(i) ∥x1, x2, . . . , xn∥ = 0 if any only if x1, x2, . . . , xn are linearly dependent, (ii) ∥x1, x2, . . . , xn∥ is invariant under any permutation, (iii) ∥x1, x2, . . . , axn∥ = |a| ∥x1, x2, . . . , xn∥, for any a ∈ R (real), (iv) ∥x1, x2, . . . , xn−1, y + z∥ = ∥x1, x2, . . . , xn−1, y∥ + ∥x1, x2, . . . , xn−1, z∥ is called an n-norm on X and the pair (X, ∥•, . . . , •∥) is called n-normed li...

Let X ∼ Np(θ, σIp) and W ∼ σχm, where both θ and σ are unknown, and X is independent of W . Optimal estimation of θ with unknown σ is a fundamental issue in applications but basic theoretical issues remain open. We consider estimation of θ under squared error loss. We develop sufficient conditions for prior density functions such that the corresponding generalized Bayes estimators for θ are adm...

Fountain codes are a class of rateless codes well-suited for communication over erasure channels with unknown erasure parameter. We analyze the decoding of LT codes, the first instance of practical, universal Fountain codes. A set of interest during LT decoding is the set of output symbols of reduced degree one (the “ripple”). The evolution of the ripple size throughout the decoding process is ...

In [1] [2], product accumulate (PA) codes were proposed and shown to be a class of simple and provably good codes for rate . This work investigates the generalized product accumulate (GPA) codes which have rates over the entire range and which are also “good” both in the maximum likelihood (ML) sense and under the iterative approach. Analysis concentrates on the weight distribution over the cod...

In this paper, we propose a new general approach to construct asymmetrical orthogonal arrays, namely generalized Kronecker product. The operation is not usual Kronecker product in the theory of matrices, but it is interesting since the interaction of two columns of asymmetrical orthogonal arrays can be often written out by the generalized Kronecker product. As an application of the method, some...

We investigate the selection and uniformization properties for classes of structures constructed by the FefermanVaught generalized product. We show that if classes K1 and K2 have the selection (respectively, uniformization) property, then the generalized product of these classes has the selection (respectively, uniformization) property.

Hierarchical-phrase based machine translation model is a popular translation model which combines advantages of phrase-based translation models and syntax-based translation models. However, since there are no linguistic constraints in the procedure of current hierarchical phrase extraction, there are a large number of redundant generalized rules extracted. In this paper, we propose two strategi...

1 Summary Conditional likelihood approach is a sensible choice for a hierarchical logistic regression model or other generalized regression models with binary data. However, its heavy computational burden limits its use, especially for the related mixed effects model. In this paper, we use modified profile likelihood as an accurate approximation to conditional likelihood, and then propose the u...

In this paper, we focus on hierarchical multiobjective linear programming problems where multiple decision makers in a hierarchical organization have their own multiple objective linear functions together with common linear constraints, and propose a fuzzy approach to obtain a satisfactory solution which reflects not only the hierarchical relationships between multiple decision makers but also ...

In this paper, we focus on hierarchical multiobjective linear programming problems where multiple decision makers in a hierarchical organization have their own multiple objective linear functions together with common linear constraints, and propose an interactive decision making method to obtain a satisfactory solution which reflects not only the hierarchical relationships between multiple deci...