arXiv subjects

Tianqing Zhang

Publications and source records attributed to Tianqing Zhang.

At least 37 records · Page 2Linked to original sources

arXiv2025

Modelling Galaxy Clustering and Tomographic Galaxy-Galaxy Lensing with HSC Y3 and SDSS using the Point-Mass Correction Model and Redshift Self-Calibration

The combination of galaxy-galaxy weak lensing and galaxy clustering is a powerful probe of the cosmological model, and exploration of how to best model and extract this information from the signals is essential. We present the measurement of the galaxy-galaxy weak lensing signals using the SDSS DR11 spectroscopic galaxies as lens galaxies, and the HSC Y3 shear catalog as source galaxies, binned into four tomographic bins by their photometric redshift. The SDSS DR11 galaxies, with a redshift range $0.15<z<0.7$, are binned into three redshift bins, each as a probe for measuring the projected correlation function, $w_p(R_p)$. We measure the galaxy-galaxy lensing signal $ΔΣ(R_p)$ in 12 lens-source bin pairs and show that there is no evidence for significant systematic biases in the measurement with null testing. We combine our $w_p(R_p)$ and $ΔΣ(R_p)$ ($2\times2$pt) data vectors and perform likelihood inference with a flat $Λ$CDM model. For $ΔΣ(R_p)$, we extend the lower limit of the scale cut compared to previous HSC Y3 analyses to $2 h^{-1}$Mpc by including a point-mass correction term in addition to the minimal bias model. We present various tests to validate our model and provide extended consistency tests. In the $Λ$CDM context, our fiducial model yields $S_8 = 0.804^{+0.051}_{-0.051}$. The $2\times2$pt data vector provides redshift parameter constraints for the third and fourth redshift bins $Δz_3 = -0.079^{+0.074}_{-0.084}$, and $Δz_4 = -0.203^{+0.167}_{-0.206}$, which is consistent with results from the previous tomographic cosmic shear studies, and serves as the foundation for a future $3\times 2$pt analysis.

astro-ph.CO↗

arXiv2025

Cosmology and Source Redshift Constraints from Galaxy Clustering and Tomographic Weak Lensing with HSC Y3 and SDSS using the Point-Mass Correction Model

The combination of galaxy clustering and weak lensing is a powerful probe of the cosmology model. We present a joint analysis of galaxy clustering and weak lensing cosmology using SDSS data as the tracer of dark matter (lens sample) and the HSC Y3 dataset as source galaxies. The analysis divides HSC Y3 galaxies into four tomographic bins for both galaxy-galaxy lensing and cosmic shear measurements, and employs a point-mass correction model to utilize galaxy-galaxy lensing signals down to 2$h^{-1}$Mpc, extending up to 70$h^{-1}$Mpc. These strategies enhance the signal-to-noise ratio of the galaxy-galaxy lensing data vector. Using a flat $Λ$CDM model, we find $S_8 = 0.780^{+0.029}_{-0.030}$, and using a $w$CDM model, we obtain $S_8 = 0.756^{+0.038}_{-0.036}$ with $w = -1.176^{+0.310}_{-0.346}$. We apply uninformative priors on the redshift mean-shift parameters for the third and fourth tomographic bins. Leveraging the self-calibration power of tomographic weak lensing, we measure $Δz_3 = -0.112^{+0.046}_{-0.049}$ and $Δz_4 = -0.185^{+0.071}_{-0.081}$, in agreement with previous HSC Y3 results. This demonstrates that weak lensing self-calibration can achieve redshift constraints comparable to other methods such as photometric and clustering redshift calibration.

astro-ph.CO↗

arXiv2025

TS-SNN: Temporal Shift Module for Spiking Neural Networks

Spiking Neural Networks (SNNs) are increasingly recognized for their biological plausibility and energy efficiency, positioning them as strong alternatives to Artificial Neural Networks (ANNs) in neuromorphic computing applications. SNNs inherently process temporal information by leveraging the precise timing of spikes, but balancing temporal feature utilization with low energy consumption remains a challenge. In this work, we introduce Temporal Shift module for Spiking Neural Networks (TS-SNN), which incorporates a novel Temporal Shift (TS) module to integrate past, present, and future spike features within a single timestep via a simple yet effective shift operation. A residual combination method prevents information loss by integrating shifted and original features. The TS module is lightweight, requiring only one additional learnable parameter, and can be seamlessly integrated into existing architectures with minimal additional computational cost. TS-SNN achieves state-of-the-art performance on benchmarks like CIFAR-10 (96.72\%), CIFAR-100 (80.28\%), and ImageNet (70.61\%) with fewer timesteps, while maintaining low energy consumption. This work marks a significant step forward in developing efficient and accurate SNN architectures.

