Towards Physical Understanding of Galaxy-Halo Alignment

We investigate the alignment of galaxy and halo orientations using the TNG300-1 hydrodynamical simulation. Our analysis reveals that the distribution of the 2D misalignment angle $\theta_{\rm{2D}}$ can be well described by a truncated shifted exponential (TSE) distribution with only {\textit{one}} free parameter across different redshifts and galaxy/halo properties. We demonstrate that the galaxy-ellipticity (GI) correlations of galaxies can be reproduced by perturbing halo orientations with the obtained $\theta_{\rm{2D}}$ distribution, with only a small bias ($<3^{\circ}$) possibly arising from unaccounted couplings between $\theta_{\rm{2D}}$ and other factors. We find that both the 2D and 3D misalignment angles $\theta_{\rm{2D}}$ and $\theta_{\rm{3D}}$ decrease with ex situ stellar mass fraction $F_{\rm{acc}}$, halo mass $M_{\rm{vir}}$ and stellar mass $M_{*}$, while increasing with disk-to-total stellar mass fraction $F_{\rm{disk}}$ and redshift. These dependences are in good agreement with our recent observational study based on the BOSS galaxy samples. Our results suggest that $F_{\rm{acc}}$ is a key factor in determining the galaxy-halo alignment. Grouping galaxies by $F_{\rm{acc}}$ nearly eliminates the dependence of $\theta_{\rm{3D}}$ on $M_{\rm{vir}}$ for all three principle axes, and also reduces the redshift dependence. For $\theta_{\rm{2D}}$, we find a more significant redshift dependence than for $\theta_{\rm{3D}}$ even after controlling $F_{\rm{acc}}$, which may be attributed to the evolution of galaxy and halo shapes. Our findings present a valuable model for observational studies and enhance our understanding of galaxy-halo alignment.Comment: 19 pages, 12 figures, submitted to Ap

Retrieving non-linear features from noisy quantum states

Accurately estimating high-order moments of quantum states is an elementary precondition for many crucial tasks in quantum computing, such as entanglement spectroscopy, entropy estimation, spectrum estimation and predicting non-linear features from quantum states. But in reality, inevitable quantum noise prevents us from accessing the desired value. In this paper, we address this issue by systematically analyzing the feasibility and efficiency of extracting high-order moments from noisy states. We first show that there exists a quantum protocol capable of accomplishing this task if and only if the underlying noise channel is invertible. We then establish a method for deriving protocols that attain optimal sample complexity using quantum operations and classical post-processing only. Our protocols, in contrast to conventional ones, incur lower overheads and avoid sampling different quantum operations due to a novel technique called observable shift, making the protocols strong candidates for practical usage on current quantum devices. The proposed method also indicates the power of entangled protocols in retrieving high-order information, whereas in the existing methods, entanglement does not help. Our work contributes to a deeper understanding of how quantum noise could affect high-order information extraction and provides guidance on how to tackle it.Comment: 23 pages, 6 figure

Evidence for baryon acoustic oscillations from galaxy-ellipticity correlations

The Baryon Acoustic Oscillations (BAO) feature in the clustering of galaxies or quasars provides a ``standard ruler" for distance measurements in cosmology. In this work, we report a $2\sim3\sigma$ signal of the BAO dip feature in the galaxy density-ellipticity (GI) cross-correlation functions using the spectroscopic sample of the Baryon Oscillation Spectroscopic Survey (BOSS) CMASS, combined with the deep DESI Legacy Imaging Surveys for precise galaxy shape measurements. We measure the GI correlation functions and model them using the linear alignment model. We constrain the distance $D_V/r_{\mathrm{d}}$ to redshift $0.57$ to a precision of $3\sim5\%$, depending on the details of modeling. The GI measurement reduces the uncertainty of distance measurement by $\sim10\%$ on top of that derived from the galaxy-galaxy (GG) correlation. More importantly, for future large and deep galaxy surveys, the independent GI measurements can help sort out the systematics in the BAO studies.Comment: Main text 3 figures + supplementary 5 figures. Published in Nature Astronom

Evaluating and Improving Tool-Augmented Computation-Intensive Math Reasoning

Chain-of-thought prompting~(CoT) and tool augmentation have been validated in recent work as effective practices for improving large language models~(LLMs) to perform step-by-step reasoning on complex math-related tasks. However, most existing math reasoning datasets may be not able to fully evaluate and analyze the ability of LLMs in manipulating tools and performing reasoning, as they may only require very few invocations of tools or miss annotations for evaluating intermediate reasoning steps. To address the issue, we construct \textbf{CARP}, a new Chinese dataset consisting of 4,886 computation-intensive algebra problems with formulated annotations on intermediate steps. In CARP, we test four LLMs with CoT prompting, and find that they are all prone to make mistakes at the early steps of the solution, leading to wrong answers. Based on this finding, we propose a new approach that can deliberate the reasoning steps with tool interfaces, namely \textbf{DELI}. In DELI, we first initialize a step-by-step solution based on retrieved exemplars, then iterate two deliberation procedures that check and refine the intermediate steps of the generated solution, from the perspectives of tool manipulation and natural language reasoning, until obtaining converged solutions or reaching the maximum turn. Experimental results on CARP and six other datasets show that the proposed DELI mostly outperforms competitive baselines, and can further boost the performance of existing CoT methods. Our data and code are available in \url{https://github.com/RUCAIBox/CARP}.Comment: 17 pages, working in progres