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Thouless pumping with nontrivial topological phases provides a powerful means for the manipulation of matter waves in one-dimensional lattice systems. The band topology is revealed by the quantization of pumped charge. In the context of Thouless pumping, we present a graphical representation for the topological phases characterized by the Chern number of an effective two-dimensional band. We illustrate how the two topological phases with distinct Zak phase is connected in the pumping process. Such a visual depiction exhibits typical patterns that is directly related to a linking number and to the Chern number, allowing for the construction of Thouless pumping schemes in a practical way. As a demonstration, we present a generalized Creutz model with tunable Peierls phase, inter-leg imbalance and diagonal hopping. Various modulation schemes for Thouless pumping are studied, focusing on their graphical representations in Bloch space, as well as the quantized pumping phenomenon in real space., Comment: 10 pages, 14 figures

We study the dynamic pricing and replenishment problems under inconsistent decision frequencies. Different from the traditional demand assumption, the discreteness of demand and the parameter within the Poisson distribution as a function of price introduce complexity into analyzing the problem property. We demonstrate the concavity of the single-period profit function with respect to product price and inventory within their respective domains. The demand model is enhanced by integrating a decision tree-based machine learning approach, trained on comprehensive market data. Employing a two-timescale stochastic approximation scheme, we address the discrepancies in decision frequencies between pricing and replenishment, ensuring convergence to local optimum. We further refine our methodology by incorporating deep reinforcement learning (DRL) techniques and propose a fast-slow dual-agent DRL algorithm. In this approach, two agents handle pricing and inventory and are updated on different scales. Numerical results from both single and multiple products scenarios validate the effectiveness of our methods.

Hallucinations in Large Language Models (LLMs) remain a major obstacle, particularly in high-stakes applications where factual accuracy is critical. While representation editing and reading methods have made strides in reducing hallucinations, their heavy reliance on specialised tools and training on in-domain samples, makes them difficult to scale and prone to overfitting. This limits their accuracy gains and generalizability to diverse datasets. This paper presents a lightweight method, Norm Voting (NoVo), which harnesses the untapped potential of attention head norms to dramatically enhance factual accuracy in zero-shot multiple-choice questions (MCQs). NoVo begins by automatically selecting truth-correlated head norms with an efficient, inference-only algorithm using only 30 random samples, allowing NoVo to effortlessly scale to diverse datasets. Afterwards, selected head norms are employed in a simple voting algorithm, which yields significant gains in prediction accuracy. On TruthfulQA MC1, NoVo surpasses the current state-of-the-art and all previous methods by an astounding margin -- at least 19 accuracy points. NoVo demonstrates exceptional generalization to 20 diverse datasets, with significant gains in over 90\% of them, far exceeding all current representation editing and reading methods. NoVo also reveals promising gains to finetuning strategies and building textual adversarial defence. NoVo's effectiveness with head norms opens new frontiers in LLM interpretability, robustness and reliability.

We propose a geometric series modulated non-Hermitian quasiperiodic lattice model, and explore its localization and topological properties. The results show that with the ever-increasing summation terms of the geometric series, multiple mobility edges and non-Hermitian point gaps with high winding number can be induced in the system. The point gap spectrum of the system has a Matryoshka doll-like structure in the complex plane, resulting in a high winding number. In addition, we analyze the limit case of summation of infinite terms. The results show that the mobility edges merge together as only one mobility edge when summation terms are pushed to the limit. Meanwhile, the corresponding point gaps are merged into a ring with winding number equal to one. Through Avila's global theory, we give an analytical expression for mobility edges in the limit of infinite summation, reconfirming that mobility edges and point gaps do merge and will result in a winding number that is indeed equal to one., Comment: main 6 pages, 7 figures

We explore a new security loophole in a practical continuous-variable quantum key distribution (CVQKD) system, which is opened by the photorefractive effect of lithium niobate-based (LN-based) modulators. By exploiting this loophole, we propose a quantum hacking strategy, i.e., the induced-photorefraction attack, which utilizes the induced photorefraction on the LN-based modulators to hide the classical intercept-resend attack. Specifically, we show that the induced photorefraction can bias the response curve of the LN-based modulator, which will affect the intensity of the modulated signal. Based on the investigation of the channel parameter estimation under above influence, we further analyze the secret key rate of the practical CVQKD system. The simulation results indicate that the communication parties will overestimate the secret key rate, which reveals that Eve can actively open the above loophole by launching the induced-photorefraction attack to successfully obtain the secret key information. To defend against this attack, we can use a random monitoring scheme for modulation variance to determine this attack, and use an improving optical power limiter to effectively mitigate the irradiation beam. Apart from these countermeasures, we also propose using the Sagnac-based IM to stabilize the practical CVQKD system, which can minimize the above effects.

