Laboratory for New Media 13th Exhibition
‘The World where “1+1≠2” - An Encouragement of Mathematical Modelling’

Laboratory for New Media Permanent Exhibition periodically updates contents of exhibitions to introduce the various possibilities of expression provided by information science and technology.
Galileo wrote that “the book of nature is written in the language of mathematics,” and in keeping with this idea, innovative research into expressing the world’s complex phenomena using mathematics is being carried out in a wide range of areas. If the world we live in was simple enough to be expressed with equations like “1+1=2,” it would certainly make understanding phenomena, predicting the future, and solving problems much easier. However, our world seems so complex and disordered. This exhibition introduces some of the researchers taking on the challenge of shedding light on our complex world by using “mathematical modelling.”

Mission 1: Prevent the spread of infectious diseases

Suppose a pandemic crisis is swiftly approaching. If the spread of infectious diseases can be described with mathematical models, it should become possible to put in place preventive measures. However, there are a multitude of factors that need to be taken into consideration, such as the type of pathogens involved, transmission routes, climate, differences between individuals, etc. When trying to consider all of these factors, it becomes too complicated to figure out the essential characteristics of the spread of infectious diseases.

Don’t hesitate to focus only on the most important factors. Good mathematical models may appear simple, but by fleshing them out when necessary it is possible to reproduce the complex behavior in the real world. Such models can be used to simulate and evaluate preventive measures.
The relevant experiment's Web "数理モデル大実験" has been released!
Collaborative researchers: Junichi Akita, Koji Iwayama, Chiyori Urabe, Keisuke Ejima, Fumiyuki Fujii, Naoya Fujiwara

Mission 2: Unlock the secrets of the brain

The human brain is a network of about 100 billion neurons. Taking lessons from chaotic phenomena found in the neurons, the “Brain with Chaotic Dynamics” was created by connecting 100 elements capable of carrying out the functions of neurons, and is able to imitate the workings of the human brain. It was created using real and simulated electronic circuits. By solving the “Let’s Make a Peaceful Zoo” problem, try to identify the humanlike behavior of the “Brain with Chaotic Dynamics.”

Although the “Let’s Make a Peaceful Zoo” problem appears simple at first, it is in fact very difficult to solve. To consider all of the possible combinations would require a huge amount of computational effort. However the human brain is capable of quickly and intuitively coming up with a satisfactory (though not necessarily the best) solution without having to go over all the possible combinations with a fine-toothed comb. Focus your attention on that characteristic of the human brain.
Collaborative researchers: Keita Tokuda, Shunsuke Horai, Yoshihiko Horio, Masato Ozawa

Mission 3: Reveal the ‘ultra’ abilities of bat sonar

Bats emit ultrasonic waves and then listen to the reflected waves to determine the direction and distance to objects. Using this ability called SONAR, bats can catch insects as small as mosquitoes while in flight. When considering bats as an acoustic system they seem very small, yet they have highly flexible and accurate signal processing abilities. If one could figure out how this ability of bats works, it could be utilized in engineering applications.

It has been noted that bats may detect multiple target-preys using sonar and then fly the route that will allow them to catch the targets in an efficient way. Based on these characteristics of bats, try to model a flight that would bring one close to multiple targets.
Collaborative researchers: Ikkyu Aihara, Shizuko Hiryu, Emyo Fujioka

Mission 4: Plan a treatment schedule

Recently, the number of patients who suffer from prostate cancer is increasing. A basic strategy for its treatment is to suppress the growth of cancer cells by medicine. But, we have to stop and restart the medicine several times because the cancer cells eventually acquire resistance to the medicine. The problem here is that there is no uniform treatment schedule that benefits every patient because the characteristics of cancer cell growth depend on each patient.

A mathematical model works effectively even under such a circumstance. A general mathematical model is used to describe the dynamics of cancer cells both when the medicine is used and when the medicine is not used. By adjusting the model to each patient, one can decide the schedule that is optimal to the patient.
Collaborative researchers: Koji Iwayama, Taiji Suzuki, Gouhei Tanaka, Yoshito Hirata, Kai Morino

Mission 5: Detect early warning signals of complex diseases

Between the “healthy” and “disease” phases or states, there is an intermediate “pre-disease” phase. This is a borderline phase from which patients can still recover to the “healthy” state with an appropriate treatment, or the patients will rapidly develop to the disease state. Thus, it is crucial to detect this pre-disease state or tipping point so as to provide effective and early treatment of the disease. The key signal lies in gene activity. However, there are so many genes whose expressions dynamically fluctuate, and it is a difficult task to identify those genes related to the disease.

There are a group of genes that display similar correlated behavior but with strong fluctuations only around the pre-disease phase. Detecting such a group of genes signals the emergence of the disease state.
Collaborative researchers: Koji Iwayama, Luonan Chen, Rui Liu

Mission 6: Forecast aftershocks

A vast number of aftershocks occur following major earthquakes. Forecasting aftershocks is strongly required to reduce seismic risks. However, it is very difficult to accurately forecast aftershocks in the early stage, because there are so many aftershocks just after the main shock that it is not possible to detect them all. There is a need for more rapid forecast using mathematical modelling.

This requires a stretch of the imagination. If you try to treat unobserved aftershocks as if they didn’t happen, your predictions will likely be inaccurate. But might it not be possible to work out the number of aftershocks that actually happened, based on incomplete observational data?
Collaborative researchers: Koji Iwayama, Takahiro Omi, Yosihiko Ogata

Mission 7: Synchronize with fireflies

Everyone has experienced situations where people who have been acting independently suddenly notice their actions have become synchronized. This phenomenon is frequently observed in the natural world also, and one of the prime examples of this is the synchronized light emissions of fireflies. Try to work out the system of synchronization by simulating the functions of fireflies using electronic circuits and setting them out in a variety of configurations.

Compare how circuits synchronize when laid out in a line and when laid out in a circle, etc. See for yourself how even the simple individual circuits can create complicated patterns when they are grouped together.
Collaborative researchers: Daisuke Ito, Keiji Okumura, Hiroshi Kawakami, Keiko Kimoto, Akinori Tsuji

Term February 19 (Wed.), 2014 - September 1 (Mon.), 2014
Exhibitors “Mathematical Theory for Modelling Complex Systems and its Transdisciplinary Applications in Science and Technology”
(FIRST, Aihara Innovative Mathematical Modelling Project)
  • The purpose of the project is to develop mathematical theory that can facilitate modelling of complex systems and to create its transdisciplinary applications in science and technology. These have been achieved on the basis of advances in mathematical engineering (a discipline originally developed in Japan) and chaos engineering (a field aimed at creating various applications with deterministic chaos, fractals, and complex networks).

  • Kazuyuki Aihara

    Professor, Institute of Industrial Science, the University of Tokyo /Director, Collaborative Research Center for Innovative Mathematical Modelling, the University of Tokyo / Professor, Graduate School of Information Science and Technology, the University of Tokyo / Professor, Graduate School of Engineering, the University of Tokyo
    He was born in 1954. He received the Ph.D. degree in electronic engineering in 1982 from the University of Tokyo. He had been Associate Professor at School of Engineering, Tokyo Denki University, Associate Professor and Professor at Faculty of Engineering, the University of Tokyo, and Research Director of ERATO Aihara Complexity Modelling Project, JST. Since 2003, he has been Professor of Institute of Industrial Science, the University of Tokyo. He has been Core Researcher of the project entitled "Mathematical Theory for Modelling Complex Systems and its Transdisciplinary Applications in Science and Technology" since 2010.
    FIRST, Aihara Innovative Mathematical Modelling Project