Ken'ichi Fujimoto

Oscillation and its inhibition in a neural oscillator model for tinnitus.

Tinnitus is a symptom of perceiving phantom sounds. As one of its treatment techniques, tinnitus retraining therapy (TRT) has been proposed. It consists of psychotherapy by counseling and physical therapy based on masking theory by external stimuli. Our interest is to explain medical effects of the physical therapy from the viewpoint of engineering. In this paper we proposed a neural oscillator model with plasticity as a model for the tinnitus generation in the auditory central nervous system and its treatment. We investigated not only oscillatory phenomena observed in the model but also inhibition of the oscillation by external stimulus

Common Lyapunov function based on Kullback-Leibler divergence for a switched nonlinear system.

Many problems with control theory have led to investigations into switched systems. One of the most urgent problems related to the analysis of the dynamics of switched systems is the stability problem. The stability of a switched system can be ensured by a common Lyapunov function for all switching modes under an arbitrary switching law. Finding a common Lyapunov function is still an interesting and challenging problem. The purpose of the present paper is to prove the stability of equilibrium in a certain class of nonlinear switched systems by introducing a common Lyapunov function; the Lyapunov function is based on generalized Kullback–Leibler divergence or Csiszars I-divergence between the state and equilibrium. The switched system is useful for finding positive solutions to linear algebraic equations, which minimize the I-divergence measure under arbitrary switching. One application of the stability of a given switched system is in developing a new approach to reconstructing tomographic images, but nonetheless, the presented results can be used in numerous other areas.

Oscillation and its inhibition in a neuronal network model for tinnitus sound therapy

Tinnitus is the perception of phantom sounds in the ears or in the head. Sound therapy techniques for tinnitus treatment have been proposed. In order to investigate mechanisms of tinnitus generation and the clinical effects of sound therapy from the viewpoint of neural engineering, we have proposed a computational model using a neural oscillator. In the present paper, we propose another model that is composed of model neurons described by simplified Hodgkin-Huxley equations. By computer simulation it was detected that this model also has a bistable state, i.e., a stable oscillatory state and a stable equilibrium (non-oscillatory) state coexist at a certain parameter region. It was also noticed that the oscillation can be inhibited by supplying constant or pulse train stimuli, which is hypothesized as an afferent signal that is employed as an acoustical signal for tinnitus treatment. By hypothesizing that the oscillation and the equilibrium correspond to generation and inhibition of tinnitus, respectively, these phenomena could explain the fact that the habituated human auditory system temporarily halts perception of tinnitus following sound therapy.

Dynamical Properties of a Plastic Neural Network Model for Tinnitus Therapy and Inhibition of Oscillation Using Noise Stimulus

Tinnitus is the perception of phantom sounds in the ears or in the head. Sound therapy techniques for tinnitus have been proposed. To account for mechanisms of tinnitus generation and the clinical effects of sound therapies from the viewpoint of neural engineering, we have proposed a plastic neural network model for the human auditory system. We found that this model has a bistable state, i.e., a stable oscillatory state and a stable equilibrium (non-oscillatory) state coexist at a certain parameter region. We also found that the oscillation can be inhibited by supplying sinusoidal stimulus, which is hypothesized as sound for treatment of tinnitus, to the model. By hypothesizing that the oscillation and the equilibrium correspond to generation and inhibition of tinnitus, respectively, we reported that these phenomena could explain the fact that the habituated human auditory system temporarily halts perception of tinnitus following sound therapy. This paper describes dynamical properties of the model and inhibition of the oscillation for two kinds of noise stimuli which correspond to sound for treatment of tinnitus in clinical. Through numerical simulations we found that adequate noise stimulus can inhibits the oscillation.

Estimation of optimal cluster number for fuzzy clustering with combined fuzzy entropy index

Without sufficient prior knowledge the identification of the optimal cluster numbers is a difficult problem for unsupervised clustering. Since fuzzy entropy is essential for measuring the information of fuzzy sets, a combined fuzzy entropy index (CFE) is developed for searching the best number of clusters kb. The CFE involves the compactness and the separation of clusters both in the data space and in the membership space. The partition of fuzzy membership sets evaluated by the ratio of the symmetric fuzzy cross entropy of membership subset pairs to the average of fuzzy entropies of clusters. The most appropriate number of clusters for a specific data set is determined by the maximum of the CFE index. In order to verify the effectiveness of the CFE in the search of kb, six artificial data sets and eight real data sets were used in the fuzzy c-means clustering. The results show the CFE index has superior performance in the estimation of the best partition of clusters than the indices PC, PE, MPC, XB, FS, Kwon, FHV and PBMF, especially for high dimensional datasets. Moreover, the CFE index can correctly find the kb for the data sets with overlapping clusters, subclusters, multi-clusters, or various density clusters.

