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The recent experiment shows the superconducting transition temperature in the Ruddlesden-Popper bilayer La$_3$Ni$_2$O$_{7}$ decreases monotonically with increasing pressure above 14 GPa. In order to unravel the underlying mechanism for this unusual dependence, we performed theoretical investigations by combining the density functional theory (DFT) and the unbiased functional renormalization group (FRG). Our DFT calculations show that the Fermi pockets are essentially unchanged with increasing pressure (above 14 GPa), but the bandwidth is enlarged, and particularly the interlayer hopping integral between the nickel $3d_{3z^2-r^2}$ orbitals is enhanced. From the DFT band structure, we construct the bilayer tight-binding model in terms of the nickel $3d_{3z^2-r^2}$ and $3d_{x^2-y^2}$ orbitals. On this basis, we investigate the superconductivity induced by correlation effects by FRG calculations. We find consistently $s_\pm$-wave pairing triggered by spin fluctuations, but the latter are weakened by pressure and lead to a decreasing transition temperature versus pressure, in qualitatively agreement with the experiment. We emphasize that the itinerancy of the $d$-orbitals is important and captured naturally in our FRG calculations, and we argue that the unusual pressure dependence would be unnatural, if not impossible, in the otherwise local-moment picture of the nickel $d$-orbitals. This sheds lights on the pertinent microscopic description of, and more importantly the mechanism of superconductivity in La$_3$Ni$_2$O$_{7}$., Comment: 8 pages, 4 figures

Quantum entanglement plays a critical role in many quantum applications, but detecting entanglement, especially in multipartite or high-dimensional quantum systems, remains a challenge. In this paper, we propose several families of entanglement criteria for detecting entanglement in multipartite or high-dimensional quantum states using generalized Wigner-Yanase skew information and variance. We also reveal a complementary character between the criteria based on generalized Wigner-Yanase skew information and an alternative one based on variance through specific examples. We illustrate the merits of these criteria and show that the combination of the entanglement criteria has a stronger detection capability, as it is capable of detecting entangled states that remain unrecognized by other criteria., Comment: 18 pages, 1 figure

Nonclassical correlation is an important concept in quantum information theory, referring to a special type of correlation that exists between quantum systems, which surpasses the scope of classical physics. In this paper, we introduce the concept of a family of information with important properties, namely the generalized Wigner-Yanase skew information, of which the famous quantum Fisher information and Wigner-Yanase skew information are special cases.We classify the local observables in the generalized Wigner-Yanase skew information into two categories (i.e., orthonormal bases and a Hermitian operator with a fixed nondegenerate spectrum), and based on this, we propose two different forms of indicators to quantify nonclassical correlations of bipartite quantum states. We have not only investigated some important properties of these two kinds of indicators but also illustrated through specific examples that they can indeed capture some nonclassical correlations. Furthermore, we find that these two types of indicators reduce to entanglement measure for bipartite pure states. Specifically, we also derive the relationship between these two indicators and the entanglement measure $I$-concurrence., Comment: 10 pages

Pursuing higher-temperature superconductors under ambient pressure continues to be a prominent topic in materials discovery. Isomorphic structures like MgB2 exhibit potential for conventional BCS-type superconductivity, but their transition temperatures (Tc) have remained below 100 K based on both experimental findings and theoretical predictions. In this study, two new two-dimensional (2D) superconductors with sandwich structures,KB2C2,featuring BC layers in AA and AB stacking configurations,are designed, whose Tc can exceed 112 K,setting a new record in 2D superconductors. The analyses suggest that electrons in {\sigma}-states covalent bonds and high-frequency E phonon modes dominated by the in-plane vibrations of B/C atoms are predominately responsible for electron-phonon coupling (EPC). An exciting robust three-gap superconducting nature stems from the strong and evident three-region distribution characteristic of electronic EPC parameters {\lambda}. When biaxial tensile strain (BTS) is applied, their Tc are boosted above 153 K. The increase in Tc originates from the softening of optical E phonon modes around the {\Gamma} point and acoustic modes around the Q point, rather than an increase of electrons at the Fermi level (EF ) as observed in other similar systems. Thus, phonon plays a more beneficial role in the EPC of BTS cases, highlighting its significance as a medium in BCS superconductors. Moreover, we find KB2C2 exhibits interesting topological properties, spin antivortex, and Ising-type spin splitting. This is the first report of the coexistence of nontrivial topology and superconductivity with such a high Tc. Therefore, KB2C2 may offer promising sandwich structures to explore higher-Tc 2D superconductors, alongside present potential avenues for investigating fundamental quantum physics., Comment: 8 pages, 3 figures

