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Yu Yu

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Published work

23 published item(s)

preprint2026arXiv

On the (In-)Security of the Shuffling Defense in the Transformer Secure Inference

For Transformer models, cryptographically secure inference ensures that the client learns only the final output, while the server learns nothing about the client's input. However, securely computing nonlinear layers remains a major efficiency bottleneck due to the substantial communication rounds and data transmission required. To address this issue, prior works reveal intermediate activations to the client, allowing nonlinear operations to be computed in plaintext. Although this approach significantly improves efficiency, exposing activations enables adversaries to extract model weights. To mitigate this risk, existing works employ a shuffling defense that reveals only randomly permuted activations to the client. In this work, we show that the shuffling defense is not as robust as previously claimed. We propose an attack that aligns differently shuffled activations to a common permutation and subsequently exploits them to extract model weights. Experiments on Pythia-70m and GPT-2 demonstrate that the proposed attack can align shuffled activations with mean squared errors ranging from $10^{-9}$ to $10^{-6}$. With a query cost of approximately \$1, the adversary can recover model weights with L1-norm differences ranging from $10^{-4}$ to $10^{-2}$ compared to the oracle weights.

preprint2022arXiv

Sensitivity tests of cosmic velocity fields to massive neutrinos

We investigate impacts of massive neutrinos on the cosmic velocity fields, employing high-resolution cosmological $N$-body simulations provided by the information-optimized CUBE code, where cosmic neutrinos are evolved using collisionless hydrodynamics and their perturbations can be accurately resolved. In this study we focus, for the first time, on the analysis of massive-neutrino induced suppression effects in various cosmic velocity field components of velocity magnitude, divergence, vorticity and dispersion. By varying the neutrino mass sum $M_ν$ from 0 -- 0.4 eV, the simulations show that, the power spectra of vorticity -- exclusively sourced by non-linear structure formation that is affected by massive neutrinos significantly -- is very sensitive to the mass sum, which potentially provide novel signatures in detecting massive neutrinos. Furthermore, using the chi-square statistic, we quantitatively test the sensitivity of the density and velocity power spectra to the neutrino mass sum. Indeed, we find that, the vorticity spectrum has the highest sensitivity, and the null hypothesis of massless neutrinos is incompatible with both vorticity and divergence spectra from $M_ν=0.1$ eV at high significance ($p$-value $= 0.03$ and $0.07$, respectively). These results demonstrate clearly the importance of peculiar velocity field measurements, in particular of vorticity and divergence components, in determination of neutrino mass and mass hierarchy.

preprint2022arXiv

Strong Conformity and Assembly Bias: Towards a Physical Understanding of the Galaxy-Halo Connection in SDSS Clusters

Understanding the physical connection between cluster galaxies and massive haloes is key to mitigating systematic uncertainties in next-generation cluster cosmology. We develop a novel method to infer the level of conformity between the stellar mass of the brightest central galaxies~(BCGs) $M_*^{BCG}$ and the satellite richness $λ$, defined as their correlation coefficient $ρ_{cc}$ at fixed halo mass, using the abundance and weak lensing of SDSS clusters as functions of $M_*^{BCG}$ and $λ$. We detect a halo mass-dependent conformity as $ρ_{cc}{=}0.60{+}0.08\ln(M_h/3{\times}10^{14}M_{\odot}/h)$. The strong conformity successfully resolves the "halo mass equality" conundrum discovered in Zu et al. 2021 -- when split by $M_*^{BCG}$ at fixed $λ$, the low and high-$M_*^{BCG}$ clusters have the same average halo mass despite having a $0.34$ dex discrepancy in average $M_*^{BCG}$. On top of the best-fitting conformity model, we develop a cluster assembly bias~(AB) prescription calibrated against the CosmicGrowth simulation, and build a conformity+AB model for the cluster weak lensing measurements. Our model predicts that with a ${\sim}20\%$ lower halo concentration $c$, the low-$M_*^{BCG}$ clusters are ${\sim}10\%$ more biased than the high-$M_*^{BCG}$ systems, in excellent agreement with the observations. We also show that the observed conformity and assembly bias are unlikely due to projection effects. Finally, we build a toy model to argue that while the early-time BCG-halo co-evolution drives the $M_*^{BCG}$-$c$ correlation, the late-time dry merger-induced BCG growth naturally produces the $M_*^{BCG}$-$λ$ conformity despite the well-known anti-correlation between $λ$ and $c$. Our method paves the path towards simultaneously constraining cosmology and cluster formation with future cluster surveys.

