Yo Horikawa

Noise effects on spike propagation in the stochastic Hodgkin-Huxley models

Effects of membrane current noise on spike propagation along a nerve fiber are studied. Additive current noise and channel noise are considered by using stochastic versions of the Hodgkin-Huxley model. The results of computer simulation show that the membrane noise causes considerable variation of the propagation time of a spike (thus changes in interspike intervals) for a small unmyelinated fiber of radius 0.1∼1 μm.

Exponential transient propagating oscillations in a ring of spiking neurons with unidirectional slow inhibitory synaptic coupling.

Transient oscillations in a ring of spiking neuron models unidirectionally coupled with slow inhibitory synapses are studied. There are stable spatially fixed steady firing-resting states and unstable symmetric propagating firing-resting states. In transients, firing-resting patterns rotate in the direction of coupling (propagating oscillations), the duration of which increases exponentially with the number of neurons (exponential transients). Further, the duration of randomly generated transient propagating oscillations is distributed in a power law form and spatiotemporal noise of intermediate strength sustains propagating oscillations. These properties agree with those of transient propagating waves in a ring of sigmoidal neuron models.

Use of Autocorrelation Kernels in Kernel Canonical Correlation Analysis for Texture Classification

Kernel canonical correlation analysis (KCCA) with autocorrelation kernels is applied to invariant texture classification. The autocorrelation kernels are the inner products of the autocorrelation functions of original data and effectively calculated with the cross-correlation functions. Classification experiment shows the autocorrelation kernels perform better than the linear and Gaussian kernels in KCCA. Further, it is shown that the generalization ability is degraded as the order of the autocorrelation kernels increases, since relative values of the kernels of different data tend to zero.

Spike propagation during the refractory period in the stochastic Hodgkin-Huxley model

The effects of noise on a spike train propagating on a nerve fiber during the relative refractory period are studied by using a stochastic version of the Hodgkin-Huxley model. Fluctuations in spike speeds due to the noise cause negative correlation between adjacent interspike intervals, while the dispersion relation due to the refractory causes positive correlation. A kinematic description of spike propagation yields expressions for changes in the autocorrelation and power spectrum of the interspike intervals during propagation. The power spectrum of the interspike intervals of an initially regular spike train first grows in proportion to 1 - cos(ω) and then becomes a white noise spectrum. Computer simulation shows that the form of the power spectrum is considerably changed on a small nerve fiber.

Pattern recognition with invariance to similarity transformations based on the third-order correlation

Invariance to similarity transformations (simultaneous shift, rotation and scaling invariance) of images based on the third-order correlation was tested on accuracy to numerical errors and on robustness to additive noise. The invariance was then applied to the estimation of the rotation angles of images.

Facial Expression Recognition using KCCA with Combining Correlation Kernels and Kansei Information

Kernel canonical correlation analysis (kCCA) with combining correlation kernels of multiple-orders and Kansei information is applied to facial expression recognition. Any explicit feature extraction is done and spatial correlation features of image data are implicitly incorporated in the correlation kernels. Further, Kansei information is included as the second feature in kCCA. Classification experiments with JAFFE database show that, although the use of Kansei information in itself gives lower classification performance than class indicators optimal for classification tasks, combining Kansei information with them makes the classification performance higher than the only use of the indicators.

Transient chaotic rotating waves in a ring of unidirectionally coupled symmetric Bonhoeffer-van der Pol oscillators near a codimension-two bifurcation point

Propagating waves in a ring of unidirectionally coupled symmetric Bonhoeffer-van der Pol (BVP) oscillators were studied. The parameter values of the BVP oscillators were near a codimension-two bifurcation point around which oscillatory, monostable, and bistable states coexist. Bifurcations of periodic, quasiperiodic, and chaotic rotating waves were found in a ring of three oscillators. In rings of large numbers of oscillators with small coupling strength, transient chaotic waves were found and their duration increased exponentially with the number of oscillators. These exponential chaotic transients could be described by a coupled map model derived from the Poincaré map of a ring of three oscillators. The quasiperiodic rotating waves due to the mode interaction near the codimension-two bifurcation point were evidently responsible for the emergence of the transient chaotic rotating waves.

Comparison of support vector machines with autocorrelation kernels for invariant texture classification

Support vector machines (SVMs) with autocorrelation kernels are applied to texture classification invariant to similarity transformations and noise. The inner product of autocorrelation functions of an arbitrary order is effectively calculated through the 2nd-order crosscorrelation of original data. Texture classification experiments show that higher performance of SVMs is achieved by exploiting the autocorrelation kernels.

Effects of asymmetric coupling and self-coupling on metastable dynamical transient rotating waves in a ring of sigmoidal neurons

Transient rotating waves in a ring of sigmoidal neurons with asymmetric bidirectional coupling and self-coupling were studied. When a pair of stable steady states and an unstable traveling wave coexisted, rotating waves propagating in a ring were generated in transients. The pinning (propagation failure) of the traveling wave occurred in the presence of asymmetric coupling and self-coupling, and its conditions were obtained. A kinematical equation for the propagation of wave fronts of the traveling and rotating waves was then derived for a large output gain of neurons. The kinematical equation showed that the duration of transient rotating waves increases exponentially with the number of neurons as that in a ring of unidirectionally coupled neurons (metastable dynamical transients). However, the exponential growth rate depended on the asymmetry of bidirectional coupling and the strength of self-coupling. The rate was equal to the propagation time of the traveling wave (a reciprocal of the propagation speed), and it increased near pinned regions. Then transient rotating waves could show metastable dynamics (extremely long duration) even in a ring of a small number of neurons.

BIFURCATIONS IN THE DECREMENTAL PROPAGATION OF A SPIKE TRAIN IN THE HODGKIN-HUXLEY MODEL OF LOW EXCITABILITY

Abstract. Response of a nerve fiber of low excitability to periodic stimulus pulses is studied with computer simulation of the Hodgkin-Huxley model. The excitability of the Hodgkin-Huxley model is reduced by decreasing the equilibrium potential for the sodium ion and by increasing the temperature, so that the decremental propagation of spikes occurs in the refractory period. It is shown that, as the period of stimulus pulses is decreased, the propagation length of the spikes is continuously changed, and period-doubling bifurcations occur. The response of a nerve fiber of low excitability is then qualitatively different from that of a normal fiber.