Although the metalization of semiconductor bulk LiBC has been experimentally achieved, various flaws, including the strong lattice distortion, the uncontrollability of phase transition under pressure, usually appear. In this work, based on the first-principles calculations, we propose a new way of hydrogenation to realize metalization. Using the fully anisotropic Migdal-Eliashberg theory, we investigate the superconducting behaviors in the stable monolayers LiBCH and LiCBH, in which C and B atoms are hydrogenated, respectively. Our findings indicate that the monolayers possess the high $T_{c}$ of 82.0 and 82.5 K, respectively, along with the interesting three-gap superconducting natures. The Fermi sheets showing the obvious three-region distribution characteristics and the abnormally strong electron-phonon coupling (EPC) are responsible for the high-$T_{c}$ three-gap superconductivity. Furthermore, the $T_{c}$ can be dramatically boosted up to 120.0 K under 3.5 \% tensile strain. To a great extent, the high $T_{c}$ is beyond the liquid nitrogen temperature ($77$ K), which is beneficial for the applications in future experiments. This study not only explores the superconducting properties of the monolayers LiBCH and LiCBH, but also offers practical insights into the search for high-$T_{c}$ superconductors., Comment: 4 figures. Comments are welcome

Recently, video generation techniques have advanced rapidly. Given the popularity of video content on social media platforms, these models intensify concerns about the spread of fake information. Therefore, there is a growing demand for detectors capable of distinguishing between fake AI-generated videos and mitigating the potential harm caused by fake information. However, the lack of large-scale datasets from the most advanced video generators poses a barrier to the development of such detectors. To address this gap, we introduce the first AI-generated video detection dataset, GenVideo. It features the following characteristics: (1) a large volume of videos, including over one million AI-generated and real videos collected; (2) a rich diversity of generated content and methodologies, covering a broad spectrum of video categories and generation techniques. We conducted extensive studies of the dataset and proposed two evaluation methods tailored for real-world-like scenarios to assess the detectors' performance: the cross-generator video classification task assesses the generalizability of trained detectors on generators; the degraded video classification task evaluates the robustness of detectors to handle videos that have degraded in quality during dissemination. Moreover, we introduced a plug-and-play module, named Detail Mamba (DeMamba), designed to enhance the detectors by identifying AI-generated videos through the analysis of inconsistencies in temporal and spatial dimensions. Our extensive experiments demonstrate DeMamba's superior generalizability and robustness on GenVideo compared to existing detectors. We believe that the GenVideo dataset and the DeMamba module will significantly advance the field of AI-generated video detection. Our code and dataset will be aviliable at \url{https://github.com/chenhaoxing/DeMamba}.

This study reveals a cutting-edge re-balanced contrastive learning strategy aimed at strengthening face anti-spoofing capabilities within facial recognition systems, with a focus on countering the challenges posed by printed photos, and highly realistic silicone or latex masks. Leveraging the HySpeFAS dataset, which benefits from Snapshot Spectral Imaging technology to provide hyperspectral images, our approach harmonizes class-level contrastive learning with data resampling and an innovative real-face oriented reweighting technique. This method effectively mitigates dataset imbalances and reduces identity-related biases. Notably, our strategy achieved an unprecedented 0.0000\% Average Classification Error Rate (ACER) on the HySpeFAS dataset, ranking first at the Chalearn Snapshot Spectral Imaging Face Anti-spoofing Challenge on CVPR 2024., Comment: We rank first at the Chalearn Snapshot Spectral Imaging Face Anti-spoofing Challenge on CVPR 2024; the paper is accepted by CVPR 2024 workshop

Text-to-image generation models have seen considerable advancement, catering to the increasing interest in personalized image creation. Current customization techniques often necessitate users to provide multiple images (typically 3-5) for each customized object, along with the classification of these objects and descriptive textual prompts for scenes. This paper questions whether the process can be made more user-friendly and the customization more intricate. We propose a method where users need only provide images along with text for each customization topic, and necessitates only a single image per visual concept. We introduce the concept of a ``multi-modal prompt'', a novel integration of text and images tailored to each customization concept, which simplifies user interaction and facilitates precise customization of both objects and scenes. Our proposed paradigm for customized text-to-image generation surpasses existing finetune-based methods in user-friendliness and the ability to customize complex objects with user-friendly inputs. Our code is available at $\href{https://github.com/zhongzero/Multi-Modal-Prompt}{https://github.com/zhongzero/Multi-Modal-Prompt}$., Comment: 11 pages, 8 figures

