# Explaining the Natural Sciences with Mathematical Models, Connecting with Other Fields of Applied Research

Kentaro Ito, Lecturer

Department of Frontier Bioscience, Faculty of Bioscience and Applied Chemistry

Posted Mar. 28, 2019

*Faculty Profile*

Lecturer Kentaro Ito researches “mathematical models” that express natural phenomena in equations, and has also won an Ig Nobel Prize for joint research on slime mold. He is now pursuing new horizons at Hosei University.

## Mathematical formulas are a universal language: Expressing natural phenomena through mathematical models

I specialize in applied mathematics. I’m currently working on developing mathematical models for the behavioral principles of living creatures.

Mathematical modeling is a research method for describing natural phenomena. In the process, you identify what are considered essential for the phenomena and express them in mathematical forms such as differential equations. For many people, equations are strongly associated with solving calculation problems. But in my field, equations are something you make by constructing mathematical expressions in the same way as you would structure a written text.

Mathematics is a universal “language” with no scope for misunderstanding. Japanese, English, and other languages used in regular communication can be interpreted in many different ways depending on the context, and sometimes the intended meaning is not conveyed accurately. Expressions in the form of equations, however, are simple and precise, so mathematical modeling can be used to clarify arguments. Moreover, using computer simulations, it’s possible to clarify cause and effect relationships between hypotheses and results.

I believe that research on mathematical modeling is not an end in itself: it can branch into various field. For example, when bats fly in groups, they avoid obstacles and don’t crash into one another even in narrow spaces. They use a mechanism that offers hints for avoiding collisions. Using mathematical modelling, it should be possible to incorporate this mechanism into automatic controls for automobiles, robots, and the like. A single mathematical model can connect with many other forms of research and extend into new applications. The wide scope for application is fascinating for me.

## What do slime mold and rail networks have in common?! Research findings awarded an Ig Nobel Prize

The development of mathematical models starts with observation of the ecology of living creatures. Based on the data gathered through this observation, you identify characteristics and tendencies, form hypotheses, and create mathematical models for them. These are then simulated on computer, and if the phenomenon can be reproduced, the research is usually considered complete. But I want to go one step further. I work closely with researchers specializing in laboratory experiments, with a view to refining both the mathematical models and the experiments that validate them.

When I was working as a researcher in the Research Institute for Electronic Science at Hokkaido University, I became interested in the behavior of slime mold (Physarum polycephalum), and continue to research it today. Slime mold is made of multinucleate single-celled organisms in the form of an amoeba. It moves slowly, changing shape as it spreads out in search of food. It envelops its food, then forms tubular transportation channels as it continues to move in search of further food. It transports both its own body (protoplasm) and its source of nutrition through these tubes. We know that tubes with high flow volumes grow larger and those with little flow degenerate, meaning that superfluous tubes are eventually reduced, leaving a more refined transportation network.

In research I published jointly in 2010 with several other researchers including Professor Toshiyuki Nakagaki, who had looked after me at Hokkaido University, we compared the transportation networks formed by slime mold with railways, a type of transportation network formed by humans. Using agar in the shape of the Kanto region, we placed food at points where major railway stations are located, and as expected, the slime mold formed transportation networks similar to those of the actual railway network. Comparisons revealed that some of the routes selected by the mold were optimal ones, achieving more efficient transportation than the railways themselves. If mathematical modeling can provide a theoretical explanation of this distinctive behavior of slime mold, we can expect it to be applied to create more efficient, low-cost transportation networks.

This research won us the Transportation Network Prize at the Ig Nobel Prizes, a parody on the Nobel Prize that recognizes research with the capacity to “make people laugh, then think.” Although this was a humorous prize, I was happy to gain recognition for our serious research efforts.

## Using mathematics to connect various types of science in pursuit of distinctive “practical wisdom”

Mathematicians might be a little out of place in the Faculty of Bioscience and Applied Chemistry. But I believe that the applied mathematics that I’ve been working on is less of a single field within the huge variety of scientific disciplines, and more of a bridge between different kinds of science. The Faculty of Bioscience and Applied Chemistry aims for organic linkage across the three fields of biology, environment, and materials, and I hope to bring fresh developments to it.

So far my research has centered on subject matter such as slime mold and bats, but I’m prepared to take on anything, as long as it can be modeled mathematically. By engaging with nature through biological experiments and comprehending natural science theories using the insight of mathematical models, I’m working toward “practical wisdom.” I hope to pursue my own style of contributing to natural science research.

## Knowledge of applied mathematics studied for physics, transferred to the unpredictable world of living things

I have enjoyed solving difficult arithmetic and other problems ever since I was small. At first I wanted to be a physicist, and studied physics at university. As I moved through the course, however, my interests shifted away from the minute world of electron, atoms, and the other things invisible to the human eye that they study in the physics department, and more toward problems on a visible scale, such as the patterns and synchronization that occur in the natural world.

I was attracted to research that used simulations to reproduce a variety of natural phenomena, biological and otherwise. For graduate school I joined an applied mathematics research lab at Hokkaido University. One of the things they studied in that lab was slime mold, and it was from this point that I developed a strong interest in interdisciplinary research that combined biology and mathematics. Even today I find it genuinely stimulating to utilize my own expertise in collaborations with people in other fields.

I was fortunate to become a doctoral researcher in the lab of Professor Toshiyuki Nakagaki, famous for his maze experiments with slime mold. There, over the course of a year or more, I gained an affinity with slime mold by feeding and experimenting on it. I was awarded an Ig Nobel Prize together with Professor Nakagaki and a large group of other co-researchers. Because they make use of living creatures, biological behavioral experiments are not like physics experiments: you cannot get the same precise results each time. This applies even to primitive organisms like slime mold. But even though perfect reproducibility can’t be expected, I enjoy the process of forming my own hypotheses in such situations and developing mathematical models that enable them to be reproduced as closely as possible.

I’ve only been at Hosei since 2017. Last year my work centered on simulation research, but from this year I’ve started doing laboratory experiments. I look forward to working with my students to explore the wonders of the natural sciences and applied mathematics.

Mathematics is a “language” that’s universal and has no scope for misunderstanding. Once you’ve mastered it, you’ll find it easy to convey to other people what you perceive as problems, and to present problems in forms that are unmistakable to anyone. I hope that my students will understand what a useful tool mathematics can be, and learn how to make effective use of it.

Kentaro Ito, Lecturer

Department of Frontier Bioscience, Faculty of Bioscience and Applied Chemistry

Born in Tokyo in 1980. PhD (Mathematics).

Graduated from the Department of Physics, School of Science at Tokyo Institute of Technology, completed the master’s and doctoral programs in the Department of Mathematics, Graduate School of Science at the Hokkaido University, then worked as a postdoctoral researcher in the Hokkaido University Research Institute for Electronic Science. Took up his present post as Lecturer in the Department of Frontier Bioscience, Faculty of Bioscience and Applied Chemistry at Hosei University in 2017 after serving as an Assistant Professor in the Department of Mathematical and Life Sciences, Graduate School of Science at Hiroshima University. Awarded an Ig Nobel Prize together with Professor Toshiyuki Nakagaki and others.