cs.NE↗

arXiv2025

Forecasting the Impact of Source Galaxy Photometric Redshift Uncertainties on the LSST $3\times2$pt Analysis

Photometric redshifts of the source galaxies are a key source of systematic uncertainty in the Rubin Observatory Legacy Survey of Space and Time (LSST)'s galaxy clustering and weak lensing analysis, i.e., the $3\times 2$pt analysis. This paper introduces a Fisher forecast code FisherA2Z for the LSST Year 10 (Y10) $3 \times 2$pt and cosmic shear analyses, utilizing a 15-parameter redshift distribution model, with one redshift bias, variance, and outlier rate per tomographic bin. FisherA2Z employs the Core Cosmology Library CCL to compute the large-scale structure power spectrum and incorporates a four-parameter nonlinear alignment model for intrinsic alignments. We evaluate the impact of marginalizing over redshift distribution parameters on weak lensing, forecast biases in cosmological parameters due to redshift errors, and assess cosmological parameter sensitivity to redshift systematic parameters using decision trees. The sensitivity study reveals that for LSST $3\times2$pt analysis, $S_8$ is most sensitive to the mean redshift of the fourth out of the five source tomographic bins, while other cosmological parameters possess different sensitivities. Additionally, we provide cosmological analysis forecasts based on different scenarios of spectroscopic training datasets. We find that the figures-of-merit for the cosmological results increase with the number of spectroscopic training galaxies, and with the completeness of the training set above $z=1.6$, assuming the redshift information comes solely from the training set galaxies without other external constraints.

astro-ph.CO↗

arXiv2025

Matching Cosmic Shear Analysis in Harmonic and Real Space

Recent cosmic shear analyses have exhibited discrepancies of up to $1σ$ between the inferred cosmological parameters when analyzing summary statistics in real space versus harmonic space. In this paper, we demonstrate the consistent measurement and analysis of cosmic shear two-point functions in harmonic and real space using the $i${\sc Master} algorithm. This algorithm provides a unified prescription to model the survey window effects and scale cuts in both real space (due to observational systematics) and harmonic space (due to model limitations), resulting in a matching estimation of the cosmic shear power spectrum from both harmonic and real space estimators. We show that the $i$\textsc{Master} algorithm gives matching results using measurements from the HSC Y1 mock shape catalogs in both real and harmonic space, resulting in matching inferences of $S_8=σ_8(Ω_m/0.3)^{0.5}$. This method provides an unbiased estimate of the cosmic shear power spectrum, and $S_8$ inference that has a correlation coefficient of 0.997 between analyses using measurements in real space and harmonic space when $S_8$ is the only free parameter. We observe the mean difference between the two inferred $S_8$ values to be 0.0004 across noise-free mock realizations, far below the observed difference of 0.042 for the published HSC Y1 analyses and well below the statistical uncertainties. While the notation employed in this paper is specific to photometric galaxy surveys, the methods are equally applicable and can be extended to spectroscopic galaxy surveys, intensity mapping, and CMB surveys.

astro-ph.CO↗

arXiv2025

Head-Tail-Aware KL Divergence in Knowledge Distillation for Spiking Neural Networks

Spiking Neural Networks (SNNs) have emerged as a promising approach for energy-efficient and biologically plausible computation. However, due to limitations in existing training methods and inherent model constraints, SNNs often exhibit a performance gap when compared to Artificial Neural Networks (ANNs). Knowledge distillation (KD) has been explored as a technique to transfer knowledge from ANN teacher models to SNN student models to mitigate this gap. Traditional KD methods typically use Kullback-Leibler (KL) divergence to align output distributions. However, conventional KL-based approaches fail to fully exploit the unique characteristics of SNNs, as they tend to overemphasize high-probability predictions while neglecting low-probability ones, leading to suboptimal generalization. To address this, we propose Head-Tail Aware Kullback-Leibler (HTA-KL) divergence, a novel KD method for SNNs. HTA-KL introduces a cumulative probability-based mask to dynamically distinguish between high- and low-probability regions. It assigns adaptive weights to ensure balanced knowledge transfer, enhancing the overall performance. By integrating forward KL (FKL) and reverse KL (RKL) divergence, our method effectively align both head and tail regions of the distribution. We evaluate our methods on CIFAR-10, CIFAR-100 and Tiny ImageNet datasets. Our method outperforms existing methods on most datasets with fewer timesteps.