Tilting planar samples for multi-zone-axes observation is a routine procedure in electron microscopy. However, this process invariably introduces optical path differences in the electron beam across different sample positions, significantly compromising image quality, particularly over large fields of view. To address this challenge, we developed path difference ptychography (PDP), a method capable of decoupling path differences from the four-dimensional data during reconstruction. This enables the acquisition of high-quality, large-scale images, facilitating a more comprehensive understanding and analysis of materials microstructure. Moreover, PDP has the potential to promote the widespread application of ptychographic tomography in the analysis of planar samples.

By using PTP and DEA methods, the study of marine fishing capacity in China revealed that it's more accurate to consider the input index as total power rather than the number of ships. The analysis clarified that the main issue with marine fishing capacity in China is the excess total power of fishing ships. The study suggested reducing the number of ships by 35.2%, the gross tonnage by 29.8%, and the total power by 37.3% to align with the catch levels of 1999. It also proposed the idea of supplementing peak years. The PTP methodology was found to be suitable for longitudinal analysis over time, while the DEA approach is better for comparing fishing capacity across different regions at the same time. Additionally, the study indicated that practical fishing capacity tends to be underestimated, so actual reductions in capacity are usually larger than calculated values.

For promoting the development of the marine economy more sustainably, based on the data envelopment analysis method and combined with the impact of the marine environment, the environmental performance of the marine economy was evaluated for Chinese coastal provinces. Firstly, the classical CCR model was used. Then, a model that considered undesirable outputs was developed to suit the Chinese marine economy. Using the two models, the economic efficiencies without environmental consideration and the environmental performance index were calculated and compared. According to the results, the empirical relationship between EPI and EE, per capita GDP, and the industrial structure was analyzed. It is useful for guiding the coastal local economy of China to a healthy way.

The fishing capacity and capacity utilization for Chinese inshore fleets over the latest 13 years were measured using the DEA method. Relevant models were then established to analyze the relationships between capacity output, capacity utilization, and income, and the function of collecting taxes to control fishing capacity was quantitatively simulated. It was pointed out that the tax system would be effective for curtailing fishing capacity and improving the efficiency of the entire fishing industry in China, provided that the tax rate is not too low. Finally, it was suggested that collecting taxes at a proper rate be implemented for Chinese inshore fishing fleets.

For controlling pollution of the marine environment while developing coastal economy, the coastal environmental performance was proposed and measured in static and dynamic methods combined with DEA and efficiency theory in this paper. With the two methods, 16 harbor cities were evaluated. The results showed the index designed in this paper can better reflect the effect to the marine environment for economy of the coastal cities.

Firstly, by establishing a prediction model for global sea-level rise and calculating with Maple, it is shown that the global sea-level rise rate in 2009 is 2.68 mm/a. The height and rate of global sea-level rise will be about 9.11 cm and 3.22 mm/a in 2020. Based on the study and the actual land subsidence in Shanghai Lingang New City, the rate of relative sea-level rise near Lingang New City is calculated to be 12.68 mm/a in 2009. Then, through setting up the extrapolation prediction model with a linear trend term and a significant tidal cycle, the rise rate of average sea-level near Lingang New City was predicted. The result showed it will be 0.33 mm/a in 2020.

Pruning is a critical strategy for compressing trained large language models (LLMs), aiming at substantial memory conservation and computational acceleration without compromising performance. However, existing pruning methods often necessitate inefficient retraining for billion-scale LLMs or rely on heuristic methods such as the optimal brain surgeon framework, which degrade performance. In this paper, we introduce FISTAPruner, the first post-training pruner based on convex optimization models and algorithms. Specifically, we propose a convex optimization model incorporating $\ell_1$ norm to induce sparsity and utilize the FISTA solver for optimization. FISTAPruner incorporates an intra-layer cumulative error correction mechanism and supports parallel pruning. We comprehensively evaluate FISTAPruner on models such as OPT, LLaMA, LLaMA-2, and LLaMA-3 with 125M to 70B parameters under unstructured and 2:4 semi-structured sparsity, demonstrating superior performance over existing state-of-the-art methods across various language benchmarks.

