Nonlinear Bias Research Articles

SYSTEMATIC EFFECTS ON THE GENUS TOPOLOGY OF THE LARGE-SCALE STRUCTURE OF THE UNIVERSE

Large-scale structure of the universe is a useful cosmological probe of the primordial non-Gaussianity and the expansion history of the universe because its topology does not change with time in the linear regime in the standard paradigm of structure formation. However, when the topology of iso-density contour surfaces is measured from an observational data, many systematic effects are introduced due to the finite size of pixels used to define the density field, non-linear gravitational evolution, redshift-space distortion, shot noise (discrete sampling), and bias in the distribution of the density field tracers. We study the various systematic effects on the genus curve to a great accuracy by using the Horizon Run 2 simulation of a {\Lambda}CDM cosmology. We numerically measure the genus curve from the gravitationally evolved matter and dark matter halo density fields. It is found that all the non-Gaussian deviations due to the systematic effects can be modeled by using a few low-order Hermite polynomials from H0 to H4. We compare our results with the analytic theories whenever possible, and find many new terms in the Hermite series that are making significant contributions to the non-Gaussian deviations. In particular, it is found that the amplitude drop of the genus curve due to the non-linear gravitational evolution can be accurately modeled by two terms H0 and H2 with coefficients both proportional to \sigma_0^2, the mean-square density fluctuation.

High-order clustering of WiggleZ galaxies

High-order statistics are a useful and complementary tool for measuring the clustering of galaxies, containing information on the non-Gaussian evolution and morphology of the large structures in the Universe. In this work, we have presented results of the 3-point correlation function in the WiggleZ spectroscopic galaxy survey, at three different epochs. Using N-body simulations to predict the clustering of matter, we have constrained the linear and nonlinear bias parameters of WiggleZ galaxies with respect to total matter, and marginalized over them to obtain constraints on σs(z), the variance of perturbations, and its evolution with redshift. These measurements are consistent with the predictions of the ΛCDM concordance cosmology and test this model in a new way.

On the baryon acoustic oscillation amplitude as a probe of radiation density

The baryon acoustic oscillation (BAO) feature in the distribution of galaxies has been widely studied as an excellent standard ruler for probing cosmic distances and expansion history, and hence dark energy. In contrast, the amplitude of the BAO feature has received relatively little study, mainly due to limited signal-to-noise, and complications due to galaxy biasing, effects of non-linear clustering and dependence on several cosmological parameters. As expected, the amplitude of the BAO feature is sensitive to the cosmic baryon fraction: for standard radiation content, the cosmic microwave background (CMB) acoustic peaks constrain this precisely and the BAO amplitude is largely a redundant cross-check. However, the CMB mainly constrains the redshift of matter-radiation equality, z_eq, and the baryon/photon ratio: if a non-standard radiation density N_eff is allowed, increasing N_eff while matching the CMB peaks leads to a reduced baryon fraction and a lower relative BAO amplitude. We construct an observable for the relative area of the BAO feature from the galaxy correlation function (Eq.~8); from linear-theory models, we find that this is mainly sensitive to N_eff and quite insensitive to other cosmological parameters. More detailed work from N-body simulations will be needed to constrain the effects of non-linearity and scale-dependent galaxy bias on this observable.

Stream Flow Response to Skilled and Non-linear Bias Corrected GCM Precipitation Change in the Wami River Sub-basin, Tanzania

