Equations, and Stochastic Analysis of - Semantic …...19 Equations, and Stochastic Analysis of...

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Research Outline

1. Research on time series analysis

The purpose of this research is to extract the underlying dynamics and nonlinear structures from the

time series data of complex phenomena: geophysical phenomena such as auroras, solar winds,

geomagnetism, earthquakes, and El Nino; economic phenomena such as stocks, foreign exchange

rates, money supply, and gross domestic product; biological phenomena such as electroencephalogram,

pulse waves, blood pressure, and electrocardiograms; and engineering phenomena such as electric

power. We focus on the underlying nonlinear structures of these phenomena, particularly their

qualitative characteristics such as stationarity, abnormality, determinacy, causality, dynamics, and

separation property. Time series analysis techniques based on the theory of KM2O-Langevin equations

for discrete-time stochastic processes are used for analyzing phenomenal data for modeling with the

philosophy of “data to model”.

2. Research on Stochastic Analysis Related to Gaussian Stationary Processes

Selected examples of fundamental research on stochastic analyses of the Markov process include

studies on the diffusion process and the corresponding diffusion equations (N. Kolmogorov) and

studies on the diffusion process and the corresponding stochastic differential equations (Ito K.); there

are other studies that combine stochastic differential equations and diffusion equations using Ito’s

formula. The aim of this research is to develop a theory of KM2O-Langevin equations for

one-dimensional continuous-time Gaussian stationary processes, which have been discussed from the

basis of the studies by N. Kolmogorov and Ito K. We also hope to derive a stochastic differential

equation (KM2O-Langevin equation with continuous time) that governs the local time evolution of

multi-dimensional continuous-time Gaussian stationary processes. Ito’s formula is applied to the

equation for deriving second-order elliptic partial differential equations with time lags related to the

Gaussian stationary processes; thus, the foundations for the stochastic analysis of Gaussian stationary

processes and a study of their applications are established.

3. Research on Riemann’s Zeta Function Based on Theory of Stationary Process

The aim of this research is to investigate Riemann zeta function, which conforms to Riemann

hypothesis and remains an unsolved analytic number theory problem, through a new approach of

using characteristics of stationary process. In particular, we focus on continuous stationary processes

with T-positivity, which can be analyzed by continuous-time KM2O-Langevin equations. That is

analyzed by the theory of continuous-time KM2O-Langevin equations, which is the source of the

theory of discrete-time KM2O-Langevin equations, to challenge and establish new theories on

Riemann hypothesis.

Theory of KM2O-Langevin Equations, Complex Phenomena Described by Equations, and Stochastic Analysis of Mathematical Phenomena

Position Title,Affiliated Department

Specialized Field, Academic Degree

Research Description

Yasunori OKABE Modeling Group Leader : : :

Fellow, MIMS; Professor, School of Science and Technology,

Meiji University

Stochastic Analysis and Time Series Analysis,

Ph. D., Osaka University

MMA of Time Series Data Mo

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Research Outline

The relation between computer and safety has essentially two aspects: safety for computers, which

protects the computer from internal and external hazard sources to ensure that the machine is able to

continue working normally, and safety by computers, which aims to build functions to maintain the

safety of other systems using computers. The former is an area of study called computer safety, while

a typical example of the latter is a new area of safety, called functional safety.

In this research, we studied the ideal functional safety (latter) as a model for establishing safety

using computers. Computers served as safety devices to monitor and control the safety of other

systems and stop them for safety purposes if necessary. To identify the process to protect safety using

computers, research focused on concepts and methods of computer and functional safety, and clarified

the differences and relationships between the two.

Although IT and software engineers may not have needed to consider safety, the findings of the

study revealed an imperative need for those working with embedded software used for systems related

to human life to fully understand safe designs when configuring systems. This is because true safety

cannot be established without knowing the characteristics of the hardware that needs to be controlled

and the details and level required by humans. Among those working with computers, engineers

developing embedded software are the closest to both mechanical systems and human beings.

References

1) Mukaidono M. (editorial supervisor), Kawaike N., Miyazaki K.: Risk assessment of machinery and

equipment. e.b. Japan Machinery Federation, Japanese Standards Association, pp.308, 2011-2.