Image inpainting, the task of reconstructing missing segments in corrupted images using available data, faces challenges in ensuring consistency and fidelity, especially under information-scarce conditions. Traditional evaluation methods, heavily dependent on the existence of unmasked reference images, inherently favor certain inpainting outcomes, introducing biases. Addressing this issue, we introduce an innovative evaluation paradigm that utilizes a self-supervised metric based on multiple re-inpainting passes. This approach, diverging from conventional reliance on direct comparisons in pixel or feature space with original images, emphasizes the principle of self-consistency to enable the exploration of various viable inpainting solutions, effectively reducing biases. Our extensive experiments across numerous benchmarks validate the alignment of our evaluation method with human judgment.

In this work, we theoretically report a new large family of two-dimensional (2D) transition metal sulfides $M$$_{2}$S with MXene structure in 2H and 1T phases, which we name as MSene. Twenty-four out of fifty-eight MSenes are proved to be stable. Notably, this family includes twelve superconducting (SC) materials, seven SC topological metals (SCTMs), four charge density wave (CDW) materials, and five magnetic materials including one ferromagnetic (FM) and four antiferromagnetic (AFM) materials. For example, 2H-Mo$_{2}$S is a SCTM which exhibits SC critical temperature ($T_{c}$) of 10.2 K and nontrivial topological properties; 1T-Hf$_{2}$S is a CDW material with the CDW originating from electron-phonon coupling. The CDW can be suppressed by compressive strain, leading to the emergence of superconductivity; 2H-Cr$_{2}$S and 1T-Mn$_{2}$S show FM and AFM properties, respectively. Thus, the new large family we predicted shows rich physical properties and significantly expands the repertoire of 2D materials. It serves as a novel platform for investigating the competition or coexistence of multiple orders such as SC, CDW, FM, AFM and topological orders in 2D materials., Comment: 6 pages, 5 figures

Two-dimensional (2D) intrinsic superconductors with nontrivial topological band and vertical ferroelectricity exhibit fascinating characteristics to achieving electrostatic control of quantum phases. While, only a few such 2D materials have been theoretically predicted. In this work, based on first principles calculations, we explore the superconductivity and ferroelectric properties in fluorinated 2D Nb2N. In the stable Nb2NF2, H3-Nb2NF2 breaks the spatial inversion symmetry, exhibiting vertical ferroelectric. More interestingly, it not only possesses intrinsic superconductivity with superconducting transition temperatures (Tc) of 10 K, but also exhibits nontrivial band topology. While, H1-Nb2NF2 shows topological band and superconductivity with Tc of 32 K, surpassing most of 2D conventional topological superconductors' candidates. Our research has enriched 2D superconducting materials with nontrivial band topology and ferroelectric properties, and provided a theoretical basis for the preparation of devices switching between superconducting and ferroelectric states with external electric field.

Pre-trained large-scale vision-language models (VLMs) have acquired profound understanding of general visual concepts. Recent advancements in efficient transfer learning (ETL) have shown remarkable success in fine-tuning VLMs within the scenario of limited data, introducing only a few parameters to harness task-specific insights from VLMs. Despite significant progress, current leading ETL methods tend to overfit the narrow distributions of base classes seen during training and encounter two primary challenges: (i) only utilizing uni-modal information to modeling task-specific knowledge; and (ii) using costly and time-consuming methods to supplement knowledge. To address these issues, we propose a Conditional Prototype Rectification Prompt Learning (CPR) method to correct the bias of base examples and augment limited data in an effective way. Specifically, we alleviate overfitting on base classes from two aspects. First, each input image acquires knowledge from both textual and visual prototypes, and then generates sample-conditional text tokens. Second, we extract utilizable knowledge from unlabeled data to further refine the prototypes. These two strategies mitigate biases stemming from base classes, yielding a more effective classifier. Extensive experiments on 11 benchmark datasets show that our CPR achieves state-of-the-art performance on both few-shot classification and base-to-new generalization tasks. Our code is avaliable at \url{https://github.com/chenhaoxing/CPR}.

