Knowledge acquisition plays a critical role in constructing a knowledge-based system (KBS). It is the most time-consuming phase and has been recognized as the bottleneck of KBS development. This paper presents a matrix representation and mapping (MRM) approach to facilitate the effectiveness of knowledge acquisition in building a KBS. The proposed MRM approach, which is based on matrix represen...

In this paper we find a unique normal form for the symplectic matrix representation of the conjugacy class of a prime order element of the mapping-class group. We find a set of generators for the fundamental group of a surface with a conformal automorphism of prime order which reflects the action the automorphism in an optimal way. This is called an adapted homotopy basis and there is a corresp...

General parametric solution to a family of generalized Sylvester matrix equations arising in linear system theory is presented by using the socalled generalized Sylvester mapping which has some elegant properties. The solution consists of some polynomial matrices satisfying certain conditions and a parametric matrix representing the degree of freedom in the solution. The results provide great c...

We show how introducing discrete Abelian flavor symmetries can produce texture zeros in the fermion mass matrices, while preserving the correct relationships with the low-energy data on quark and lepton masses. We outline a procedure for defining texture zeros as suppressed entries in Yukawa matrices. These texture zeros can account for the coexistence of the observed large mixing in atmospheri...

The periodicity of a texture is one of its important visual characteristics. The inertias of co-occurrence matrices of the texture have been often used to detect the visual periodicity. However, it is time-consuming to explicitly construct these matrices. In this paper, we propose the distance matching function to avoid constructing the matrices due to our new interpretation of an inertia. For ...

(a) Define a linear mapping R2h h : R 5 → R3 according to the full weighting scheme (see Lecture slides). Setup the respective matrix R2h h . (b) Define a linear mapping Ph 2h : R 3 → R5 which prolongates a solution vector from the coarse to the fine grid using linear interpolation (see Lecture slides). Setup the respective matrix Ph 2h. (c) Based on the matrices R2h h , P h 2h and Ah, compute ...

When modelling code-switched speech (utterances that contain a mixture of languages), the embedded language often contains phones not found in the matrix language. These are typically dealt with by either extending the phone set or mapping each phone to a matrix language counterpart. We use acoustic log likelihoods to assist us in identifying the optimal mapping strategy at a context-dependent ...

Through eigenanalysis of communication matrices, we develop a new objective function formulation for mapping tasks to parallel computers with cellular networks. This new formulation significantly speeds up the solution process through consideration of the symmetries in the supply matrix of a network and a transformation of the demand matrix of any application. The extent of the speedup is not e...