Particle swarm optimization (PSO) is a swarm intelligence algorithm and has good search performance and simplicity in implementation. Because of its properties, PSO has been applied to various optimization problems. However, the search performance of the classical PSO (CPSO) depends on reference frame of solution spaces for each objective function. CPSO is an invariant algorithm through translation and scale changes to reference frame of solution spaces but is a rotationally variant algorithm. As such, the search performance of CPSO is worse in solving rotated problems than in solving non-rotated problems. In the reference frame invariance, the search performance of an optimization algorithm is independent on rotation, translation, or scale changes to reference frame of solution spaces, which is a property of preferred optimization algorithms. In our previous study, piecewise-linear particle swarm optimizer (PPSO) has been proposed, which is effective in solving rotated problems. Because PPSO particles can move in solution spaces freely without depending on the coordinate systems, PPSO algorithm may have rotational invariance. However, theoretical analysis of reference frame invariance of PPSO has not been done. In addition, although behavior of each particle depends on PPSO parameters, good parameter conditions in solving various optimization problems have not been sufficiently clarified. In this paper, we analyze the reference frame invariance of PPSO theoretically, and investigated whether or not PPSO is invariant under reference frame alteration. We clarify that control parameters of PPSO which affect movement of each particle and performance of PPSO through numerical simulations.

In this paper, we propose a new paradigm of deterministic PSO, named piecewise-linear particle swarm optimizer (PPSO). In PPSO, each particle has two search dynamics, a convergence mode and a divergence mode. The trajectory of each particle is switched between the two dynamics and is controlled by parameters. We analyze convergence condition of each particle and investigate parameter conditions to allow particles to converge to an equilibrium point through numerical experiments. We further compare solving performances of PPSO. As a result, we report here that the solving performances of PPSO are substantially the same as or superior to those of PSO.

This paper proposes the application of tree-structured clustering to the processing of noisy speech collected under various SNR conditions in the framework of piecewise-linear transformation (PLT)-based HMM adaptation for noisy speech. Three kinds of clustering methods are described: a one-step clustering method that integrates noise and SNR conditions and two two-step clustering methods that construct trees for each SNR condition. According to the clustering results, a noisy speech HMM is made for each node of the tree structure. Based on the likelihood maximization criterion, the HMM that best matches the input speech is selected by tracing the tree from top to bottom, and the selected HMM is further adapted by linear transformation. The proposed methods are evaluated by applying them to a Japanese dialogue recognition system. The results confirm that the proposed methods are effective in recognizing digitally noise-added speech and actual noisy speech issued by a wide range of speakers under various noise conditions. The results also indicate that the one-step clustering method gives better performance than the two-step clustering methods.

Recently, efficient algorithms have been proposed for finding all characteristic curves of one-port piecewise-linear resistive circuits. Using these algorithms, a middle scale one-port circuit can be represented by a piecewise-linear resistor that is neither voltage nor current controlled. In this letter, an efficient algorithm is proposed for finding all dc operating points of piecewise-linear circuits containing such neither voltage nor current controlled resistors.

We consider the problem of constructing nonlinear dynamical systems that realize an arbitrary prescribed tree sources. We give a construction of dynamical systems by using piecewise-linear maps. Furthermore, we examine the obtained dynamical system to show that the structure of the memory of tree sources is characterized with some geometrical property of the constructed dynamical systems. Using a similar method, we also construct a dynamical system generating an arbitrary prescribed reverse tree source and show that the obtained dynamical system has some interesting geometrical property explicitly reflecting the tree structure of the memory of the reverse tree source.

An efficient algorithm is proposed for finding all dc solutions of piecewise-linear (PWL) circuits. This algorithm is based on a powerful test (termed the LP test) for nonexistence of a solution to a system of PWL equations in a given region using the dual simplex method. The proposed algorithm also uses a special technique that decreases the number of regions on which the LP test is performed. By numerical examples, it is shown that the proposed algorithm could find all solutions of large scale problems, including those where the number of variables is 500 and the number of linear regions is 10500, in practical computation time.

In this paper, a simple chaotic circuit using two RC phase shift oscillators and a diode is proposed and analyzed. By using a simpler model of the original circuit, the mechanism of generating chaos is explained and the exact solutions are derived. The exact expression of the Poincare map and its Jacobian matrix make it possible to confirm the generation of chaos using the Lyapunov exponents and to investigate the related bifurcation phenomena.

Recently there have been several attempts to construct a Markov information source based on chaotic dynamics of the PLM (piecewise-linear-monotonic) onto maps. Study, however, soon informs us that Kalman's 1956 embedding of a Markov chain is to be highly appreciated. In this paper Kalman's procedure for embedding a prescribed Markov chain into chaotic dynamics of the PLM onto map is revisited and improved by using the PLM onto map with the minimum number of subintervals.

In this study, we investigate two oscillators which have the same natural frequency, mutually coupled by N-type piecewise-linear negative resistor. In this system, according to the negative range of the coupling negative resistor, the various inter-esting synchronization phenomena which are in-phase, opposite phase and doublemode-like oscillations are observed. Especially, we show doublemode-like oscillations that are not observed until now in mutually coupled van der Pol oscillators with the smooth cubic characteristics, although the ones with same natural frequencies are coupled. And we show the differences of the phenomena between two oscillators coupled by the smooth cubic negative resistor and the ones coupled by the piecewise-linear negative resistor.

