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arXiv 2024年

作者： Sun, Zejun Zheng, Guang-Hui School of Mathematics Hunan University Changsha410082 China School of Mathematics Hunan Provincial Key Laboratory of Intelligent Information Processing and Applied Mathematics Hunan University Changsha410082 China

In this article, we propose a new dimensionality-independent and gradient-free sampler, called Geometric Optics Approximation Sampling, which is based on the reflector antenna system. The core idea is to construct a reflecting surface that redirects rays from a source with a predetermined simpler measure towards a output domain while achieving a desired distribution defined by the projection of a complex target measure of interest. Given a such reflecting surface, one can generate arbitrarily many independent and uncorrelated samples from the target measure simply by dual re-simulating or rays tracing the reflector antenna system and then projecting the traced rays onto target domain. In order to obtain a desired reflecting surface, we use the method of supporting paraboloid to solve the reflector antenna problem that does not require a gradient information regarding the density of the target measure. Furthermore, within the supporting paraboloid method, we utilize a low-discrepancy sequence or a random sequence to discretize the target measure, which in turn yields a dimensionality-independent approach for constructing the reflecting surface. Meanwhile, we present a dual re-simulation or ray tracing method based on its dual reflecting surface, which enables drawing samples from the target measure using the reflector antenna system obtained through the dimensionality-independent method. In theory, we define a geometric optics approximation measure by means of the reflecting surfaces, that is the pushforward of the source measure. We give its well-defined result. In particular, we prove the stability of this measure with respect to the target domain, which in turn ensures the robustness of the numerical sampling. In addition, we establish error bounds between the projection of the numerical geometric optics approximation measure and the target measure under the Wasserstein metrics. Several examples and numerical experiments comparing with measure transport samplers a

关键词： Reflection

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Bayesian inference via geometric optics approximation

arXiv

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arXiv 2024年

Markov chain Monte Carlo (MCMC) simulations have been widely used to generate samples from the complex posterior distribution in Bayesian inferences. However, these simulations often require multiple computations of the forward model in the likelihood function for each drawn sample. This computational burden renders MCMC sampling impractical when the forward model is computationally expensive, such as in the case of partial differential equation models. In this paper, we propose a novel sampling approach called the geometric optics approximation method (GOAM) for Bayesian inverse problems, which entirely circumvents the need for MCMC simulations. Our method is rooted in the problem of reflector shape design, which focuses on constructing a reflecting surface that redirects rays from a source, with a predetermined density, towards a target domain while achieving a desired density distribution. The key idea is to consider the unnormalized Bayesian posterior as the density on the target domain within the optical system and define a geometric optics approximation measure with respect to posterior by a reflecting surface. Consequently, once such a reflecting surface is obtained, we can utilize it to draw an arbitrary number of independent and uncorrelated samples from the posterior measure for Bayesian inverse problems. In theory, we have shown that the geometric optics approximation measure is well-posed. The efficiency and robustness of our proposed sampler, employing the geometric optics approximation method, are demonstrated through several numerical examples provided in this paper. Copyright © 2024, The Authors. All rights reserved.

关键词： Numerical methods

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Corona theorem for the Dirichlet-type space

arXiv

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arXiv 2023年

作者： Luo, Shuaibing School of Mathematics Hunan Provincial Key Laboratory of Intelligent Information Processing and Applied Mathematics Hunan University Changsha410082 China

This paper utilizes Cauchy’s transform and duality for the Dirichlet-type space D(µ) with positive superharmonic weight Uµ on the unit disk D to establish the corona theorem for the Dirichlet-type multiplier algebra (formula presented) then (formula presented) thereby generalizing Carleson’s corona theorem for M(H2) = H∞ in [7] and Xiao’s corona theorem for M(D) ⊂ H∞ in [25] thanks to (formula presented);Copyright © 2023, The Authors. All rights reserved.

