The digital spiking neuron (DSN) consists of digital state cells and behaves like a simplified neuron model. By adjusting wirings among the cells, the DSN can generate spike-trains with various characteristics. In this paper we present a theorem that clarifies basic relations between change of wirings and change of characteristics of the spike-train. Also, in order to explore learning potential of the DSN, we propose a learning algorithm for generating spike-trains that are suited to an application example. We then show significances and basic roles of the presented theorem in the learning dynamics.

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.

This paper studies a chaotic spiking oscillator consisting of two capacitors, two voltage-controlled current sources of signum shape and one impulsive switch. The vector field of circuit equation is piecewise constant and embedded return map is piecewise linear. Using the map parameter condition for chaos generation is given. Using a simple test circuit typical phenomena can be confirmed experimentally.

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.

This paper addresses the parameter estimation problem of an interval-based hybrid dynamical system (interval system). The interval system has a two-layer architecture that comprises a finite state automaton and multiple linear dynamical systems. The automaton controls the activation timing of the dynamical systems based on a stochastic transition model between intervals. Thus, the interval system can generate and analyze complex multivariate sequences that consist of temporal regimes of dynamic primitives. Although the interval system is a powerful model to represent human behaviors such as gestures and facial expressions, the learning process has a paradoxical nature: temporal segmentation of primitives and identification of constituent dynamical systems need to be solved simultaneously. To overcome this problem, we propose a multiphase parameter estimation method that consists of a bottom-up clustering phase of linear dynamical systems and a refinement phase of all the system parameters. Experimental results show the method can organize hidden dynamical systems behind the training data and refine the system parameters successfully.

There is increasing evidence from in vivo recordings in monkeys trained to respond to stimuli by making left- or rightward eye movements, that firing rates in certain groups of neurons in oculo-motor areas mimic drift-diffusion processes, rising to a (fixed) threshold prior to movement initiation. This supplements earlier observations of psychologists, that human reaction-time and error-rate data can be fitted by random walk and diffusion models, and has renewed interest in optimal decision-making ideas from information theory and statistical decision theory as a clue to neural mechanisms. We review results from decision theory and stochastic ordinary differential equations, and show how they may be extended and applied to derive explicit parameter dependencies in optimal performance that may be tested on human and animal subjects. We then briefly describe a biophysically-based model of a pool of neurons in locus coeruleus, a brainstem nucleus implicated in widespread norepinephrine release. This neurotransmitter can effect transient gain changes in cortical circuits of the type that the abstract drift-diffusion analysis requires. We also describe how optimal gain schedules can be computed in the presence of time-varying noisy signals. We argue that a rational account of how neural spikes give rise to simple behaviors is beginning to emerge.

Some plants have air purification ability. This purification ability of plants is considered a promising method for indoor air purification because of the low cost and high purification performance. Therefore, several studies have been carried out to investigate the relationship between the air purification ability of plants and environmental conditions. Nevertheless, the purification mechanism and process have not been clarified yet. In this paper, we investigated the air purification process in plants by bioelectrical potential analysis using linear and nonlinear analysis methods. First, we showed that two types of plants have a high air purification ability; Schefflera and Boston fern. Next, we measured AC bioelectrical potential during the purifying process of plants for pollutant gas. Then, we evaluated the power spectra of time series data of the bioelectrical potential. We found that the power spectra shifted to a lower level after gas injection over all frequencies. Thus, the higher power spectrum came from possible higher physiological activities of the plant. Finally, we introduced a nonlinear analysis method from the dynamical system theory. We transformed the time series data of the potential to a higher dimensional state space using a delay coordinate, which is often used in the field of nonlinear time series analysis. The results show that the orbits in the reconstructed state space have a large variation in gas injection. These experimental results suggest that the measurement of bioelectrical potential could become a useful method for evaluating the air purification ability of plants.

In this paper we study the large deviation property for chaotic binary sequences generated by one-dimensional maps displaying chaos and thresholds functions. We deal with the case when nonlinear maps are the r-adic maps. The large deviation theory for dynamical systems is useful for investigating this problem.

The PLC (Programmable Logic Controller) has been widely used in the industrial world as a controller for manufacturing systems, as a process controller and so on. The conventional PLC has been designed and verified as a pure Discrete Event System (DES) by using an abstract model of a controlled plant. In verifying the PLC, however, it is also important to take into account the physical behavior (e.g. dynamics, shape of objects) of the controlled plant in order to guarantee such important factors as safety. This paper presents a new verification technique for the PLC-based control system, which takes into account these physical behaviors, based on a Hybrid Dynamical System (HDS) framework. The other key idea described in the paper is the introduction of the concept of signed distance which not only measures the distance between two objects but also checks whether two objects interfere with each other. The developed idea is applied to illustrative material handling problems, and its usefulness is demonstrated.

