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This paper proposes FAST-LIVO2: a fast, direct LiDAR-inertial-visual odometry framework to achieve accurate and robust state estimation in SLAM tasks and provide great potential in real-time, onboard robotic applications. FAST-LIVO2 fuses the IMU, LiDAR and image measurements efficiently through an ESIKF. To address the dimension mismatch between the heterogeneous LiDAR and image measurements, we use a sequential update strategy in the Kalman filter. To enhance the efficiency, we use direct methods for both the visual and LiDAR fusion, where the LiDAR module registers raw points without extracting edge or plane features and the visual module minimizes direct photometric errors without extracting ORB or FAST corner features. The fusion of both visual and LiDAR measurements is based on a single unified voxel map where the LiDAR module constructs the geometric structure for registering new LiDAR scans and the visual module attaches image patches to the LiDAR points. To enhance the accuracy of image alignment, we use plane priors from the LiDAR points in the voxel map (and even refine the plane prior) and update the reference patch dynamically after new images are aligned. Furthermore, to enhance the robustness of image alignment, FAST-LIVO2 employs an on-demanding raycast operation and estimates the image exposure time in real time. Lastly, we detail three applications of FAST-LIVO2: UAV onboard navigation demonstrating the system's computation efficiency for real-time onboard navigation, airborne mapping showcasing the system's mapping accuracy, and 3D model rendering (mesh-based and NeRF-based) underscoring the suitability of our reconstructed dense map for subsequent rendering tasks. We open source our code, dataset and application on GitHub to benefit the robotics community., Comment: 30 pages, 31 figures, due to the limitation that 'The abstract field cannot exceed 1,920 characters', the abstract presented here is shorter than the one in the PDF file

Recent advances in unsupervised deep graph clustering have been significantly promoted by contrastive learning. Despite the strides, most graph contrastive learning models face challenges: 1) graph augmentation is used to improve learning diversity, but commonly used random augmentation methods may destroy inherent semantics and cause noise; 2) the fixed positive and negative sample selection strategy is limited to deal with complex real data, thereby impeding the model's capability to capture fine-grained patterns and relationships. To reduce these problems, we propose the Clustering-guided Curriculum Graph contrastive Learning (CCGL) framework. CCGL uses clustering entropy as the guidance of the following graph augmentation and contrastive learning. Specifically, according to the clustering entropy, the intra-class edges and important features are emphasized in augmentation. Then, a multi-task curriculum learning scheme is proposed, which employs the clustering guidance to shift the focus from the discrimination task to the clustering task. In this way, the sample selection strategy of contrastive learning can be adjusted adaptively from early to late stage, which enhances the model's flexibility for complex data structure. Experimental results demonstrate that CCGL has achieved excellent performance compared to state-of-the-art competitors.

Clustering is a fundamental task in machine learning and data science, and similarity graph-based clustering is an important approach within this domain. Doubly stochastic symmetric similarity graphs provide numerous benefits for clustering problems and downstream tasks, yet learning such graphs remains a significant challenge. Marcus theorem states that a strictly positive symmetric matrix can be transformed into a doubly stochastic symmetric matrix by diagonal matrices. However, in clustering, learning sparse matrices is crucial for computational efficiency. We extend Marcus theorem by proposing the Marcus mapping, which indicates that certain sparse matrices can also be transformed into doubly stochastic symmetric matrices via diagonal matrices. Additionally, we introduce rank constraints into the clustering problem and propose the Doubly Stochastic Adaptive Neighbors Clustering algorithm based on the Marcus Mapping (ANCMM). This ensures that the learned graph naturally divides into the desired number of clusters. We validate the effectiveness of our algorithm through extensive comparisons with state-of-the-art algorithms. Finally, we explore the relationship between the Marcus mapping and optimal transport. We prove that the Marcus mapping solves a specific type of optimal transport problem and demonstrate that solving this problem through Marcus mapping is more efficient than directly applying optimal transport methods.