The reliability of stream flow projection under changing climate cannot be guaranteed if the General Circulation Model (GCM) used for the projection of future climate does not predict well its past climate. In this study stream flows in the Wami River sub-basin were simulated under changing climate by the skilled and non-linear bias corrected GCM using a physically based and semi distributed rainfall runoff model, SWAT. The SWAT model was setup using the terrain, land use, soil, precipitation and temperature data. The baseline water uses were used to naturalise stream flows and the SWAT model was calibrated and validated using the historical stream flows. In addressing future runoff projections the domestic, livestock, irrigation and industrial water demands in the subbasin were projected to the year 2039 using the current irrigation area growth rates, Tanzania vision 2025 and development plans for the Wami River sub-basin. The GCMs were incorporated in the hydrological model so as to factor in the effects of climate change. Precipitation was selected as the changing climatic variable for projection because runoff is very sensitive to precipitation as compared to other climatic variables like temperature. A total of twenty four GCMs from CMIP3 database representing twentieth century precipitation were interpolated into forty five sub-catchments in the subOriginal Research Article British Journal of Environment & Climate Change, 4(4): 389-408, 2014 390 basin and evaluated for their skills. The HADCM3 model was selected due to its highest skill score in predicting past climate. Then the HADCM3 precipitation signal of scenario A2, was corrected by Non-linear Bias Correction (NBC) in the forty five sub-catchments in the sub-basin and used to simulate future stream flow. The results of stream flow simulated using skilled and non-linear corrected HADCM3 precipitation signal shows that stream flow is projected to increase for the near term climatology (2010 – 2039).

Modelling baryon acoustic oscillations with perturbation theory and stochastic halo biasing

Abstract In this work we investigate the generation of mock halo catalogues based on perturbation theory and non-linear stochastic biasing with the novel patchy code. In particular, we use Augmented Lagrangian Perturbation Theory (ALPT) to generate a dark matter density field on a mesh starting from Gaussian fluctuations and to compute the peculiar velocity field. ALPT is based on a combination of second order LPT (2LPT) on large scales and the spherical collapse model on smaller scales. We account for the systematic deviation of perturbative approaches from N-body simulations together with halo biasing adopting an exponential bias model. We then account for stochastic biasing by defining three regimes: a low-, an intermediate- and a high-density regime, using a Poisson distribution in the intermediate regime and the negative binomial distribution – including an additional parameter – to model over-dispersion in the high-density regime. Since we focus in this study on massive haloes, we suppress the generation of haloes in the low-density regime. The various non-linear and stochastic biasing parameters, and density thresholds, are calibrated with the large BigMultiDark N-body simulation to match the power spectrum of the corresponding halo population. Our model effectively includes only five parameters, as they are additionally constrained by the halo number density. Our mock catalogues show power spectra, in both real- and redshift-space, which are compatible with N-body simulations within about 2 per cent up to k ∼ 1 h Mpc−1 at z = 0.577 for a sample of haloes with the typical Baryon Oscillation Spectroscopic Survey (BOSS) CMASS (constant stellar mass galaxy sample) galaxy number density. The corresponding correlation functions are compatible down to a few Mpc. We also find that neglecting over-dispersion in high-density regions produces power spectra with deviations of 10 per cent at k ∼ 0.4 h Mpc−1. These results indicate the need to account for an accurate statistical description of the galaxy clustering for precise studies of large-scale surveys.

Calibration verification of a low-cost method for MEMS accelerometers

This paper presents a new low-cost method for calibration of microelectromechanical system accelerometers. A guide way with low friction that can provide a one-directional linear transversal motion is used. For collecting data sets, the accelerometer is moved manually from one reference point to another, and this movement is measured. A function is developed that relates this movement to acceleration. To verify the proposed calibration method, a three-axis table is used to collect data sets and a least-squares algorithm is applied to find the appropriate function. With this low-cost method, the scale factor matrix, the sensitivity matrix, the non-linear scale factor matrix and bias vector are found.

Practical estimate of gradient nonlinearity for implementation of apparent diffusion coefficient bias correction

To describe an efficient procedure to empirically characterize gradient nonlinearity and correct for the corresponding apparent diffusion coefficient (ADC) bias on a clinical magnetic resonance imaging (MRI) scanner. Spatial nonlinearity scalars for individual gradient coils along superior and right directions were estimated via diffusion measurements of an isotropicic e-water phantom. Digital nonlinearity model from an independent scanner, described in the literature, was rescaled by system-specific scalars to approximate 3D bias correction maps. Correction efficacy was assessed by comparison to unbiased ADC values measured at isocenter. Empirically estimated nonlinearity scalars were confirmed by geometric distortion measurements of a regular grid phantom. The applied nonlinearity correction for arbitrarily oriented diffusion gradients reduced ADC bias from 20% down to 2% at clinically relevant offsets both for isotropic and anisotropic media. Identical performance was achieved using either corrected diffusion-weighted imaging (DWI) intensities or corrected b-values for each direction in brain and ice-water. Direction-average trace image correction was adequate only for isotropic medium. Empiric scalar adjustment of an independent gradient nonlinearity model adequately described DWI bias for a clinical scanner. Observed efficiency of implemented ADC bias correction quantitatively agreed with previous theoretical predictions and numerical simulations. The described procedure provides an independent benchmark for nonlinearity bias correction of clinical MRI scanners.