In this paper, an iterative decoding algorithm for channels with additive linear dynamical noise is presented. The proposed algorithm is based on the tightly coupled two inference algorithms: the sum-product algorithm which infers the information symbols of an low density parity check (LDPC) code and the Kalman smoothing algorithm which infers the channel states. The linear dynamical noise are the noise generated from a linear dynamical system. We often encounter such noise (i.e., additive colored noise) in practical communication and storage systems. The conventional iterative decoding algorithms such as the sum-product algorithm cannot derive full potential of turbo codes nor LDPC codes over such a channel because the conventional algorithms are designed under the independence assumption on the noise. Several simulations have been performed to assess the performance of the proposed algorithm. From the simulation results, it can be concluded that the Kalman smoothing algorithm deserves to be implemented in a decoder when the linear dynamical part of the linear dynamical noise is dominant rather than the white Gaussian noise part. In such a case, the performance of the proposed algorithm is far superior to that of the conventional algorithm.

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.

This letter introduces a chaotic circuit consisting of one linear 2-port VCCS, one hysteresis 2-port VCCS, and two capacitors. The circuit has double screw attractors, quad screw attractors and co-existence states of them. Since the system is piecewise linear, attractors existence condition can be described using exact piecewise solutions. Using a simple test circuit, typical phenomena are verified in the laboratory.

There are several attempts to generate chaotic binary sequences by using one-dimensional maps. From the standpoint of engineering applications, it is necessary to evaluate statistical properties of sample sequences of finite length. In this paper we attempt to evaluate the statistics of chaotic binary sequences of finite length. The large deviation theory for dynamical systems is useful for investigating this problem.

In this paper, we present new stability conditions for a class of large-scale hybrid dynamical systems composed of a number of interconnected hybrid subsystems. The stability conditions are given in terms of discontinuous Lyapunov functions of the stable hybrid subsystems. Furthermore, the stability conditions are represented by LMIs (Linear Matrix Inequalities) which are computationally tractable.

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.

We here consider an extension of the validity of classical criteria ensuring the robustness of the statistical features of discrete time dynamical systems with respect to implementation inaccuracies and noise. The result is achieved by proving that, whenever a discrete time dynamical system is robust, all the discrete time dynamical systems topologically conjugate with it are also robust. In particular, this result offer an explanation for the stochastic robustness of the logistic map, which is confirmed by the reported experimental measurements.

We are working on an algorithm to optimize the logic circuits that can be realized on the super fine-grain parallel processing architecture. As a part of this work, we have developed an inverter reduction algorithm. This algorithm is based on modeling logic circuits as dynamical systems. We implement the algorithm in the PARTHENON system, which is the high level synthesis system developed in NTT's laboratories, and evaluate it using ISCAS85 benchmarks. We also compare the results with both the existing algorithm of PARTHENON and the algorithm of Jain and Bryant.

We investigate bifurcations of the periodic solution observed in a phase converter circuit. The system equations can be considered as a nonlinear coupled system with Duffing's equation and an equation describing a parametric excitation circuit. In this system there are two types of solutions. One is with x = y = 0 which is the same as the solution of Duffing's equation (correspond to uncoupled case), another solution is with xy0. We obtain bifurcation sets of both solutions and discuss how does the coupling change the bifurcation structure. From numerical analysis we obtain a codimension two bifurcation which is intersection of double period-doubling bifurcations. Pericdic solutions generated by these bifurcations become chaotic states through a cascade of codimension three bifurcations which are intersections of D-type of branchings and period-doubling bifurcations.

It is well known that the Hopfield Model (HM) for neural networks to solve the TSP suffers from three major drawbacks: (D1) it can converge to non-optimal local minimum solutions; (D2) it can also converge to non-feasible solutions; (D3) results are very sensitive to the careful tuning of its parameters. A number of methods have been proposed to overcome (D1) well. In contrast, work on (D2) and (D3) has not been sufficient; techniques have not been generalized to larger classes of optimization problems with constraint including the TSP. We first construct Extended HMs (E-HMs) that overcome both (D2) and (D3). The extension of the E-HM lies in the addition of a synapse dynamical system cooperated with the corrent HM unit dynamical system. It is this synapse dynamical system that makes the TSP constraint hold at any final states for whatever choices of the HM parameters and an initial state. We then generalize the E-HM further into a network that can solve a larger class of continuous optimization problems with a constraint equation where both of the objective function and the constraint function are non-negative and continuously differentiable.

We propose an equivalent circuit model described by the Rössler equation. Then we can consider a coupled Rössler system with a physical meaning on the connection. We consider an oscillatory circuit such that two identical Rössler circuits are coupled by a resistor. We have studied three routes to entirely and almost synchronized chaotic attractors from phase-locked periodic oscillations. Moreover, to simplify understanding of synchronization phenomena in the coupled Rössler system, we investigate a mutually coupled map that shows analogous locking properties to the coupled Rössler System.