About Takayasu Lab.

Financial Market
Under Construction

Dealer Model

financial Market
Under Construction

Bubbles and Crashes

Financial Market
Under Construction

Order Book Analysis

Financial Market
Under Construction

PUCK Model

Complex Network
Under Construction

Inter-firm Trading Network

SNS DataUnder Construction

Social Media

POS DataUnder Construction

Sales Data Analysis

GPS DataUnder Construction

COVID-19 Prediction

GPS DataUnder Construction

Human Mobility Models

Intestinal Flora
Under Construction

Ecological Models of Microbiota

About Takayasu Lab.

At the Takayasu Laboratory, we analyze phenomena in a broad range of fields using various methods developed in statistical physics, statistical science, and information science. The themes of research conducted in this laboratory are as follows.
1. Modeling of universal phenomena observed across various fields and analysis of their characteristics
2. Data analysis and modeling of economic and social systems caused by complex interactions among many people
3. Data analysis and modeling of complex systems found in the life sciences
Today, with the development of computers, these research themes are topics of interest in cutting-edge information science, statistical physics, econophysics, sociophysics, and complex systems science. With the advent of the era of big data, it has become possible to accurately observe the activities of humans and companies as microscopic components, as well as their interactions and time evolution in human society. In addition, improvements in computer performance and developments in statistical science and information science have made it possible to analyze large-scale data, and modeling from the viewpoint of the relationship between micro (components) and macro (phenomena) has become possible to investigate how micro components affect macro phenomena. From these micro and macro perspectives, data on human society and biological systems are a treasure house of new discoveries. At the Takayasu Laboratory, we take on the challenge of elucidating such complex phenomena while creating cutting-edge knowledge.

“We are taking on the challenge of developing the research fields necessary for a super smart society.”

Obtaining accurate and sufficient observational data and reproducible analysis results are major prerequisites for research subjects to be widely accepted by the public as empirical science. In the super smart society, the accumulation of big data enables precise observations on humans, society, and the economy, and new scientific fields are emerging. Many universal human behaviors have been reported, obtaining similar results in different countries and regions. New science is emerging from analyzing these vast amounts of human and social data.

The development of science has a long history of responding to the social needs of the times. New fields develop significantly when the scientists’ curiosity and discoveries coincide with industry needs. For example, during the Age of Discovery in the 17th century, research on planetary motion, which was necessary for measuring the position of ships (astronomical observation), led to classical mechanics; the invention of the heat engine in the 18th century led to research on heat and temperature, which led to the development of thermodynamics; the invention of the motor and the telephone in the 19th century led to the development of electromagnetics; and in the early 20th century, iron manufacturing technology sustained the country, and the issue of measuring blast furnace temperatures led to quantum mechanics. Then the atom was discovered, and the foundations of statistical physics were established. Being sensitive to the social needs of the times is also an important factor that is indispensable for developing new scientific fields.

So, what kinds of research fields will develop as a new science in the super smart society? It will be essential to fulfill the conditions that enable precise observation and meet social needs.

When considering these fields, we must recognize the development of infrastructure brought about by the advanced information technology that made significant progress at the end of the 20th century. A vast information network connects the world; smartphones and tablets have enabled each individual to communicate in real time. Economic activities and people's lives have changed significantly as a result. As symbolized by Internet-based net banking, PoS systems, electronic money, and computer trading, computer systems have been widely introduced into economic activities. The world's economic activities have become faster and more complex, and the linkage of financial markets and other financial institutions has also become faster. In addition, in our daily lives, we live in a society where each individual can connect with people worldwide and disseminate information through social media and video sites. Smart home appliances linked to smartphones and tablets, self-driving cars, etc., are being implemented. In these times, it has become essential to analyze and utilize big data, a vast record of human activities, from multiple angles at high speed to maintain a stable social life (research on econophysics and sociophysics). (Research on Econophysics and Sociophysics)

Due to major changes in the means of communication in our daily lives, the “quantity” and “quality” of information have become new social issues. The issues related to the quantity of information include the increasing complexity of network structures due to the expansion of the scale of the Internet, the increase in the quantity of data used, and the issue of reduced communication efficiency that occurs during disasters. Research on what communication control methods should be used to make the system as robust as possible and high transport efficiency in a vast autonomous distributed system is an essential basic research theme related to constructing information communication systems. Furthermore, in the future, this is expected to be closely related to the elucidation of the issue of how a vast quantity of information is communicated in the massive network of neurons in the brain (research on transport systems in autonomous distributed systems). Regarding the quality of information, there is the issue of how to find meaningful information out of the information that is being carelessly and rapidly flooded on the Web. Quality of information is developing into a groundbreaking field that reveals new universal rules of human behavior, such as how hoaxes and fads are formed as part of human group psychology (analysis of social media information).

