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

Group Chase and Escape (List of Papers)

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.

Delayed Stochastic Control (List of Papers)

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.

Delayed Stochastic Systems (List of Papers)

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.

Stochastic Neurodyanamics (List of Papers)

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.

Profile and Other publications

In Japanese

Math3 at Tokyo Univ. Lect1

Math3 at Tokyo Univ. Lect2

Math3 at Tokyo Univ. Lect3

Math3 at Tokyo Univ. Lect4

Math3 at Tokyo Univ. Lect5

Math3 at Tokyo Univ. Lect6

Math3 at Tokyo Univ. Lect7

Math3 at Tokyo Univ. Lect8

Math3 at Tokyo Univ. Lect9

Math3 at Tokyo Univ. Lect10