Ensemble learning is a method that leverages weak learners to produce a strong learner. However, obtaining a large number of base learners requires substantial time and computational resources. Therefore, it is meaningful to study how to achieve the performance typically obtained with many base learners using only a few. We argue that to achieve this, it is essential to enhance both classification performance and generalization ability during the ensemble process. To increase model accuracy, each weak base learner needs to be more efficiently integrated. It is observed that different base learners exhibit varying levels of accuracy in predicting different classes. To capitalize on this, we introduce confidence tensors $\tilde{\mathbf{\Theta}}$ and $\tilde{\mathbf{\Theta}}_{rst}$ signifies the degree of confidence that the $t$-th base classifier assigns the sample to class $r$ while it actually belongs to class $s$. To the best of our knowledge, this is the first time an evaluation of the performance of base classifiers across different classes has been proposed. The proposed confidence tensor compensates for the strengths and weaknesses of each base classifier in different classes, enabling the method to achieve superior results with a smaller number of base learners. To enhance generalization performance, we design a smooth and convex objective function that leverages the concept of margin, making the strong learner more discriminative. Furthermore, it is proved that in gradient matrix of the loss function, the sum of each column's elements is zero, allowing us to solve a constrained optimization problem using gradient-based methods. We then compare our algorithm with random forests of ten times the size and other classical methods across numerous datasets, demonstrating the superiority of our approach.

A novel approach for describing the evolution of nucleon structure from the low-$Q^2$ regime to the high-$Q^2$ asymptotic region is proposed. This infrared-safe scheme modifies the parton distribution evolution equations to incorporate the corrections from emergent hadron mass mechanisms and parton-parton recombination at low $Q^2$. The effective parton mass, generated by dynamical chiral symmetry breaking, slows the evolution of parton distributions in the infrared region, causing the DGLAP evolution to freeze when $Q^2\ll M_{\rm q/g}$. Notably, this scheme renders the high-$Q^2$ parton distributions insensitive to the choice of input hadronic scale. The parton-parton recombination effect is crucial in suppressing the rapid growth of parton distributions at small $x$, consistent with experimental data. When applied to three valence quark distributions derived from a quark model, our scheme yields parton distributions that agree well with deep-inelastic scattering data in both large-$x$ and small-$x$ regions, providing a unified description of nucleon structure across the entire $Q^2$ range., Comment: 10 pages, 5 figures

The development of different theories of discourse structure has led to the establishment of discourse corpora based on these theories. However, the existence of discourse corpora established on different theoretical bases creates challenges when it comes to exploring them in a consistent and cohesive way. This study has as its primary focus the conversion of PDTB annotations into dependency structures. It employs refined BERT-based discourse parsers to test the validity of the dependency data derived from the PDTB-style corpora in English, Chinese, and several other languages. By converting both PDTB and RST annotations for the same texts into dependencies, this study also applies ``dependency distance'' metrics to examine the correlation between RST dependencies and PDTB dependencies in English. The results show that the PDTB dependency data is valid and that there is a strong correlation between the two types of dependency distance. This study presents a comprehensive approach for analyzing and evaluating discourse corpora by employing discourse dependencies to achieve unified analysis. By applying dependency representations, we can extract data from PDTB, RST, and SDRT corpora in a coherent and unified manner. Moreover, the cross-linguistic validation establishes the framework's generalizability beyond English. The establishment of this comprehensive dependency framework overcomes limitations of existing discourse corpora, supporting a diverse range of algorithms and facilitating further studies in computational discourse analysis and language sciences.