2) Mukaidono M., Kitano M., Komatsubara A., Kikuchi M., Yamamoto T., Otake Y.: Why are accidents

caused by products?: Review of the safety of familiar products. Kenseisha, pp.214, 2011-3.

3) Mukaidono M.: Transition of safety technology and outlook for the future. Japan Industrial Safety and

Health Association. Safety and Health. vol.12. No.1 2011，pp.2932, 2011-1.

4) Mukaidono M: Computer Safety and Functional Safety. Institute of Electronics, Information and

Communication Engineers. IEICE Fundamentals Review. Vol.4, No.2, pp.129135, 2010-10.

5) Mukaidono M: Safety design to prevent aging degradation. National Institute of Technology and

Evaluation. Life and Safety Journal. Vol.10, pp.811, 2010-10.

Study on Modeling for Establishing Safety using Computers




Masao MUKAIDONO

: : :

Deputy Director, MIMS; Professor, School of Science and

Technology, Meiji University

Safety Study, Ph.D., Meiji University

Modeling and Analysis on uncertainty systems

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Research Outline

This study focuses on various problems related to financial mathematics from the realistic standpoint

of studying and modeling financial phenomena. It also includes the modeling of socioeconomic

phenomena.

The interest rate analysis study team was formed at the Meiji Institute for Advanced Study of

Mathematical Sciences (MIMS). The team is responsible for analyzing changes in the term structure of

interest rates before and after a financial crisis based on the government bond pricing model, which was

developed by Kariya and Tsuda (95) (the following figure shows changes in interest rates on the basis

of government bond prices). We are also interested in modeling phenomena in which financial asset

values are closely correlated

to downward fluctuations of

the market, which is a

characteristic of the

fluctuation structure in times

of financial crisis. This is an

important issue in

measurement methods of

value-at-risk (VaR) as it is

not taken into account in the current financial risk management procedures. The team is involved in the

demonstration of corporate bond pricing models that take into account the fact that the business of one

company may be related to several industries. It is hoped that the term structure of the probability of

default derived from the results will enable the pricing of various credit risk products. Another aim of

the research is to determine the fluctuation structure of credit risks in financial crisis.

A separate study will be conducted with doctoral students to investigate the problems of games on

the superiority of the authority between managers and those working under them and games on

information screening, as well as business risk management, such as the relation between business and

temperature. A handbook on economic time series analysis is currently being edited.

Modeling and Risk Management of Financial and Economic Phenomena




Takeaki KARIYA

: : :

Fellow, MIMS; Professor, Graduate School of Global

Business, Meiji University

Financial Technology,

Ph.D., University of Minnesota, Kyushu University

MMA of Finance

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Research Outline

During this fiscal year, as our studies on the intelligent optimization of smart grids, the intelligent

multi-objective optimization was applied to power transmission and distribution networks. In the area

of power transmission networks, we researched economic load dispatching (ELD) for the

multi-objective optimization of thermal power plants. ELD is a constrained optimization problem in

power systems, which determines the electrical power to be generated by the generating units, so as to

minimize the total fuel costs of thermal power generators while satisfying the total output of the power

generators required by the power transmission networks. The CO2 emissions as well as the total fuel

cost were minimized.

Such solutions are called the Pareto solution set, which have been difficult to directly obtain with the

existing procedures. Thus, as a method of evaluating the solution set, particle swarm optimization (PSO) of

meta-heuristics was examined. Meta-heuristics is a class of optimization methods for obtaining highly

accurate approximate solutions to global optimal solutions by repeating simple rules and heuristics. PSO is a

heuristic method with multipoint search rules like the behavior of swarms of birds, fish, or honeybees in

searching for food. PSO was expanded to evolutionary PSO, which adaptively adjusts the PSO parameters,

for multi-objective optimization, and a method that incorporates improving the strength pareto evolutionary

algorithm (SPEA2) strategies was developed, producing excellent results. Secondly, we also explored the

formulation of optimized allocation problem of the step voltage regulator (SVR), as a multi-objective

optimization problem in the distribution network. With the liberalization of power in recent years,

consumers can now select the power company of their choice, for example, according to economic

viability, reliability, and quality. On the other hand, suppliers face growing demand for sophisticated

and stable supply due to increasing complexity and diversity of distribution networks. In addition,

stochastic reverse power flows caused by dispersed power sources of renewable energy lead to the

uncertainty of load, which is feared to cause interference to the specified voltage maintained in the

power system. In this study, minimization of the deviation of node voltage and of the installation costs

of SVRs as the objective functions were examined. Additionally, a scenario for load through Monte