preprint2022arXiv

The DESI $N$-body Simulation Project -- II. Suppressing sample variance with fast simulations

Dark Energy Spectroscopic Instrument (DESI) will construct a large and precise three-dimensional map of our Universe. The survey effective volume reaches $\sim20\Gpchcube$. It is a great challenge to prepare high-resolution simulations with a much larger volume for validating the DESI analysis pipelines. \textsc{AbacusSummit} is a suite of high-resolution dark-matter-only simulations designed for this purpose, with $200\Gpchcube$ (10 times DESI volume) for the base cosmology. However, further efforts need to be done to provide a more precise analysis of the data and to cover also other cosmologies. Recently, the CARPool method was proposed to use paired accurate and approximate simulations to achieve high statistical precision with a limited number of high-resolution simulations. Relying on this technique, we propose to use fast quasi-$N$-body solvers combined with accurate simulations to produce accurate summary statistics. This enables us to obtain 100 times smaller variance than the expected DESI statistical variance at the scales we are interested in, e.g. $k < 0.3\hMpc$ for the halo power spectrum. In addition, it can significantly suppress the sample variance of the halo bispectrum. We further generalize the method for other cosmologies with only one realization in \textsc{AbacusSummit} suite to extend the effective volume $\sim 20$ times. In summary, our proposed strategy of combining high-fidelity simulations with fast approximate gravity solvers and a series of variance suppression techniques sets the path for a robust cosmological analysis of galaxy survey data.

preprint2021arXiv

Authentication of Metropolitan Quantum Key Distribution Network with Post-quantum Cryptography

Quantum key distribution (QKD) provides information theoretically secures key exchange requiring authentication of the classic data processing channel via pre-sharing of symmetric private keys. In previous studies, the lattice-based post-quantum digital signature algorithm Aigis-Sig, combined with public-key infrastructure (PKI) was used to achieve high-efficiency quantum security authentication of QKD, and its advantages in simplifying the MAN network structure and new user entry were demonstrated. This experiment further integrates the PQC algorithm into the commercial QKD system, the Jinan field metropolitan QKD network comprised of 14 user nodes and 5 optical switching nodes. The feasibility, effectiveness and stability of the post-quantum cryptography (PQC) algorithm and advantages of replacing trusted relays with optical switching brought by PQC authentication large-scale metropolitan area QKD network were verified. QKD with PQC authentication has potential in quantum-secure communications, specifically in metropolitan QKD networks.

preprint2021arXiv

Numerical investigation of non-Gaussianities in the phase and modulus of density Fourier modes

We numerically investigate non-Gaussianities in the late-time cosmological density field in Fourier space. We explore various statistics, including the two-point and three-point probability distribution function (PDF) of phase and modulus, and two \& three-point correlation function of of phase and modulus. We detect significant non-Gaussianity for certain configurations. We compare the simulation results with the theoretical expansion series of \citet{2007ApJS..170....1M}. We find that the $\mathcal{O}(V^{-1/2})$ order term alone is sufficiently accurate to describe all the measured non-Gaussianities in not only the PDFs, but also the correlations. We also numerically find that the phase-modulus cross-correlation contributes $\sim 50\%$ to the bispectrum, further verifying the accuracy of the $\mathcal{O}(V^{-1/2})$ order prediction. This work demonstrates that non-Gaussianity of the cosmic density field is simpler in Fourier space, and may facilitate the data analysis in the era of precision cosmology.

preprint2021arXiv

The DESI $N$-body Simulation Project I: Testing the Robustness of Simulations for the DESI Dark Time Survey

