Tetsuo Nishi

Topological criteria for nonlinear resistive circuits containing controlled sources to have a unique solution

This paper gives a definitive solution to the following fundamental problem: When does a network containing nonlinear monotone resistors (characterized by strictly increasing onto function), dc sources (voltage and current sources), and linear controlled sources (all 4 types) possess a unique solution? Our uniqueness criteria is couched in strictly topological terms. In particular, the uniqueness of a large class of practical nonlinear circuits can be determined, often by inspection, by checking for the presence of a new and fundamental topological structure called a cactus graph.

An efficient method to find all solutions of piecewise-linear resistive circuits

An efficient method is presented for solving a system of piecewise-linear equations, F(x)=y, each element of which is a piecewise-linear function of one variable. Let n denote the dimension of x and L the number of regions of x in which F is linear. Then it is shown that the multiplications required to solve L linear simultaneous equations obtained from F(x)=y are O(Ln) for large n.<<ETX>>

Rigorous proof of termination of SMO algorithm for support vector Machines

Sequential minimal optimization (SMO) algorithm is one of the simplest decomposition methods for learning of support vector machines (SVMs). Keerthi and Gilbert have recently studied the convergence property of SMO algorithm and given a proof that SMO algorithm always stops within a finite number of iterations. In this letter, we point out the incompleteness of their proof and give a more rigorous proof.

Graph-theoretical approach to 2-switch DC-DC converters

SUMMARY This paper presents a graph-theoretic approach to analyse and synthesize switch mode DC–DC converters. The result is based on the state-space averaging equation and the fundamental graph theory. Hence our proposed method is applied to various kinds of DC–DC converters with two switches and topological conditions for two-switch DC–DC converters are obtained systematically. Copyright ? 2005 John Wiley & Sons, Ltd.

On the number of solutions of a class of nonlinear resistive circuits

The author deals with the number of solutions of equations of nonlinear resistive circuits composed of linear and nonlinear one-port resistors, linear active elements, and DC sources. By referring to the V-I characteristics of real diodes it is assumed that the second derivative as well as the first derivative of the V-I characteristics of nonlinear resistors are positive. The necessary and sufficient conditions are given for the equation to have a finite number (<or=2/sup n/) of solutions. The extension of this result is discussed.<<ETX>>

Global Convergence of Decomposition Learning Methods for Support Vector Machines

Decomposition methods are well-known techniques for solving quadratic programming (QP) problems arising in support vector machines (SVMs). In each iteration of a decomposition method, a small number of variables are selected and a QP problem with only the selected variables is solved. Since large matrix computations are not required, decomposition methods are applicable to large QP problems. In this paper, we will make a rigorous analysis of the global convergence of general decomposition methods for SVMs. We first introduce a relaxed version of the optimality condition for the QP problems and then prove that a decomposition method reaches a solution satisfying this relaxed optimality condition within a finite number of iterations under a very mild condition on how to select variables

An Efficient Method for Simplifying Decision Functions of Support Vector Machines

A novel method to simplify decision functions of support vector machines (SVMs) is proposed in this paper. In our method, a decision function is determined first in a usual way by using all training samples. Next those support vectors which contribute less to the decision function are excluded from the training samples. Finally a new decision function is obtained by using the remaining samples. Experimental results show that the proposed method can effectively simplify decision functions of SVMs without reducing the generalization capability.

Uniqueness of solution for nonlinear resistive circuits containing CCCS's or VCVS's whose controlling coefficients are finite

Necessary and sufficient conditions are given for the uniqueness of solution of nonlinear resistive circuits made of strictly monotoneincreasing nonlinear resistors, dc sources, and k linear current-controlled current sources (CCCSs) or linear voltage-controlled voltage sources (VCVSs) whose controlling coefficients {alpha}_{mu} are bounded by 0 . These conditions are cast in explicit topological terms and are therefore easy to check.

A learning algorithm for improving the classification speed of support vector machines

A novel method for training support vector machines (SVMs) is proposed to speed up the SVMs in test phase. It has three main steps. First, an SVM is trained on all the training samples, thereby producing a number of support vectors. Second, the support vectors, which contribute less to the shape of the decision surface, are excluded from the training set. Finally, the SVM is re-trained only on the remaining samples. Compared to the initially trained SVM, the efficiency of the finally trained SVM is highly improved, without system degradation.

Necessary and Sufficient Condition for a Class of Planar Dynamical Systems Related to CNNs to be Completely Stable

We study global dynamical behavior of cellular neural networks (CNNs) consisting of two cells. Since the output characteristic of each cell is expressed by a piecewise-linear function, a CNN with two cells is considered as a planar piecewise-linear dynamical system. We present the necessary and sufficient condition for such a CNN to be completely stable under the assumptions that: 1) self-coupling coefficients take the same value greater than one and 2) biases are set to zero. The condition is explicitly expressed in terms of coupling coefficients between cells