Recent advancements in personalizing text-to-image (T2I) diffusion models have shown the capability to generate images based on personalized visual concepts using a limited number of user-provided examples. However, these models often struggle with maintaining high visual fidelity, particularly in manipulating scenes as defined by textual inputs. Addressing this, we introduce ComFusion, a novel approach that leverages pretrained models generating composition of a few user-provided subject images and predefined-text scenes, effectively fusing visual-subject instances with textual-specific scenes, resulting in the generation of high-fidelity instances within diverse scenes. ComFusion integrates a class-scene prior preservation regularization, which leverages composites the subject class and scene-specific knowledge from pretrained models to enhance generation fidelity. Additionally, ComFusion uses coarse generated images, ensuring they align effectively with both the instance image and scene texts. Consequently, ComFusion maintains a delicate balance between capturing the essence of the subject and maintaining scene fidelity.Extensive evaluations of ComFusion against various baselines in T2I personalization have demonstrated its qualitative and quantitative superiority.

The extraordinary ability of generative models enabled the generation of images with such high quality that human beings cannot distinguish Artificial Intelligence (AI) generated images from real-life photographs. The development of generation techniques opened up new opportunities but concurrently introduced potential risks to privacy, authenticity, and security. Therefore, the task of detecting AI-generated imagery is of paramount importance to prevent illegal activities. To assess the generalizability and robustness of AI-generated image detection, we present a large-scale dataset, referred to as WildFake, comprising state-of-the-art generators, diverse object categories, and real-world applications. WildFake dataset has the following advantages: 1) Rich Content with Wild collection: WildFake collects fake images from the open-source community, enriching its diversity with a broad range of image classes and image styles. 2) Hierarchical structure: WildFake contains fake images synthesized by different types of generators from GANs, diffusion models, to other generative models. These key strengths enhance the generalization and robustness of detectors trained on WildFake, thereby demonstrating WildFake's considerable relevance and effectiveness for AI-generated detectors in real-world scenarios. Moreover, our extensive evaluation experiments are tailored to yield profound insights into the capabilities of different levels of generative models, a distinctive advantage afforded by WildFake's unique hierarchical structure.

The recent discovery of bulk superconductivity in trilayer nickelate La$_4$Ni$_3$O$_{10}$ with the critical temperature $T_c$ near $30$K under high pressure is attracting a new wave of research interest, after the breakthrough of bilayer La$_3$Ni$_2$O$_7$ with $T_c$ near $80$K. The similarities and differences of electronic structure and superconducting mechanism in these two systems are urgent theoretical issues. In this Letter, we study the electronic band structure and construct a minimal trilayer tight-binding model for the high-pressure phase of La$_4$Ni$_3$O$_{10}$ in terms of the nickel $3d_{x^2-y^2}$ and $3d_{3z^2-r^2}$ orbitals, and study the superconducting mechanism due to local Coulomb interactions by the unbiased functional renormalization group. We find antiferromagnetic correlations between the outer layers instead of neighboring ones, apart from the inplane correlations. The effective interaction induces Cooper pairing with the $s_\pm$-wave symmetry, which changes sign across the Fermi pockets. We find $T_c$ in La$_4$Ni$_3$O$_{10}$ is systematically lower than that in La$_3$Ni$_2$O$_7$, and electron doping can enhance $T_c$., Comment: 4 pages, 4 figures, 1 table

Painterly image harmonization aims to harmonize a photographic foreground object on the painterly background. Different from previous auto-encoder based harmonization networks, we develop a progressive multi-stage harmonization network, which harmonizes the composite foreground from low-level styles (e.g., color, simple texture) to high-level styles (e.g., complex texture). Our network has better interpretability and harmonization performance. Moreover, we design an early-exit strategy to automatically decide the proper stage to exit, which can skip the unnecessary and even harmful late stages. Extensive experiments on the benchmark dataset demonstrate the effectiveness of our progressive harmonization network., Comment: Accepted by AAAI 2024

Given a composite image with photographic object and painterly background, painterly image harmonization targets at stylizing the composite object to be compatible with the background. Despite the competitive performance of existing painterly harmonization works, they did not fully leverage the painterly objects in artistic paintings. In this work, we explore learning from painterly objects for painterly image harmonization. In particular, we learn a mapping from background style and object information to object style based on painterly objects in artistic paintings. With the learnt mapping, we can hallucinate the target style of composite object, which is used to harmonize encoder feature maps to produce the harmonized image. Extensive experiments on the benchmark dataset demonstrate the effectiveness of our proposed method., Comment: Accepted by AAAI 2024