Animating stylized characters to match a reference motion sequence is a highly demanded task in film and gaming industries. Existing methods mostly focus on rigid deformations of characters' body, neglecting local deformations on the apparel driven by physical dynamics. They deform apparel the same way as the body, leading to results with limited details and unrealistic artifacts, e.g. body-apparel penetration. In contrast, we present a novel method aiming for high-quality motion transfer with realistic apparel animation. As existing datasets lack annotations necessary for generating realistic apparel animations, we build a new dataset named MMDMC, which combines stylized characters from the MikuMikuDance community with real-world Motion Capture data. We then propose a data-driven pipeline that learns to disentangle body and apparel deformations via two neural deformation modules. For body parts, we propose a geodesic attention block to effectively incorporate semantic priors into skeletal body deformation to tackle complex body shapes for stylized characters. Since apparel motion can significantly deviate from respective body joints, we propose to model apparel deformation in a non-linear vertex displacement field conditioned on its historic states. Extensive experiments show that our method produces results with superior quality for various types of apparel. Our dataset is released in https://github.com/rongakowang/MMDMC., Comment: Accepted to ECCV 2024

Three-nucleon short-range correlation ($3N$ SRC) represents a rare and intriguing part of the nuclear dynamics at short distance, beyond the two-nucleon short-range correlation ($2N$ SRC). To search its existence is a hot topic in the ongoing and future high-energy nuclear experiments and the developments of nuclear theory. In this study, we found a positive sign of $3N$ SRC in nuclei, by analyzing the correlation between the per-nucleon nuclear mass and the probability of a nucleon in $2N$ SRC state, with the current experimental measurements of $^2$H, $^3$He, $^4$He, $^9$Be, $^{12}$C, $^{27}$Al, $^{56}$Fe, Cu, $^{197}$Au and $^{208}$Pb from SLAC, CLAS, and JLab Hall C collaborations. The effective masses of the nucleons in $2N$ SRC and $3N$ SRC are also extracted from the analysis, which provide some references for the nuclear medium effect study. The probability of $3N$ SRC is much smaller than that of $2N$ SRC, thus requiring high-luminosity experiments to confirm its existence., Comment: 7 pages, 3 figures

As a Goldstone boson with zero quantum number and zero SM charge, the decays of long-lived $\eta$ ($\eta^{\prime}$) meson provide a unique window to search new physics beyond the standard model and new sources of CP violation, to test the low-energy QCD theory, and to measure the fundamental parameters of light quarks. For such goals in the physics frontiers we discuss a plan of building a super $\eta$ factory at HIAF high-energy terminal or at CiADS after upgrade. The high-intensity proton beam at HIAF provides a great opportunity of producing a huge number of $\eta$ samples of more than $10^{13}$ events per year, with multiple layers of thin targets of light nucleus. The physics goals, the first-version conceptual design of the spectrometer, and the preliminary simulation results are present., Comment: 19 pages, 9 figures

The traditional personality models only yield binary results. This paper presents a novel approach for training personality detection models that produce continuous output values, using mixed strategies. By leveraging the PANDORA dataset, which includes extensive personality labeling of Reddit comments, we developed models that predict the Big Five personality traits with high accuracy. Our approach involves fine-tuning a RoBERTa-base model with various strategies such as Multi-Layer Perceptron (MLP) integration, and hyperparameter tuning. The results demonstrate that our models significantly outperform traditional binary classification methods, offering precise continuous outputs for personality traits, thus enhancing applications in AI, psychology, human resources, marketing and health care fields.

In quantum Shannon theory, various kinds of quantum entropies are used to characterize the capacities of noisy physical systems. Among them, min-entropy and its smooth version attract wide interest especially in the field of quantum cryptography as they can be used to bound the information obtained by an adversary. However, calculating the exact value or non-trivial bounds of min-entropy are extremely difficult because the composite system dimension may scale exponentially with the dimension of its subsystem. Here, we develop a one-shot lower bound calculation technique for the min-entropy of a classical-quantum state that is applicable to both finite and infinite dimensional reduced quantum states. Moreover, we show our technique is of practical interest in at least two situations. First, it gives an alternative tight finite-data analysis for the well-known BB84 quantum key distribution protocol. More importantly, it provides a security proof for a novel source-independent continuous-variable quantum random number generation protocol. These show the effectiveness and wide applicability of our approach.

