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Galaxy clusters identified with optical imaging tend to suffer from projection effects, which impact richness (the number of member galaxies in a cluster) and lensing coherently. Physically unassociated galaxies can be mistaken as cluster members due to the significant uncertainties in their line-of-sight distances, thereby changing the observed cluster richness; at the same time, projection effects alter the weak gravitational lensing signals of clusters, leading to a correlated scatter between richness and lensing at a given halo mass. As a result, the lensing signals for optically selected clusters tend to be biased high. This optical selection bias problem of cluster lensing is one of the key challenges in cluster cosmology. Fortunately, recently available multiwavelength observations of clusters provide a solution. We analyze a simulated data set mimicking the observed lensing of clusters identified by both optical photometry and gas properties, aiming to constrain this selection bias. Assuming a redMaPPer sample from the Dark Energy Survey with South Pole Telescope Sunyaev-Zeldovich effect observations, we find that an overlapping survey of 1300 square deg, 0.2 < z < 0.65, can constrain the average lensing bias to an accuracy of 5 percent. This provides an exciting opportunity for directly constraining optical selection bias from observations. We further show that our approach can remove the optical selection bias from the lensing signal, paving the way for future optical cluster cosmology analyses., Comment: 16 pages, 5 figures. Submitted to PRD

We present an investigation into a hitherto unexplored systematic that affects the accuracy of galaxy cluster mass estimates with weak gravitational lensing. Specifically, we study the covariance between the weak lensing signal, $\Delta\Sigma$, and the "true" cluster galaxy number count, $N_{\rm gal}$, as measured within a spherical volume that is void of projection effects. By quantifying the impact of this covariance on mass calibration, this work reveals a significant source of systematic uncertainty. Using the MDPL2 simulation with galaxies traced by the SAGE semi-analytic model, we measure the intrinsic property covariance between these observables within the 3D vicinity of the cluster, spanning a range of dynamical mass and redshift values relevant for optical cluster surveys. Our results reveal a negative covariance at small radial scales ($R \lesssim R_{\rm 200c}$) and a null covariance at large scales ($R \gtrsim R_{\rm 200c}$) across most mass and redshift bins. We also find that this covariance results in a $2-3\%$ bias in the halo mass estimates in most bins. Furthermore, by modeling $N_{\rm gal}$ and $\Delta\Sigma$ as multi-(log)-linear equations of secondary halo properties, we provide a quantitative explanation for the physical origin of the negative covariance at small scales. Specifically, we demonstrate that the $N_{\rm gal}$-$\Delta\Sigma$ covariance can be explained by the secondary properties of halos that probe their formation history. We attribute the difference between our results and the positive bias seen in other works with (mock)-cluster finders to projection effects. These findings highlight the importance of accounting for the covariance between observables in cluster mass estimation, which is crucial for obtaining accurate constraints on cosmological parameters.

The recent Dark Energy Survey Year 1 (DES-Y1) analysis of galaxy cluster abundances and weak lensing produced $\Omega_{\rm m}$ and $\sigma_8$ constraints in 5.6$\sigma$ tension with Planck. It is suggested in that work that this tension is driven by unmodelled systematics in optical cluster selection. We present a novel simulation-based forward modeling framework that explicitly incorporates cluster selection into its model predictions. Applying this framework to the DES-Y1 data we find consistency with Planck, resolving the tension found in the DES-Y1 analysis. An extension of this approach to the final DES data set will produce robust constraints on $\Lambda$CDM parameters and correspondingly strong tests of cosmological models., Comment: 6 pages, 2 figures, 1 table, Supplemental material with 2 figures. Submitted to Physical Review Letters