Inhibition of Oscillation in a Neural Oscillator Model for Sound Therapy of Tinnitus

Abstract Perception of continuous or intermittent sounds ringing in the ears without any external source is referred to as tinnitus. For the management of tinnitus one of the most effective approaches is sound therapy. Previously, we demonstrated a conceptual and computational plastic neural oscillator model for the mechanisms of tinnitus generation and the clinical effects of sound therapy on tinnitus. The proposed model has a stable oscillatory state and a stable equilibrium (non-oscillatory) state. It can be hypothesized that the oscillation state corresponds to the generation of tinnitus and the equilibrium state corresponds to the state in which the tinnitus is inhibited. Through numerical simulations of this model it was found that the oscillation can be inhibited by supplying band-pass noise (BN) stimuli, which clinically has been used as a stimulus for treatment of tinnitus (i.e., sound therapy). The current paper describes the inhibition of the oscillation by yet two different types of noise stimuli: Gaussian white noise (GWN) and additive uniform noise (AUN). This investigation shows that only smaller RMS value of GWN input could inhibit the oscillation. When larger RMS values of GWN were employed the inhibition of oscillation was not frequent. It was observed that AUN can inhibit the oscillation with higher possibility than GWN or BN. It is an interesting result although it does not directly suggest that AUN is better than GWN or BN in clinic.

Analysis of A Neural Oscillator Model with Plasticity for Treatment of Tinnitus

Tinnitus is a symptom of perceiving phantom sounds. The majority of tinnitus cases are caused by misinterpreting null sounds from ears as significant nervous signals in the cerebral limbic system. There are two typical sound therapies for tinnitus: Tinnitus Masking (TM) and Tinnitus Retraining Therapy (TRT). Their effects have been discussed from clinical assessments. To account for the mechanism of perceiving tinnitus and the clinical effects from the viewpoint of engineering, this paper describes a neural oscillator model with a plastic coupling for a cerebral limbic system and its dynamic behavior. We observed a bi-stable state such that a stable equilibrium and a stable oscillation coexist in a certain range of parameters. It was also discovered that the value of the plastic coupling changes by external stimulation, and then the oscillation is inhibited. This could explain the fact that the retrained cerebral limbic system temporarily stops perceiving tinnitus after sound therapy.

Parametric Control to Avoid Bifurcation Based on Maximum Local Lyapunov Exponent

This chapter presents a parametric controller to avoid bifurcations of stable periodic points in nonlinear discrete-time dynamical systems. The parameter regulation in the controller can be theoretically derived from the optimization of the maximum local Lyapunov exponent (MLLE) that is closely related to the stability index of stable fixed and periodic points. Differently from the stability index, the MLLE is differentiable with respect to system parameters in general and can be computed in real time without finding the exact position of fixed and periodic points. The computation of parameter updating to avoid bifurcations can be also realized along the passage of time. Therefore, the parametric controller we propose can detect the approach of parameter values to bifurcation points by monitoring the MLLE and avoid the bifurcation points by suppressing the MLLE below a prescribed negative value even when unexpected parameter variation causing bifurcations occurs. The outline of our controller and experimental results to evaluate whether our controller is effective for avoiding bifurcations are presented.

Collapse of mixed-mode oscillations and chaos in the extended Bonhoeffer-van Der pol oscillator under weak periodic perturbation

Mixed-mode oscillations in a slow-fast dynamical system under weak perturbation are studied numerically. First, we make a band-limited extremely weak Gaussian noise, and apply this noise to this oscillator. Then, we observe random phenomenon from numerical study even if the noise is extremely weak. The mixed-mode oscillations are submerged by chaos due to extremely weak noise. We imagine that mixed-mode oscillations in a slow-fast systems are delicate to the noise. In order to make clear the mechanism of generation of chaos, we assume that weak perturbation is periodic. From this assumption, we can calculate Lyapunov exponent, and draw a bifurcation diagram. In this bifurcation diagram, period-doubling bifurcations take place when the amplitude of the periodic perturbation is extremely small. We suspect the observability of the mixed-mode oscillation of the slow-fast dynamical system by experiment from this numerical result.

BIFURCATION ANALYSIS OF ITERATIVE IMAGE RECONSTRUCTION METHOD FOR COMPUTED TOMOGRAPHY

Of the iterative image reconstruction algorithms for computed tomography (CT), the power multiplicative algebraic reconstruction technique (PMART) is known to have good properties for speeding convergence and maximizing entropy. We analyze here bifurcations of fixed and periodic points that correspond to reconstructed images observed using PMART with an image made of multiple pixels and we investigate an extended PMART, which is a dynamical class for accelerating convergence. The convergence process for the state in the neighborhood of the true reconstructed image can be reduced to the property of a fixed point observed in the dynamical system. To investigate the speed of convergence, we present a computational method of obtaining parameter sets in which the given real or absolute values of the characteristic multiplier are equal. The advantage of the extended PMART is verified by comparing it with the standard multiplicative algebraic reconstruction technique (MART) using numerical experiments.