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pp2-linear codes: rank and kernel

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arXiv 2022年

作者： Shi, Minjia Wang, Shukai Li, Xiaoxiao Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education School of Mathematics Sciences Anhui University Anhui Hefei China

A code C is called pp2-linear if it is the Gray image of a pp2-additive code, where p > 2 is prime. In this paper, the rank and the dimension of the kernel of pp2-linear codes are studied. Two bounds of the rank of a Z3Z9-linear code and the dimension of the kernel of a pp2-linear code are given, respectively. For each value of these bounds, we give detailed construction of the corresponding code. Finally, pairs of rank and the dimension of the kernel of 39-linear codes are also *** Codes 94B05 © 2022, CC0.

关键词： Additives

A Novel Underdetermined Blind Source Separation Algorithm of Frequency-hopping signals via Time-frequency Analysis

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TechRxiv

TechRxiv 2023年

作者： Li, Yingsong Wang, Yifan Li, Yibing Sun, Qian The College of Information and Communication Engineering Harbin Engineering University Harbin150001 China The Key Laboratory of Intelligent Computing and Signal Processing Ministry of Education Anhui University Hefei230601 China

To address the significant performance degradation of conventional underdetermined blind source separation algorithms for frequency-hopping (FH) signals under time-frequency (TF) overlapping conditions, this paper presents a novel three-stage scheme based on the TF distribution of FH signals. In the first stage, key parameters of the FH signal are estimated using a TF binary graph. In the second step, the initial mixing matrix is estimated for non-overlapping and overlapping carrier frequencies employing density peaks clustering and tensor decomposition methods, respectively. In the third step, the final mixing matrix, directions of arrival (DOA), and source signals are estimated using the expectation-maximization algorithm within the nonnegative matrix factorization model. Finally, different segments of the FH signals are spliced together based on the DOAs of different source signals. Comprehensive experimental results demonstrate the superior performance of the proposed algorithm compared to state-of-the-art algorithms. Even at a signal-to-noise ratio of 5 dB, the correlation coefficient of the estimated source signals can still reach 0.91. © 2023, CC BY.

关键词： Blind source separation

Research on Multi-Agent Question Answering Based on Large Language Models 25

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Research on Multi-Agent Question Answering Based on Large La...

Proceedings of the 2025 3rd International Conference on Communication Networks and Machine Learning

作者： Xinpeng Lei Fucheng Wan Key Laboratory of Linguistic and Cultural Computing Ministry of Education Northwest Minzu University Lanzhou Gansu China Key Laboratory of Minzu Languages and Cultures Intelligent Information Processing Northwest Minzu University Lanzhou Gansu China

ISBN: (纸本)9798400713231

The continuous development of large language models has led to tremendous performance improvement and has made them increasingly more important. More and more researchers are starting to explore the use of these large language models in developing artificial intelligence agents. The goal of this research is to develop a question-answering system based on a multi-agent setup with the open-source large language model Qwen2.5. In this multi-agent setup, the two agents include a student and a teacher where the student solves issues with guidance from the teacher. We evaluate accuracy difference between a single-agent and a multi-agent setup with the Chinese evaluation data, C-Eval. This is a departure from other approaches like fine-tuning large models or utilizing methods like chain of thought (CoT) and n-shot learning that are tailor-made to improve model performance. Rather, it is a more general approach aimed at further testing the abilities of large language models and thereby improve their logical reasoning capabilities. The experimental results demonstrate a significant improvement in accuracy in multi-agent systems compared to single-agent setup. In particular, improvement in accuracy over various subjects is around 2.5%. In addition, it has been found that improvement is directly proportional to model parameter size; for example, a model with a parameter size of 14 billion has a 22.18% improvement in accuracy for hard cases and reflects a significant improvement in performance.

关键词： Multi-agent

Low Coupling Sparse Array Based on Uniform Linear Array Fitting Method

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Low Coupling Sparse Array Based on Uniform Linear Array Fitt...

IEEE International Conference on Electronic Information and Communication Technology (ICEICT)

作者： Yichang Yao Yingsong Li Liping Li Nikola Zlatanov College of Information and Communication Engineering Harbin Engineering University Harbin China Key Laboratory of Intelligent Computing and Signal Processing Ministry of Education Anhui University China Faculty of Computer and Engineering Sciences Innopolis University Innopolis Russia

ISBN: (数字)9798350384437

ISBN: (纸本)9798350384444

In order to solve the problem that traditional sparse arrays only emphasize high degrees of freedom and ignore low coupling, uniform array fitting method can design arrays with low coupling. However, the existing array coupling based on uniform array fitting method still has room for decline, and the value of weight function is not the minimum, so the performance of array DOA estimation needs to be further optimized. Therefore, based on the uniform matrix fitting method, a uniform matrix fitting 6-base-layer array is designed. By extending the spacing of each subarray of the uniform subarray in the base layer, the number of small array element spacing pairs in the differential cooperative array is reduced, and the coupling between the elements of the whole sparse array is reduced as a whole. The performance of DOA estimation of the designed array is simulated and analyzed by using spatial smoothing multiple signal classification algorithm.

