An Introduction to Semi-Tensor Product of Matrices and Its Applications

Cheng, Daizhan; Qi, Hongsheng; Zhao, Yin

doi:10.1142/8323

Cited by 334 publications

(268 citation statements)

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“…Instead of this representation, we may use the matrix-based representation proposed in [4], [5], [6], [23], where the semi-tensor product (STP) of matrices is used. Since in this paper, manipulation of matrices using the STP is not needed, we use a simple matrix-based representation based on truth tables.…”

Section: B Matrix-based Representation For Pbnsmentioning

confidence: 99%

“…where the concentration level (high or low) of the gene WNT5A is denoted by x 1 , the concentration level of the gene pirin by x 2 , the concentration level of the gene S100P by x 3 , the concentration level of the gene RET1 by x 4 , the concentration level of the gene MART1 by x 5 , the concentration level of the gene HADHB by x 6 , and the concentration level of the gene STC2 by x 7 . See [29] for further details.…”

Section: B Biological Examplementioning

confidence: 99%

“…This representation is an extension of that for BNs [18], and can be obtained from truth tables and selection probabilities. A matrix-based representation obtained by the semi-tensor product (STP) method [4], [5], [6], [23] can be also used. However, since manipulation of matrices using the STP method is not needed in this paper, we use a simple matrix-based representation based on truth tables.…”

Section: Introductionmentioning

confidence: 99%

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Design of Probabilistic Boolean Networks Based on Network Structure and Steady-State Probabilities

Kobayashi

Hiraishi

2017

IEEE Trans. Neural Netw. Learning Syst.

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Abstract-In this paper, we consider the problem of finding a probabilistic Boolean network (PBN) based on network structure and desired steady-state properties. In systems biology and synthetic biology, such problems are important as an inverse problem. Using a matrix-based representation of PBNs, a solution method for this problem is proposed. The problem of finding a Boolean network (BN) has been studied so far. In the problem of finding a PBN, we must calculate not only Boolean functions, but also the probabilities of selecting a Boolean function and the number of candidates of Boolean functions. Hence, the problem of finding a PBN is more difficult than that of finding a BN. The effectiveness of the proposed method is presented by numerical examples.Index Terms-gene regulatory network, network structure, probabilistic Boolean network, systems biology.

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Section: B Matrix-based Representation For Pbnsmentioning

confidence: 99%

Section: B Biological Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Design of Probabilistic Boolean Networks Based on Network Structure and Steady-State Probabilities

Kobayashi

Hiraishi

2017

IEEE Trans. Neural Netw. Learning Syst.

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“…In [21,22], the STP is presented as an extension of the conventional matrix product. For a conventional matrix product, if Col (A) ≠ Row (B), then matrices A and B are multiplicative.…”

Section: Semi-tensor Productmentioning

confidence: 99%

“…The proposed algorithm is based on the semi-tensor product (STP) [21,22], a novel matrix product that works by extending the conventional matrix product in cases of unequal dimensions. Our algorithm generates a random matrix, with dimensions that are smaller than M and N, where M is the length of the sampling vector and N is the length of signal that we want to reconstruct.…”

Section: Introductionmentioning

confidence: 99%

Low storage space for compressive sensing: semi-tensor product approach

Wang

Ruan

et al. 2017

J Image Video Proc.

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Random measurement matrices play a critical role in successful recovery with the compressive sensing (CS) framework. However, due to its randomly generated elements, these matrices require massive amounts of storage space to implement a random matrix in CS applications. To effectively reduce the storage space of the random measurement matrix for CS, we propose a random sampling approach for the CS framework based on the semi-tensor product (STP). The proposed approach generates a random measurement matrix, where the dimensions of the random measurement matrix are reduced to a quarter (or 1/16, 1/64, and even 1/256) of the number of dimensions, which are used for conventional CS. We then estimate the values of the sparse vector with a modified iteratively re-weighted least-squares (IRLS) algorithm. The results of numerical simulations showed that the proposed approach can reduce the storage space of a random matrix to at least a quarter while maintaining quality of reconstruction. All results confirmed that the proposed approach significantly influences the physical implementation of the CS in images, especially on embedded system and field programmable gate array (FPGA), where storage is limited.

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Minimum‐Time State Feedback Stabilization of Constrained Boolean Control Networks

Li¹,

Wang²

2015

Asian Journal of Control

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This paper investigates the state feedback stabilization of Boolean control networks (BCNs) with state and input constraints by using the semi-tensor product of matrices. Firstly, a kind of constrained input-state incidence matrix is proposed for constrained BCNs, which contains all the reachability information of the constrained systems. Secondly, based on the constrained input-state incidence matrix, a necessary and sufficient condition is presented for the stabilization of constrained BCNs via state feedback. Thirdly, a general procedure is proposed to design all possible minimum-time state feedback stabilizers. The study of an illustrative example shows that the new results obtained are effective in analyzing the stabilization of constrained BCNs.

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An Introduction to Semi-Tensor Product of Matrices and Its Applications

Cited by 334 publications

References 0 publications

Design of Probabilistic Boolean Networks Based on Network Structure and Steady-State Probabilities

Design of Probabilistic Boolean Networks Based on Network Structure and Steady-State Probabilities

Low storage space for compressive sensing: semi-tensor product approach

Minimum‐Time State Feedback Stabilization of Constrained Boolean Control Networks

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