A fast maximum likelihood nonlinear feature transformation method for GMM–HMM speaker adaptation

We describe a novel maximum likelihood nonlinear feature bias compensation method for Gaussian mixture model–hidden Markov model (GMM–HMM) adaptation. Our approach exploits a single-hidden-layer neural network (SHLNN) that, similar to the extreme learning machine (ELM), uses randomly generated lower-layer weights and linear output units. Different from the conventional ELM, however, our approach optimizes the SHLNN parameters by maximizing the likelihood of observing the features given the speaker-independent GMM–HMM. We derive a novel and efficient learning algorithm for optimizing this criterion. We show, on a large vocabulary speech recognition task, that the proposed approach can cut the word error rate (WER) by 13% over the feature maximum likelihood linear regression (fMLLR) method with bias compensation, and can cut the WER by more than 5% over the fMLLR method with both bias and rotation transformations if applied on top of the fMLLR. Overall, it can reduce the WER by more than 27% over the speaker-independent system with 0.2 real-time adaptation time.

Nonlinear stochastic biasing of halos: Analysis of cosmologicalN-body simulations and perturbation theories

It is crucial to understand and model a behavior of galaxy biasing for future ambitious galaxy redshift surveys. Using 40 large cosmological N-body simulations for a standard LambdaCDM cosmology, we study the cross-correlation coefficient between matter and the halo density field, which is an indicator of the stochasticity of bias, over a wide redshift range 0\le z \le 3. The cross-correlation coefficient is important to extract information on the matter density field, e.g., by combining galaxy clustering and galaxy-galaxy lensing measurements. We compare the simulation results with integrated perturbation theory (iPT) proposed by one of the present authors and standard perturbation theory (SPT) combined with a phenomenological model of local bias. The cross-correlation coefficient derived from the iPT agrees with N-body simulation results down to r~15 (10) h^{-1}Mpc within 0.5 (1.0) % for all redshifts and halo masses we consider. The SPT with local bias does not explain complicated behaviors on quasilinear scales at low redshifts, while roughly reproduces the general behavior of the cross-correlation coefficient on fully nonlinear scales. The iPT is powerful to predict the cross-correlation coefficient down to quasilinear regimes with a high precision.

An accurate tool for the fast generation of dark matter halo catalogues

We present a new parallel implementation of the PINpointing Orbit Crossing-Collapsed HIerarchical Objects (PINOCCHIO) algorithm, a quick tool, based on Lagrangian Perturbation Theory, for the hierarchical build-up of Dark Matter halos in cosmological volumes. To assess its ability to predict halo correlations on large scales, we compare its results with those of an N-body simulation of a 3 Gpc/h box sampled with 2048^3 particles taken from the MICE suite, matching the same seeds for the initial conditions. Thanks to the FFTW libraries and to the relatively simple design, the code shows very good scaling properties. The CPU time required by PINOCCHIO is a tiny fraction (~1/2000) of that required by the MICE simulation. Varying some of PINOCCHIO numerical parameters allows one to produce a universal mass function that lies in the range allowed by published fits, although it underestimates the MICE mass function of FoF halos in the high mass tail. We compare the matter-halo and the halo-halo power spectra with those of the MICE simulation and find that these 2-point statistics are well recovered on large scales. In particular, when catalogs are matched in number density, agreement within ten per cent is achieved for the halo power spectrum. At scales k>0.1 h/Mpc, the inaccuracy of the Zel'dovich approximation in locating halo positions causes an underestimate of the power spectrum that can be modeled as a Gaussian factor with a damping scale of d=3 Mpc/h at z=0, decreasing at higher redshift. Finally, a remarkable match is obtained for the reduced halo bispectrum, showing a good description of nonlinear halo bias. Our results demonstrate the potential of PINOCCHIO as an accurate and flexible tool for generating large ensembles of mock galaxy surveys, with interesting applications for the analysis of large galaxy redshift surveys.