关键词： Algebra

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SCENERY:a lightweight block cipher based on Feistel structure

引用

Frontiers of Computer Science 2022年第3期16卷 193-202页

作者： Jingya FENG Lang LI Hunan Provincial Key Laboratory of Intelligent Information Processing and Application Hengyang Normal UniversityHengyang 421002China College of Information Science and Engineering Hunan Normal UniversityChangsha 410081China College of Computer Science and Technology Hengyang Normal UniversityHengyang 421002China

In this paper,we propose a new lightweight block cipher called *** main purpose of SCENERY design applies to hardware and software *** is a 64-bit block cipher supporting 80-bit keys,and its data processing consists of 28 *** round function of SCENERY consists of 84×4 S-boxes in parallel and a 32× 32 binary matrix,and we can implement SCENERY with some basic logic *** hardware implementation of SCENERY only requires 1438 GE based on 0.18 um CMOS technology,and the software implementation of encrypting or decrypting a block takes approximately 1516 clock cycles 0118-bit microcontrollers and 364 clock cycles on 64-bit *** with other encryption algorithms,the performance of SCENERY is well balanced for both hardware and *** the security analyses,SCENERY can achieve enough security margin against known attacks,such as differential cryptanalysis,linear cryptanalysis,impossible differential cryptanalysis and related-key attacks.

关键词： lightweight block cipher feistel structure cryptanalysis internet of things

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Side-channel analysis attacks based on deep learning network

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Frontiers of Computer Science 2022年第2期16卷 35-45页

作者： Yu OU Lang LI Hunan Provincial Key Laboratory of Intelligent Information Processing and Application Hengyang Normal UniversityHengyang 421002China College of Information Science and Engineering Hunan Normal UniversityChangsha 410081China College of Computer Science and Technology Hengyang Normal UniversityHengyang 421002China

There has been a growing interest in the sidechannel analysis(SCA)field based on deep learning(DL)*** DL network or model has been developed to improve the efficiency of ***,few studies have investigated the impact of the different models on attack results and the exact relationship between power consumption traces and intermediate *** on the convolutional neural network and the autoencoder,this paper proposes a Template Analysis Pre-trained DL Classification model named TAPDC which contains three *** TAPDC model detects the periodicity of power trace,relating power to the intermediate values and mining the deeper features by the multi-layer convolutional *** implement the TAPDC model and compare it with two classical models in a fair *** evaluative results show that the TAPDC model with autoencoder and deep convolution feature extraction structure in SCA can more effectively extract information from power consumption ***,Using the classifier layer,this model links power information to the probability of intermediate *** completes the conversion from power trace to intermediate values and greatly improves the efficiency of the power attack.

关键词： side-channel analysis template attack machine learning deep learning

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The Mean Time to Absorption on Horizontal Partitioned Sierpinski Gasket Networks

引用

Analysis in Theory and Applications 2024年第1期40卷 1-21页

作者： Zhizhuo Zhang Bo Wu Zuguo Yu School of Mathematics Southeast UniversityNanjingJianagsu 211189China School of Applied Mathematics Nanjing University of Finance and EconomicsNanjingJiangsu 210023China Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education and Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityXiangtanHunan 411105China

The random walk is one of the most basic dynamic properties of complex networks,which has gradually become a research hotspot in recent years due to its many applications in actual *** important characteristic of the random walk is the mean time to absorption,which plays an extremely important role in the study of topology,dynamics and practical application of complex *** the mean time to absorption on the regular iterative self-similar network models is an important way to explore the inﬂuence of self-similarity on the properties of random walks on the *** existing literatures have proved that even local self-similar structures can greatly affect the properties of random walks on the global network,but they have failed to prove whether these effects are related to the scale of these self-similar *** this article,we construct and study a class of Horizontal Par-titioned Sierpinski Gasket network model based on the classic Sierpinski gasket net-work,which is composed of local self-similar structures,and the scale of these structures will be controlled by the partition coefﬁcient ***,the analytical expressions and approximate expressions of the mean time to absorption on the network model are obtained,which prove that the size of the self-similar structure in the network will directly restrict the inﬂuence of the self-similar structure on the properties of random walks on the ***,we also analyzed the mean time to absorption of different absorption nodes on the network toﬁnd the location of the node with the highest absorption efﬁciency.

