We present generic expressions for the integrands of canonical bases under maximal cut in elliptic Feynman integral families with multiple kinematic scales. Such integrals frequently arise in phenomenologically relevant scattering processes. The derivation of our results starts from the Legendre normal form of elliptic curves, where the geometric properties of the curves are simple and explicit, and further kinematic singularities are presented as marked points. The simplicity of the normal form allows a straightforward construction of canonical bases with an arbitrary number of marked points. They can then be mapped into any univariate elliptic integral families via an appropriate Möbius transformation, leading to universal expressions for the integrands. As a demonstration, we discuss the application of our method to several concrete examples, including two new integral families whose canonical bases were not available in the literature. In several examples, we derive canonical bases for the full integral families without any cuts, demonstrating the simplicity of the sub-sector dependence of our canonical bases.

Multivariate time series forecasting enables the prediction of future states by leveraging historical data, thereby facilitating decision-making processes. Each data node in a multivariate time series encompasses a sequence of multiple dimensions. These nodes exhibit interdependent relationships, forming a graph structure. While existing prediction methods often assume a fixed graph structure, many real-world scenarios involve dynamic graph structures. Moreover, interactions among time series observed at different time scales vary significantly. To enhance prediction accuracy by capturing precise temporal and spatial features, this paper introduces the Temporal Attention Evolutional Graph Convolutional Network (TAEGCN). This novel method not only integrates causal temporal convolution and a multi-head self-attention mechanism to learn temporal features of nodes, but also construct the dynamic graph structure based on these temporal features to keep the consistency of the changing in spatial feature with temporal series. TAEGCN adeptly captures temporal causal relationships and hidden spatial dependencies within the data. Furthermore, TAEGCN incorporates a unified neural network that seamlessly integrates these components to generate final predictions. Experimental results conducted on two public transportation network datasets, METR-LA and PEMS-BAY, demonstrate the superior performance of the proposed model.

Keyphrase extraction (KPE) is an important task in Natural Language Processing for many scenarios, which aims to extract keyphrases that are present in a given document. Many existing supervised methods treat KPE as sequential labeling, span-level classification, or generative tasks. However, these methods lack the ability to utilize keyphrase information, which may result in biased results. In this study, we propose Diff-KPE, which leverages the supervised Variational Information Bottleneck (VIB) to guide the text diffusion process for generating enhanced keyphrase representations. Diff-KPE first generates the desired keyphrase embeddings conditioned on the entire document and then injects the generated keyphrase embeddings into each phrase representation. A ranking network and VIB are then optimized together with rank loss and classification loss, respectively. This design of Diff-KPE allows us to rank each candidate phrase by utilizing both the information of keyphrases and the document. Experiments show that Diff-KPE outperforms existing KPE methods on a large open domain keyphrase extraction benchmark, OpenKP, and a scientific domain dataset, KP20K.

In the medical field, accurate diagnosis of lung cancer is crucial for treatment. Traditional manual analysis methods have significant limitations in terms of accuracy and efficiency. To address this issue, this paper proposes a deep learning network framework based on the pre-trained MobileNetV2 model, initialized with weights from the ImageNet-1K dataset (version 2). The last layer of the model (the fully connected layer) is replaced with a new fully connected layer, and a softmax activation function is added to efficiently classify three types of lung cancer CT scan images. Experimental results show that the model achieves an accuracy of 99.6% on the test set, with significant improvements in feature extraction compared to traditional this http URL the rapid development of artificial intelligence technologies, deep learning applications in medical image processing are bringing revolutionary changes to the healthcare industry. AI-based lung cancer detection systems can significantly improve diagnostic efficiency, reduce the workload of doctors, and occupy an important position in the global healthcare market. The potential of AI to improve diagnostic accuracy, reduce medical costs, and promote precision medicine will have a profound impact on the future development of the healthcare industry.

Real world datasets often contain noisy labels, and learning from such datasets using standard classification approaches may not produce the desired performance. In this paper, we propose a Gaussian Mixture Discriminant Analysis (GMDA) with noisy label for each class. We introduce flipping probability and class probability and use EM algorithms to solve the discriminant problem with label noise. We also provide the detail proofs of convergence. Experimental results on synthetic and real-world datasets show that the proposed approach notably outperforms other four state-of-art methods.