The WiggleZ Dark Energy Survey: constraining galaxy bias and cosmic growth with three-point correlation functions

Higher-order statistics are a useful and complementary tool for measuring the clustering of galaxies, containing information on the non-gaussian evolution and morphology of large-scale structure in the Universe. In this work we present measurements of the three-point correlation function (3PCF) for 187,000 galaxies in the WiggleZ spectroscopic galaxy survey. We explore the WiggleZ 3PCF scale and shape dependence at three different epochs z=0.35, 0.55 and 0.68, the highest redshifts where these measurements have been made to date. Using N-body simulations to predict the clustering of dark matter, we constrain the linear and non-linear bias parameters of WiggleZ galaxies with respect to dark matter, and marginalise over them to obtain constraints on sigma_8(z), the variance of perturbations on a scale of 8 Mpc/h and its evolution with redshift. These measurements of sigma_8(z), which have 10-20% accuracies, are consistent with the predictions of the LCDM concordance cosmology and test this model in a new way.

Analysis and correction of gradient nonlinearity bias in apparent diffusion coefficient measurements

Gradient nonlinearity of MRI systems leads to spatially dependent b-values and consequently high non-uniformity errors (10-20%) in apparent diffusion coefficient (ADC) measurements over clinically relevant field-of-views. This work seeks practical correction procedure that effectively reduces observed ADC bias for media of arbitrary anisotropy in the fewest measurements. All-inclusive bias analysis considers spatial and time-domain cross-terms for diffusion and imaging gradients. The proposed correction is based on rotation of the gradient nonlinearity tensor into the diffusion gradient frame where spatial bias of b-matrix can be approximated by its Euclidean norm. Correction efficiency of the proposed procedure is numerically evaluated for a range of model diffusion tensor anisotropies and orientations. Spatial dependence of nonlinearity correction terms accounts for the bulk (75-95%) of ADC bias for FA = 0.3-0.9. Residual ADC non-uniformity errors are amplified for anisotropic diffusion. This approximation obviates need for full diffusion tensor measurement and diagonalization to derive a corrected ADC. Practical scenarios are outlined for implementation of the correction on clinical MRI systems. The proposed simplified correction algorithm appears sufficient to control ADC non-uniformity errors in clinical studies using three orthogonal diffusion measurements. The most efficient reduction of ADC bias for anisotropic medium is achieved with non-lab-based diffusion gradients.

Cosmological parameter constraints from galaxy–galaxy lensing and galaxy clustering with the SDSS DR7

Recent studies have shown that the cross-correlation coefficient between galaxies and dark matter is very close to unity on scales outside a few virial radii of galaxy halos, independent of the details of how galaxies populate dark matter halos. This finding makes it possible to determine the dark matter clustering from measurements of galaxy-galaxy weak lensing and galaxy clustering. We present new cosmological parameter constraints based on large-scale measurements of spectroscopic galaxy samples from the Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7). We generalise the approach of Baldauf et al. (2010) to remove small scale information (below 2 and 4 Mpc/h for lensing and clustering measurements, respectively), where the cross-correlation coefficient differs from unity. We derive constraints for three galaxy samples covering 7131 sq. deg., containing 69150, 62150, and 35088 galaxies with mean redshifts of 0.11, 0.28, and 0.40. We clearly detect scale-dependent galaxy bias for the more luminous galaxy samples, at a level consistent with theoretical expectations. When we vary both \sigma_8 and \Omega_m (and marginalise over non-linear galaxy bias) in a flat LCDM model, the best-constrained quantity is \sigma_8 (\Omega_m/0.25)^{0.57}=0.80 +/- 0.05 (1-sigma, stat. + sys.), where statistical and systematic errors have comparable contributions, and we fixed n_s=0.96 and h=0.7. These strong constraints on the matter clustering suggest that this method is competitive with cosmic shear in current data, while having very complementary and in some ways less serious systematics. We therefore expect that this method will play a prominent role in future weak lensing surveys. When we combine these data with WMAP7 CMB data, constraints on \sigma_8, \Omega_m, H_0, w_{de} and \sum m_{\nu} become 30--80 per cent tighter than with CMB data alone, since our data break several parameter degeneracies.