To empirically study the policy impact of a National New Area on the local economy, this paper evaluates the effect of the Zhoushan Archipelago New Area on local GDP growth rate and economic efficiency. By collecting input and output data from 20 prefectural-level cities in Jiangsu, Zhejiang, and Anhui provinces from 1995 to 2015, we estimate the economic efficiency of these cities using data envelopment analysis. Subsequently, we construct counterfactuals for Zhoushan by selecting comparable cities from the dataset, excluding Zhoushan, and applying a panel data approach. The difference between the actual and counterfactual values for GDP growth rate and economic efficiency in Zhoushan is analyzed to determine the treatment effect of the National New Area policy. The research reveals that in the initial four years, the New Area policy enhanced Zhoushan's economic efficiency but negatively affected its GDP growth rate. This influence gradually disappeared after four years. Further analysis suggests that the policy's effect on GDP growth rate varies with the level of economic development in different regions, having a more substantial impact in less developed areas. Therefore, we conclude that establishing a New Area in relatively undeveloped zones is more advantageous.

The photorealistic reconstruction and rendering of architectural scenes have extensive applications in industries such as film, games, and transportation. It also plays an important role in urban planning, architectural design, and the city's promotion, especially in protecting historical and cultural relics. The 3D Gaussian Splatting, due to better performance over NeRF, has become a mainstream technology in 3D reconstruction. Its only input is a set of images but it relies heavily on geometric parameters computed by the SfM process. At the same time, there is an existing abundance of raw 3D models, that could inform the structural perception of certain buildings but cannot be applied. In this paper, we propose a straightforward method to harness these raw 3D models to guide 3D Gaussians in capturing the basic shape of the building and improve the visual quality of textures and details when photos are captured non-systematically. This exploration opens up new possibilities for improving the effectiveness of 3D reconstruction techniques in the field of architectural design.

Large model training has been using recomputation to alleviate the memory pressure and pipelining to exploit the parallelism of data, tensor, and devices. The existing recomputation approaches may incur up to 40% overhead when training real-world models, e.g., the GPT model with 22B parameters. This is because they are executed on demand in the critical training path. In this paper, we design a new recomputation framework, Lynx, to reduce the overhead by overlapping the recomputation with communication occurring in training pipelines. It consists of an optimal scheduling algorithm (OPT) and a heuristic-based scheduling algorithm (HEU). OPT achieves a global optimum but suffers from a long search time. HEU was designed based on our observation that there are identical structures in large DNN models so that we can apply the same scheduling policy to all identical structures. HEU achieves a local optimum but reduces the search time by 99% compared to OPT. Our comprehensive evaluation using GPT models with 1.3B-20B parameters shows that both OPT and HEU outperform the state-of-the-art recomputation approaches (e.g., Megatron-LM and Checkmake) by 1.02-1.53x. HEU achieves a similar performance as OPT with a search time of 0.16s on average., Comment: 13 pages

With an extremely high dimensionality, the spatial degree of freedom of entangled photons is a key tool for quantum foundation and applied quantum techniques. To fully utilize the feature, the essential task is to experimentally characterize the multiphoton spatial wave function including the entangled amplitude and phase information at different evolutionary stages. However, there is no effective method to measure it. Quantum state tomography is costly, and quantum holography requires additional references. Here we introduce quantum Shack-Hartmann wavefront sensing to perform efficient and reference-free measurement of the biphoton spatial wave function. The joint probability distribution of photon pairs at the back focal plane of a microlens array is measured and used for amplitude extraction and phase reconstruction. In the experiment, we observe that the biphoton amplitude correlation becomes weak while phase correlation shows up during free-space propagation. Our work is a crucial step in quantum physical and adaptive optics and paves the way for characterizing quantum optical fields with high-order correlations or topological patterns., Comment: Main text: 6 pages, 4 figures; Supplemental Material: 13 pages, 11 figures. (c) 2024 American Physical Society

The expanding applications call for novel new-generation wide-bandgap semiconductors. Here, we show that a compound only composed of the ordinary elements Na and Cl, namely three-dimensional NaCl2 crystal, is a wide-bandgap semiconductor. This finding benefits from the breaking of conventional stoichiometry frameworks in the theoretical design, leading to the discovery of three-dimensional XY2 (X = Na, Li, K; Y = Cl, F, Br, I) crystals, with covalent bonds of Y pairs inducing the wide bandgap from 2.24 to 4.45 eV. Crucially, such an unexpected NaCl2 crystal was successfully synthesized under ambient conditions. The unconventional stoichiometric strategy with other chemical elements potentially yields more wide-bandgap semiconductors, offering the capability for bandgap tuning. These unconventional stoichiometric materials may also exhibit superconductivity, transparent inorganic electrides, high-energy-density, and beyond.