Machine Translation (MT) Quality Estimation (QE) assesses translation reliability without reference texts. This study introduces "textual similarity" as a new metric for QE, using sentence transformers and cosine similarity to measure semantic closeness. Analyzing data from the MLQE-PE dataset, we found that textual similarity exhibits stronger correlations with human scores than traditional metrics (hter, model evaluation, sentence probability etc.). Employing GAMMs as a statistical tool, we demonstrated that textual similarity consistently outperforms other metrics across multiple language pairs in predicting human scores. We also found that "hter" actually failed to predict human scores in QE. Our findings highlight the effectiveness of textual similarity as a robust QE metric, recommending its integration with other metrics into QE frameworks and MT system training for improved accuracy and usability.

Automated essay scoring (AES) involves predicting a score that reflects the writing quality of an essay. Most existing AES systems produce only a single overall score. However, users and L2 learners expect scores across different dimensions (e.g., vocabulary, grammar, coherence) for English essays in real-world applications. To address this need, we have developed two models that automatically score English essays across multiple dimensions by employing fine-tuning and other strategies on two large datasets. The results demonstrate that our systems achieve impressive performance in evaluation using three criteria: precision, F1 score, and Quadratic Weighted Kappa. Furthermore, our system outperforms existing methods in overall scoring.

With built-in eye-tracking cameras, the recently released Apple Vision Pro (AVP) mixed reality (MR) headset features gaze-based interaction, eye image rendering on external screens, and iris recognition for device unlocking. One of the technological advancements of the AVP is its heavy reliance on gaze- and gesture-based interaction. However, limited information is available regarding the technological specifications of the eye-tracking capability of the AVP, and raw gaze data is inaccessible to developers. This study evaluates the eye-tracking accuracy of the AVP with two sets of tests spanning both MR and virtual reality (VR) applications. This study also examines how eye-tracking accuracy relates to user-reported usability. The results revealed an overall eye-tracking accuracy of 1.11{\deg} and 0.93{\deg} in two testing setups, within a field of view (FOV) of approximately 34{\deg} x 18{\deg}. The usability and learnability scores of the AVP, measured using the standard System Usability Scale (SUS), were 75.24 and 68.26, respectively. Importantly, no statistically reliable correlation was found between eye-tracking accuracy and usability scores. These results suggest that eye-tracking accuracy is critical for gaze-based interaction, but it is not the sole determinant of user experience in VR/AR., Comment: 16 pages, 6 figures and 3 tables

Ordinal regression is a specialized supervised problem where the labels show an inherent order. The order distinguishes it from normal multi-class problem. Support Vector Ordinal Regression, as an outstanding ordinal regression model, is widely used in many ordinal regression tasks. However, like most supervised learning algorithms, the design of SVOR is based on the assumption that the training data are real and reliable, which is difficult to satisfy in real-world data. In many practical applications, outliers are frequently present in the training set, potentially leading to misguide the learning process, such that the performance is non-optimal. In this paper, we propose a novel capped $\ell_{p}$-norm loss function that is theoretically robust to both light and heavy outliers. The capped $\ell_{p}$-norm loss can help the model detect and eliminate outliers during training process. Adhering to this concept, we introduce a new model, Capped $\ell_{p}$-Norm Support Vector Ordinal Regression(CSVOR), that is robust to outliers. CSVOR uses a weight matrix to detect and eliminate outliers during the training process to improve the robustness to outliers. Moreover, a Re-Weighted algorithm algorithm which is illustrated convergence by our theoretical results is proposed to effectively minimize the corresponding problem. Extensive experimental results demonstrate that our model outperforms state-of-the-art(SOTA) methods, particularly in the presence of outliers.

