TR on Systems with noise and dealy

[Toru Ohira]

The following TRs are available from Sony Computer Science Lab.
http://www.csl.sony.co.jp/person/ohira/drw.html

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
(1)		Oscillatory Correlation of Delayed Random Walks
		
		Toru Ohira (Sony CSL)
	        SCSL-TR-96-014

(Tentatively scheduled to appear as Rapid Communincation in Phys. Rev. E. Feb., 1997;
also regitared at Los Alamos National Lab Archive, cond-mat/9701066)


(2)		Delay Estimation from Noisy Time Series

		Toru Ohira (Sony CSL) 
		Ryusuke Sawatari (Computer Science Dept. Keio Univ.)
		SCSL-TR-96-017

(Tentatively scheduled to appear as Rapid Communincation in Phys. Rev. E. March, 1997;
also regitared at Los Alamos National Lab Archive, cond-mat/9701193)
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

These papers are aimed to analytically capture the behavior of 
systems with noise and delay, which includes neural networks.
As it stands these works are more of formal theory, and we welcome
suggestion and comments toward application to neural networks.
(For preliminary application to neuro-muscular control asssociated with
human posture control, please see SCSL-TR-94-026, "Delayed Random Walks" 
(Ohira and Milton), Phys. Rev. E. vol.52, pp.3277,1995).

Sincerely,

Toru Ohira
ohira at csl.sony.co.jp
Sony Computer Science Lab.

++++++++++++++++++Abstracts++++++++++++++++

Oscillatory Correlation of Delayed Random Walks
(Ohira)

We investigate analytically and numerically the statistical properties of a random
walk model with delayed transition probability dependence (delayed random walk).
The characteristic feature of such a model is the oscillatory behavior of its 
correlation function. We investigate a model whose transient and stationary
oscillatory behavior is analytically tractable. The corresppondence of the model
with a Langevin equation with delay is also considered.


Delay Estimation From Noisy Time Series
(Ohira and Sawatari)

We propose here a method to estimate a delay from a time series taking advantage
of analysis of random walks with delay. This method is applicable to a time series
coming out of a system which is or can be approximated as a linear feedback system
with delay and noise. We successfully test the method with a time series generated 
by discrete Langevin equation with delay.