Analysis of large galaxy surveys requires confidence in the robustness of numerical simulation methods. The simulations are used to construct mock galaxy catalogs to validate data analysis pipelines and identify potential systematics. We compare three $N$-body simulation codes, ABACUS, GADGET, and SWIFT, to investigate the regimes in which their results agree. We run $N$-body simulations at three different mass resolutions, $6.25\times10^{8}$, $2.11\times10^{9}$, and $5.00\times10^{9}~h^{-1}$M$_{\odot}$, matching phases to reduce the noise within the comparisons. We find systematic errors in the halo clustering between different codes are smaller than the DESI statistical error for $s > 20\, h^{-1}$Mpc in the correlation function in redshift space. Through the resolution comparison we find that simulations run with a mass resolution of $2.1\times10^{9}~h^{-1}$M$_{\odot}$ are sufficiently converged for systematic effects in the halo clustering to be smaller than the DESI statistical error at scales larger than $20 \, h^{-1}$Mpc. These findings show that the simulations are robust for extracting cosmological information from large scales which is the key goal of the DESI survey. Comparing matter power spectra, we find the codes agree to within 1% for $k \leq 10~h$Mpc$^{-1}$. We also run a comparison of three initial condition generation codes and find good agreement. In addition, we include a quasi-$N$-body code, FastPM, since we plan use it for certain DESI analyses. The impact of the halo definition and galaxy-halo relation will be presented in a follow up study.

preprint2020arXiv

A Differential Approach for Gaze Estimation

Non-invasive gaze estimation methods usually regress gaze directions directly from a single face or eye image. However, due to important variabilities in eye shapes and inner eye structures amongst individuals, universal models obtain limited accuracies and their output usually exhibit high variance as well as biases which are subject dependent. Therefore, increasing accuracy is usually done through calibration, allowing gaze predictions for a subject to be mapped to his/her actual gaze. In this paper, we introduce a novel image differential method for gaze estimation. We propose to directly train a differential convolutional neural network to predict the gaze differences between two eye input images of the same subject. Then, given a set of subject specific calibration images, we can use the inferred differences to predict the gaze direction of a novel eye sample. The assumption is that by allowing the comparison between two eye images, annoyance factors (alignment, eyelid closing, illumination perturbations) which usually plague single image prediction methods can be much reduced, allowing better prediction altogether. Experiments on 3 public datasets validate our approach which constantly outperforms state-of-the-art methods even when using only one calibration sample or when the latter methods are followed by subject specific gaze adaptation.

preprint2020arXiv

Multimode silicon photonics using on-chip geometrical-optics

On-chip optical interconnect has been widely accepted as a promising technology to realize future large-scale multiprocessors. Mode-division multiplexing (MDM) provides a new degree of freedom for optical interconnects to dramatically increase the link capacity. Present on-chip multimode devices are based on traditional wave-optics. Although large amount of computation and optimization are adopted to support more modes, mode-independent manipulation is still hard to be achieved due to severe mode dispersion. Here, we propose a universal solution to standardize the design of fundamental multimode building blocks, by introducing a geometrical-optics-like concept adopting waveguide width larger than the working wavelength. The proposed solution can tackle a group of modes at the same time with very simple processes, avoiding demultiplexing procedure and ensuring compact footprint. Compare to conventional schemes, it is scalable to larger mode channels without increasing the complexity and whole footprint. As a proof of concept, we demonstrate a set of multimode building blocks including crossing, bend, coupler and switches. Low losses of multimode waveguide crossing and bend are achieved, as well as ultra-low power consumption of the multimode switch is realized since it enables reconfigurable routing for a group of modes simultaneously. Our work promotes the multimode photonics research and makes the MDM technique more practical.

preprint2020arXiv

Neutrino effects on the morphology of cosmic large-scale structure

In this work, we propose a powerful probe of neutrino effects on the large-scale structure (LSS) of the Universe, i.e., Minkowski functionals (MFs). The morphology of LSS can be fully described by four MFs. This tool, with strong statistical power, is robust to various systematics and can comprehensively probe all orders of N-point statistics. By using a pair of high-resolution N-body simulations, for the first time, we comprehensively studied the subtle neutrino effects on the morphology of LSS. For an ideal LSS survey of volume $\sim1.73$ Gpc$^3$/$h^3$, neutrino signals are mainly detected from void regions with a significant level up to $\thicksim 10σ$ and $\thicksim 300σ$ for CDM and total matter density fields, respectively. This demonstrates its enormous potential for much improving the neutrino mass constraint in the data analysis of up-coming ambitious LSS surveys.