We review arguably the simplest solution for the Hubble tension -- the possibility that we live in a void. In this scenario, the local Hubble constant $H_0$ is higher than the global value, thus potentially explaining why $H_0$ measured locally by the distance ladder including Type Ia supernovae (SNIa) would be larger than the value inferred from the cosmic microwave background and other cosmological probes. In addition, since the local supernova sample is sparse and highly inhomogeneous, the error bars in the local Hubble constant might be larger than previously estimated. These two effects -- local matter density and sample inhomogeneity -- constitute the sample variance (or the cosmic variance) of the local Hubble constant measurements. To investigate these effects explicitly, we have mocked up SNIa observations by exactly matching their actual spatial distribution in a large N-body simulation. We have then investigated whether the sample variance is large enough to explain the Hubble tension. The answer is resoundingly negative: the typical local variation in $H_0$ is far smaller than what would be required to explain the Hubble tension; the latter would require a 20-$\sigma$ deviation from the expected sample variance. Equivalently, the void required to explain the Hubble tension would need to be so empty ($\delta\approx-0.8$ on a scale 120 $h^{-1}{\rm Mpc}$) that it would be incompatible with the large-scale structure in a $\Lambda$CDM universe. Therefore, the possibility that we live in a void does not come close to explaining the Hubble tension., Comment: Invited chapter for the edited book Hubble Constant Tension (Eds. E. Di Valentino and D. Brout, Springer Singapore, expected in 2024)

We study the one-parameter family of Fredholm determinants $\det(I-\rho^2\mathcal{K}_{n,x})$, $\rho\in\mathbb{R}$, where $\mathcal{K}_{n,x}$ stands for the integral operator acting on $L^2(x,+\infty)$ with the higher order Airy kernel. This family of determinants represents a new universal class of distributions which is a higher order analogue of the classical Tracy-Widom distribution. Each of the determinants admits an integral representation in terms of a special real solution to the $n$-th member of the Painlev\'{e} II hierarchy. Using the Riemann-Hilbert approach, we establish asymptotics of the determinants and the associated higher order Painlev\'{e} II transcendents as $x\to -\infty$ for $0<|\rho|<1$ and $|\rho|>1$, respectively. In the case of $0<|\rho|<1$, we are able to calculate the constant term in the asymptotic expansion of the determinants, while for $|\rho|>1$, the relevant asymptotics exhibit singular behaviors. Applications of our results are also discussed, which particularly include asymptotic statistical properties of the counting function for the random point process defined by the higher order Airy kernel., Comment: 39 pages, 7 figures

Simulation of surface processes is a key part of computational chemistry that offers atomic-scale insights into mechanisms of heterogeneous catalysis, diffusion dynamics, as well as quantum tunneling phenomena. The most common theoretical approaches involve optimization of reaction pathways, including semiclassical tunneling pathways (called instantons). However, the computational effort can be demanding, especially for instanton optimizations with ab initio electronic structure. Recently, machine learning has been applied to accelerate reaction-pathway optimization, showing great potential for a wide range of applications. However, previous methods suffer from practical issues such as unfavorable scaling with respect to the size of the descriptor, and were mostly designed for reactions in the gas phase. We propose an improved framework based on Gaussian process regression for general transformed coordinates, which can alleviate the size problem. The descriptor combines internal and Cartesian coordinates, which improves the performance for modeling surface processes. We demonstrate with eleven instanton optimizations in three example systems that the new approach makes ab initio instanton optimization significantly cheaper, such that it becomes not much more expensive than a classical transition-state theory calculation.