Carlo Simulation was created, which takes into account the correlation of the nodes in the distribution

network, and the flexible optimum layout of the SVRs was determined. To solve multi-objective

optimization problems, we focused on SPEA2, which is one of multi-objective heuristics. As a result of

these efforts, we were able to come up with several power system planning solutions, provide the operators

with choices of planning solutions, which incorporate tradeoffs, and propose effective SVR locations for

network planners by Monte Carlo Simulation.

Study on Intelligent and Multi-objective Optimization of Smart Grids




Hiroyuki MORI

: : :


Meiji University

Intellectual Informatics, Ph.D., Waseda University

MMA of Intelligent Systems

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Research Outline

We are currently involved in research for the Core Research for Evolutional Science & Technology

(CREST) project, the goal of which is to build robots which can move lithely and robustly like living

organisms in complex, uncertain, and realistic environments based on the observations of living organisms.

The research team is comprised of biologists, mathematicians, and engineers. To achieve our goal, robots

need to be rendered with the large degree of freedom, and controlled in a sophisticated manner. One key to

achieving this goal is the self-organization of locomotion based on autonomous distributed control. However,

in the current situation, autonomous distributed control lacks design principles for linking autonomous

agents with the whole body. Therefore, the extraction of these design principles from unicellular organisms

such as true slime mold and amoeba was attempted. This is because unicellular organisms lack nervous

system and their locomotion is the direct manifestation of autonomous distributed control. The approach in

this project is clear. Focus is given to the locomotion of even more complicated multicellular organizations

as the future direction of the project, based on the findings for the unicellular organisms as the starting point.

Applying the concept of discrepancy function extracted from models on the locomotion of true slime

molds, an amoeboid robot moving completely by autonomous distributed control was designed. Simulation

results showed that adaptive locomotion is spontaneously generated through the phase shift by discrepancy

function and global interactions as a result of the conservation of protoplasmic mass.

Understanding and reproducing the locomotion of snakes are important goals in the project as their

movements are full of suggestions, considering the way they are able to make full use of the large degrees of

freedom of the body, and the balance between control from the brain and autonomous distributed control.

Simulations using coupled oscillators as the controller were carried out, based on autonomous distributed

control combining phasic and tonic control, and the effectiveness of the framework was confirmed. To verify

the validity of the framework, a snake-shaped robot was built; through experiments, smooth serpentine

motions were reproduced successfully, showing that snakes have outstanding adaptability as well as fault

tolerance by contingently associating the phase relation of the movements of each somite and the degree of

muscle tone.

The cleavage model proposed during the last year is based on the hypothesis that the locomotion of the

central body is controlled by two diffusible morphogens produced by the vegetal and animal poles. With

cooperation from specialists of mass spectrometry, we have started searching for morphogens in actual sea

urchin eggs. At the same time, modeling using a phase field model designed for multicellular systems was

carried out to mathematically describe realistic cleavage processes up to the shape change stage.

Study on Morphogenesis and Locomotion of Living Organisms




Ryo KOBAYASHI Sub-leader of all researches : : :

Fellow, MIMS; Professor, Department of Mathematical and

Life Sciences, Graduate School of Science, Hiroshima University

Mathematical Modeling and Analysis,

Ph.D., The University of Tokyo

Mathematical study of structure formation, locomotion and

information processing of living organisms

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Research Outline

Our research on humanity in visual information systems focuses on the following two topics:

(1) Proposal of image processing method taking into account human subjective assessment

(2) Assessment of human mental state by electroencephalogram analysis during text reading

