A sample program of the phase converter model

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Contributor:NIJC Administrator (nijcadmin)  |  Created Date: Mar 16, 2011 13:59:26  |  Visits:1853  |  Runs:7
Free Keywords: adaptive filter, granular layer, phase converter model
ID 39
Title A sample program of the phase converter model
Free Keywords adaptive filter, granular layer, phase converter model
Description This is an implementation of the phase converter model proposed
by Fujita (1982). Specifically, the granular layer, the phase
lead-lag generator of granule cell activity, is implemented.
This is our implementation of the cerebellar model presented in the
following paper:

M. Fujita (1982).
Adaptive filter model of the cerebellum.
Biological Cybernetics. Vol.45, pp.195--206.

This implementation is independent of the original version developed by Fujita (1982).

* About the model

** Model description without Laplace transform

Let u(t) be the mossy fiber signal at time t. x_{i}(t), the activity
of granule cell i at time t, is calculated as

x_{i}(t) = [ w_{i} u(t) - y(t) ]+,

where [x]+ = x if x > 0 and 0 otherwise, w_{i} is the weight of
mossy fiber synapses at the granule cell, and y(t) is the activity
of the Golgi cell at time t. Notice that only one Golgi cell is
incorpoated in the model.

The Golgi cell is a leaky integrator: y(t) is calculated as

y(t) = \int_{0}^{t} \exp(-(t-s)/\tau) (w_{pf}\sum_{i}x_{i}(s) + u(s)) ds,

where \tau is the integration constant and w_{pf} is the parallel-fiber
synaptic weight.

** How does the model work?

For simplicity, let's consider the case of sinusoidally oscillating
mossy fiber signals:

u(t) = sin(2pi f t),

where f is the oscillation frequency. Also, let's consider the case
that the Golgi cell receives inputs only from mossy fibers, namely,
w_{pf} = 0.

Then, because the Golgi cell is an integrator, if \tau is large enough,
the output of the cell becomes

y(t) = c cos(2pi f t),

where c is constant. Now, the activity of granule cell i is given

x_{i}(t) = [ w_{i} sin(2pi f t) - c cos(2pi f t) ]+
= [ sin(2pi f t - phi_{i}) ]+,


where phi_{i} = atan(c/w_{i}). Therefore, granule cells become active
sinusoidally with various phases. Notice that the phase variation
is generated through the variation of mossy fiber synaptic weights
across cells.

Next, let's consider the case of w_{pf} > 0. If granule cells
become active one by one sequentially, the parallel-fiber input signals
to the Golgi cell may become almost constant. Thus, the Golgi cell
inhibit granule cells tonically, which controls the threshold of
granule cells' activity, as argued by Marr (1969) and Albus (1971).

* Files

This folder contains the following files:

readme.txt :: This file
Makefile :: Makefile
adaptive_filter.c :: The source code written in C.
gr.dat :: responses of granule cells to sinusoidal MF signals
go.dat :: response of a Golgi cell to sinusoidal MF signals
mf.dat :: MF signals
plot.gp :: The script to plot gr.dat, go.dat, mf dat using gnuplot

* Usage

Parameters can be set at the head of the program.

% make
% ./adaptive_filter

mf.dat, gr.dat, go.dat are generated

% gnuplot plot.gp (if you have gnuplot)

mf.dat, gr.dat and go.dat are plotted.

* Authors

Takeru Honda and Tadashi Yamazaki

TH: Dept. of Information and Communication Engineering, University of
Electro-communications. TY: Lab. for Motor Learning Control, RIKEN
Brain Science Institute.

* Copyright

Copyright (c) 2007 RIKEN (The Institute of Physical and Chemical
Research) Some rights reversed.

* License

CC-BY

This work is licensed under the Creative Commons Attribution 3.0
License. To view a copy of this license, visit
http://creativecommons.org/licenses/by/3.0/ or send a letter to
Creative Commons, 171 Second Street, Suite 300, San Francisco,
California, 94105, USA.
Last Modified Date Mar 21, 2013 13:58:47
Created Date Mar 16, 2011 13:59:26
Contributor NIJC Administrator (nijcadmin)
Item Type Online Simulation
Change Log(History)
Mar 21, 2013 Modified; Contents URL.
Feb 12, 2012 Modified; Description, Simulator Name.
Mar 24, 2011 Modified; Index.
Mar 23, 2011 Modified; Preview.
Mar 16, 2011 Modified; Simulator, Model site name.
Model Contents URL http://cerebellum.neuroinf.jp/modules/xoonips/detail.php?item_id=403
Hits:2
Model Site Name Cerebellar Platform
Simulator Name Original C program
Simulator Version
Index
/ Public / Title / A-E


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