cs.AI↗

arXiv2025

Chromatic Effects on the PSF and Shear Measurement for the Roman Space Telescope High-Latitude Wide Area Survey

Weak gravitational lensing (WL) is a key cosmological probe that requires precise measurement of galaxy images to infer shape distortions, or shear, and constrain cosmology. Accurate estimation of the Point Spread Function (PSF) is crucial for shear measurement, but the wavelength dependence of the PSF introduces chromatic biases that can systematically impact shear inference. We focus on biases arising from spectral energy distribution (SED) differences between stars, used for PSF modeling, and galaxies, used for shear measurement. We investigate these effects in $\textit{Roman's}$ four design reference mission WL bands (Y106, J129, H158, F184) and wide filter (W146). Using $\textit{Roman}$-like image simulations, we quantify the induced shear biases and compare them to requirements on those biases. Multiplicative biases over all galaxies hover around $\sim$0.2% in the WL bands and 2% in the wide filter, exceeding the mission requirement of $|m| < 0.032\%$ and relaxed requirement of $|m| < 0.1\%$. In individual redshift bins, biases can reach 0.4$\unicode{x2013}$0.9% for the WL bands and 3$\unicode{x2013}$6% for the wide filter. Additive biases remain acceptable in the WL bands but exceed systematic limits in the wide filter. We develop and test PSF-level corrections, showing that a first-order correction reduces biases within survey requirements for the WL bands; however, higher-order terms are necessary for the wide filter. Our results highlight the necessity of chromatic corrections for precision WL with $\textit{Roman}$ and provide a framework for mitigating these biases. Finally, we compare analytical color-based corrections to self-organizing maps (SOMs) and find that both methods effectively reduce biases.

astro-ph.CO↗

arXiv2025

STAA-SNN: Spatial-Temporal Attention Aggregator for Spiking Neural Networks

Spiking Neural Networks (SNNs) have gained significant attention due to their biological plausibility and energy efficiency, making them promising alternatives to Artificial Neural Networks (ANNs). However, the performance gap between SNNs and ANNs remains a substantial challenge hindering the widespread adoption of SNNs. In this paper, we propose a Spatial-Temporal Attention Aggregator SNN (STAA-SNN) framework, which dynamically focuses on and captures both spatial and temporal dependencies. First, we introduce a spike-driven self-attention mechanism specifically designed for SNNs. Additionally, we pioneeringly incorporate position encoding to integrate latent temporal relationships into the incoming features. For spatial-temporal information aggregation, we employ step attention to selectively amplify relevant features at different steps. Finally, we implement a time-step random dropout strategy to avoid local optima. As a result, STAA-SNN effectively captures both spatial and temporal dependencies, enabling the model to analyze complex patterns and make accurate predictions. The framework demonstrates exceptional performance across diverse datasets and exhibits strong generalization capabilities. Notably, STAA-SNN achieves state-of-the-art results on neuromorphic datasets CIFAR10-DVS, with remarkable performances of 97.14%, 82.05% and 70.40% on the static datasets CIFAR-10, CIFAR-100 and ImageNet, respectively. Furthermore, our model exhibits improved performance ranging from 0.33\% to 2.80\% with fewer time steps. The code for the model is available on GitHub.

cs.CV↗

arXiv2025

Temporal Separation with Entropy Regularization for Knowledge Distillation in Spiking Neural Networks