Many recent studies focus on developing mechanisms to explain the black-box behaviors of neural networks (NNs). However, little work has been done to extract the potential hidden semantics (mathematical representation) of a neural network. A succinct and explicit mathematical representation of a NN model could improve the understanding and interpretation of its behaviors. To address this need, we propose a novel symbolic regression method for neural works (called SRNet) to discover the mathematical expressions of a NN. SRNet creates a Cartesian genetic programming (NNCGP) to represent the hidden semantics of a single layer in a NN. It then leverages a multi-chromosome NNCGP to represent hidden semantics of all layers of the NN. The method uses a (1+$\lambda$) evolutionary strategy (called MNNCGP-ES) to extract the final mathematical expressions of all layers in the NN. Experiments on 12 symbolic regression benchmarks and 5 classification benchmarks show that SRNet not only can reveal the complex relationships between each layer of a NN but also can extract the mathematical representation of the whole NN. Compared with LIME and MAPLE, SRNet has higher interpolation accuracy and trends to approximate the real model on the practical dataset.

We establish a general convergence theory of the Rayleigh--Ritz method and the refined Rayleigh--Ritz method for computing some simple eigenpair $(\lambda_{*},x_{*})$ of a given analytic regular nonlinear eigenvalue problem (NEP). In terms of the deviation $\varepsilon$ of $x_{*}$ from a given subspace $\mathcal{W}$, we establish a priori convergence results on the Ritz value, the Ritz vector and the refined Ritz vector. The results show that, as $\varepsilon\rightarrow 0$, there exists a Ritz value that unconditionally converges to $\lambda_*$ and the corresponding refined Ritz vector does so too but the Ritz vector converges conditionally and it may fail to converge and even may not be unique. We also present an error bound for the approximate eigenvector in terms of the computable residual norm of a given approximate eigenpair, and give lower and upper bounds for the error of the refined Ritz vector and the Ritz vector as well as for that of the corresponding residual norms. These results nontrivially extend some convergence results on these two methods for the linear eigenvalue problem to the NEP. Examples are constructed to illustrate the main results.

The porous media community extensively utilizes digital rock images for core analysis. High-resolution digital rock images that possess sufficient quality are essential but often challenging to acquire. Super-resolution (SR) approaches enhance the resolution of digital rock images and provide improved visualization of fine features and structures, aiding in the analysis and interpretation of rock properties, such as pore connectivity and mineral distribution. However, there is a current shortage of real paired microscopic images for super-resolution training. In this study, we used two types of Scanning Electron Microscopes (SEM) to obtain the images of shale samples in five regions, with 1X, 2X, 4X, 8X and 16X magnifications. We used these real scanned paired images as a reference to select the optimal method of image generation and validated it using Enhanced Deep Super Resolution (EDSR) and Very Deep Super Resolution (VDSR) methods. Our experiments show that the bilinear algorithm is more suitable than the commonly used bicubic method, for establishing low-resolution datasets in the SR approaches, which is partially attributed to the mechanism of Scanning Electron Microscopes (SEM).

In this paper, the branches of recursive and recurrent neural networks are classified in detail according to the network structure, training objective function and learning algorithm implementation. They are roughly divided into three categories: The first category is General Recursive and Recurrent Neural Networks, including Basic Recursive and Recurrent Neural Networks, Long Short Term Memory Recursive and Recurrent Neural Networks, Convolutional Recursive and Recurrent Neural Networks, Differential Recursive and Recurrent Neural Networks, One-Layer Recursive and Recurrent Neural Networks, High-Order Recursive and Recurrent Neural Networks, Highway Networks, Multidimensional Recursive and Recurrent Neural Networks, Bidirectional Recursive and Recurrent Neural Networks; the second category is Structured Recursive and Recurrent Neural Networks, including Grid Recursive and Recurrent Neural Networks, Graph Recursive and Recurrent Neural Networks, Temporal Recursive and Recurrent Neural Networks, Lattice Recursive and Recurrent Neural Networks, Hierarchical Recursive and Recurrent Neural Networks, Tree Recursive and Recurrent Neural Networks; the third category is Other Recursive and Recurrent Neural Networks, including Array Long Short Term Memory, Nested and Stacked Recursive and Recurrent Neural Networks, Memory Recursive and Recurrent Neural Networks. Various networks cross each other and even rely on each other to form a complex network of relationships. In the context of the development and convergence of various networks, many complex sequence, speech and image problems are solved. After a detailed description of the principle and structure of the above model and model deformation, the research progress and application of each model are described, and finally the recursive and recurrent neural network models are prospected and summarized.

Federated reinforcement learning (FRL) methods usually share the encrypted local state or policy information and help each client to learn from others while preserving everyone's privacy. In this work, we propose that sharing the approximated behavior metric-based state projection function is a promising way to enhance the performance of FRL and concurrently provides an effective protection of sensitive information. We introduce FedRAG, a FRL framework to learn a computationally practical projection function of states for each client and aggregating the parameters of projection functions at a central server. The FedRAG approach shares no sensitive task-specific information, yet provides information gain for each client. We conduct extensive experiments on the DeepMind Control Suite to demonstrate insightful results.