preprint2020arXiv

PrivPy: Enabling Scalable and General Privacy-Preserving Machine Learning

We introduce PrivPy, a practical privacy-preserving collaborative computation framework, especially optimized for machine learning tasks. PrivPy provides an easy-to-use and highly compatible Python programming front-end which supports high-level array operations and different secure computation engines to allow for security assumptions and performance trade-offs. With PrivPy, programmers can write modern machine learning algorithms conveniently and efficiently in Python. We also design and implement a new efficient computation engine, with which people can use competing cloud providers to efficiently perform general arithmetics over real numbers. We demonstrate the usability and scalability of PrivPy using common machine learning models (e.g. logistic regression and convolutional neural networks) and real-world datasets (including a 5000-by-1-million matrix).

preprint2020arXiv

Probing Primordial Chirality with Galaxy Spins

Chiral symmetry is maximally violated in weak interactions, and such microscopic asymmetries in the early Universe might leave observable imprints on astrophysical scales without violating the cosmological principle. In this Letter, we propose a helicity measurement to detect primordial chiral violation. We point out that observations of halo-galaxy angular momentum directions (spins), which are frozen in during the galaxy formation process, provide a fossil chiral observable. From the clustering mode of large scale structure of the Universe, we construct a spin mode in Lagrangian space and show in simulations that it is a good probe of halo-galaxy spins. In standard model, a strong symmetric correlation between the left and right helical components of this spin mode and galaxy spins is expected. Measurements of these correlations will be sensitive to chiral breaking, providing a direct test of chiral symmetry breaking in the early Universe.

preprint2020arXiv

The copula of the cosmological matter density field is non-Gaussian

Non-Gaussianity of the cosmological matter density field can be largely reduced by a local Gaussianization transformation (and its approximations such as the logrithmic transformation). Such behavior can be recasted as the Gaussian copula hypothesis, and has been verified to very high accuracy at two-point level. On the other hand, statistically significant non-Gaussianities in the Gaussianized field have been detected in simulations. We point out that, this apparent inconsistency is caused by the very limited degrees of freedom in the copula function, which make it misleading as a diagnosis of residual non-Gaussianity in the Gaussianized field. Using the copula density, we highlight the departure from Gaussianity. We further quantify its impact in the predicted n-point correlation functions. We explore a remedy of the Gaussian copula hypothesis, which alleviates but not completely solves the above problems.

preprint2020arXiv

Unsupervised Representation Learning for Gaze Estimation

Although automatic gaze estimation is very important to a large variety of application areas, it is difficult to train accurate and robust gaze models, in great part due to the difficulty in collecting large and diverse data (annotating 3D gaze is expensive and existing datasets use different setups). To address this issue, our main contribution in this paper is to propose an effective approach to learn a low dimensional gaze representation without gaze annotations, which to the best of our best knowledge, is the first work to do so. The main idea is to rely on a gaze redirection network and use the gaze representation difference of the input and target images (of the redirection network) as the redirection variable. A redirection loss in image domain allows the joint training of both the redirection network and the gaze representation network. In addition, we propose a warping field regularization which not only provides an explicit physical meaning to the gaze representations but also avoids redirection distortions. Promising results on few-shot gaze estimation (competitive results can be achieved with as few as <= 100 calibration samples), cross-dataset gaze estimation, gaze network pretraining, and another task (head pose estimation) demonstrate the validity of our framework.

preprint2019arXiv

Nonlinear Reconstruction of the Velocity Field

We propose a new velocity reconstruction method based on the displacement estimation by recently developed methods. The velocity is first reconstructed by transfer functions in Lagrangian space and then mapped into Eulerian space. High resolution simulations are used to test the performance. We find that the new reconstruction method outperforms the standard velocity reconstruction in the sense of better cross-correlation coefficient, less velocity misalignment and smaller amplitude difference. We conclude that this new method has the potential to improve the large-scale structure sciences involving a velocity reconstruction, such as kinetic Sunyaev-Zel'dovich measurement and supernova cosmology.