Bias dependent NO2 sensitivity of SnO2 thin films at room temperature

Abstract Amorphous granular SnO2 thin films were investigated from a standpoint of an NO2 gas sensor working at room temperature. The films were deposited using pulsed laser deposition method with substrate at room temperature and ∼90 nm thick SnO2 films with amorphous structure were obtained as a result. SnO2 films deposited on Pt electrode substrates formed a sensor structure that showed response Iair/Igas to 4 ppm NO2 up to ∼8000. I–V characteristics of the sensor structure were described by the power law dependence, whereas the power indexes were different for measurements in pure air and in the presence of NO2. As a result, the sensor response was highly dependent on bias voltage between the sensor electrodes. It was demonstrated that the nonlinear electrical characteristics and bias dependent gas sensitivity were the inherent properties of thin films and the contacts were ohmic.

Probing Electric Fields in Polymer Tandem and Single Junction Cells with Electroabsorption Spectroscopy

For polymer tandem solar cells it is not easy to determine the individual internal electric fields across each of the two individual photoactive layers because the intermediate contact is often buried in the device stack and cannot be contacted. Here we explore electroabsorption (EA) spectroscopy as a possible tool to investigate these electric fields in polymer tandem solar cells. EA spectroscopy is a noninvasive electro-optical technique that can be used to probe internal electrical fields in organic thin film devices. The tandem cell investigated consists of a wide band gap front cell and a small band gap back cell, connected via an intermediate recombination contact. We demonstrate that the EA spectra of the individual subcells and their dependence on applied external bias can be distinguished in the EA spectrum of the tandem cells but that a quantitative interpretation of the EA spectra in terms of individual internal fields is hampered by a nonlinear bias dependence of the EA intensity on the applie...

Material selection considerations for coaxial, ferrimagnetic-based nonlinear transmission lines

The growing need for solid-state high power microwave sources has renewed interest in nonlinear transmission lines (NLTLs). This article focuses specifically on ferrimagnetic-based NLTLs in a coaxial geometry. Achieved peak powers exceed 30 MW at 30 kV incident voltage with rf power reaching 4.8 MW peak and pulse lengths ranging from 1–5 ns. The presented NLTL operates in S-band with the capability to tune the center frequency of oscillation over the entire 2–4 GHz band and bandwidths of approximately 30%, placing the NLTL into the ultra-wideband–mesoband category of microwave sources. Several nonlinear materials were tested and the relationship between NLTL performance and material parameters is discussed. In particular, the importance of the material's ferromagnetic resonance linewidth and its relationship to microwave generation is highlighted. For a specific nonlinear material, it is shown that an optimum relation between incident pulse magnitude and static bias magnitude exists. By varying the nonlinear material's bias magnetic field, active delay control was demonstrated.

Bias Correction of Regional Climate Model Simulations in a Region of Complex Orography

AbstractThis study presents a method to correct regional climate model (RCM) outputs using observations from automatic weather stations. The correction applies a nonlinear procedure, which recently appeared in the literature, to both precipitation and temperature on a monthly basis in a region of complex orography. To assess the temporal stability of such a correction, the correcting parameters of each variable are investigated using different time periods within the observational record. The RCM simulations used in this study to evaluate the bias-correction method are the publicly available “Reg-CM3” experiments from the Ensemble-Based Predictions of Climate Changes and Their Impacts (ENSEMBLES) project. They provide daily precipitation and temperature time series on a raster with spatial resolution of 0.22°. The analysis is performed in the Rhone catchment, located in southwestern Switzerland and characterized by highly complex orography. The results show that the nonlinear bias correction increases dramatically the accuracy not only of the RCM mean daily precipitation and temperature but also of values across the entire domain of the probability distribution. Moreover, the correction parameters seem to be reasonably independent from the sample used for their calibration, especially in the case of temperature. The good performance of the method over the considered mountainous region during the evaluation period points to the suitability of this technique for correcting RCM biases regardless of the stationarity of the climate and, therefore, also for future climate and in regions characterized by marked orography.

