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Applied Mathematics (Mathematical Biology, Nonlinear Mathematics, and Foundations of Quantum Theory) Lab
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Research that uses mathematical models to explore delays, fluctuations, and the chase-and-escape behavior of groups.
AboutAbout the lab
Building mathematical models from real phenomena
Prof. Ohira builds mathematical models from concrete natural and social phenomena.
The core of the research is taking up problems that are not yet part of mathematics and shaping them into mathematical problems.
The lab works on the mathematics of systems involving delay and fluctuation (noise) in information transmission, and on "collective pursuit and evasion," in which groups chase and flee.
Prof. Ohira believes that building mathematical models also requires sensibilities from outside mathematics, such as those gained from experiments and observation, as well as collaboration with people in other fields.
Key terms
- Mathematical model
- A simplified representation of how a phenomenon works, expressed with equations and rules.
- Random walk
- A model of erratic motion in which the direction of each step is determined by probability.
- Autocorrelation function
- A function that expresses how similar data at one time is to data a little later.
- Feedback
- A mechanism in which the result of a movement is observed and fed back to adjust the next movement.
NewsLab news
Published a paper on a phenomenon in which amplitude is greatly amplified in nonautonomous delay differential equations
Published a paper on a method for solving nonautonomous delay differential equations using the Fourier transform
Published a paper on a model of transient return phenomena in delay differential equations
Published a paper on a model of the mechanisms by which patterns on the skin of living organisms form and disappear
ResearchResearch themes
With systems such as neural circuits and the immune system in mind, where many interacting elements produce complex behavior, the lab theoretically studies the effects of delay and fluctuation in information transmission. It has also proposed a new problem, collective pursuit and evasion.
*Illustrative imageCollective Pursuit and Evasion
The lab proposed combining the long-studied mathematical problem of "pursuit and evasion" with research on collective behavior such as schools of fish, animal herds, and traffic jams. Even simple models show surprisingly complex behavior when groups chase and flee.
*Illustrative imageSystems with Delay and Fluctuation
As a basis for studying systems that contain both delay and noise, the lab proposes the "delayed random walk." It is a random walk whose transition probability is determined by the position a fixed time earlier, and when the delay exceeds a certain value, oscillations appear in the autocorrelation function. The lab has also devised a method for estimating delay from noisy time series.
*Illustrative imageDelayed Stochastic Control
Human reactions take several hundred milliseconds, yet people can sometimes control objects that move faster than that. The lab proposes the "delayed stochastic control" hypothesis, which holds that an appropriate amount of fluctuation and feedback delay helps with such control. It also found that when balancing a stick on a fingertip, shaking an object with the other hand makes balancing easier.
*Illustrative imageApplications of Delay and Noise
These are attempts to apply the theory of phenomena brought about by delay and noise to information processing. The lab has proposed a cryptographic model that uses the complexity of coupled delay dynamics, an analysis of exchange rate movements, and a model in which network structures emerge from interactions with delay.
MembersFaculty
- ProfessorToru Ohira
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Blackbird-sunset-03” Jerry Segraves (en:User:Jsegraves99) / Public domain (cropped)
- Collective Pursuit and Evasion: “Border Collie sheepdog trial” Scot Campbell / CC BY-SA 2.0 (cropped)
- Systems with Delay and Fluctuation: “Brownian trajectory” Roque345 / CC BY 3.0 (cropped)
- Delayed Stochastic Control: “Feedback control system” Controlsystemintro / CC BY-SA 4.0 (cropped)
- Applications of Delay and Noise: “Network graph visualization showing bibliography and keywords” Ecpp / CC BY-SA 4.0 (cropped)
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- Related lab (Nakanishi Lab): “Root system A2 with labels” Mark L MacDonald; derivative of work of User:Smithers888 and User:Maksim / CC BY-SA 3.0 (cropped)
- Related lab (Representation Theory and Infinite-Dimensional Integrable Systems Lab): “Dynkin diagram Dn” Rogilbert / Public domain (cropped)
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