Takahide Matsuoka

Fractal dimension of dendritic tree of cerebellar Purkinje cell during onto- and phylogenetic development

The cerebellar Purkinje cell has highly branched dendrites extending in a transverse plane to the cerebellar folium. Branching patterns of the dendrites were subjected to fractal analysis to obtain a quantitative measure of their intricacy. Using a square-covering method, we found that dendrites have a statistical self-similarity so that their fractal dimension can be evaluated. In postnatal mouse, dimensions of Golgi-stained Purkinje cells increased as dendrites developed. The time course of the dimension increase was correlated with development of the width and area of the dendritic fields. After the dimension reached the maximum value at postnatal day 20, the width and area further continued to grow until day 100. In human cerebellum, dimensions of Purkinje cell dendrites increased greatly during pregnancy and reached 97% of the adult value at birth. On the other hand, 41% of the adult dendritic field width and 11% of the adult area had been attained at birth. The physical size of dendrites increased in a more lagged phase than the dimensions, and growth proceeded mainly after birth. These observations indicate that after the maximum complexity and fundamental tree pattern have been attained, the overall tree size further increases. It is observed that phylogenetic development of dendritic trees of Purkinje cells in several species of vertebrates showed a correlation with the increase in dimensions. These studies demonstrated the potency of the fractal analysis in evaluating development of dendritic trees of neurons.

Perception of missing fundamental and consideration on its characteristics

It is considered that pitch of f/sub 0/ is produced in the auditory center when we hear a complex tone of f/sub 1/ = n f/sub 0/ and T/sub 2/= (n+k) f/sub 0/. f/sub 0/ is known as missing fundamental. We confirm, by psycho-acoustic experiments, that we can hear missing fundamental. Furthermore, we investigate how a/sub i/f/sub i/, and /spl theta//sub i/, in complex tones a/sub 1/sin(2/spl pi/f/sub 1/t+/spl theta//sub 1/)+a/sub 2/sin(2/spl pi/f/sub 2/t+/spl theta//sub 2/) in low frequency region, influence on producing f/sub 0/ . The low frequency region ( 250 Hz/spl sim/1000 Hz ) is chosen for considering the mechanism of perceiving missing fundamental without influence of spontaneous discharge and refractory period. The results of experiments are discussed by significant difference test. Finally, we confirm, by psycho-acoustic experiments, that we can hear missing fundamental in frequency region higher than 1000 Hz.

Significance of distributed representation in the output layer of a neural network in a pattern recognition task.

In the cerebral cortex, it is assumed that information is represented by the activity pattern of an assembly of neurons and the synaptic efficacies among them. A distributed representation of pattern is incorporated in the output layer of a neural network with an error back-propagation algorithm, in order to study its technological merits. The network has three layers, which consist of a 32×32 array of units (1024) for the input layer, 6–25 units for the hidden layer and 12 units for the output layer. 12 triangular patterns with a variety of parameters are presented to the input layer. Three output-layer units are assigned to each input figure. After initial learning, the network responds to the learned pattern with high accuracy. In addition, it responds with high accuracy to similar but unpresented patterns, showing a generalisation for patterns. The network shows resistance to unit de-activation procedures. When the input layer is exposed to the learned pattern, the hidden-layer units show associative activation pattern. These results indicate that the organisation of information representation in the output layer in a neural network strongly influences both the performance of the whole network and information representation in the hidden layer.

Phase-locking by integral pulse frequency modulation and the information of the missing fundamental in pulse trains

We showed theoretically that a synchronous phenomenon occurs (i.e. 1 synchronous pulse per n periods of an input periodic signal occurs) by integral pulse frequency modulation with a refractory period. It is investigated how the information of the missing fundamental of a complex sound is contained in the phase-locked output pulse train from a primary auditory nerve which performs integral pulse frequency modulation. It has been found that the information explicitly appears in the aggregated autocorrelogram of the pulse trains.