Within the $\Lambda$CDM cosmology, dark matter haloes are comprised of both a smooth component and a population of smaller, gravitationally bound subhaloes. These components are often treated as a single halo when halo properties, such as density profiles, are extracted from simulations. Recent work has shown that density profiles change substantially when subhalo mass is excluded. In this paper, we expand on this result by analysing the change in three specific host halo properties -- concentration ($c_{\rm{NFW}}$), spin ($\lambda_{\rm Bullock}$), and shape ($c/a$), -- when calculated only from the smooth component of the halo. This analysis is performed on both Milky Way-mass haloes and cluster-mass haloes in high-resolution, zoom-in, $N$-body simulations. We find that when subhaloes are excluded the median value of (1) $c_{\rm{NFW}}$ is enhanced by $\approx 38 \pm 12\%$ and $\approx 88 \pm 7.7\%$ for Milky Way mass ($10^{12.1}\,\text{M}_\odot$) and cluster mass ($10^{14.8}\,\text{M}_\odot$) haloes respectively, (2) $\lambda_{\rm Bullock}$ is reduced for Milky Way mass by $\approx 16 \pm 6.8\%$ and cluster mass haloes by $\approx 32 \pm 8.9\%$. Additionally, with the removal of subhaloes, cluster mass haloes tend to become more spherical as the ratio of minor-to-major axis, $c/a$, increases by $\approx 12 \pm 4\%$, whereas Milky Way mass haloes remain approximately the same shape with $c/a$ changed by $\approx 1.2 \pm 5.6\%$. The fractional change of each of these properties depends primarily on the amount of mass that is removed from the halo system and, to a lesser extent, mass accretion history. Our findings demonstrate that the properties of the smooth components of dark matter haloes are biased relative to the total mass of the halo including subhaloes., Comment: Accepted to MNRAS 09/26/2023

We present the Cardinal mock galaxy catalogs, a new version of the Buzzard simulation that has been updated to support ongoing and future cosmological surveys, including DES, DESI, and LSST. These catalogs are based on a one-quarter sky simulation populated with galaxies out to a redshift of $z=2.35$ to a depth of $m_{\rm{r}}=27$. Compared to the Buzzard mocks, the Cardinal mocks include an updated subhalo abundance matching (SHAM) model that considers orphan galaxies and includes mass-dependent scatter between galaxy luminosity and halo properties. This model can simultaneously fit galaxy clustering and group--galaxy cross-correlations measured in three different luminosity threshold samples. The Cardinal mocks also feature a new color assignment model that can simultaneously fit color-dependent galaxy clustering in three different luminosity bins. We have developed an algorithm that uses photometric data to improve the color assignment model further and have also developed a novel method to improve small-scale lensing below the ray-tracing resolution. These improvements enable the Cardinal mocks to accurately reproduce the abundance of galaxy clusters and the properties of lens galaxies in the Dark Energy Survey data. As such, these simulations will be a valuable tool for future cosmological analyses based on large sky surveys. The cardinal mock will be released upon publication at https://chunhaoto.com/cardinalsim., Comment: 37 pages; 20 figures. See figure 1 for summary and appendix K for a list of main differences between Cardinal and Buzzard. To be submitted to APJ; Comments welcome. Highlights can be found at https://chunhaoto.com/cardinalsim

The clustering signals of galaxy clusters are known to be powerful tools for self-calibrating the mass-observable relation and are complementary to cluster abundance and lensing. In this work, we explore the possibility of combining three correlation functions -- cluster lensing, the cluster-galaxy cross-correlation function, and the galaxy auto-correlation function -- to self-calibrate optical cluster selection bias, the boosted clustering and lensing signals in a richness-selected sample mainly caused by projection effects. We develop mock catalogues of redMaGiC-like galaxies and redMaPPer-like clusters by applying Halo Occupation Distribution (HOD) models to N-body simulations and using counts-in-cylinders around massive haloes as a richness proxy. In addition to the previously known small-scale boost in projected correlation functions, we find that the projection effects also significantly boost 3D correlation functions out to scales 100 $h^{-1} \mathrm{Mpc}$. We perform a likelihood analysis assuming survey conditions similar to that of the Dark Energy Survey (DES) and show that the selection bias can be self-consistently constrained at the 10% level. We discuss strategies for applying this approach to real data. We expect that expanding the analysis to smaller scales and using deeper lensing data would further improve the constraints on cluster selection bias., Comment: 12 pages, 10 figures; replaced to match published version