关键词： Mean time to absorption self-similar network Sierpinski Gasket

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ADHD diagnosis guided by functional brain networks combined with domain knowledge

引用

Computers in Biology and Medicine 2024年 177卷 108611-108611页

作者： Cao, Chunhong Fu, Huawei Li, Gai Wang, Mengyang Gao, Xieping MOE Key Laboratory of Intelligent Computing and Information Processing Xiangtan University Xiangtan411100 China Hunan Provincial Key Laboratory of Intelligent Computing and Language Information Processing Hunan Normal University Changsha410081 China

Utilizing functional magnetic resonance imaging (fMRI) to model functional brain networks (FBNs) is increasingly prominent in attention-deficit/hyperactivity disorder (ADHD) research, revealing neural impact and mechanisms through the exploration of activated brain regions. However, current FBNs-based methods face two major challenges. The primary challenge stems from the limitations of existing modeling methods in accurately capturing both regional correlations and long-distance dependencies (LDDs) within the dynamic brain, thereby affecting the diagnostic accuracy of FBNs as biomarkers. Additionally, limited sample size and class imbalance also pose a challenge to the learning performance of the model. To address the issues, we propose an automated diagnostic framework, which integrates modeling, multimodal fusion, and classification into a unified process. It aims to extract representative FBNs and efficiently incorporate domain knowledge to guide ADHD classification. Our work mainly includes three-fold: 1) A multi-head attention-based region-enhancement module (MAREM) is designed to simultaneously capture regional correlations and LDDs across the entire sequence of brain activity, which facilitates the construction of representative FBNs. 2) The multimodal supplementary learning module (MSLM) is proposed to integrate domain knowledge from phenotype data with FBNs from neuroimaging data, achieving information complementarity and alleviating the problems of insufficient medical data and unbalanced sample categories. 3) An ADHD automatic diagnosis framework guided by FBNs and domain knowledge (ADF-FAD) is proposed to help doctors make more accurate decisions, which is applied to the ADHD-200 dataset to confirm its effectiveness. The results indicate that the FBNs extracted by MAREM perform well in modeling and classification. After with MSLM, the model achieves accuracy of 92.4%, 74.4%, and 80% at NYU, PU, and KKI, respectively, demonstrating its ability to effecti

关键词： Domain Knowledge

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Fuzzy information Quantity Measurement and Feature Selection by Macrogranular Entropy

IEEE Transactions on Artificial Intelligence

引用

IEEE Transactions on Artificial Intelligence 2025年

作者： Zhu, Zhilin Zhang, Chucai Dai, Jianhua Hunan Normal University Hunan Provincial Key Laboratory of Intelligent Computing and Language Information Processing College of Information Science and Engineering Changsha410081 China

Feature selection is an important data preprocessing process in artificial intelligence, which aims to eliminate redundant features while retaining essential features. Measuring feature significance and relevance between features is a significant challenge. Fuzzy information entropy is an extension of Shannon entropy. It is widely used for quantifying the information of fuzzy divisions. However, it has significant limitations, notably the lack of monotonicity in fuzzy conditional entropy measure of decision uncertainty in the feature selection process. We introduce a novel measurement Macrogranular Entropy (ME) and construct some generalized forms, such as conditional macrogranular entropy, mutual macrogranular information, and joint macrogranular entropy. The conditional macrogranular entropy exhibits monotonicity when measuring decision uncertainty. Additionally, we propose two feature selection algorithms: one based on Monotonic Conditional Macrogranular Entropy (MCME), and the other based on the Degree of Symmetric Association (ADSA). The ADSA algorithm and the MCME algorithm are compared against eight other feature selection algorithms through a series of experiments. The comparison was conducted based on classification performance using SVM and NB classifiers, as well as evaluation metrics including F1-score and Recall. In terms of all four evaluation metrics, ADSA and MCME achieved the top two rankings, respectively. Specifically, on the NB and SVM classifiers, the ADSA algorithm improves the average accuracy by 12.22% and 2.88% compared to the original feature set, while MCME improves the accuracy by 10.07% and 1.01%, respectively. Experimental comparisons demonstrate that ADSA algorithm effectively removes redundant information from the dataset during feature selection. © 2025 IEEE.

