Phase structure of nonlinear dynamical system is governed by the vector field and decides the trajectories. Accordingly, the power spectra of trajectories include the structural field effect on the phase space. In this paper, we develop a method for analyzing phase structure using power spectra of trajectories and reconstitute a potential function in the system.

Quad-core cpus have been a common desktop configuration for today's office. The increasing number of processors on a single chip opens new opportunity for parallel computing. Our goal is to make use of the multi-core as well as multi-processor architectures to speed up large-scale data mining algorithms. In this paper, we present a general parallel learning framework, Cut-And-Stitch, for training hidden Markov chain models. Particularly, we propose two model-specific variants, CAS-LDS for learning linear dynamical systems (LDS) and CAS-HMM for learning hidden Markov models (HMM). Our main contribution is a novel method to handle the data dependencies due to the chain structure of hidden variables, so as to parallelize the EM-based parameter learning algorithm. We implement CAS-LDS and CAS-HMM using OpenMP on two supercomputers and a quad-core commercial desktop. The experimental results show that parallel algorithms using Cut-And-Stitch achieve comparable accuracy and almost linear speedups over the traditional serial version.

In this paper, we propose a variational method to derive the coefficients of piecewise-linear (PWL) models able to accurately approximate nonlinear functions, which are vector fields of autonomous dynamical systems described by continuous-time state-space models dependent on parameters. Such dynamical systems admit limit cycles, and the supercritical Hopf bifurcation normal form is chosen as an example of a system to be approximated. The robustness of the approximations is checked, with a view to circuit implementations.

Acoustic modeling in speech recognition uses very little knowledge of the speech production process. At many levels our models continue to model speech as a surface phenomenon. Typically, hidden Markov model (HMM) parameters operate primarily in the acoustic space or in a linear transformation thereof; state-to-state evolution is modeled only crudely, with no explicit relationship between states, such as would be afforded by the use of phonetic features commonly used by linguists to describe speech phenomena, or by the continuity and smoothness of the production parameters governing speech. This survey article attempts to provide an overview of proposals by several researchers for improving acoustic modeling in these regards. Such topics as the controversial Motor Theory of Speech Perception, work by Hogden explicitly using a continuity constraint in a pseudo-articulatory domain, the Kalman filter based Hidden Dynamic Model, and work by many groups showing the benefits of using articulatory features instead of phones as the underlying units of speech, will be covered.

A merged analog-digital circuit architecture is proposed for implementing intelligence in SoC systems. Pulse modulation signals are introduced for time-domain massively parallel analog signal processing, and also for interfacing analog and digital worlds naturally within the SoC VLSI chip. Principles and applications of pulse-domain linear arithmetic processing are explored, and the results are expanded to the nonlinear signal processing, including an arbitrary chaos generation and continuous-time dynamical systems with nonlinear oscillation. Silicon implementations of the circuits employing the proposed architecture are fully described.