Spiking Neural Networks (SNNs), inspired by the human brain, offer significant computational efficiency through discrete spike-based information transfer. Despite their potential to reduce inference energy consumption, a performance gap persists between SNNs and Artificial Neural Networks (ANNs), primarily due to current training methods and inherent model limitations. While recent research has aimed to enhance SNN learning by employing knowledge distillation (KD) from ANN teacher networks, traditional distillation techniques often overlook the distinctive spatiotemporal properties of SNNs, thus failing to fully leverage their advantages. To overcome these challenge, we propose a novel logit distillation method characterized by temporal separation and entropy regularization. This approach improves existing SNN distillation techniques by performing distillation learning on logits across different time steps, rather than merely on aggregated output features. Furthermore, the integration of entropy regularization stabilizes model optimization and further boosts the performance. Extensive experimental results indicate that our method surpasses prior SNN distillation strategies, whether based on logit distillation, feature distillation, or a combination of both. The code will be available on GitHub.

cs.CV↗

arXiv2025

EIoU-EMC: A Novel Loss for Domain-specific Nested Entity Recognition

In recent years, research has mainly focused on the general NER task. There still have some challenges with nested NER task in the specific domains. Specifically, the scenarios of low resource and class imbalance impede the wide application for biomedical and industrial domains. In this study, we design a novel loss EIoU-EMC, by enhancing the implement of Intersection over Union loss and Multiclass loss. Our proposed method specially leverages the information of entity boundary and entity classification, thereby enhancing the model's capacity to learn from a limited number of data samples. To validate the performance of this innovative method in enhancing NER task, we conducted experiments on three distinct biomedical NER datasets and one dataset constructed by ourselves from industrial complex equipment maintenance documents. Comparing to strong baselines, our method demonstrates the competitive performance across all datasets. During the experimental analysis, our proposed method exhibits significant advancements in entity boundary recognition and entity classification. Our code are available here.

cs.CL↗

arXiv2025

DeepDISC-photoz: Deep Learning-Based Photometric Redshift Estimation for Rubin LSST

Photometric redshifts will be a key data product for the Rubin Observatory Legacy Survey of Space and Time (LSST) as well as for future ground and space-based surveys. The need for photometric redshifts, or photo-zs, arises from sparse spectroscopic coverage of observed galaxies. LSST is expected to observe billions of objects, making it crucial to have a photo-z estimator that is accurate and efficient. To that end, we present DeepDISC photo-z, a photo-z estimator that is an extension of the DeepDISC framework. The base DeepDISC network simultaneously detects, segments, and classifies objects in multi-band coadded images. We introduce photo-z capabilities to DeepDISC by adding a redshift estimation Region of Interest head, which produces a photo-z probability distribution function for each detected object. On simulated LSST images, DeepDISC photo-z outperforms traditional catalog-based estimators, in both point estimate and probabilistic metrics. We validate DeepDISC by examining dependencies on systematics including galactic extinction, blending and PSF effects. We also examine the impact of the data quality and the size of the training set and model. We find that the biggest factor in DeepDISC photo-z quality is the signal-to-noise of the imaging data, and see a reduction in photo-z scatter approximately proportional to the image data signal-to-noise. Our code is fully public and integrated in the RAIL photo-z package for ease of use and comparison to other codes at https://github.com/LSSTDESC/rail_deepdisc

astro-ph.IM↗

arXiv2025

The Blending ToolKit: A simulation framework for evaluation of galaxy detection and deblending

We present an open source Python library for simulating overlapping (i.e., blended) images of galaxies and performing self-consistent comparisons of detection and deblending algorithms based on a suite of metrics. The package, named Blending Toolkit (BTK), serves as a modular, flexible, easy-to-install, and simple-to-use interface for exploring and analyzing systematic effects related to blended galaxies in cosmological surveys such as the Vera Rubin Observatory Legacy Survey of Space and Time (LSST). BTK has three main components: (1) a set of modules that perform fast image simulations of blended galaxies, using the open source image simulation package GalSim; (2) a module that standardizes the inputs and outputs of existing deblending algorithms; (3) a library of deblending metrics commonly defined in the galaxy deblending literature. In combination, these modules allow researchers to explore the impacts of galaxy blending in cosmological surveys. Additionally, BTK provides researchers who are developing a new deblending algorithm a framework to evaluate algorithm performance and make principled comparisons with existing deblenders. BTK includes a suite of tutorials and comprehensive documentation. The source code is publicly available on GitHub at https://github.com/LSSTDESC/BlendingToolKit.

astro-ph.IM↗

arXiv2025

FSTA-SNN:Frequency-based Spatial-Temporal Attention Module for Spiking Neural Networks

