In this paper, we write down the separable Werner state in a two-qubit system as a convex combination of product states explicitly. The Werner state in a two-qubit system has a single real parameter and varies from inseparable state to separable state according to the value of its parameter. The convex combination of product states gives a hidden variable model to the separable Werner state.

In this report, we propose a new partitioned variable metric method for minimizing nonsmooth partially separable functions. After a short introduction, the complete algorithm is introduced and some implementation details are given. We prove that this algorithm is globally convergent under standard mild assumptions. Computational experiments given confirm efficiency and robustness of the new met...

Variable selection for clustering is an important and challenging problem in high-dimensional data analysis. Existing variable selection methods for model-based clustering select informative variables in a "one-in-all-out" manner; that is, a variable is selected if at least one pair of clusters is separable by this variable and removed if it cannot separate any of the clusters. In many applicat...

We present an alternating augmented Lagrangian method for convex optimization problems where the cost function is the sum of two terms, one that is separable in the variable blocks, and a second that is separable in the difference between consecutive variable blocks. Examples of such problems include Fused Lasso estimation, total variation denoising, and multiperiod portfolio optimization with ...

In this paper, we write down the separable Werner state in a two-qubit system explicitly as a convex combination of product states, which is different from the convex combination obtained byWootters’ method. TheWerner state in a two-qubit system has a single real parameter and varies from inseparable state to separable state according to the value of its parameter. We derive a hidden variable m...

This paper considers the identification problem of continuous-time systems with unknown time delays from sampled input-output data. An iterative global separable nonlinear least-squares (GSEPNLS) method which estimates the time delays and transfer function parameters separably is derived, by using stochastic global-optimization technique to avoid convergence to a local minimum. Futhermore, the ...

We develop a separable-kernel decomposition method for approximating the double-square-root DSR continuation operator in one-way migrations in this paper. This new approach is a further development of separable approximations of the single-square-root SSR operator. The separable approximation of the DSR operator generally involves solving a complicated nonlinear system of integral equations. In...

This paper considers the identification problem of continuous-time systems with unknown time delay from sampled input-output data. By using a digital prefilter, an approximated discrete-time estimation model is first derived, in which the system parameters remain in their original form and the time delay need not be an integral multiple of the sampling period. Then an iterative separable nonlin...

This paper proposes a design method of separable denominator 2-D variable digital filters with high frequency tuning accuracy. In the proposed method, a parallel allpass structure with complex coefficients is used as a prototype structure of the 2-D variable digital filters. The proposed 2-D variable digital filters are composed of first-order complex allpass sections. To improve the frequency ...