The Peres-Horodecki criterion of positivity under partial transpose is studied in the context of separability of bipartite continuous variable states. The partial transpose operation admits, in the continuous case, a geometric interpretation as mirror reflection in phase space. This recognition leads to uncertainty principles, stronger than the traditional ones, to be obeyed by all separable st...

This paper proposed a novel classification model which introduced the kernel function into the original Multiple Criteria Linear Programming (MCLP) model. MCLP model is used as a classification method which can only solve linear separable problems in data mining. However, the proposed kernel-based MCLP model can deal with non-linear cases. Meanwhile, unlike some other complicated models, this m...

We consider convex-concave saddle point problems with a separable structure and non-strongly convex functions. We propose an efficient stochastic block coordinate descent method using adaptive primal-dual updates, which enables flexible parallel optimization for large-scale problems. Our method shares the efficiency and flexibility of block coordinate descent methods with the simplicity of prim...

Learning hash functions/codes for similarity search over multi-view data is attracting increasing attention, where similar hash codes are assigned to the data objects characterizing consistently neighborhood relationship across views. Traditional methods in this category inherently suffer three limitations: 1) they commonly adopt a two-stage scheme where similarity matrix is first constructed, ...

This paper aims to study the α-volume of K, an arbitrary subset of the set of N ×N density matrices. The α-volume is a generalization of the Hilbert-Schmidt volume and the volume induced by partial trace. We obtain two-side estimates for the α-volume of K in terms of its Hilbert-Schmidt volume. The analogous estimates between the Bures volume and the α-volume are also established. We employ our...

T H E German Government has commissioned me to communicate to this Congress the assurances of its good-will, and to participate in your transactions. In this official capacity allow me to repeat here the invitation given already in the general session to visit at some convenient time the German university exhibit in the Liberal Arts Building. I have also the honor to lay before you a considerab...

This paper details a systematic method for significantly enhancing the noise margins of very fast threshold gates. The method is based on adding nonlinear terms determined from the Boolean form of the linearly separable (threshold) function to be implemented. It follows that linearly separable functions can be computed with high noise immunity by higher order perceptrons. Simulation results sup...

An analytic and empirical study of line iterative methods for solving the discrete convection-diffusion equation is performed. The methodology consists of performing one step of the cyclic reduction method, followed by iteration on the resulting reduced system using line orderings of the reduced grid. Two classes of iterative methods are considered: block stationary methods, such as the block G...

This paper presents a methodology for identifying groups of products that exhibit similar patterns in demand and responsiveness to changes in price using store-level sales data. We use the concept of economic separability as an identification condition for different product groups, and build a weakly separable model of aggregate demand. A common issue with separable demand models is that the pa...

This special class of a nonlinear mathematical programming problem which is addressed in this paper has a structure characterized by a subset of variables restricted to assume discrete values, which are linear and separable from the continuous variables. The strategy of releasing nonbasic variables from their bounds, combined with the “active constraint” method and the notion of superbasics, ha...