We present DeepSeek-V2, a strong Mixture-of-Experts (MoE) language model characterized by economical training and efficient inference. It comprises 236B total parameters, of which 21B are activated for each token, and supports a context length of 128K tokens. DeepSeek-V2 adopts innovative architectures including Multi-head Latent Attention (MLA) and DeepSeekMoE. MLA guarantees efficient inference through significantly compressing the Key-Value (KV) cache into a latent vector, while DeepSeekMoE enables training strong models at an economical cost through sparse computation. Compared with DeepSeek 67B, DeepSeek-V2 achieves significantly stronger performance, and meanwhile saves 42.5% of training costs, reduces the KV cache by 93.3%, and boosts the maximum generation throughput to 5.76 times. We pretrain DeepSeek-V2 on a high-quality and multi-source corpus consisting of 8.1T tokens, and further perform Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL) to fully unlock its potential. Evaluation results show that, even with only 21B activated parameters, DeepSeek-V2 and its chat versions still achieve top-tier performance among open-source models.

The identification of new materials with superconducting properties is the pursuit in the realm of superconductivity research. Here, excitedly, we show that the simplest salt daily used can be made a superconductor at normal pressure only by adjusting its stoichiometry of Na and Cl as Na3Cl at normal pressure based on first-principles calculations. This bulk stable abnormal Na-Cl stoichiometric crystal of 3:1, the first 'magic' ratio, includes metallic (Na) atoms in the core as well as hybridization of ionic and metallic bonding, facilitating the electron-phonon-coupling for superconductivity with a critical temperature Tc of 0.13 K. The flat bands and van Hove singularities near the Fermi level produce large densities of states, similar to H3S and LaH10, which is beneficial for the emergence of superconductivity. The crystal composed of with abnormal Na-Cl magic stoichiometry is a precisely tunable, purely sodium and chloride-based, three-dimensional bulk superconductor, which is therefore an ideal material for designing and understanding abnormal stoichiometric crystals. The methodology of constructing this bulk abnormal crystal may be general to almost all elements, which could lead to insights into the physics of other conventional superconductors and even high-critical-temperature superconductors.

Large-scale cosmic filaments may have played an important role in shaping the properties of galaxies. Meanwhile, cosmic filaments are believed to harbor a substantial portion of the missing baryons at redshift z < 2. To inspect the role of filaments in these issues, many properties of filaments need to be examined, including their lengths, thicknesses, and density profiles. However, measuring some of these properties poses challenges. This study concentrates on estimating filament width/thickness, investigating potential correlations between the local width of filaments and the properties of dark matter halos within filaments. We find that the local width of filaments generally increases with the mass of dark matter halos embedded in filaments per unit length, roughly following a secondorder polynomial, although with notable scatter. We probe and discuss means that may refine our findings. After further verification and improvements, this relation could be applied to filament samples constructed from the observed galaxy distribution, aiding in understanding the roles of cosmic filaments in galaxy evolution and uncovering the missing baryons., Comment: 11 pages, 7 figures, accepted to ApJ

As deep learning models exponentially increase in size, optimizers such as Adam encounter significant memory consumption challenges due to the storage of first and second moment data. Current memory-efficient methods like Adafactor and CAME often compromise accuracy with their matrix factorization techniques. Addressing this, we introduce Adapprox, a novel approach that employs randomized low-rank matrix approximation for a more effective and accurate approximation of Adam's second moment. Adapprox features an adaptive rank selection mechanism, finely balancing accuracy and memory efficiency, and includes an optional cosine similarity guidance strategy to enhance stability and expedite convergence. In GPT-2 training and downstream tasks, Adapprox surpasses AdamW by achieving 34.5% to 49.9% and 33.8% to 49.9% memory savings for the 117M and 345M models, respectively, with the first moment enabled, and further increases these savings without the first moment. Besides, it enhances convergence speed and improves downstream task performance relative to its counterparts.