关键词： Feature Selection

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Online Multi-label Streaming Feature Selection with Missing Features by Dual-Space Consistency information Measurement

IEEE Transactions on Artificial Intelligence

引用

IEEE Transactions on Artificial Intelligence 2025年

作者： Dai, Jianhua Wang, Jie Hunan Normal University Hunan Provincial Key Laboratory of Intelligent Computing and Language Information Processing College of Information Science and Engineering Changsha410081 China

Multi-label feature selection is critical to address the challenges of high dimensionality and computational complexity in multi-label learning. However, in some practical applications, a more complex challenge is the dynamic generation of features, known as streaming features. Although some scholars have studied multi-label streaming feature selection methods, the problem of missing features during dynamic feature generation in multi-label data is rarely considered. Hence, we propose an online multi-label streaming feature selection method for multilabel data containing missing features by dual-space consistency information measurement. Firstly, we construct the dual-space consistency information measurement, which can effectively capture the relationships between features and labels. Specifically, we consider it from the perspective of instance correlation, and propose a fuzzy α-tolerance relation in the feature space to directly deal with missing features, and introduce an improved neighbour similarity relation in the label space to capture the instance similarity between the label combinations. Secondly, based on the dual-space consistency information, we further introduce the consistency gain index to help identify those features with important information during the streaming feature selection process. Thirdly, by combining online significance analysis, online relevance analysis, and online redundancy analysis, a new streaming feature selection framework is constructed, which can comprehensively evaluate the newly arrived features in terms of strong consistency, weak consistency and irrelevance, so as to identify the most representative features in the continuously arriving feature streams. Finally, a series of comparative experiments on multiple benchmark datasets demonstrate the effectiveness and superiority of our proposed method. © 2025 IEEE.

关键词： Data consistency

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Online Multi-Label Streaming Feature Selection by Label Enhancement and Fuzzy Synergistic Discrimination information

引用

IEEE Transactions on Fuzzy Systems 2025年

作者： Zou, Ligeng Zhou, Tong Dai, Jianhua Hunan Normal University Hunan Provincial Key Laboratory of Intelligent Computing and Language Information Processing College of Information Science and Engineering Changsha410081 China

Online streaming feature selection is an effective approach for handling large-scale streaming data in real-world applications. However, many existing online streaming feature selection studies do not effectively leverage the correlation and hidden information in the label space. The measures used in streaming feature selection often face challenges such as computational complexity and insufficient information exploitation. To address these issues, we propose an online streaming feature selection method based on label enhancement and fuzzy synergistic discrimination information. Firstly, we define a novel label enhancement method based on label correlation, which does not require any prior knowledge of feature space. Secondly, we propose a new measure to evaluate the discriminative ability of multiple feature subsets for labels in fuzzy environment, called fuzzy synergistic discrimination information. It is bounded and has many interesting properties. The fuzzy synergistic discrimination information is computed directly based on fuzzy similarity relations, so the calculation is relatively simple. Thirdly, based on label enhancement and proposed fuzzy synergistic discrimination information, we construct a three-stage online multi-label streaming feature selection method, including online significance analysis, online relevance analysis and online redundancy analysis. Finally, comparative experiments on 12 datasets demonstrate the effectiveness and superiority of the proposed method. The influences of different feature sequences and these components on the algorithm's performance are further analyzed. © 1993-2012 IEEE.

关键词： information hiding

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