preprint2016arXiv

Fast generation of weak lensing maps by the inverse-Gaussianization method

To take full advantage of the unprecedented power of upcoming weak lensing surveys, understanding the noise, such as cosmic variance and geometry/mask effects, is as important as understanding the signal itself. Accurately quantifying the noise requires a large number of statistically independent mocks for a variety of cosmologies. This is impractical for weak lensing simulations, which are costly for simultaneous requirements of large box size (to cover a significant fraction of the past light cone) and high resolution (to robustly probe the small scale where most lensing signal resides). Therefore fast mock generation methods are desired and are under intensive investigation. We propose a new fast weak lensing map generation method, named the inverse-Gaussianization method, based on the finding that a lensing convergence field can be Gaussianized to excellent accuracy by a local transformation [Yu et al, Phys. Rev. D 84, 023523 (2011)]. Given a simulation, it enables us to produce as many as infinite statistically independent lensing maps as fast as producing the simulation initial conditions. The proposed method is tested against simulations for each tomography bin centered at lens redshift $z \sim 0.5$, 1, and 2, with various statistics. We find that the lensing maps generated by our method have reasonably accurate power spectra, bispectra, and power spectrum covariance matrix. Therefore, it will be useful for weak lensing surveys to generate realistic mocks. As an example of application, we measure the probability distribution function of the lensing power spectrum, from 16384 lensing maps produced by the inverse-Gaussianization method.

preprint2016arXiv

Measurement of Neutrino Masses from Relative Velocities

We present a new technique to measure neutrino masses using their flow field relative to dark matter. Present day streaming motions of neutrinos relative to dark matter and baryons are several hundred km/s, comparable with their thermal velocity dispersion. This results in a unique dipole anisotropic distortion of the matter-neutrino cross power spectrum, which is observable through the dipole distortion in the cross correlation of different galaxy populations. Such a dipole vanishes if not for this relative velocity and so it is a clean signature for neutrino mass. We estimate the size of this effect and find that current and future galaxy surveys may be sensitive to these signature distortions.

preprint2015arXiv

Kriging Interpolating Cosmic Velocity Field

[abridged] Volume-weighted statistics of large scale peculiar velocity is preferred by peculiar velocity cosmology, since it is free of uncertainties of galaxy density bias entangled in mass-weighted statistics. However, measuring the volume-weighted velocity statistics from galaxy (halo/simulation particle) velocity data is challenging. For the first time, we apply the Kriging interpolation to obtain the volume-weighted velocity field. Kriging is a minimum variance estimator. It predicts the most likely velocity for each place based on the velocity at other places. We test the performance of Kriging quantified by the E-mode velocity power spectrum from simulations. Dependences on the variogram prior used in Kriging, the number $n_k$ of the nearby particles to interpolate and the density $n_P$ of the observed sample are investigated. First, we find that Kriging induces $1\%$ and $3\%$ systematics at $k\sim 0.1h{\rm Mpc}^{-1}$ when $n_P\sim 6\times 10^{-2} ({\rm Mpc}/h)^{-3}$ and $n_P\sim 6\times 10^{-3} ({\rm Mpc}/h)^{-3}$, respectively. The deviation increases for decreasing $n_P$ and increasing $k$. When $n_P\lesssim 6\times 10^{-4} ({\rm Mpc}/h)^{-3}$, a smoothing effect dominates small scales, causing significant underestimation of the velocity power spectrum. Second, increasing $n_k$ helps to recover small scale power. However, for $n_P\lesssim 6\times 10^{-4} ({\rm Mpc}/h)^{-3}$ cases, the recovery is limited. Finally, Kriging is more sensitive to the variogram prior for lower sample density. The most straightforward application of Kriging on the cosmic velocity field does not show obvious advantages over the nearest-particle method (Zheng et al. 2013) and could not be directly applied to cosmology so far. However, whether potential improvements may be achieved by more delicate versions of Kriging is worth further investigation.

preprint2015arXiv

The source-lens clustering effect in the context of lensing tomography and its self-calibration

Cosmic shear can only be measured where there are galaxies. This source-lens clustering (SLC) effect has two sources, intrinsic source clustering and cosmic magnification (magnification/size bias). Lensing tomography can suppress the former. However, this reduction is limited by the existence of photo-z error and nonzero redshift bin width. Furthermore, SLC induced by cosmic magnification cannot be reduced by lensing tomography. Through N-body simulations, we quantify the impact of SLC on the lensing power spectrum in the context of lensing tomography. We consider both the standard estimator and the pixel-based estimator. We find that none of them can satisfactorily handle both sources of SLC. (1) For the standard estimator, SLC induced by both sources can bias the lensing power spectrum by O(1)-O(10)%. Intrinsic source clustering also increases statistical uncertainties in the measured lensing power spectrum. However, the standard estimator suppresses intrinsic source clustering in the cross-spectrum. (2) In contrast, the pixel-based estimator suppresses SLC through cosmic magnification. However, it fails to suppress SLC through intrinsic source clustering and the measured lensing power spectrum can be biased low by O(1)-O(10)%. In short, for typical photo-z errors (sigma_z/(1+z)=0.05) and photo-z bin sizes (Delta_z^P=0.2), SLC alters the lensing E-mode power spectrum by 1-10%, with ell~10^3$ and z_s~1 being of particular interest to weak lensing cosmology. Therefore the SLC is a severe systematic for cosmology in Stage-IV lensing surveys. We present useful scaling relations to self-calibrate the SLC effect.