The deposition and intercalation of metal atoms can induce superconductivity in monolayer and bilayer graphenes. For example, it has been experimentally proved that Li-deposited graphene is a superconductor with critical temperature $T_{c}$ of 5.9 K, Ca-intercalated bilayer graphene C$_{6}$CaC$_{6}$ and K-intercalated epitaxial bilayer graphene C$_{8}$KC$_{8}$ are superconductors with $T_{c}$ of 2-4 K and 3.6 K, respectively. However, the $T_{c}$ of them are relatively low. To obtain higher $T_{c}$ in graphene-based superconductors, here we predict a new Ca-intercalated bilayer graphene C$_{2}$CaC$_{2}$, which shows higher Ca concentration than the C$_{6}$CaC$_{6}$. It is proved to be thermodynamically and dynamically stable. The electronic structure, electron-phonon coupling (EPC) and superconductivity of C$_{2}$CaC$_{2}$ are investigated based on first-principles calculations. The EPC of C$_{2}$CaC$_{2}$ mainly comes from the coupling between the electrons of C-$p_{z}$ orbital and the high- and low-frequency vibration modes of C atoms. The calculated EPC constant $\lambda$ of C$_{2}$CaC$_{2}$ is 0.75, and the superconducting $T_{c}$ is 18.9 K, which is much higher than other metal-intercalated bilayer graphenes. By further applying -4\% biaxial compressive strain to C$_{2}$CaC$_{2}$, the $T_{c}$ can be boosted to 26.6 K. Thus, the predicted C$_{2}$CaC$_{2}$ provides a new platform for realizing superconductivity with the highest $T_{c}$ in bilayer graphenes., Comment: 29 pages,11 figures

Audio-visual zero-shot learning aims to recognize unseen classes based on paired audio-visual sequences. Recent methods mainly focus on learning multi-modal features aligned with class names to enhance the generalization ability to unseen categories. However, these approaches ignore the obscure event concepts in class names and may inevitably introduce complex network structures with difficult training objectives. In this paper, we introduce a straightforward yet efficient framework called KnowleDge-Augmented audio-visual learning (KDA), which aids the model in more effectively learning novel event content by leveraging an external knowledge base. Specifically, we first propose to utilize the knowledge contained in large language models (LLMs) to generate numerous descriptive sentences that include important distinguishing audio-visual features of event classes, which helps to better understand unseen categories. Furthermore, we propose a knowledge-aware adaptive margin loss to help distinguish similar events, further improving the generalization ability towards unseen classes. Extensive experimental results demonstrate that our proposed KDA can outperform state-of-the-art methods on three popular audio-visual zero-shot learning datasets.Our code will be avaliable at \url{https://github.com/chenhaoxing/KDA}.

Image compositing plays a vital role in photo editing. After inserting a foreground object into another background image, the composite image may look unnatural and inharmonious. When the foreground is photorealistic and the background is an artistic painting, painterly image harmonization aims to transfer the style of background painting to the foreground object, which is a challenging task due to the large domain gap between foreground and background. In this work, we employ adversarial learning to bridge the domain gap between foreground feature map and background feature map. Specifically, we design a dual-encoder generator, in which the residual encoder produces the residual features added to the foreground feature map from main encoder. Then, a pixel-wise discriminator plays against the generator, encouraging the refined foreground feature map to be indistinguishable from background feature map. Extensive experiments demonstrate that our method could achieve more harmonious and visually appealing results than previous methods., Comment: Accepted by WACV2024

Kuiper's $V_n$ statistic, a measure for comparing the difference of ideal distribution and empirical distribution, is of great significance in the goodness-of-fit test. However, Kuiper's formulae for computing the cumulative distribution function, false positive probability and the upper tail quantile of $V_n$can not be applied to the case of small sample capacity $n$ since the approximation error is $\mathcal{O}(n^{-1})$. In this work, our contributions lie in three perspectives: firstly the approximation error is reduced to $\mathcal{O}(n^{-(k+1)/2})$ where $k$ is the expansion order with the \textit{high order expansion} (HOE) for the exponent of differential operator; secondly, a novel high order formula with approximation error $\mathcal{O}(n^{-3})$ is obtained by massive calculations; thirdly, the fixed-point algorithms are designed for solving the Kuiper pair of critical values and upper tail quantiles based on the novel formula. The high order expansion method for Kuiper's $V_n$-statistic is applicable for various applications where there are more than $5$ samples of data. The principles, algorithms and code for the high order expansion method are attractive for the goodness-of-fit test., Comment: arXiv admin note: text overlap with arXiv:2308.09463