“Developing Interdisciplinary Fields and Pioneering New Fields”

At today’s cutting edge, the boundaries of existing academic disciplines are becoming unclear. This is because it has been recognized that multifaceted research (interdisciplinary research) is necessary to elucidate the nature and phenomena of things. Our research is no exception. The Takayasu Laboratory has pioneered the interdisciplinary fields of econophysics and sociophysics, which combine the foundations of big data analysis from advanced information and statistical science with modeling methods from statistical physics, complex systems science, and systems science, as well as knowledge from economics and sociology. This is because we have come to realize that the knowledge of material science is useful for elucidating social and economic phenomena caused by the complex interaction of human activities. In individual human behavior, the diversity brought about by individuality can be observed. However, it has become clear through big data analysis that there are universal laws in group behavior.

In particular, assuming that we know the properties of individual components (micro), when we observe the properties of a system as a whole (macro) in which many components interact in a complex manner, the study of subjects in which non-trivial phenomena are detected has been an active part of the field of statistical physics. Statistical physics is a research field that developed from the successful derivation of the equation of the state of a gas filled with a macroscopic system consisting of many molecules from the motion of individual gas molecules and has been used to formulate and clarify phase transitions and self-organized critical phenomena in materials. Currently, the concept has been extended to include biological, informational, economic, and social phenomena (construction and analysis of basic mathematical models). Biophysics, for example, is one of the interdisciplinary fields that is making significant progress. In terms of the concept of micro and macro mentioned earlier, for example, each nerve cell is a micro that constitutes a vast network of nerve cells called the brain. Although the electrophysiological characteristics of the neurons that make up the microscopic structure have come to be understood in detail, research has only just begun to elucidate the high-order functions of the brain, such as thoughts and emotions, which are macro functions created by the complex network of these functions. In addition, in economic and social phenomena, the micro is each individual human being. The group behavior of many people can be observed as a phenomenon because each individual's actions affect each other. Research in econophysics and sociophysics, which seeks to elucidate the complex interactions of many people, is also deeply related to advanced research in statistical physics of non-equilibrium open systems such as fractured and cohesive phenomena, which has advanced with the development of computers (Research in Econophysics and Sociophysics).

"Specific Examples of Research Themes"

check Construction and Analysis of Basic Mathematical Models

Focusing on spatiotemporal self-similar patterns and power distributions, this research aims to understand generation mechanisms using mathematical models.

  1. Research on the Random Multiplication Process and Power Distribution
    Physical Review Letters 1997, Journal of Statistical Physics 2014, Entropy 2017, Entropy 2021
  2. Research on the Self-modulation Process and Long-time Correlation
    Physica A 2003
  3. Research on Nonlinear Transport Phenomena and Diffusion/Aggregation Transition on Complex Networks
    International Journal of Modern Physics 2012, Pnysical Review E 2015
  4. Research on the Formation Models of Complex Networks
    Physical Review Letters 2012, Journal of Statistical Mechanics 2017
  5. Research on Phase Transitions in Complex Networks
    Scientific Reports 2018, Journal of Statistical Physics 2022
  6. Research on Methods for Extracting Critical Explanatory Variables from Many Explanatory Variables for Objective Variables
    Entropy 2018
  7. Research on Methods for Detecting Change Points in Time Series
    Scientific Reports 2022
  8. Research on Methods for the Trend Decomposition of Time Series
    PloS One 2020
  9. Research on Methods for Extracting Densely Accumulated Areas from High-dimensional Big Data under Certain Conditions
    Entropy 2023

check Research on Econophysics and Sociophysics

The field of econophysics and sociophysics began around the 1990s when researchers in statistical physics analyzed the electronic data of financial market prices that had just become available. Econophysics and sociophysics are data-based research fields that elucidate economic and social phenomena caused by the interaction of many people, companies, nations, and other entities. We analyze big data on the economy and human society and clarify their characteristics, such as statistical properties and relationships between variables. We then build the simplest, data-driven models that reproduce observed system characteristics. After validating the model, we conduct applied research using the model, such as forecasting and elucidating system vulnerabilities.

We currently envision the following specific themes for econophysics and sociophysics.