Spiking Neural Networks (SNNs) are emerging as a promising alternative to Artificial Neural Networks (ANNs) due to their inherent energy efficiency. Owing to the inherent sparsity in spike generation within SNNs, the in-depth analysis and optimization of intermediate output spikes are often neglected. This oversight significantly restricts the inherent energy efficiency of SNNs and diminishes their advantages in spatiotemporal feature extraction, resulting in a lack of accuracy and unnecessary energy expenditure. In this work, we analyze the inherent spiking characteristics of SNNs from both temporal and spatial perspectives. In terms of spatial analysis, we find that shallow layers tend to focus on learning vertical variations, while deeper layers gradually learn horizontal variations of features. Regarding temporal analysis, we observe that there is not a significant difference in feature learning across different time steps. This suggests that increasing the time steps has limited effect on feature learning. Based on the insights derived from these analyses, we propose a Frequency-based Spatial-Temporal Attention (FSTA) module to enhance feature learning in SNNs. This module aims to improve the feature learning capabilities by suppressing redundant spike features.The experimental results indicate that the introduction of the FSTA module significantly reduces the spike firing rate of SNNs, demonstrating superior performance compared to state-of-the-art baselines across multiple datasets.

cs.NE↗

arXiv2025

DA-LIF: Dual Adaptive Leaky Integrate-and-Fire Model for Deep Spiking Neural Networks

Spiking Neural Networks (SNNs) are valued for their ability to process spatio-temporal information efficiently, offering biological plausibility, low energy consumption, and compatibility with neuromorphic hardware. However, the commonly used Leaky Integrate-and-Fire (LIF) model overlooks neuron heterogeneity and independently processes spatial and temporal information, limiting the expressive power of SNNs. In this paper, we propose the Dual Adaptive Leaky Integrate-and-Fire (DA-LIF) model, which introduces spatial and temporal tuning with independently learnable decays. Evaluations on both static (CIFAR10/100, ImageNet) and neuromorphic datasets (CIFAR10-DVS, DVS128 Gesture) demonstrate superior accuracy with fewer timesteps compared to state-of-the-art methods. Importantly, DA-LIF achieves these improvements with minimal additional parameters, maintaining low energy consumption. Extensive ablation studies further highlight the robustness and effectiveness of the DA-LIF model.

cs.NE↗

arXiv2024

Impact of survey spatial variability on galaxy redshift distributions and the cosmological $3\times2$-point statistics for the Rubin Legacy Survey of Space and Time (LSST)

We investigate the impact of spatial survey non-uniformity on the galaxy redshift distributions for forthcoming data releases of the Rubin Observatory Legacy Survey of Space and Time (LSST). Specifically, we construct a mock photometry dataset degraded by the Rubin OpSim observing conditions, and estimate photometric redshifts of the sample using a template-fitting photo-$z$ estimator, BPZ, and a machine learning method, FlexZBoost. We select the Gold sample, defined as $i<25.3$ for 10 year LSST data, with an adjusted magnitude cut for each year and divide it into five tomographic redshift bins for the weak lensing lens and source samples. We quantify the change in the number of objects, mean redshift, and width of each tomographic bin as a function of the coadd $i$-band depth for 1-year (Y1), 3-year (Y3), and 5-year (Y5) data. In particular, Y3 and Y5 have large non-uniformity due to the rolling cadence of LSST, hence provide a worst-case scenario of the impact from non-uniformity. We find that these quantities typically increase with depth, and the variation can be $10-40\%$ at extreme depth values. Using Y3 as an example, we propagate the variable depth effect to the weak lensing $3\times2$pt analysis, and assess the impact on cosmological parameters via a Fisher forecast. We find that galaxy clustering is most susceptible to variable depth, and non-uniformity needs to be mitigated below $3\%$ to recover unbiased cosmological constraints. There is little impact on galaxy-shear and shear-shear power spectra, given the expected LSST Y3 noise.

astro-ph.CO↗

arXiv2024

Exploring the baryonic effect signature in the Hyper Suprime-Cam Year 3 cosmic shear two-point correlations on small scales: the $S_8$ tension remains present