Data-driven approaches have revolutionized scientific research. Machine learning and statistical analysis are commonly utilized in this type of research. Despite their widespread use, these methodologies differ significantly in their techniques and objectives. Few studies have utilized a consistent dataset to demonstrate these differences within the social sciences, particularly in language and cognitive sciences. This study leverages the Buckeye Speech Corpus to illustrate how both machine learning and statistical analysis are applied in data-driven research to obtain distinct insights. This study significantly enhances our understanding of the diverse approaches employed in data-driven strategies.

In recent years, the neural network backdoor hidden in the parameters of the federated learning model has been proved to have great security risks. Considering the characteristics of trigger generation, data poisoning and model training in backdoor attack, this paper designs a backdoor attack method based on federated learning. Firstly, aiming at the concealment of the backdoor trigger, a TrojanGan steganography model with encoder-decoder structure is designed. The model can encode specific attack information as invisible noise and attach it to the image as a backdoor trigger, which improves the concealment and data transformations of the backdoor trigger.Secondly, aiming at the problem of single backdoor trigger mode, an image poisoning attack method called combination trigger attack is proposed. This method realizes multi-backdoor triggering by multiplexing combined triggers and improves the robustness of backdoor attacks. Finally, aiming at the problem that the local training mechanism leads to the decrease of the success rate of backdoor attack, a dual model replacement backdoor attack algorithm based on federated learning is designed. This method can improve the success rate of backdoor attack while maintaining the performance of the federated learning aggregation model. Experiments show that the attack strategy in this paper can not only achieve high backdoor concealment and diversification of trigger forms under federated learning, but also achieve good attack success rate in multi-target attacks.door concealment and diversification of trigger forms but also achieve good results in multi-target attacks.

This study employs deep learning techniques to explore four speaker profiling tasks on the TIMIT dataset, namely gender classification, accent classification, age estimation, and speaker identification, highlighting the potential and challenges of multi-task learning versus single-task models. The motivation for this research is twofold: firstly, to empirically assess the advantages and drawbacks of multi-task learning over single-task models in the context of speaker profiling; secondly, to emphasize the undiminished significance of skillful feature engineering for speaker recognition tasks. The findings reveal challenges in accent classification, and multi-task learning is found advantageous for tasks of similar complexity. Non-sequential features are favored for speaker recognition, but sequential ones can serve as starting points for complex models. The study underscores the necessity of meticulous experimentation and parameter tuning for deep learning models.

The majority of research in computational psycholinguistics has concentrated on the processing of words. This study introduces innovative methods for computing sentence-level metrics using multilingual large language models. The metrics developed sentence surprisal and sentence relevance and then are tested and compared to validate whether they can predict how humans comprehend sentences as a whole across languages. These metrics offer significant interpretability and achieve high accuracy in predicting human sentence reading speeds. Our results indicate that these computational sentence-level metrics are exceptionally effective at predicting and elucidating the processing difficulties encountered by readers in comprehending sentences as a whole across a variety of languages. Their impressive performance and generalization capabilities provide a promising avenue for future research in integrating LLMs and cognitive science.

Amidst the rapid evolution of LLMs, the significance of evaluation in comprehending and propelling these models forward is increasingly paramount. Evaluations have revealed that factors such as scaling, training types, architectures and other factors profoundly impact the performance of LLMs. However, the extent and nature of these impacts continue to be subjects of debate because most assessments have been restricted to a limited number of models and data points. Clarifying the effects of these factors on performance scores can be more effectively achieved through a statistical lens. Our study embarks on a thorough re-examination of these LLMs, targeting the inadequacies in current evaluation methods. With the advent of a uniform evaluation framework, our research leverages an expansive dataset of evaluation results, introducing a comprehensive statistical methodology. This includes the application of ANOVA, Tukey HSD tests, GAMM, and clustering technique, offering a robust and transparent approach to deciphering LLM performance data. Contrary to prevailing findings, our results challenge assumptions about emergent abilities and the influence of given training types and architectures in LLMs. These findings furnish new perspectives on the characteristics, intrinsic nature, and developmental trajectories of LLMs. By providing straightforward and reliable methods to scrutinize and reassess LLM performance data, this study contributes a nuanced perspective on LLM efficiency and potentials.