For (1), studies on a system for removing impulsive noise in color images and that for beautifying

human face images by making the face look sharp were launched in FY2009. During the current fiscal

year, we improved these features. Both systems apply interactive evolutionary computation to carry out

optimum image processing based on the subjective criteria of users. In order to remove impulsive noise

from color images, we proposed a method applying interactive evolutionary computation to optimize a

switching median filter that comprehensively examines the respective amounts of several local

characteristics around each pixel in FY2009. In cases where the noise occurrence rate is low, the

interpolation method is known to be more effective than the median filtering method. We hence

proposed a method of estimating the probability of noise generation around each pixel and switching

between the median filter and interpolation to minimize both image blurring and noise effectively, and

have already demonstrated its effectiveness. The new system for removing impulsive noise from color

images also applies interactive evolutionary computation to ensure effective and optimum noise

removal settings while taking human subjective assessment into account.

Activities for human face image beautification included subjective assessment experiments and

studies on how to reduce computational complexity of the system developed last year in order to

implement it as i-appli program. In the experiments, different facial images of a female subject in her

20s and another in her 50s were prepared: images of their faces made up by themselves, those of their

faces made up by professional makeup artists, and those processed by the proposed beautification

system. Twenty subjects subjectively assessed the images. The results found that the facial images

processed by the system were rated higher than the face made up by professional makeup artists. As to

the reduction of computational complexity, the two-dimensional ε filter in the beautification system was

created by combining horizontal and vertical one-dimensional ε filters to increase the speed of the

filtering process.

For (2), we conducted objective assessments of the mental stress during reading text on paper media

and electronic displays, using brain waves. Specifically, we extracted brain waves of subjects reading

text with different size letters on paper medium and electronic displays, and calculated the feature value

of alpha and beta waves. The results showed that considerable beta waves occurs more when reading

small letters; in particular, the ratio of the amount of beta wave to that of alpha wave increases when

reading small letters, with a significant difference from reading large letters. Other studies have

suggested that the ratio indicates the degree of mental stress in humans. We found that this stress does

not differ much according to the size of letters in the case of paper medium, but increases significantly

when reading small letters on electronic displays.

Humanity in Visual Information System




Kaoru ARAKAWA : : :


Meiji University

Image and Speech Processing, Ph.D., The University of Tokyo

MMA of Perception Systems

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Research Outline

In nature, there are various types of groups: fish, birds, and insects are well-known examples. In human

society, there are movements of various groups, or collective motion. The degree of flow or congestion of

groups of automobiles or pedestrians has a substantial impact on the productivity of society in general.

Isolated sand dunes, otherwise known as barchans, cause huge damage to roads, pipelines, and other

man-made structures by collective motion. In this way, the collective motion has a complexity and diversity

unimaginable from the movement of individual elements. Most conventional theoretical studies on collective

motion have expressed the movement of elements using relatively simple rules and comparing complex

movements seen in a group in general. However, in reality, the complex internal freedom of elements has a

crucial impact on the movement of the whole group. In FY2010, we thus focused on the relation between the

movement and functions of a whole group and the internal freedom of elements, and conducted the

following four studies:

1. Analysis of the mechanism deciding the priority order of using individual chemical or visual

information in the group foraging behavior of ants

2. Construction of new mathematical models for understanding the formation and movements of

barchans and transverse dunes in a consistent manner

3. Mathematical analysis of the non-uniformity of fluctuations given to elements and resonance

efficiency of the whole group in groups of elements causing stochastic resonance

4. Analysis of traffic flow and jams of camphor boats in annular conduits through experiments and

mathematical models

For 1, quantitative analysis through experiments, image analysis of experiment data, and mathematical

models have demonstrated that ants (garden ants) carry out foraging activities using not only chemical

information based on pheromones, but also visual information. We also investigated how ants use the two

types of information according to the situation. For 2, we succeeded in explaining the mechanism by which

dunes of different shapes are sequentially formed according to changes in environmental parameters as a

dynamical bifurcation phenomenon. For 3, we demonstrated that stochastic resonance phenomena with a

high degree of resonance is reproduced by adding white noise with differing amplitude according to the

element, as responses to the external stimulation of multiple FHN elements simulating the dynamics of

neural ignition. For 4, in collaboration with Nobuhiko Suematsu, a postdoctoral fellow of the Global COE