The baryonic feedback effect is considered as a possible solution to the so-called $S_8$ tension indicated in cosmic shear cosmology. The baryonic effect is more significant on smaller scales, and affects the cosmic shear two-point correlation functions (2PCFs) with different scale- and redshift-dependencies from those of the cosmological parameters. In this paper, we use the Hyper Suprime-Cam Year 3 (HSC-Y3) data to measure the cosmic shear 2PCFs ($ξ_{\pm}$) down to 0.28 arcminutes, taking full advantage of the high number density of source galaxies in the deep HSC data, to explore a possible signature of the baryonic effect. While the published HSC analysis used the cosmic shear 2PCFs on angular scales, which are sensitive to the matter power spectrum at $k\lesssim 1~h{\rm Mpc}^{-1}$, the smaller scale HSC cosmic shear signal allows us to probe the signature of matter power spectrum up to $k\simeq 20~h{\rm Mpc}^{-1}$. Using the accurate emulator of the nonlinear matter power spectrum, DarkEmulator2, we show that the dark matter-only model can provide an acceptable fit to the HSC-Y3 2PCFs down to the smallest scales. In other words, we do not find any clear signature of the baryonic effects or do not find a systematic shift in the $S_8$ value with the inclusion of the smaller-scale information as would be expected if the baryonic effect is significant. Alternatively, we use a flexible 6-parameter model of the baryonic effects, which can lead to both enhancement and suppression in the matter power spectrum compared to the dark matter-only model, to perform the parameter inference of the HSC-Y3 2PCFs. We find that the small-scale HSC data allow only a fractional suppression of up to 5 percent in the matter power spectrum at $k\sim 1~h{\rm Mpc}^{-1}$, which is not sufficient to reconcile the $S_8$ tension.

astro-ph.CO↗

arXiv2024

Simulating image coaddition with the Nancy Grace Roman Space Telescope: II. Analysis of the simulated images and implications for weak lensing

One challenge for applying current weak lensing analysis tools to the Nancy Grace Roman Space Telescope is that individual images will be undersampled. Our companion paper presented an initial application of Imcom - an algorithm that builds an optimal mapping from input to output pixels to reconstruct a fully sampled combined image - on the Roman image simulations. In this paper, we measure the output noise power spectra, identify the sources of the major features in the power spectra, and show that simple analytic models that ignore sampling effects underestimate the power spectra of the coadded noise images. We compute the moments of both idealized injected stars and fully simulated stars in the coadded images, and their 1- and 2-point statistics. We show that the idealized injected stars have root-mean-square ellipticity errors (1 - 6) x 10-4 per component depending on the band; the correlation functions are >= 2 orders of magnitude below requirements, indicating that the image combination step itself is using a small fraction of the overall Roman 2nd moment error budget, although the 4th moments are larger and warrant further investigation. The stars in the simulated sky images, which include blending and chromaticity effects, have correlation functions near the requirement level (and below the requirement level in a wide-band image constructed by stacking all 4 filters). We evaluate the noise-induced biases in the ellipticities of injected stars, and explain the resulting trends with an analytical model. We conclude by enumerating the next steps in developing an image coaddition pipeline for Roman.

astro-ph.IM↗

arXiv2024

Simulating image coaddition with the Nancy Grace Roman Space Telescope: I. Simulation methodology and general results

The upcoming Nancy Grace Roman Space Telescope will carry out a wide-area survey in the near infrared. A key science objective is the measurement of cosmic structure via weak gravitational lensing. Roman data will be undersampled, which introduces new challenges in the measurement of source galaxy shapes; a potential solution is to use linear algebra-based coaddition techniques such as Imcom that combine multiple undersampled images to produce a single oversampled output mosaic with a desired "target" point spread function (PSF). We present here an initial application of Imcom to 0.64 square degrees of simulated Roman data, based on the Roman branch of the Legacy Survey of Space and Time (LSST) Dark Energy Science Collaboration (DESC) Data Challenge 2 (DC2) simulation. We show that Imcom runs successfully on simulated data that includes features such as plate scale distortions, chip gaps, detector defects, and cosmic ray masks. We simultaneously propagate grids of injected sources and simulated noise fields as well as the full simulation. We quantify the residual deviations of the PSF from the target (the "leakage"), as well as noise properties of the output images; we discuss how the overall tiling pattern as well as Moiré patterns appear in the final leakage and noise maps. We include appendices on interpolation algorithms and the interaction of undersampling with image processing operations that may be of broader applicability. The companion paper ("Paper II") explores the implications for weak lensing analyses.

astro-ph.IM↗