Reference-frame-independent (RFI) quantum key distribution (QKD) presents promising advantages, especially for mobile-platform-based implementations, as it eliminates the need for active reference frame calibration. While RFI-QKD has been explored in various studies, limitations in key rate and distance persist due to finite data collection. In this study, we experimentally demonstrate an improved RFI-QKD protocol proposed by Zhu \textit{et al.} [Opt. Lett. 47, 4219 (2022)], featuring a statistical quantity for bounding information leaked to Eve that exhibits more insensitivity to statistical fluctuations and more robustness to variations in the reference frame. Taking into account finite-size considerations and potential general attacks, RFI-QKD is implemented over a distance of 175 \si{\kilo\meter} in this work. We believe that our study extends the communication distance achievable by RFI-QKD, thereby constituting a notable advancement for its practical application., Comment: 9 pages, 3 figures

The streamline pattern of planar polynomial velocity field is far from fully understood. In the community of fluid mechanics, most studies simply focus on the velocity gradient, or the linear part of the velocity field, but few studies on high-order terms. This paper is concerned with the local streamline pattern (LSP) of velocity field around an isotropic point. In virtue of the concept and method of dynamical systems, where the streamline pattern is equivalent to the phase portrait, we make clear the classification of LSPs of planar velocity fields with nonzero linear part, especially the cases where the determinant of velocity gradient vanishes at the isotropic point., Comment: 20 pages, 4 figures, 4 tables

Given a holonomic sequence $F(n)$, we characterize rational functions $r(n)$ so that $r(n)F(n)$ can be summable. We provide upper and lower bounds on the degree of the numerator of $r(k)$ and show the denominator of $r(n)$ can be read from annihilators of $F(k)$. This illustration provides the so-called rational reductions which can be used to generate new multi-sum equalities and congruences from known ones.

We present the gluon distribution functions of pion and kaon in small-$x$ and large-$x$ regions, and compare them with the results obtained from lattice QCD and continuum Schwinger function methods. Whether in the small-$x$ region or the large-$x$ region, our gluon distribution of pion is consistent with the results of lattice QCD and continuum Schwinger function method. In addition, the first four moments of gluon distributions of pion and kaon at different $Q^{2}$ scales are calculated. Furthermore, we present the mass decompositions of pion and kaon with the dynamical parton distribution functions calculated by the DGLAP equation with parton-parton recombination corrections. The mass structures of pion and kaon are totally different from that of the proton., Comment: 7 figures

Support Vector Machine (SVM) stands out as a prominent machine learning technique widely applied in practical pattern recognition tasks. It achieves binary classification by maximizing the "margin", which represents the minimum distance between instances and the decision boundary. Although many efforts have been dedicated to expanding SVM for multi-class case through strategies such as one versus one and one versus the rest, satisfactory solutions remain to be developed. In this paper, we propose a novel method for multi-class SVM that incorporates pairwise class loss considerations and maximizes the minimum margin. Adhering to this concept, we embrace a new formulation that imparts heightened flexibility to multi-class SVM. Furthermore, the correlations between the proposed method and multiple forms of multi-class SVM are analyzed. The proposed regularizer, akin to the concept of "margin", can serve as a seamless enhancement over the softmax in deep learning, providing guidance for network parameter learning. Empirical evaluations demonstrate the effectiveness and superiority of our proposed method over existing multi-classification methods.Code is available at https://github.com/zz-haooo/M3SVM.