Application Of Synchronous Phenomenon In A Nervous System To The Pitch Period Detection Of Speech

It has been f ound t hat an integral pulse frequency m odulation ( denoted I PFM) with an absolute refractory period (denoted ARP), [defined as a period d uring which an input s ignal is n ot integrated], in a nervous system generates 1 for n synchronous phenomenon ( in t hat s tate, 1 synchronous p ulse p er n periods of input periodic signal occurs). The mechanism o f t he synchronization has become clear f or an input sine wave. The experiments of the pitch period detection of quasi-speech were carried out by use of IPFM with ARP. The method to realize a synchronous state rapidly, when the amplitude and the pitch period of quasi-speech change on a large s cale, i s l eft f or future research.

On the Occurrence of Phase-locked Pulse Train in the Peripheral Auditory System

The missing fundamental is not in the frequency band of one channel of a telephone line (from 300Hz to 3400Hz), but we can perceived it over the telephone. It is considered that the missing fundamental f0 is produced in the auditory center, when we listen to a complex tone of f1=nf0 and f2=(n+k)f0. f0 is known as the missing fundamental. Some phenomena, which were made clear by psycho-acoustic experiments, have no evidence data of electrophysiology. The missing fundamental phenomenon is one of the phenomena. By making physiological models we are trying to make clear the mechanism how the missing fundamental is produced. We already showed how the information of the missing fundamental f0 explicitly appeared on the aggregated autocorrelogram of the output pulse train for input signal f1 to one cochlear model and the output pulse train for input signal f2 to another cochlear model. We have made clear that the models have the following characteristics about the models of two neurons (Primary Auditory Nerve (Integrate-and-Fire unit with spontaneous discharge) and Anteroventral Cochlear Nucleus (agreement detector)) that play an important role in producing the information of the missing fundamental. The model of Primary Auditory Nerve generates the pulse train (quasi periodic pulse train) adding spontaneous discharge to periodic pulses for input periodic signal. The model of Anteroventral Cochlear Nucleus works as agreement detector of pulses of the input pulse trains (above-mentioned quasi periodic pulse trains (21 quasi periodic pulse trains in Fig.1)) and generates a periodic pulse train (a phase-locked pulse train) which synchronizes an periodic signal to an cochlear model.The afferent nerves from right Cochlear Nucleus and left Cochlear Nucleus is aggregated at Superior Olivary Complex. We suppose that each periodic pulse train from each ear is fed to Superior Olivary Complex.

Anteroventral Cochlear Nucleus Models for Considering on the Missing Fundamental

Several phenomena, which were made clear by psycho-acoustic experiments, have not electric physiologic evidence data. The missing fundamental phenomenon is one of the phenomena. We try making clear the mechanism how the missing fundamental is produced. By psycho-acoustic experiments and cochlear models experiments, we investigated its fundamental characteristics in the low frequency range where the influence of spontaneous discharge of primary auditory nerves and the influence of refractory period of primary auditory nerves can be ignored. In order to investigate the mechanism of the missing fundamental in the frequency range where these influence can not be ignored, we have made anteroventral cochlear nucleus models (AVCN models). In this report, cochlear models - AVCN models is mentioned. And it is also mentioned that the frequency information of the missing fundamental of input signals lower than 900 Hz explicitly appeared in the interspike-interval histogram of the aggregated autocorrelogram of output pulse trains from cochlear models AVCN models. To confirm it by the perceptual experiments, psychoacoustic experiments will be carried out in the future

Investigation on missing fundamental by a cochlea model generating spontaneous discharge

It is considered that the pitch (f/sub 0/) is produced in auditory centers when we hear a complex tone of f/sub 1/=n f/sub 0/, and f/sub 2/=(n+1) f/sub 0/. f/sub 0/ is known as missing fundamental. By a cochlea model we try to make clear the mechanism of how the missing fundamental is generated. The following signal is applied to the cochlea model: a/sub 1//spl square/sin (2/spl part/f/sub 1/ t) + a/sub 2//spl square/sin (2/spl part/f/sub 2/ t). We make an aggregated autocorreleogram of output pulse trains from a cochlea model. We investigate methodically the relation between the information of the missing fundamental in the output pulse trains and the values a/sub 1/, and n, k in f/sub 1/=n f/sub 0/, f/sub 2/=(n+k) f/sub 0/ by the aggregated autocorreleogram.