Research (Under Construction)


To be Announced

Representative publications


"確確率論 講義ノート:場合の数から確率微分方程式まで" 森北出版  (Text Book in Japanese, "Probability Theory: Lecture Note", Morikita Publishing, Tokyo, Japan), 2017/3.

"「ゆらぎ」と「遅れ」:不確実さの数理学" 新潮選書 (Book in Japanese, "Fluctuation and Delay: Mathematics of Uncertainty", Shincho Publishing, Tokyo, Japan), 2015/5. (訂正表

"Mathematics as a Laboratory Tool: Dynamics, Delays and Noise ", J. G. Milton and T. Ohira, Springer 2014.

"Theory of Noise and Delay " (Book in Japanese「ノイズと遅れの数理」共立出版), 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).

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

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

"Delayed Random Walks", T. Ohira and J. G. Milton, Physical Review E, vol. 52, 3277 (1995).

"Master-equation approach to stochastic neurodynamics" , T. Ohira and J. D. Cowan, Physical Review E Vol.48, pp.2259, 1993

"Perfect Disturbing Measuremnts", T. Ohira and P. Pearle, American Journal of Physics, vol. 56, 692 (1988).

Books (Editor)

"Mathematical Approaches to Biological Systems: Networks, Oscillations, and Collective Motions",  T. Ohira and T. Uzawa (eds), Springer 2015.

Reviews in Japanese

遅れのあるランダムウォーク,  大平徹 「シミュレーション」Vol 32, pp. 55-57, 2013.

集団追跡と逃避,   上村淳, 大平徹「日本物理学会誌」Vol.66, pp.205-208, 2011.

時間軸上の非局所性とゆらぎ:確率共鳴を通じて,  大平徹「日本物理学会誌」Vol.62, pp.260-264, 2007.

「遅れ」と「ノイズ」の周辺で,  大平徹「数理科学」No.467, pp. 79-83,May 2002.

ノイズと遅れの共鳴現象,  大平徹, 佐藤譲「日本物理学会誌」Vol.55, pp.360-363, 2000.

News in Media

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

"Front Runner" in Japanse edition of Sicentific American, (「フロントランナー 挑む」日経サイエンス)October Issue, 2013 (link)

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) )

(この研究はNature の"News and Views"に Prof. T. Vicsekによる紹介をいただきました。 Nature, vol. 466 p. 43 (2010)(link) )

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.


Delayed Stochastic Control (List of Papers) (Video

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. (see Video)

ここでは、遅れ確率制御(delayed stochastic control)の仮説の提案をしています。人間の反応時間は数100ミリのオーダーです。しかし、たとえば倒立棒の制御などそれよりも速い動きをする、状況や物体の制御をすることも見られます。通常はこれらはフィードバックと予測制御をくみあわせたものであると考えられますが、はたしてそれだけでしょうか? たとえば、このように「遅い」反応時間をもちながらも、一輪車にのれるようなロボットを伝統的な制御手法の組み合わせだけでつくれるでしょうか? ここでの解析では斥力をもつ遅れランダムウォークの結果からちょうどよい揺らぎと遅れの組み合わせがより安定した状況をもたらす可能性が示唆されています。このような「共鳴」の活用が生体制御にも存在するのではないかというのがここでの仮説です。また、ここではあらたに、人が指先の上で棒のバランスをとるときに反対の手で物体を振ったり、足を揺らしたりするとより安定感が得られることができるという現象を見つけました。これは上記の遅れ確率制御の一つのサポートになるとともに医療や運動機能のリハビリなどへの応用を探る可能性をもっています。 (Video を御覧ください)

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.


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.

ここでは、私が非局所性と揺らぎを時間軸上でとりあつかう時の概念的な枠組みを議論しています。時間的な非局所性の例としては 遅れ力学と関連するトピックを研究してきましたが、新たに予測力学を提案考察しています。また、時間を確率変数として 考える方向として、「確率的時間」を持つような力学モデルを提案しています。

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.


Other Topics (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) Topics from random walks and probability theories. (4) Quantum Theories and Measurements