Quantum random number generator harnesses the power of quantum mechanics to generate true random numbers, making it valuable for various scientific applications. However, real-world devices often suffer from imperfections that can undermine the integrity and privacy of generated randomness. To combat this issue, we present a novel quantum random number generator and experimentally demonstrate it. Our approach circumvents the need for exhaustive characterization of measurement devices, even in the presence of a quantum side channel. Additionally, we also do not require detailed characterization of the source, relying instead on reasonable assumptions about encoding dimension and noise constraints. Leveraging commercially available all-fiber devices, we achieve a randomness generation rate of 40 kbps., Comment: 16 pages, 9 figures

We propose a way to split a given bivariate P-recursive sequence into a summable part and a non-summable part in such a way that the non-summable part is minimal in some sense. This decomposition gives rise to a new reduction-based creative telescoping algorithm based on the concept of integral bases., Comment: 20 pages

This paper addresses the task of 3D pose estimation for a hand interacting with an object from a single image observation. When modeling hand-object interaction, previous works mainly exploit proximity cues, while overlooking the dynamical nature that the hand must stably grasp the object to counteract gravity and thus preventing the object from slipping or falling. These works fail to leverage dynamical constraints in the estimation and consequently often produce unstable results. Meanwhile, refining unstable configurations with physics-based reasoning remains challenging, both by the complexity of contact dynamics and by the lack of effective and efficient physics inference in the data-driven learning framework. To address both issues, we present DeepSimHO: a novel deep-learning pipeline that combines forward physics simulation and backward gradient approximation with a neural network. Specifically, for an initial hand-object pose estimated by a base network, we forward it to a physics simulator to evaluate its stability. However, due to non-smooth contact geometry and penetration, existing differentiable simulators can not provide reliable state gradient. To remedy this, we further introduce a deep network to learn the stability evaluation process from the simulator, while smoothly approximating its gradient and thus enabling effective back-propagation. Extensive experiments show that our method noticeably improves the stability of the estimation and achieves superior efficiency over test-time optimization. The code is available at https://github.com/rongakowang/DeepSimHO., Comment: Accepted to NeurIPS 2023

In this note, we apply the power-partible reduction to show the following arithmetic properties of large Schr\"oder polynomials $S_n(z)$ and little Schr\"oder polynomials $s_n(z)$: for any odd prime $p$, nonnegative integer $r\in\mathbb{N}$, $\varepsilon\in\{-1,1\}$ and $z\in\mathbb{Z}$ with $\gcd(p,z(z+1))=1$, we have \[ \sum_{k=0}^{p-1}(2k+1)^{2r+1}\varepsilon^k S_k(z)\equiv 1\pmod {p}\quad \text{and} \quad \sum_{k=0}^{p-1}(2k+1)^{2r+1}\varepsilon^k s_k(z)\equiv 0\pmod {p}. \], Comment: 11

Accurate detection of oral cancer is crucial for improving patient outcomes. However, the field faces two key challenges: the scarcity of deep learning-based image segmentation research specifically targeting oral cancer and the lack of annotated data. Our study proposes OCU-Net, a pioneering U-Net image segmentation architecture exclusively designed to detect oral cancer in hematoxylin and eosin (H&E) stained image datasets. OCU-Net incorporates advanced deep learning modules, such as the Channel and Spatial Attention Fusion (CSAF) module, a novel and innovative feature that emphasizes important channel and spatial areas in H&E images while exploring contextual information. In addition, OCU-Net integrates other innovative components such as Squeeze-and-Excite (SE) attention module, Atrous Spatial Pyramid Pooling (ASPP) module, residual blocks, and multi-scale fusion. The incorporation of these modules showed superior performance for oral cancer segmentation for two datasets used in this research. Furthermore, we effectively utilized the efficient ImageNet pre-trained MobileNet-V2 model as a backbone of our OCU-Net to create OCU-Netm, an enhanced version achieving state-of-the-art results. Comprehensive evaluation demonstrates that OCU-Net and OCU-Netm outperformed existing segmentation methods, highlighting their precision in identifying cancer cells in H&E images from OCDC and ORCA datasets.