An efficient algorithm is proposed for finding all solutions of piecewise-linear resistive circuits The algorithm is based on the idea of "contraction" of the solution domain using a sign test. The proposed algorithm is efficient because many large super-regions containing no solution are eliminated in early steps.

This paper presents a new piecewise-linear dc model of the MOSFET. The proposed model is derived for long channel MOSFETs from the Shichman-Hodges equations, with emphasis on the accurate modeling of the major electrical characteristics, and is extended for short channel MOSFETs. The performance of the model is evaluated by comparing current-voltage characteristics and voltage transfer characteristics with those of the SPICE level-l and Sakurai models. The experimental results, using three or fewer piecewise-linear region boundaries on the axes of VGS, VGD and VSB, demonstrate that the proposed model provides enough accuracy for practical use with digital circuits.

An efficient algorithm is given for finding all solutions of piecewise-linear resistive circuits containing nonseparable transistor models such as the Gummel-Poon model or the Shichman-Hodges model. The proposed algorithm is simple and can be easily programmed using recursive functions.

An efficient algorithm is presented for finding all solutions of piecewise-linear resistive circuits containing sophisticated transistor models such as the Gummel-Poon model or the Shichman-Hodges model. When a circuit contains these nonseparable models, the hybrid equation describing the circuit takes a special structure termed pairwise-separability (or tuplewise-separability). This structure is effectively exploited in the new algorithm. A numerical example is given, and it is shown that all solutions are computed very rapidly.

A globally and quadratically convergent algorithm is presented for solving nonlinear resistive networks containing transistors modeled by the Gummel-Poon model or the Shichman-Hodges model. This algorithm is based on the Katzenelson algorithm that is globally convergent for a broad class of piecewise-linear resistive networks. An effective restart technique is introduced, by which the algorithm converges to the solutions of the nonlinear resistive networks quadratically. The quadratic convergence is proved and also verified by numerical examples.

An efficient algorithm is presented for solving nonlinear resistive networks. In this algorithm, the techniques of the piecewise-linear homotopy method are introduced to the Katzenelson algorithm, which is known to be globally convergent for a broad class of piecewise-linear resistive networks. The proposed algorithm has the following advantages over the original Katzenelson algorithm. First, it can be applied directly to nonlinear (not piecewise-linear) network equations. Secondly, it can find the accurate solutions of the nonlinear network equations with quadratic convergence. Therefore, accurate solutions can be computed efficiently without the piecewise-linear modeling process. The proposed algorithm is practically more advantageous than the piecewise-linear homotopy method because it is based on the Katzenelson algorithm that is very popular in circuit simulation and has been implemented on several circuit simulators.

Recently, efficient algorithms that exploit the separability of nonlinear mappings have been proposed for finding all solutions of piecewise-linear resistive circuits. In this letter, it is shown that these algorithms can be extended to circuits containing piecewise-linear resistors that are neither voltage nor current controlled. Using the parametric representation for these resistors, the circuits can be described by systems of nonlinear equations with separable mappings. This separability is effectively exploited in finding all solutions. A numerical example is given, and it is demonstrated that all solutions are computed very rapidly by the new algorithm.

An efficient algorithm is presented for finding all solutions of piecewise-linear resistive circuits. In this algorithm, a simple sign test is performed to eliminate many linear regions that do not contain a solution. This makes the number of simultaneous linear equations to be solved much smaller. This test, in its original form, is applied to each linear region; but this is time-consuming because the number of linear regions is generally very large. In this paper, it is shown that the sign test can be applied to super-regions consisting of adjacent linear regions. Therefore, many linear regions are discarded at the same time, and the computational efficiency of the algorithm is substantially improved. The branch-and-bound method is used in applying the sign test to super-regions. Some numerical examples are given, and it is shown that all solutions are computed very rapidly. The proposed algorithm is simple, efficient, and can be easily programmed.

Finding DC solutions of nonlinear networks is one of the most difficult tasks in circuit simulation, and many circuit designers experience difficulties in finding DC solutions using Newton's method. Piecewise-linear analysis has been studied to overcome this difficulty. However, efficient piecewiselinear algorithms have not been proposed for nonlinear resistive networks containing the Gummel-Poon models or the Shichman-Hodges models. In this paper, a new piecewise-linear algorithm is presented for solving nonlinear resistive networks containing these sophisticated transistor models. The basic idea of the algorithm is to exploit the special structure of the nonlinear network equations, namely, the pairwise-separability. The proposed algorithm is globally convergent and much more efficient than the conventional simplical-type piecewise-linear algorithms.

In this article, we consider a hysteresis oscillator which includes periodic thresholds. This oscillator relates to a model of human's sleep-wake cycles. Deriving a one dimensional return map rigorously, we can clarify existence regions of various periodic attractors in some parameter subspace. Also, we clarify co-existence regions of periodic attractors and existence regions of quasi-periodic attractors. Some of theoretical results are confirmed by laboratory measurements.

An efficient algorithm is presented for finding all solutions of piecewise-linear resistive circuits. In this algorithm, a simple sign test is performed to eliminate many linear regions that do not contain a solution. Therefore, the number of simultaneous linear equations to be solved is substantially decreased. This test, in its original form, requires O(Ln2) additions and comparisons in the worst case, where n is the number of variables and L is the number of linear regions. In this paper, an effective technique is proposed that reduces the computational complexity of the sign test to O(Ln). Some numerical examples are given, and it is shown that all solutions can be computed very efficiently. The proposed algorithm is simple and can be easily programmed by using recursive functions.