Article
Mathematics
Shuling Wang, Haitao Li
Summary: The paper examines a method for resolving FRIs and proposes a general procedure for FRIs with Boolean semi-tensor product composition, obtaining all possible solutions by finding all possible parameter set solutions. Two examples are used to demonstrate the effectiveness of the method.
Article
Mathematics, Applied
Ying Wang, Yuning Yang
Summary: This paper considers generalizing the t-SVD of third-order tensors to tensors of arbitrary order N and introduces the Hot-SVD as a tensor-tensor product version of the higher order SVD (HOSVD). The existence of Hot-SVD is proved by introducing the small-t transpose for third-order tensors. Various properties of Hot-SVD and its truncated versions are established, and numerical examples are provided to validate them.
COMPUTATIONAL & APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Shaoyu Dai, Bowen Li, Jianquan Lu, Jie Zhong, Yang Liu
Summary: This article proposes a unified method for studying the general robust property of probabilistic Boolean control networks (PBCNs). It suggests that the investigation on the robust property of a given PBCN with probability one can be transformed into the investigation on the corresponding Boolean control network (BCN). The paper also presents an application of the method in studying the robust set stabilization of PBCNs with positive time-varying probability distribution.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Engineering, Electrical & Electronic
Fen Liu, Jianfeng Chen, Kemeng Li, Jisheng Bai, Weijie Tan, Chang Cai, Muhammad Saad Ayub
Summary: In this paper, a semi-tensor product-based multi-modal factorized multilinear (STP-MFM) pooling method is proposed for information fusion in sentiment analysis. Experimental results demonstrate that the proposed method outperforms baselines in terms of accuracy, training speed, and model complexity.
DIGITAL SIGNAL PROCESSING
(2024)
Article
Automation & Control Systems
Fengqiu Liu, Xun Shen, Sotiris Moschoyiannis, Yuhu Wu
Summary: This article studies an algebra-logic mixed representation of gate networks and its application to stuck-at fault diagnosis. The gate network is characterized by a logic expression and described based on 2-to-1 multiplexers. A novel algebra-logic mixed representation is proposed through the logic expression and system structure, using the semi-tensor product of matrices. A novel stuck-at fault diagnosis algorithm is presented, where the fault testability is equivalent to the solution existence of linear equations. The effectiveness and feasibility of the proposed approach and algorithms are demonstrated through the fault diagnosis of a 4-bit carry look-ahead adder.
ASIAN JOURNAL OF CONTROL
(2023)
Review
Computer Science, Information Systems
Yongyi Yan, Daizhan Cheng, Jun-E. Feng, Haitao Li, Jumei Yue
Summary: Algebraic state space theory (ASST) based on the semi-tensor product (STP) provides an algebraic analysis approach for logical systems. This study focuses on the applications of the ASST method to finite state machines (FSMs), including deterministic, nondeterministic, probabilistic, networked, and controlled and combined FSMs. Other related applications such as FSM in Boolean control networks and graph theory in FSMs are also surveyed. Potential research directions in the FSM field with respect to the ASST method are predicted.
SCIENCE CHINA-INFORMATION SCIENCES
(2023)
Article
Computer Science, Artificial Intelligence
Xiaowu Deng, Yuanquan Shi, Dunhong Yao
Summary: Due to the development and popularization of Internet technologies, the amount of data in various fields is increasing and showing complex characteristics. Tensor algebra provides a mathematical tool for processing high-dimensional heterogeneous data. This article presents advances in tensor theories, algorithms, and applications, including tensor operation, decomposition theory, supervised and unsupervised learning, deep learning, and their application research. The opportunities and challenges of tensor learning are also briefly discussed.
APPLIED INTELLIGENCE
(2023)
Article
Computer Science, Information Systems
Wenhui Kong, Jianghua Zhong, Dongdai Lin
Summary: This paper discusses the observability of Galois NFSRs and presents necessary and/or sufficient conditions using the semi-tensor product-based Boolean network theory. A new observability matrix is proposed to facilitate the determination of observability.
SCIENCE CHINA-INFORMATION SCIENCES
(2022)
Article
Computer Science, Artificial Intelligence
Wang Qiang, Yuwang Ji
Summary: In this paper, a new tensor product based linear layer is presented, which can replace the original convolution layer, fully-connected layer, and vector FC layer in capsule networks without tensor rank selection. This approach can effectively reduce the amount of model parameters.
APPLIED INTELLIGENCE
(2022)
Article
Computer Science, Artificial Intelligence
Linye Wu, Jitao Sun
Summary: In this paper, we investigate the optimal preview control problem of Boolean Networks (BNs). An augmented system, established through a model transformation based on the semi-tensor product of matrices and the Exclusive-Or operator, can control BNs with a minimal cost function. We then provide an optimal preview controller equipped with various features such as state feedback, integrator, and preview feedforward for BNs. The proposed optimal preview controller of BNs is validated through a numerical example.
NEURAL PROCESSING LETTERS
(2023)
Article
Computer Science, Information Systems
Yang Liu, Jie Zhong, Daniel W. C. Ho, Weihua Gui
Summary: This study investigates the minimum observability of Boolean networks using the semi-tensor product of matrices. It presents necessary and sufficient conditions for observability, algorithm for designing an observer, and necessary condition for determining the minimum number of directly measurable nodes. Examples are provided to demonstrate the effectiveness of the results.
SCIENCE CHINA-INFORMATION SCIENCES
(2022)
Article
Computer Science, Artificial Intelligence
Wei Wang, Guoqiang Sun, Siwen Zhao, Yujun Li, Jianli Zhao
Summary: Tensor decomposition is widely used in context-aware recommendation, but current models have limitations such as fewer parameters in CP decomposition and high computational complexity in Tucker decomposition. To address these issues, we propose a bias Tensor Ring decomposition framework for context-aware recommendation, which achieves a better balance between recommendation performance and computational complexity.
EXPERT SYSTEMS WITH APPLICATIONS
(2023)
Article
Mathematics, Applied
Xinrong Yang, Qilong Sun, Haitao Li, Xiangshan Kong
Summary: This paper discusses the design of impulsive sequence for the set stabilizability of impulsive probabilistic Boolean networks (IPBNs). By converting the dynamics of IPBNs into the corresponding probabilistic Boolean control networks, the state feedback impulsive sequence design is transformed into the state feedback control design. Several criteria are obtained for the set stabilizability in finite time with probability one and set stabilizability in distribution of IPBNs, respectively, by designing the state feedback impulsive sequences.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Computer Science, Artificial Intelligence
Zhe Gao, Biao Wang, Jun-e Feng, Tiantian Li
Summary: This paper investigates the reconstructibility of switched Boolean control networks, proposes new definitions and algorithms, and demonstrates their effectiveness through an example.
Article
Mathematics, Applied
Shih Yu Chang, Yimin Wei
Summary: This paper focuses on establishing new probability bounds for sums of random, independent T-product tensors. The study characterizes the large-deviation behavior of the extreme eigenvalue of these sums and applies Laplace transform method and Lieb's concavity theorem to generalize classical bounds. The paper also derives tail bounds for the norm of a sum of random rectangular T-product tensors.
COMPUTATIONAL & APPLIED MATHEMATICS
(2022)