We present Symphony, a compilation of $262$ cosmological, cold-dark-matter-only zoom-in simulations spanning four decades of host halo mass, from $10^{11}$$-$$10^{15}~M_{\mathrm{\odot}}$. This compilation includes three existing simulation suites at the cluster and Milky Way$-$mass scales, and two new suites: $39$ Large Magellanic Cloud-mass ($10^{11}~M_{\mathrm{\odot}}$) and $49$ strong-lens-analog ($10^{13}~M_{\mathrm{\odot}}$) group-mass hosts. Across the entire host halo mass range, the highest-resolution regions in these simulations are resolved with a dark matter particle mass of $\approx 3\times 10^{-7}$ times the host virial mass and a Plummer-equivalent gravitational softening length of $\approx 9\times 10^{-4}$ times the host virial radius, on average. We measure correlations between subhalo abundance and host concentration, formation time, and maximum subhalo mass, all of which peak at the Milky Way host halo mass scale. Subhalo abundances are $\approx 50\%$ higher in clusters than in lower-mass hosts at fixed sub-to-host halo mass ratios. Subhalo radial distributions are approximately self-similar as a function of host mass and are less concentrated than hosts' underlying dark matter distributions. We compare our results to the semianalytic model $\mathrm{\texttt{Galacticus}}$, which predicts subhalo mass functions with a higher normalization at the low-mass end and radial distributions that are slightly more concentrated than Symphony. We use $\mathrm{\texttt{UniverseMachine}}$ to model halo and subhalo star formation histories in Symphony, and we demonstrate that these predictions resolve the formation histories of the halos that host nearly all currently observable satellite galaxies in the universe. To promote open use of Symphony, data products are publicly available at http://web.stanford.edu/group/gfc/symphony., Comment: 39 pages, 20 figures, 2 tables. Updated to published version

Geometry diagram parsing plays a key role in geometry problem solving, wherein the primitive extraction and relation parsing remain challenging due to the complex layout and between-primitive relationship. In this paper, we propose a powerful diagram parser based on deep learning and graph reasoning. Specifically, a modified instance segmentation method is proposed to extract geometric primitives, and the graph neural network (GNN) is leveraged to realize relation parsing and primitive classification incorporating geometric features and prior knowledge. All the modules are integrated into an end-to-end model called PGDPNet to perform all the sub-tasks simultaneously. In addition, we build a new large-scale geometry diagram dataset named PGDP5K with primitive level annotations. Experiments on PGDP5K and an existing dataset IMP-Geometry3K show that our model outperforms state-of-the-art methods in four sub-tasks remarkably. Our code, dataset and appendix material are available at https://github.com/mingliangzhang2018/PGDP., Comment: Accepted to IJCAI 2022

Bayesian posterior inference of modern multi-probe cosmological analyses incurs massive computational costs. For instance, depending on the combinations of probes, a single posterior inference for the Dark Energy Survey (DES) data had a wall-clock time that ranged from 1 to 21 days using a state-of-the-art computing cluster with 100 cores. These computational costs have severe environmental impacts and the long wall-clock time slows scientific productivity. To address these difficulties, we introduce LINNA: the Likelihood Inference Neural Network Accelerator. Relative to the baseline DES analyses, LINNA reduces the computational cost associated with posterior inference by a factor of 8--50. If applied to the first-year cosmological analysis of Rubin Observatory's Legacy Survey of Space and Time (LSST Y1), we conservatively estimate that LINNA will save more than US $\$300,000$ on energy costs, while simultaneously reducing $\rm{CO}_2$ emission by $2,400$ tons. To accomplish these reductions, LINNA automatically builds training data sets, creates neural network surrogate models, and produces a Markov chain that samples the posterior. We explicitly verify that LINNA accurately reproduces the first-year DES (DES Y1) cosmological constraints derived from a variety of different data vectors with our default code settings, without needing to retune the algorithm every time. Further, we find that LINNA is sufficient for enabling accurate and efficient sampling for LSST Y10 multi-probe analyses. We make LINNA publicly available at https://github.com/chto/linna, to enable others to perform fast and accurate posterior inference in contemporary cosmological analyses., Comment: 21 pages, 12 figures, submitted to JCAP, comments are welcome