Convolution Lagrangian perturbation theory for biased tracers

We present a new formulation of Lagrangian perturbation theory which allows accurate predictions of the real- and redshift-space correlation functions of the mass field and dark matter halos. Our formulation involves a non-perturbative resummation of Lagrangian perturbation theory and indeed can be viewed as a partial resummation of the formalism of Matsubara (2008a,b) in which we keep exponentiated all of the terms which tend to a constant at large separation. One of the key features of our method is that we naturally recover the Zel'dovich approximation as the lowest order of our expansion for the matter correlation function. We compare our results against a suite of N-body simulations and obtain good agreement for the correlation functions in real-space and for the monopole correlation function in redshift space. The agreement becomes worse for higher multipole moments of the redshift-space, halo correlation function. Our formalism naturally includes non-linear bias and explains the strong bias-dependence of the multipole moments of the redshift-space correlation function seen in N-body simulations.

The 21-cm radiation from minihaloes as a probe of small primordial non-Gaussianity

Abstract We present a new probe of primordial non-Gaussianity via the 21-cm radiation from minihaloes at high redshifts. We calculate the fluctuations in the brightness temperature (measured against the cosmic microwave background) of the 21-cm background from minihaloes containing H i at redshift ∼6–20, and find a significant enhancement due to small non-Gaussianity with amplitude fNL ≲ 1. This enhancement can be attributed to the non-linear bias which is strongly increased in the presence of non-Gaussianity. We show that our results are robust against changes in the assumed mass function and some physical aspects of minihalo formation, but are nevertheless sensitive to the presence of strong radiation sources within or around the minihaloes. Our findings are relevant for constraining and searching for small primordial non-Gaussianity with upcoming radio telescopes such as Low-Frequency Array (LOFAR) and Square Kilometre Array (SKA).

On combining galaxy clustering and weak lensing to unveil galaxy biasing via the halo model

Galaxies are (biased) tracers of the dark matter in theUniverse. This mapping can be conveniently divided into two parts: the connection between galaxies and dark matter haloes (halo occupation statistics) and the relation between haloes and the underlying matter distribution. The former is the focus of this paper in which we formulate the concept of non-linear and stochastic galaxy biasing in the framework of halo occupation statistics. Using two-point statistics in projection, we define the galaxy bias function, bg(rp), and the galaxy–dark matter cross-correlation function, , where rp is the projected distance. We use the analytical halo model to predict how the scale dependence of is the projected distance. We use the analytical halo model to predict how the scale dependence of bg and , over the range 0.1 ≲ rp ≲ 30 h−1 Mpc, depends on the non-linearity and stochasticity in halo occupation models. In particular, we quantify the effect due to the presence of central galaxies, the assumption for the radial distribution of satellite galaxies, the richness of the halo and the Poisson character of the probability to have a certain number of satellite galaxies in the halo of a certain mass. Overall, brighter galaxies reveal a stronger scale dependence, and out to a larger radius. In real space, we find that galaxy bias becomes scale independent, with Mpc, depending on luminosity. However, galaxy bias is scale dependent out to much larger radii when one uses the projected quantities defined in this paper. These projected bias functions have the advantage that they are more easily accessible observationally and that their scale dependence carries a wealth of information regarding the properties of galaxy biasing. To observationally constrain the parameters of the halo model and to unveil the origin of galaxy biasing, we propose the use of the bias function . This function is obtained via a combination of weak gravitational lensing and galaxy clustering, and it can be measured using existing and forthcoming imaging and spectroscopic galaxy surveys.