Solving logic equation via matrix expression

2009 ◽  
Vol 4 (3) ◽  
pp. 259-269 ◽  
Author(s):  
Daizhan Cheng ◽  
Zhiqiang Li
Keyword(s):  
Logic Equation ◽  
Matrix Expression

ALGEBRAIC APPROACH TO DYNAMICS OF MULTIVALUED NETWORKS

2010 ◽  
Vol 20 (03) ◽  
pp. 561-582 ◽  
Author(s):  
ZHIQIANG LI ◽  
DAIZHAN CHENG
Keyword(s):  
Discrete Time ◽  
Transition Matrix ◽  
Algebraic Approach ◽  
Bilinear System ◽  
Logical Function ◽  
Control Networks ◽  
Logical Network ◽  
Multilinear Mapping ◽  
Network Transition ◽  
Matrix Expression

Using semi-tensor product of matrices, a matrix expression for multivalued logic is proposed, where a logical variable is expressed as a vector, and a logical function is expressed as a multilinear mapping. Under this framework, the dynamics of a multivalued logical network is converted into a standard discrete-time linear system. Analyzing the network transition matrix, easily computable formulas are obtained to show (a) the number of equilibriums; (b) the numbers of cycles of different lengths; (c) transient period, the minimum time for all points to enter the set of attractors, respectively. A method to reconstruct the logical network from its network transition matrix is also presented. This approach can also be used to convert the dynamics of a multivalued control network into a discrete-time bilinear system. Then, the structure and the controllability of multivalued logical control networks are revealed.

Knockdown of IRF3 inhibits extracellular matrix expression in keloid fibroblasts

2017 ◽  
Vol 88 ◽  
pp. 1064-1068 ◽  
Author(s):  
Yi Zhang ◽  
Li Zhang ◽  
Xiao-hua Lin ◽  
Zhi-ming Li ◽  
Qi-yu Zhang
Keyword(s):  
Extracellular Matrix ◽  
Matrix Expression ◽  
Keloid Fibroblasts

Extracellular matrix expression of human prolapsed vaginal wall

2009 ◽  
Vol 29 (4) ◽  
pp. 582-586 ◽  
Author(s):  
Elizabeth Mosier ◽  
Victor K. Lin ◽  
Philippe Zimmern
Keyword(s):  
Extracellular Matrix ◽  
Vaginal Wall ◽  
Matrix Expression

Aw expanded logic equation list for checkout

1969 ◽  
Author(s):  
J. A. Rader ◽  
D. A. Isaak
Keyword(s):  
Logic Equation

Finding Cut-Edges and the Minimum Spanning Tree via Semi-Tensor Product Approach

2018 ◽  
Vol 6 (5) ◽  
pp. 459-472
Author(s):  
Xujiao Fan ◽  
Yong Xu ◽  
Xue Su ◽  
Jinhuan Wang
Keyword(s):  
Tensor Product ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
The Matrix ◽  
Product Approach ◽  
Matrix Expression ◽  
Necessary And Sufficient ◽  
Logical Functions

Abstract Using the semi-tensor product of matrices, this paper investigates cycles of graphs with application to cut-edges and the minimum spanning tree, and presents a number of new results and algorithms. Firstly, by defining a characteristic logical vector and using the matrix expression of logical functions, an algebraic description is obtained for cycles of graph, based on which a new necessary and sufficient condition is established to find all cycles for any graph. Secondly, using the necessary and sufficient condition of cycles, two algorithms are established to find all cut-edges and the minimum spanning tree, respectively. Finally, the study of an illustrative example shows that the results/algorithms presented in this paper are effective.

scholarly journals A MicroRNA-29 Mimic (Remlarsen) Represses Extracellular Matrix Expression and Fibroplasia in the Skin

2019 ◽  
Vol 139 (5) ◽  
pp. 1073-1081 ◽  
Author(s):  
Corrie L. Gallant-Behm ◽  
Joseph Piper ◽  
Joshua M. Lynch ◽  
Anita G. Seto ◽  
Seok Jong Hong ◽  
...  
Keyword(s):  
Extracellular Matrix ◽  
Matrix Expression
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