【Research on Financial Markets】
Research on random walks, including Brownian motion, led to the discovery of the atom in the early 20th century and is a topic of great interest even to statistical physicists. Brownian motion, the mystery of which was solved with the discovery of the atom, has dramatically advanced the field to find answers to the following questions of scientific curiosity: What human behavior has its nature as the root of random walks in financial markets? When does a deviation from a random walk occur? Many properties that deviate from random walks have been discovered by analyzing the time-series data of market prices in seconds (currently in milliseconds) in financial markets such as stocks and foreign exchange using various methods. Econophysics inductively derives the dynamic effects that create market instability from vast amounts of data and elucidates phenomena by going back to the fundamental questions of why and how fluctuations occur.
The research themes consist of the following five areas.

  1. Analysis and Modeling of Market Price Fluctuations in Financial Markets
    In our laboratory, we are developing our own model (Potential of Unbalanced Complex Kinetics (PUCK) model). This model formulates a random walk in the potential, which can reproduce surges and crashes with acceleration from a random walk, and so on. The relationship between the parameters of the model and those of the dealer model is also analyzed. By applying time renormalization, it is also possible to derive exponential and double exponential functions known for surges, crashes, inflation, etc. The model's parameters can be estimated sequentially using particle filters.
    Pysica A 2006, Progress of Theoretical Physics 2009, Physical Review E 2009, Journal of Statistical Computation and Simulation 2014, Journal of Statistical Mechanics 2019, "Computation and Society (Iwanami koza keisan kagaku. 6) Chapter 2," Physics Reports 2022
  2. Analysis and Modeling of Board Information
    This is research to analyze transaction information called board information, which indicates the number of sell orders and buy orders placed by participants in the financial market at what prices, and to extract the factors of market price instability.
    Physical Review Letters 2014, Physical Review E 2015, Physical Review Letters 2018, Physical Review E 2018, PloS One 2018, PloS One 2019
  3. Dealer Model Research
    This is research to explore the mechanisms of surges and crashes observed as macro phenomena by linking the dynamic behavior of financial market prices with the strategies of dealers (market participants), which are micro components.。
    Physical Review E 2009,Transactions of the Japanese Society for Artificial Intelligence 2012, Physical Review E 2018, Physical Review Letters 2018, Journal of Statistical Physics 2023
  4. Research on Interactions among Multiple Markets
    Although electronic trading has made it possible to buy and sell at high speed in financial markets, it is known that crashes in financial market prices are linked to and spread to other markets. For example, in the foreign exchange market, a crash originating from one currency can spread and cause a multi-currency crash, such as a currency crisis.
    Physica A 2006, PloS One 2020
  5. 5. Research on the Origin of Random Fluctuation from Board Information Data
    This is research that analyzes board information to deepen the understanding of what kind of trading behavior of market participants causes fluctuations that cause market price changes and dissipation that stops changes.
    Physical Review Letters 2014. Physical Review E 2015, Physical Review Letters 2018

【Analysis and Modeling of Corporate Information】
By analyzing corporate financial and transaction data, it has become possible to model the life cycles of companies of various sizes in various industries, from foundation to bankruptcy. By analyzing what kinds of companies that newly established companies start trading as, it has been found that there is a tendency to start trading as a company that already has many transactions and that there is a mechanism (preferential selection) by which larger ones become larger. This mechanism is also famous for the unequal power distribution of the number of followers on social media, etc., in research on connections between people (complex networks). However, this was initially a law discovered in the field of crystal growth in physics. Furthermore, it is known that business-to-business transaction networks are large-scale complex networks. By observing the flows of money, goods, and services on that network structure and modeling those flows, it is now possible to estimate the amount of damage caused to sales in the event of a disaster.

