# Toru Ohira

Representative publications.

"Theory of Noise and Delay" (in Japanese), Kyoritsu Publishing, Tokyo, Japan, 2006/1.

"Group Chase and Escape", A. Kamimura and T. Ohira, New Journal
of Physics, vol. 12, 053013 (2010).

"Stochasticity and Non-locality of Time", T. Ohira, Physica A,
vol. 379, 483 (2007).

"Resonance with Noise and Delay", T. Ohira and Y. Sato, Physical Review Letters, vol. 82, 2811 (1999).

"Delayed Stochastic Systems", T. Ohira and T. Yamane, Physical Review E, vol. 61, 1247 (2000).

## Research Activities

We have proposed a new topic by combining two fields. One is the study of "Chase and Escape"
which has a long history in mathematics. The other is a recent interests
in collective behaviors such as fish, animals and traffic jams. We have
proposed simple models which nohtheless show rather complex behavir when
chase and escapes are performed in groups.

(Covered in "News and Views" by Prof. T. Vicsek, Nature, vol. 466 p. 43 (2010)(link) )

### Non-locality and Fluctuation of Time
(List of Papers)

Here, I have tried to laid out a conceptual framework of
my approach to non-locality and fluctuations.
As an example of non-locality on time, I have been working on
delayed dynamical systems. I have recently started working on
"predictive dynamical models" as other examples.
I am also proposing a simple dynamical model with "stochastic
time", in which time is considered as a stochastic variable.
I conjecture and propose the concept of "delayed stochastic control''. The main motivation of such a hypothesis is the fact that humans can often handle situations or objects whose time constant is much faster than their reaction time. Compared to artificial systems, humans are "very slow" with a reaction time of a few hundred mili-seconds. Of course, one cannot only rely on feedback,
predictive control is also important.
However, the key question is whether they are enough or not. For example, by
combining these traditional control schemes, can we create a robot with a reaction time of that of a human (approximately 100 mili-seconds), and which can ride a unicycle ? Recent experiments, for example, a human balancing a stick on the fingertips began to pose these questions. Most of the fluctuating movement of the stick is much
faster than 100 mili-seconds. Delayed stochastic control is a new scheme, which takes advantage of resonant phenomena with an appropriate amount of noise level and feedback delay time. We
analyzed this resonant phenomena by considering the stability of repulsive delayed random walks. We also discovered a new effect: someone can better balance the stick on the fingertips, if they
move an object with the other hand in a fluctuating manner. This is likely to be a piece of supporting evidence for
delayed stochastic control.
I propose the concept of "delayed random walks'' as a mathematical
framework for studying systems containing both "noise'' and "delay''.
A delayed random walk is a random walk in which
the transition probability depends on the
position of the walker at a fixed time interval in the past.
It has been used
to model human postural controls and neural activities
in comparison to experimental data.
Typically, ocillatory autocorrelation function is associated
with delayed random walks of sufficiently long delay.
To study
such oscillatory behavior in stationary and transient states,
we have studied analytically tractable models.
On the basis of his theory, we have also devised a method of
estimating delay from noisy time series coming out of linear delayed feedback
systems.
### Applications of Effects of Noise and Delay
(List of Papers)

On
the basis of understanding gaind from theoretical studies, we now seek possible applications of delayed stochastic systems,
delayed systems, and stochastic sytems
to information processing methods or systems. We have thus
proposed and studied the following systems. (1) An encryption
model which takes advantage of the complexity of coupled delayed
dynamics. (2) A stochastic binary element with a delayed
memory showing a resonance between noise and delay.
(3) Analysis of yen-dollar exchange dynamics.
(4) Emergent network structure formation with delayed interactions.
We are investigating a master equation approach to stochastic neurodynamics.
We write the master equation in a
second quantized form which is analogous to the
Schoroedinger equation. Both exact and approximate
expressions for the moment generating functions
and associated moments are obtained by taking various approaches to
investigating the master equation: differential equations, the BBGKY-like hierarchy,
a neural path integral, and its associated diagram expansion.
The formal expressions for each approach are presented together
with Monte Carlo simulations.
### Emergent Autonomous Computational Systems
(List of Papers)

In biological systems, information processing is often
performed in the form of emergent activities arising from
an interaction of many simple elements. I am looking for
hints from such natural information processing systems to enable one to
design an autonomous open distributed system that can produce
a useful emergent computation.
Ideas are borrowed from the neural and immune system and also from field theory
in physics: (1) A distributed traffic control models for model computer
networks and motorways in analogy with neural networks.
(2) A pattern learning model is constructed in an
analogous manner, i.e., with the recognition mechanism of antigens by
antibodies in the immune system. (3) The concept of
the "computational field" is extended and made concrete through the exchange of
basic particles called "Computon''. An autonomous
load balancing system using Computon exchange is being
constructed.