(Center of Excellence) Program (as well as specially appointed lecturer of Meiji University and research

collaborator of Meiji University GCOE), we have succeeded in reproducing traffic jams similar to those of

automobiles on highways by arranging camphor boats in water channels that self-drive using the difference

in the surface tension in front and at the back of the boats, and describing the basic mechanism of the traffic

jam phenomenon using mathematical models. Further experiments also discovered a new type of collective

motion mode (cluster state) not seen in automobile traffic jams, the mechanism of which was theoretically

analyzed. These results have been widely introduced not only in the journals of the Physical Society of Japan

and the American Institute of Physics, but also in the Nikkei newspaper and The Science News.

Clarification of Dynamics and Functions of Moving Group of Elements




Hiraku NISHIMORI

: : :

Fellow, MIMS; Professor, Department of Mathematical and Life

Science, Graduate School of Science, Hiroshima University

Non-equilibrium Physics, Ph.D., Tokyo Institute of Technology

MMA of Cooperative Phenomena

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Research Outline As our information-oriented society becomes even more highly networked in the 21st century,

researchers are now able to obtain detailed records of massive human economic activities which could

not be documented accurately in the past. Econophysics is the study of mathematically modeling the

characteristics of the collective human activity based on such detailed data. It started in the latter half of

the 1990s as a result of spreading the scope of research by theoretical physicists, including myself, to

an economic phenomenon. Both areas of research and the population of researchers in this field have

since been constantly growing as more data becomes available.

The most significant progress in econophysics is found in the field of financial markets such as

foreign and stock exchange markets. On financial markets, face to face trading practice has been shifted

to buying and selling via computer networks thanks to the advent of computerization. Computer

algorithmic trading, which is completed in a minimal time of 1/1000 seconds, is increasing shares in

most markets. It also allows investors to monitor not only prices at which deals were done but also the

distribution of buy and sell orders called the order-book. Methods to analyze such data have been

developed, and mathematical models have been constructed from different approaches. As a result, we

now have a better idea of which data to process, which models to use for estimating parameters, and

what forecasts to make based on this. Econophysics research is also progressing in other areas such as

research on allowing the monitoring of business networks, the statistical property of fluctuations in

sales, and POS data, which allows for the identification of consumer purchase activities by article.

Once we are able to mathematically describe phenomena, we will next shift our focus to applied

research such as forecasts and control. Already at the forefront of econophysics research, various

applied research efforts are being attempted on a trial and error basis. For instance, topics for financial

market studies include: predicting changes to increase profits, a target that is easily understandable to

all; methods to control excessive fluctuations of the financial market; and methods to encourage the

supply of money gathering in the financial market to the actual economy. Once these new applications

are successful through advanced mathematical models based on data, it is no exaggeration to say that

mathematical science will indeed change society.

As applied research themes I have been working on a basket-type electronic money system taking

corporate financial data into account, and a novel financing system without the perspective of interest

rates. There are a countless number of other new themes to investigate, such as an estimation of money

flow by restoration programs for damages caused by the Great East Japan Earthquake.

Explaining Social and Economic Phenomena with Science based on Data




Hideki TAKAYASU

: : :

Fellow, MIMS; Visiting Professor, Organization for the

Strategic Coordination of Research and Intellectual Property,

Meiji University

Econophysics and Fractals, Ph.D., Nagoya University

MMA of Economic Phenomena and Fractals

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Research Outline

The progress of measurement technology has been gradually elucidating the dynamics of functional

processes, such as the structural formation and information processing in cells and tissues during

development and reproduction. Such dynamical phenomena are produced as a result of the combined

contribution of numerous elements such as molecules and genes. This has led to the growing need for

integrated studies based on system theories to understand the mechanism and design principles in the

complex phenomena of living things, which requires the progress of mathematical methodologies

linked to sophisticated measurement technologies. The aim of our studies is hence to challenge

emerging themes in life science using mathematical concepts and methodologies related to physics and

mathematical science.