The Hurst exponent is a significant indicator for characterizing the self-similarity and long-term memory properties of time sequences. It has wide applications in physics, technologies, engineering, mathematics, statistics, economics, psychology and so on. Currently, available methods for estimating the Hurst exponent of time sequences can be divided into different categories: time-domain methods and spectrum-domain methods based on the representation of time sequence, linear regression methods and Bayesian methods based on parameter estimation methods. Although various methods are discussed in literature, there are still some deficiencies: the descriptions of the estimation algorithms are just mathematics-oriented and the pseudo-codes are missing; the effectiveness and accuracy of the estimation algorithms are not clear; the classification of estimation methods is not considered and there is a lack of guidance for selecting the estimation methods. In this work, the emphasis is put on thirteen dominant methods for estimating the Hurst exponent. For the purpose of decreasing the difficulty of implementing the estimation methods with computer programs, the mathematical principles are discussed briefly and the pseudo-codes of algorithms are presented with necessary details. It is expected that the survey could help the researchers to select, implement and apply the estimation algorithms of interest in practical situations in an easy way., Comment: 46 pages, 8 figures, 4 tables, 24 algorithms with pseudo-codes

The detection of multipartite entanglement in multipartite quantum systems is a fundamental and key issue in quantum information theory. In this paper, we investigate $k$-nonseparability and $k$-partite entanglement of $N$-partite quantum systems from the perspective of the generalized Wigner-Yanase skew information introduced by Yang $et$ $al$. [\href{https://doi.org/10.1103/PhysRevA.106.052401 }{Phys. Rev. A \textbf{106}, 052401 (2022)}]. More specifically, we develop two different approaches in form of inequalities to construct entanglement criteria, which are expressed in terms of the generalized Wigner-Yanase skew information. Any violation of these inequalities by a quantum state reveals its $k$-nonseparability or $k$-partite entanglement, so these inequalities present the hierarchic classifications of $k$-nonseparability or $k$-partite entanglement for all $N$-partite quantum states from $N$-nonseparability to $2$-nonseparability or from $2$-partite entanglement to $N$-partite entanglement, which are more refined than well-known ways. It is shown that our results reveal some $k$-nonseparability and $k$-partite entanglement that remain undetected by other methods, and these are illustrated through some examples., Comment: 12 pages, 2 figures

Image composition targets at synthesizing a realistic composite image from a pair of foreground and background images. Recently, generative composition methods are built on large pretrained diffusion models to generate composite images, considering their great potential in image generation. However, they suffer from lack of controllability on foreground attributes and poor preservation of foreground identity. To address these challenges, we propose a controllable image composition method that unifies four tasks in one diffusion model: image blending, image harmonization, view synthesis, and generative composition. Meanwhile, we design a self-supervised training framework coupled with a tailored pipeline of training data preparation. Moreover, we propose a local enhancement module to enhance the foreground details in the diffusion model, improving the foreground fidelity of composite images. The proposed method is evaluated on both public benchmark and real-world data, which demonstrates that our method can generate more faithful and controllable composite images than existing approaches. The code and model will be available at https://github.com/bcmi/ControlCom-Image-Composition.

Kuiper's statistic is a good measure for the difference of ideal distribution and empirical distribution in the goodness-of-fit test. However, it is a challenging problem to solve the critical value and upper tail quantile, or simply Kuiper pair, of Kuiper's statistics due to the difficulties of solving the nonlinear equation and reasonable approximation of infinite series. In this work, the contributions lie in three perspectives: firstly, the second order approximation for the infinite series of the cumulative distribution of the critical value is used to achieve higher precision; secondly, the principles and fixed-point algorithms for solving the Kuiper pair are presented with details; finally, finally, a mistake about the critical value $c^\alpha_n$ for $(\alpha, n)=(0.01,30)$ in Kuiper's distribution table has been labeled and corrected where $n$ is the sample capacity and $\alpha$ is the upper tail quantile. The algorithms are verified and validated by comparing with the table provided by Kuiper. The methods and algorithms proposed are enlightening and worth of introducing to the college students, computer programmers, engineers, experimental psychologists and so on., Comment: 20 pages, 6 figures, 5 tables, code available on GitHub