Cosmological constraints from current and upcoming galaxy cluster surveys are limited by the accuracy of cluster mass calibration. In particular, optically identified galaxy clusters are prone to selection effects that can bias the weak lensing mass calibration. We investigate the selection bias of the stacked cluster lensing signal associated with optically selected clusters, using clusters identified by the redMaPPer algorithm in the Buzzard simulations as a case study. We find that at a given cluster halo mass, the residuals of redMaPPer richness and weak lensing signal are positively correlated. As a result, for a given richness selection, the stacked lensing signal is biased high compared with what we would expect from the underlying halo mass probability distribution. The cluster lensing selection bias can thus lead to overestimated mean cluster mass and biased cosmology results. We show that the lensing selection bias exhibits a strong scale-dependence and is approximately 20 to 60 percent for $\Delta\Sigma$ at large scales. This selection bias largely originates from spurious member galaxies within +/- 20 to 60 Mpc/h along the line of sight, highlighting the importance of quantifying projection effects associated with the broad redshift distribution of member galaxies in photometric cluster surveys. While our results qualitatively agree with those in the literature, accurate quantitative modelling of the selection bias is needed to achieve the goals of cluster lensing cosmology and will require synthetic catalogues covering a wide range of galaxy-halo connection models., Comment: 16 pages, 16 figures; replaced to match published version

Counts of galaxy clusters offer a high-precision probe of cosmology, but control of systematic errors will determine the accuracy of this measurement. Using Buzzard simulations, we quantify one such systematic, the triaxiality distribution of clusters identified with the redMaPPer optical cluster finding algorithm, which was used in the Dark Energy Survey Year-1 (DES Y1) cluster cosmology analysis. We test whether redMaPPer selection biases the clusters' shape and orientation and find that it only biases orientation, preferentially selecting clusters with their major axes oriented along the line of sight. Modeling the richness-mass relation as a log-linear relation, we find that the log-richness amplitude $\ln(A)$ is boosted from the lowest to highest orientation bin with a significance of $14\sigma$, while the orientation dependence of the richness-mass slope and intrinsic scatter is minimal. We also find that the weak lensing shear-profile ratios of cluster-associated dark halos in different orientation bins resemble a "bottleneck" shape that can be quantified with a Cauchy function. We test the correlation of orientation with two other leading systematics in cluster cosmology -- miscentering and projection -- and find a null correlation. Analytic templates for the triaxiality bias of observed-richness and lensing profiles are mapped as corrections to the observable of richness-binned lensing profiles for redMaPPer clusters. The resulting mass bias confirms the DES Y1 finding that triaxiality is a leading source of bias in cluster cosmology. However, the richness-dependence of the bias confirms that triaxiality does not fully resolve the tension at low-richness between DES Y1 cluster cosmology and other probes. Our model can be used for quantifying the impact of triaxiality bias on cosmological constraints for upcoming weak lensing surveys of galaxy clusters.

Approximating distributions from their samples is a canonical statistical-learning problem. One of its most powerful and successful modalities approximates every distribution to an $\ell_1$ distance essentially at most a constant times larger than its closest $t$-piece degree-$d$ polynomial, where $t\ge1$ and $d\ge0$. Letting $c_{t,d}$ denote the smallest such factor, clearly $c_{1,0}=1$, and it can be shown that $c_{t,d}\ge 2$ for all other $t$ and $d$. Yet current computationally efficient algorithms show only $c_{t,1}\le 2.25$ and the bound rises quickly to $c_{t,d}\le 3$ for $d\ge 9$. We derive a near-linear-time and essentially sample-optimal estimator that establishes $c_{t,d}=2$ for all $(t,d)\ne(1,0)$. Additionally, for many practical distributions, the lowest approximation distance is achieved by polynomials with vastly varying number of pieces. We provide a method that estimates this number near-optimally, hence helps approach the best possible approximation. Experiments combining the two techniques confirm improved performance over existing methodologies., Comment: 19 pages, 12 figures