Multi-Agent Path Finding (MAPF), which involves finding collision-free paths for multiple robots, is crucial in various applications. Lifelong MAPF, where targets are reassigned to agents as soon as they complete their initial targets, offers a more accurate approximation of real-world warehouse planning. In this paper, we present a novel mechanism named Caching-Augmented Lifelong MAPF (CAL-MAPF), designed to improve the performance of Lifelong MAPF. We have developed a new type of map grid called cache for temporary item storage and replacement, and created a locking mechanism to improve the planning solution's stability. A task assigner (TA) is designed for CAL-MAPF to allocate target locations to agents and control agent status in different situations. CAL-MAPF has been evaluated using various cache replacement policies and input task distributions. We have identified three main factors significantly impacting CAL-MAPF performance through experimentation: suitable input task distribution, high cache hit rate, and smooth traffic. In general, CAL-MAPF has demonstrated potential for performance improvements in certain task distributions, map and agent configurations.

In this paper, we set out to construct a set of reference mock galaxy redshift surveys (MGRSs) for the future Chinese Space-station Survey Telescope (CSST) observation, where subsequent survey selection effects can be added and evaluated. This set of MGRSs is generated using the dark matter subhalos extracted from a high-resolution Jiutian $N$-body simulation of the standard $\Lambda$CDM cosmogony with $\Omega_m=0.3111$, $\Omega_{\Lambda}=0.6889$, and $\sigma_8=0.8102$. The simulation has a boxsize of $1~h^{-1} {\rm Gpc}$, and consists of $6144^3$ particles with mass resolution $3.723 \times 10^{8} h^{-1} M_\odot $. In order to take into account the effect of redshift evolution, we first use all 128 snapshots in the Jiutian simulation to generate a light-cone halo/subhalo catalog. Next, galaxy luminosities are assigned to the main and subhalo populations using the subhalo abundance matching (SHAM) method with the DESI $z$-band luminosity functions at different redshifts. Multi-band photometries, as well as images, are then assigned to each mock galaxy using a 3-dimensional parameter space nearest neighbor sampling of the DESI LS observational galaxies and groups. Finally, the CSST and DESI LS survey geometry and magnitude limit cuts are applied to generate the required MGRSs. As we have checked, this set of MGRSs can generally reproduce the observed galaxy luminosity/mass functions within 0.1 dex for galaxies with $L > 10^8 L_\odot$ (or $M_* > 10^{8.5} M_\odot$) and within 1-$\sigma$ level for galaxies with $L < 10^8L_\odot$ (or $M_* < 10^{8.5} M_\odot$). Together with the CSST slitless spectra and redshifts for our DESI LS seed galaxies that are under construction, we will set out to test various slitless observational selection effects in subsequent probes., Comment: 13 pages, 9 figures, accepted for publication in MNRAS

We introduce a deep reinforcement learning (DRL) approach for solving management problems including inventory management, dynamic pricing, and recommendation. This DRL approach has the potential to lead to a large management model based on certain transformer neural network structures, resulting in an artificial general intelligence paradigm for various management tasks. Traditional methods have limitations for solving complex real-world problems, and we demonstrate how DRL can surpass existing heuristic approaches for solving management tasks. We aim to solve the problems in a unified framework, considering the interconnections between different tasks. Central to our methodology is the development of a foundational decision model coordinating decisions across the different domains through generative decision-making. Our experimental results affirm the effectiveness of our DRL-based framework in complex and dynamic business environments. This work opens new pathways for the application of DRL in management problems, highlighting its potential to revolutionize traditional business management.

The unique property of tantalum (Ta), particularly its long coherent lifetime in superconducting qubits and its exceptional resistance to both acid and alkali, makes it promising for superconducting quantum processors. It is a notable advantage to achieve high-performance quantum processors with neat and unified fabrication of all circuit elements, including coplanar waveguides (CPW), qubits, and airbridges, on the tantalum film-based platform. Here, we propose a reliable tantalum airbridges with separate or fully-capped structure fabricated via a novel lift-off method, where a barrier layer with aluminium (Al) film is first introduced to separate two layers of photoresist and then etched away before the deposition of tantalum film, followed by cleaning with piranha solution to remove the residual photoresist on the chip. We characterize such tantalum airbridges as the control line jumpers, the ground plane crossovers and even coupling elements. They exhibit excellent connectivity, minimal capacitive loss, effectively suppress microwave and flux crosstalk and offer high freedom of coupling. Besides, by presenting a surface-13 tunable coupling superconducting quantum processor with median $T_1$ reaching above 100 $\mu$s, the overall adaptability of tantalum airbridges is verified. The median single-qubit gate fidelity shows a tiny decrease from about 99.95% for the isolated Randomized Benchmarking to 99.94% for the simultaneous one. This fabrication method, compatible with all known superconducting materials, requires mild conditions of film deposition compared with the commonly used etching and grayscale lithography. Meanwhile, the experimental achievement of non-local coupling with controlled-Z (CZ) gate fidelity exceeding 99.2% may further facilitate qLDPC codes, laying a foundation for scalable quantum computation and quantum error correction with entirely tantalum elements., Comment: 15 pages, 10 figures