In the field of chemical engineering, traditional data-processing and prediction methods face significant challenges. Machine-learning and large-language models (LLMs) also have their respective limitations. This paper explores the application of the Chain-of-Thought (CoT) reasoning model in chemical engineering, starting from 30 experimental data points. By integrating traditional surrogate models like Gaussian processes and random forests with powerful LLMs such as DeepSeek-R1, a hierarchical architecture is proposed. Two CoT-building methods, Large Language Model-Chain of Thought (LLM-CoT) and Machine Learning-Large Language Model-Chain of Thought (ML-LLM-CoT), are studied. The LLM-CoT combines local models DeepSeek-r1:14b and Qwen2:7b with Ollama. The ML-LLM-CoT integrates a pre-trained Gaussian ML model with the LLM-based CoT framework. Our results show that during construction, ML-LLM-CoT is more efficient. It only has 2 points that require rethink and a total of 4 rethink times, while LLM-CoT has 5 points that need to be re-thought and 34 total rethink times. In predicting the solubility of 20 molecules with dissimilar structures, the number of molecules with a prediction deviation higher than 100\% for the Gaussian model, LLM-CoT, and ML-LLM-CoT is 7, 6, and 4 respectively. These results indicate that ML-LLM-CoT performs better in controlling the number of high-deviation molecules, optimizing the average deviation, and achieving a higher success rate in solubility judgment, providing a more reliable method for chemical engineering and molecular property prediction. This study breaks through the limitations of traditional methods and offers new solutions for rapid property prediction and process optimization in chemical engineering.

Multi-view learning attempts to generate a model with a better performance by exploiting the consensus and/or complementarity among multi-view data. However, in terms of complementarity, most existing approaches only can find representations with single complementarity rather than complementary information with diversity. In this paper, to utilize both complementarity and consistency simultaneously, give free rein to the potential of deep learning in grasping diversity-promoting complementarity for multi-view representation learning, we propose a novel supervised multi-view representation learning algorithm, called Self-Attention Multi-View network with Diversity-Promoting Complementarity (SAMVDPC), which exploits the consistency by a group of encoders, uses self-attention to find complementary information entailing diversity. Extensive experiments conducted on eight real-world datasets have demonstrated the effectiveness of our proposed method, and show its superiority over several baseline methods, which only consider single complementary information.

Medical data mainly includes various types of biomedical signals and medical images, which can be used by professional doctors to make judgments on patients' health conditions. However, the interpretation of medical data requires a lot of human cost and there may be misjudgments, so many scholars use neural networks and deep learning to classify and study medical data, which can improve the efficiency and accuracy of doctors and detect diseases early for early diagnosis, etc. Therefore, it has a wide range of application prospects. However, traditional neural networks have disadvantages such as high energy consumption and high latency (slow computation speed). This paper presents recent research on signal classification and disease diagnosis based on a third-generation neural network, the spiking neuron network, using medical data including EEG signals, ECG signals, EMG signals and MRI images. The advantages and disadvantages of pulsed neural networks compared with traditional networks are summarized and its development orientation in the future is prospected.

This groundbreaking research extracted DNA from petroleum using nanoparticle affinity bead technology, yielding 3,159,020 petroleum DNA (pDNA) sequences, primarily environmental DNA. While most original in situ DNA (oriDNA) was lost, ancient DNA (aDNA) from petroleum offers an important source of ecological and evolutionary information, surpassing traditional fossils. This study reveals that oil, mainly sourced from algae and lower aquatic plants, now serves as a new type of fossil, providing detailed insights into Earth's hidden history, including unclassified species and ancient events, revolutionizing petroleum geology and paleontology.

Abstract. Most of the real world data we encounter are asynchronous event sequence, so the last decades have been characterized by the implementation of various point process into the field of social networks,electronic medical records and financial transactions. At the beginning, Hawkes process and its variants which can simulate simultaneously the self-triggering and mutual triggering patterns between different events in complex sequences in a clear and quantitative way are more popular.Later on, with the advances of neural network, neural Hawkes process has been proposed one after another, and gradually become a research hotspot. The proposal of the transformer Hawkes process (THP) has gained a huge performance improvement, so a new upsurge of the neural Hawkes process based on transformer is set off. However, THP does not make full use of the information of occurrence time and type of event in the asynchronous event sequence. It simply adds the encoding of event type conversion and the location encoding of time conversion to the source encoding. At the same time, the learner built from a single transformer will result in an inescapable learning bias. In order to mitigate these problems, we propose a tri-transformer Hawkes process (Tri-THP) model, in which the event and time information are added to the dot-product attention as auxiliary information to form a new multihead attention. The effectiveness of the Tri-THP is proved by a series of well-designed experiments on both real world and synthetic data.