavelength wave manipulation, with the design, fabrication and size advantages associated with surface excitation. An important topic within metasurfaces is the tailored rainbow trapping and selective spatial frequency separation of electromagnetic and acoustic waves using graded metasurfaces. This frequency dependent trapping and spatial frequency segregation has implications for energy concentrators and associated energy harvesting, sensing and wave filtering techniques. Different demonstrations of acoustic and electromagnetic rainbow devices have been performed, however not for deep elastic substrates that support both shear and compressional waves, together with surface Rayleigh waves; these allow not only for Rayleigh wave rainbow effects to exist but also for mode conversion from surface into shear waves. Here we demonstrate experimentally not only elastic Rayleigh wave rainbow trapping, by taking advantage of a stop-band for surface waves, but also selective mode conversion of surface Rayleigh waves to shear waves. These experiments performed at ultrasonic frequencies, in the range of 400–600 kHz, are complemented by time domain numerical simulations. The metasurfaces we design are not limited to guided ultrasonic waves and are a general phenomenon in elastic waves that can be translated across scales