preprint2014arXiv

Satellite Alignment: I. Distribution of Substructures and Their Dependence On Assembly History From N-Body Simulations

Observations have shown that the spatial distribution of satellite galaxies is not random, but aligned with the major axes of central galaxies. This alignment is dependent on galaxy properties, such that red satellites are more strongly aligned than blue satellites. Theoretical work done to interpret this phenomena has found that it is due to the non-spherical nature of dark matter halos. However, most studies over-predict the alignment signal under the assumption that the central galaxy shape follows the shape of the host halo. It is also not clear whether the color dependence of alignment is due to an assembly bias or an evolution effect. In this paper we study these problems using a cosmological N-body simulation. Subhalos are used to trace the positions of satellite galaxies. It is found that the shape of dark matter halos are mis-aligned at different radii. If the central galaxy shares the same shape as the inner host halo, then the alignment effect is weaker and agrees with observational data. However, it predicts almost no dependence of alignment on the color of satellite galaxies, though the late accreted subhalos show stronger alignment with the outer layer of the host halo than their early accreted counterparts. We find that this is due to the limitation of pure N-body simulations that satellites galaxies without associated subhalos ('orphan galaxies') are not resolved. These orphan (mostly red) satellites often reside in the inner region of host halos and should follow the shape of the host halo in the inner region.

preprint2013arXiv

Weak lensing reconstruction through cosmic magnification. II. Improved power spectrum determination and map-making

The existence of galaxy intrinsic clustering severely hampers the weak lensing reconstruction from cosmic magnification. In paper I \citep{Yang2011}, we proposed a minimal variance estimator to overcome this problem. By utilizing the different dependences of cosmic magnification and galaxy intrinsic clustering on galaxy flux, we demonstrated that the otherwise overwhelming galaxy intrinsic clustering can be significantly suppressed such that lensing maps can be reconstructed with promising accuracy. This procedure relies heavily on the accuracy of determining the galaxy bias from the same data. Paper I adopts an iterative approach, which degrades toward high redshift. The current paper presents an alternative method, improving over paper I. We prove that the measured galaxy clustering between flux bins allows for simultaneous determination of the lensing power spectrum and the flux dependence of galaxy bias, at this redshift bin. Comparing to paper I, the new approach is not only more straightforward, but also more robust. It identifies an ambiguity in determining the galaxy bias and further discovers a mathematically robust way to suppress this ambiguity to non-negligible level ($\sim 0.1%$). The accurately determined galaxy bias can then be applied to the minimal variance estimator proposed in paper I to improve the lensing map-making. The gain at high redshift is significant. These maps can be used to measure other statistics, such as cluster finding and peak statistics. Furthermore, by including galaxy clustering measurement between different redshift bins, we can also determine the lensing cross power spectrum between these bins, up to a small and correctable multiplicative factor.

preprint2012arXiv

Gaussianizing the non-Gaussian lensing convergence field II: the applicability to noisy data

In paper I (Yu et al. [1]), we show through N-body simulation that a local monotonic Gaussian transformation can significantly reduce non-Gaussianity in a noise-free lensing convergence field. This makes the Gaussianization a promising theoretical tool to understand high-order lensing statistics. Here we present a study of its applicability in lensing data analysis, in particular when shape measurement noise is presented in lensing convergence maps. (i) We find that shape measurement noise significantly degrades the Gaussianization performance and the degradation increases for shallower surveys. (ii) The Wiener filter is efficient in reducing the impact of shape measurement noise. The Gaussianization of the Wiener-filtered lensing maps is able to suppress skewness, kurtosis, and the 5th- and 6th-order cumulants by a factor of 10 or more. It also works efficiently to reduce the bispectrum to zero.

preprint2011arXiv

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 $κ$. It performs a local monotonic transformation $κ\rightarrow y$ 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 $κ$ 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.