Improving the Solution of Least Squares Support Vector Machines with Application to a Blast Furnace System

The solution of least squares support vector machines (LS-SVMs) is characterized by a specific linear system, that is, a saddle point system. Approaches for its numerical solutions such as conjugate methods Sykens and Vandewalle (1999) and null space methods Chu et al. (2005) have been proposed. To speed up the solution of LS-SVM, this paper employs the minimal residual (MINRES) method to solve the above saddle point system directly. Theoretical analysis indicates that the MINRES method is more efficient than the conjugate gradient method and the null space method for solving the saddle point system. Experiments on benchmark data sets show that compared with mainstream algorithms for LS-SVM, the proposed approach significantly reduces the training time and keeps comparable accuracy. To heel, the LS-SVM based on MINRES method is used to track a practical problem originated from blast furnace iron-making process: changing trend prediction of silicon content in hot metal. The MINRES method-based LS-SVM can effectively perform feature reduction and model selection simultaneously, so it is a practical tool for the silicon trend prediction task

The norms of Bloch vectors and classification of four qudits quantum states

We investigate the norms of the Bloch vectors for any quantum state with subsystems less than or equal to four. Tight upper bounds of the norms are obtained, which can be used to derive tight upper bounds for entanglement measure defined by the norms of Bloch vectors. By using these bounds a trade-off relation of the norms of Bloch vectors is discussed. Theses upper bounds are then applied on separability. Necessary conditions are presented for different kinds of separable states in four-partite quantum systems. We further present a complete classification of quantum states for four qudits quantum systems.Comment: 8 pages, 1 figur

Selective ion removal by capacitive deionization (CDI)-based technologies

Severe freshwater shortages and global pollution make selective removal of target ions from solutions of great significance for water purification and resource recovery. Capacitive deionization (CDI) removes charged ions and molecules from water by applying a low applied electric field across the electrodes and has received much attention due to its lower energy consumption and sustainability. Its application field has been expanding in the past few years. In this paper, we report an overview of the current status of selective ion removal in CDI. This paper also discusses the prospects of selective CDI, including desalination, water softening, heavy metal removal and recovery, nutrient removal, and other common ion removal techniques. The insights from this review will inform the implementation of CDI technology

The data of 9 figures in PONE-D-18-18118

The data of 9 figures in PONE-D-18-1811