Matrix expression and reachability analysis of finite automata

In this paper, we propose a matrix-based approach for finite automata and then study the reachability conditions. Both the deterministic and nondeterministic automata are expressed in matrix forms, and the necessary and sufficient conditions on reachability are given using semitensor product of matrices. Our results show that the matrix expression provides an effective computational way for the reachability analysis of finite automata.

Logic and logic-based control

This paper gives a matrix expression of logic. Under the matrix expression, a general description of the logical operators is proposed. Using the semi-tensor product of matrices, the proofs of logical equivalences, implications, etc., can be simplified a lot. Certain general properties are revealed. Then, based on matrix expression, the logical operators are extended to multi-valued logic, which provides a foundation for fuzzy logical inference. Finally, we propose a new type of logic, called mix-valued logic, and a new design technique, called logic-based fuzzy control. They provide a numerically computable framework for the application of fuzzy logic for the control of fuzzy systems.

A New Expression of the Hermitian Solutions to a System of Matrix Equations with Applications

In this paper, a new necessary and sufficient condition for the existence of a Hermitian solution as well as a new expression of the general Hermitian solution to the system of matrix equations A1X = C1 and A3XB3 = C3 are derived. The max-min ranks and inertias of these Hermitian solutions with some interesting applications are shown. In particular, the max-min ranks and inertias of the Hermitian part of the general solution to this system are presented.

Algorithmic tangent modulus at finite strains based on multiplicative decomposition

The algorithmic tangent modulus at finite strains in current configuration plays an important role in the nonlinear finite element method. In this work, the exact tensorial forms of the algorithmic tangent modulus at finite strains are derived in the principal space and their corresponding matrix expressions are also presented. The algorithmic tangent modulus consists of two terms. The first term depends on a specific yield surface, while the second term is independent of the specific yield surface. The elastoplastic matrix in the principal space associated with the specific yield surface is derived by the logarithmic strains in terms of the local multiplicative decomposition. The Drucker-Prager yield function of elastoplastic material is used as a numerical example to verify the present algorithmic tangent modulus at finite strains.

Contracted product of hypermatrices via STP of matrices

An equivalent definition of hypermatrices is introduced.The matrix expression of hypermatrices is proposed.Using permu-tation matrices,the conversion between different matrix expressions is revealed.The various kinds of contracted products of hypermatrices are realized by semi-tensor products(STP)of matrices via matrix expressions of hypermatrices.

SUBic:A Scalable Unsupervised Framework for Discovering High Quality Biclusters

A biclustering algorithm extends conventional clustering techniques to extract all of the meaningful subgroups of genes and conditions in the expression matrix of a microarray dataset. However, such algorithms are very sensitive to input parameters and show poor scalability. This paper proposes a scalable unsupervised biclustering framework, SUBic, to find high quality constant-row biclusters in an expression matrix effectively. A one-dimensional clustering algorithm is proposed to partition the attributes, that is, columns of an expression matrix into disjoint groups based on the similarity of expression values. These groups form a set of short transactions and are used to discover a set of frequent itemsets each of which corresponds to a bicluster. However, a bicluster may include any attribute whose expression value is not similar enough to others, so a bicluster refinement is used to enhance the quality of a bicluster by removing those attributes based on its distribution of expression values. The performance of the proposed method is comparatively analyzed through a series of experiments on synthetic and real datasets.