关键词： Couplings Mutual coupling Direction-of-arrival estimation Smoothing methods Simulation Fitting Estimation

Hyperbolic Hierarchical Knowledge Graph Embeddings for Link Prediction in Low Dimensions

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arXiv 2022年

作者： Zheng, Wenjie Wang, Wenxue Zhao, Shu Qian, Fulan Nanjing University of Science and Technology China Key Laboratory of Intelligent Computing and Signal Processing Ministry of Education Anhui University China

Knowledge graph embeddings (KGE) have been validated as powerful methods for inferring missing links in knowledge graphs (KGs) that they typically map entities into Euclidean space and treat relations as transformations of entities. Recently, some Euclidean KGE methods have been enhanced to model semantic hierarchies commonly found in KGs, improving the performance of link prediction. To embed hierarchical data, hyperbolic space has emerged as a promising alternative to traditional Euclidean space, offering high fidelity and lower memory consumption. Unlike Euclidean, hyperbolic space provides countless curvatures to choose from. However, it is difficult for existing hyperbolic KGE methods to obtain the optimal curvature settings manually, thereby limiting their ability to effectively model semantic hierarchies. To address this limitation, we propose a novel KGE model called Hyperbolic Hierarchical KGE (HypHKGE). This model introduces attention-based learnable curvatures for hyperbolic space, which helps preserve rich semantic hierarchies. Furthermore, to utilize the preserved hierarchies for inferring missing links, we define hyperbolic hierarchical transformations based on the theory of hyperbolic geometry, including both inter-level and intra-level modeling. Experiments demonstrate the effectiveness of the proposed HypHKGE model on the three benchmark datasets (WN18RR, FB15K-237, and YAGO3-10). The source code will be publicly released at https://***/wjzheng96/HypHKGE. Copyright © 2022, The Authors. All rights reserved.

关键词： Knowledge graph

Equivalence and Duality of Polycyclic Codes Associated with Trinomials over Finite Fields

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arXiv 2022年

作者： Shi, Minjia Lu, Haodong Zhou, Shuang Xu, Jiarui Zhu, Yuhang The Key Laboratory of Intelligent Computing and Signal Processing Ministry of Education School of Mathematical Sciences Anhui University Hefei230601 China

In this paper, several conjectures proposed in [2] are studied, involving the equivalence and duality of polycyclic codes associated with trinomials. According to the results, we give methods to construct isodual and self-dual polycyclic codes, and study the self-orthogonal and dual-containing polycyclic codes over F2MSC Codes 94B05, 05E30 © 2022, CC0.

关键词： Algebra

Gray Images of Cyclic Codes over p2 and pp2

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arXiv 2022年

作者： Wang, Xuan Shi, Minjia Key Laboratory of Intelligent Computing and Signal Processing Ministry of Education School of Mathematical Sciences Anhui University Hefei230601 China

In the paper, we firstly study the algebraic structures of ppk-additive cyclic codes and give the generator polynomials and the minimal spanning set of these codes. Secondly, a necessary and sufficient condition for the pp2-additive cyclic code whose Gray image is linear (not necessarily cyclic) over p is given. Moreover, as for some special families of cyclic codes over p2 and pp2, the linearity of the Gray images is *** Codes 94B05 © 2022, CC0.

关键词： Additives

A NEURAL MULTIGRID SOLVER FOR HELMHOLTZ EQUATIONS WITH HIGH WAVENUMBER AND HETEROGENEOUS MEDIA

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arXiv 2024年

作者： Cui, Chen Jiang, Kai Shu, Shi Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

Solving high-wavenumber and heterogeneous Helmholtz equations presents a longstanding challenge in scientific computing. In this paper, we introduce a deep learning-enhanced multigrid solver to address this issue. By conducting error analysis on standard multigrid applied to a discrete Helmholtz equation, we devise a strategy to handle errors with different frequencies separately. For error components with frequencies distant from the wavenumber, we perform simple smoothing based on local operations at different levels to eliminate them. On the other hand, to address error components with frequencies near the wavenumber, we utilize another multigrid V-cycle to solve an advection-diffusion-reaction (ADR) equation at a coarse scale. The resulting solver, named Wave-ADR-NS, involves parameters learned through unsupervised training. Numerical results demonstrate that Wave-ADR-NS effectively resolves heterogeneous 2D Helmholtz equation with wavenumber up to 2000. Comparative experiments against classical multigrid preconditioners and existing deep learning-based multigrid preconditioners reveals the superior performance of *** Codes 65N22, 65N55, 68T07 Copyright © 2024, The Authors. All rights reserved.

关键词： Helmholtz equation

Near-field Source DOA Estimation Algorithm Based on De-impact Function under Impulse Noise

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Near-field Source DOA Estimation Algorithm Based on De-impac...

IEEE International Conference on Electronic Information and Communication Technology (ICEICT)

作者： Xingchao Xu Baohe Pang Yingsong Li Liping Li Dingcheng Zou Nikola Zlatanov College of Information and Communication Engineering Harbin Engineering University Harbin China Key Laboratory of Intelligent Computing and Signal Processing Ministry of Education Anhui University China Faculty of Computer and Engineering Sciences Innopolis University Innopolis Russia

ISBN: (数字)9798350384437

ISBN: (纸本)9798350384444

In addressing the issue of localizing near-field source signals in the presence of impulse noise, this manuscript introduces a novel de-impact function designed for preprocessing received signals to alleviate the interference caused by impulse noise. Simulation experiments verify the effectiveness of the proposed de-impact function in effectively suppressing impulse noise. Furthermore, to augment estimation precision, a novel algorithm for near-field source localization is proposed. Building upon the framework of correlation entropy theory, a new correntropy covariance matrix is formulated to replace the original signal covariance matrix for signal processing. Through a succession of low-bias approximations between near-field and far-field scenarios, the algorithm converts the original 2-D search into 1-D operations. Additionally, the conventional spectral peak search is replaced by polynomial solving to further mitigate the computational complexity of the algorithm.

关键词： Location awareness Direction-of-arrival estimation Noise signal processing algorithms Estimation Interference Approximation algorithms