Recently, there have been many reports that spatiotemporal pattern formations take place in a cell

with mechanisms similar to reaction-diffusion systems. These include temporal oscillations, spatial

patterns, and multistability, each of which is responsible for important functions in their respective

contexts. As cell-level reactions are highly probabilistic, these mechanisms for structural formation

must be robust against probabilistic noises. On the other hand, these mechanisms also have the

seemingly contradictory nature of giving diversity to the behavior of cells by amplifying the

probabilistic nature of individual reactions to the macroscopic level. We are currently conducting

research on how these phenomena are actually possible, through the analysis of the florescent image

data of a single cell, and by developing and analyzing mathematical models.

Development is the process of forming structures with spatial harmony by activating the program

within a cell accurately to generate various types of cells from a single cell. Mechanical processes such

as the viscoelastic body, whose basic unit is the cell, are involved in the formation of tissue structures,

and these in turn interact with the reaction-diffusion process of genes and signals. With the cooperation

of the groups in RIKEN Center for Developmental Biology and Hiroshima University, we are

attempting to understand the development process using mathematical and quantitative methods.

Tatsuo SHIBATA Position Title,Affiliated Department



: : :

Fellow, MIMS; Associate Professor, Department of Mathematical

and Life Sciences, Graduate School of Science, Hiroshima

University

Mathematical Life Science,

Doctor of Philosophy, The University of Tokyo

Modeling and analysis of the inner- and inter-cellular process

Physical Biology

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Research Outline

During the current fiscal year, I continued to investigate mathematical models to explain the phenomena

of biological evolution. Currently, I am involved in two major projects:

Theoretical research: Japan Science and Technology Agency (JST) (Life modeling) Unified

understanding of two major theories of biological evolution

Applied research: Scientific Research Fund (New research area exploration) Replacement of

Neanderthals by Homo sapiens

The aim of my theoretical project is to pursue the unified understanding of inclusive fitness theory (IFT)

and adaptive dynamics theory (ADT). In particular, the remarkable progress of IFT in recent years has raised

the slightly philosophical question, “What exactly is kin selection?”, which has become an actively debated

topic in journals such as Nature. Because it is highly likely that IFT is still misunderstood, my aim for the

current fiscal year was to identify the facts of IFT as well as its strong and weak points, and reconstruct IFT,

which has been described only instinctively in the past, as a mathematical theory[1].

For applied research, I am presently involved in a major project on the evolution of humankind. Focusing

on the replacement drama of Neanderthals by Homo sapiens 50,000 years ago, this large-scale

multidisciplinary project is participated by researchers from a wide range of academic fields, from physical

anthropologists studying fossil human bones, to archaeologists researching ruins, brain scientists studying

the learning capacities unique to Homo sapiens, paleoclimatologists calculating the environment in those

days, and cultural anthropologists studying modern day hunters and gatherers. The framework of the project

is based on the learning hypothesis that explains that Homo sapiens replaced Neanderthals with their

superior individual leaning abilities. The hypothesis, established by theoretical studies, is indirectly

supported in that stone tools suddenly changed (progressed) since the era of the Homo sapiens, but it still not

known why individual learning abilities only evolved in Homo sapiens. In collaboration with Professor

Kenichi Aoki and Dr. Wataru Nakahashi, I have been studying models on the evolution of learning abilities.

Based on experience gained through the work, I attempted to build models expressing the frequency

dynamics of genes and culture during the expansion of distribution, using reaction-diffusion equations.

Findings showed that individual learning abilities tend to evolve easily when distribution expands rapidly[2].

Considering that more than half of the history of Homo sapiens evolution spanned several tens of thousands

of years after early human migration out of Africa, my model supports the learning hypothesis that the early

human migration out of Africa helped evolve individual learning abilities.

[1] Wakano JY, Ohtsuki H, Kobayashi Y. Non-experts' guide to the inclusive fitness theory: a mathematical description.

(Submitted)

[2] Wakano JY, Kawasaki K, Shigesada N, Aoki K. Coexistence of individual and social learners during range-expansion.

(Submitted)

Research on Biological Evolution: Theory and Applications




Joe Yuichiro WAKANO : : :

Fellow, MIMS; Associate Professor, Organization for the

Strategic Coordination of Research and Intellectual Property,

Meiji University

Mathematical Biology, Ph.D. (Science), Kyoto University

MMA of Macrobiology and Ecosystems

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