The baryonic feedback effect is an important systematic error in the weak lensing (WL) analysis. It contributes partly to the $S_8$ tension in the literature. With the next generations of large scale structure (LSS) and CMB experiments, the high signal-to-noise kinetic Sunyaev-Zel'dovich (kSZ) effect detection can tightly constrain the baryon distribution in and around dark matter halos, and quantify the baryonic effect in the weak lensing statistics. In this work, we apply the Fisher matrix technique to predict the future kSZ constraints on 3 kSZ-sensitive Baryon Correction Model (BCM) parameters. Our calculations show that, in combination with next generation LSS surveys, the 3rd generation CMB experiments such as AdvACT and Simon Observatory can constrain the matter power spectrum damping $S(k)$ to the precision of $\sigma_S(k)<0.8\%\sqrt{37.8{\rm Gpc}^3h^{-3}/V}$ at $k\lesssim 10h/$Mpc, where $V$ is the overlapped survey volume between the future LSS and CMB surveys. For the 4th generation CMB surveys such as CMB-S4 and CMB-HD, the constraint will be enhanced to $\sigma_S(k)<0.4\%\sqrt{37.8{\rm Gpc}^3h^{-3}/V}$. If extra-observations, e.g. X-ray detection and thermal SZ observation, can effectively fix the gas density profile slope parameter $\delta$, the constraint on $S(k)$ will be further boosted to $\sigma_S(k)<0.3\%\sqrt{37.8{\rm Gpc}^3h^{-3}/V}$ and $\sigma_S(k)<0.1\%\sqrt{37.8{\rm Gpc}^3h^{-3}/V}$ for the 3rd and 4th generation CMB surveys., Comment: 22 pages, 10 figures, minor revisions, JCAP accepted

We report a $\sim5.2\sigma$ detection of the kinetic Sunyaev-Zel'dovich (kSZ) effect in Fourier space, by combining the DESI galaxy groups and the Planck data. We use the density-weighted pairwise kSZ power spectrum as the summary statistic, and the detailed procedure of its measurement is presented in this paper. Meanwhile, we analyze the redshift space group density power spectrum to constrain its bias parameters and photo-z uncertainties. These best-fitted parameters are substituted to a nonlinear kSZ model, and we fit the measured kSZ power spectrum with this model to constrain the group optical depth $\bar{\tau}$. Selected by a varying lower mass threshold $M_{\rm th}$, the galaxy group catalogs with different median masses ($\tilde{M}$) are constructed from the DR9 data of the DESI Legacy Imaging Surveys. $\tilde{M}$ spans a wide range of $\sim10^{13}-10^{14}M_\odot/h$ and the heaviest $\tilde{M}\sim10^{14} M_\odot/h$ is larger than those of most other kSZ detections. When the aperture photometric filter radius $\theta_{\rm AP}$ is set to be $4.2$ arcmin, the $\tilde{M}=1.75\times10^{13}M_\odot/h$ group sample at the median redshift $\tilde{z}=0.64$ has the highest kSZ detection ${\rm S/N}=5.2$. By fitting $\bar{\tau}$s from various samples against their $\tilde{M}$s, we obtain a linear $\log\bar{\tau}-\log \tilde{M}$ relation: $\log\bar{\tau} = \gamma(\log \tilde{M}-14)+\log\beta$, in which $\gamma=0.55\pm0.1$. We also vary the aperture photometric filter radius and measure the $\bar{\tau}$ profiles of group samples, whose constraints on the baryon distribution within and around dark matter halos will be discussed in a companion paper., Comment: 25 pages, 14 figures, ApJS accepted