  1. Research on Characteristics of Business-to-Business Transaction Networks
    Business-to-business networks are known as large complex networks. Analysis of the network's properties and robustness (such as percolation) are essential sciences for maintaining and developing supply chains.
    Annual Report of the Earth Simulator Center2007, Scientific Reports 2017, Physical Review E 2015, PloS One 2015
  2. Modeling Transport Phenomena on Business-to-Business Transaction Networks
    It is now possible to observe the amount of money transacted between neighboring companies on a transaction network, and the transport equation for the money flow is derived in a data-driven manner (gravitational interaction model). Combining this model with real-world network information assimilates four model parameters into the data so that company sales can be correctly estimated. This model can be used to estimate the impact of bankruptcies on large companies and the amount of damage to sales in the event of a disaster.
    International Journal of Modern Physics 2012, Artificial Life and Robotics 2019
  3. Time Evolution Model of Business-to-Business Transaction Networks
    We can observe the time evolution of business-to-business transaction networks. It is now possible to simulate the time evolution of a company’s transaction network by examining what size of companies in the network new entrants (start-ups) start doing business with, what types of companies merge or spin-off, and what kinds of companies go bankrupt. When used together with the gravitational interaction model, many statistical properties can be reproduced, including the distribution of company sales, the distribution of company growth rates, the distribution of company life spans, the scaling relationship between sales and the number of trading partners, and the change in the number of trading partners with company age. This research aims to serve as an excellent example of Evidence-Based Policy Making, in which when the government proposes a policy to a company, the effect of that policy can be evaluated through simulation.
  4. Research on Company Life Cycle
    It is known that the three variables of sales, number of employees, and number of trading partners as company parameters neatly satisfy the power-law scaling relationship with each other. In the phase space of these three variables, when we describe a flow diagram that indicates which way companies tend to proceed with age, we found that stable companies tend to cluster near the scaling line and that companies tend to go bankrupt when they deviate from the scaling line.
    New Journal of Physics 2019, Entropy 2021, Physical Review E 2022
  5. Proposal of Analysis Method for Corporate Data
    The development of methods for extracting essential parameters for bankruptcies, chain bankruptcies, and rapid growth from corporate financial data and transaction network information
    Entropy 2023
  6. 【Research on Social Media】
    Social media, represented by blogs and Twitter, allows anyone to transmit, share, and spread information through the Internet, and its use is increasing worldwide. The information posted on social media is stored and used for academic research after being processed in a way that protects privacy policies, such as anonymization. Although many individual posts are of personal interest or gossipy chatter, when the number of users reaches tens of millions, we can find various macro non-trivial characteristics based on the frequency of words in the daily posts. The following studies are underway.
    Phys Rev E 2013, "Econophysics of Social Media" Nippon Hyoron Sha 2012

    1. Research on Quantitative Detection of Public Feelings
      Some words are associated with feelings such as anger and joy, and we have developed a method to quantitatively assess overall public feelings based on the distribution of words in articles posted on social media. We can observe how public feelings change depending on what kind of events are happening. We have been conducting a detailed analysis of how public feelings have changed since the outbreak of COVID-19 in early 2020, the subsequent pandemic, the government's imposition of behavioral restrictions, and vaccinations.
      PloS One 2019, Scientific Reports 2022
    2. Research on the Propagation of Fake News
      By considering each user as a node and followers as links, the diffusion of information can be described by a diffusion model on the network structure. We found that there is a difference in the network structure between the propagation of correct information and misinformation. We can also simulate the spread of information in social media by applying the basic mathematical model of contact-propagated infectious diseases on the network.
      PloS One 2015, Euro Physics Journal Data Science 2020
    3. Research on the Frequency of Hashtag Usage
      Social networking services (SNS) such as Twitter and Weibo use hashtags to mark comments, and observations of the creation, increase, decay, and disappearance of hashtags have shown that there are universal characteristics. We have been working on building a model to describe how information posted by individuals spreads.

    【Research on Retail Data】
    Goods in convenience stores and supermarkets have barcodes, and the POS system automatically records the sales price and quantity. By analyzing such retail data, we can refine forecasts of the number of sales.

    1. Research on the Law of Fluctuation of the Number of Sales
      The event when goods with a small average number of sales sells can be approximated by a Poisson process, and the variance of the number of sales is proportional to the average. However, for goods with a large average number of sales above a certain level, it is known that the variance is proportional to the square of the average value, which is a more significant fluctuation than that of the Poisson process. We will analyze the sales data of various goods and clarify the characteristics of fluctuations.
      PloS One 2016
    2. Research on Forecasting the Number of Sales per Goods
      Based on the characteristics of the fluctuations described above, we will build a mathematical model for forecasting the number of sales that can respond to rapid changes in the number of sales by using methods such as particle filters.
      Stats 2019
    3. Research on Strategies to Reduce Waste and Increase Profits
      If production is reduced to reduce the amount of waste due to unsold goods, there is a high possibility of reducing profits through lost opportunities. We will explore the optimal way to reduce waste and increase profits using mathematical models.
      Sustainability 2019
    4. Research on Commodity Ecosystems
      Although convenience stores have thousands of different goods on display at all times, a quasi-steady state is maintained in which some goods are replaced daily. We will analyze the entire goods’ temporal fluctuations from the ecosystem’s perspective and build a mathematical model.
      Entropy 2020
    5. 【Research on GPS Data】
      GPS data from smartphones has come to be used in academic research, and it has become possible to observe people's movements. In our laboratory, we have stored an enormous amount of data for several years, in which the positions of approximately 1 million users in Japan were recorded at intervals of about 10 minutes. It is possible to quantitatively measure how many people are moving from where to where, the morning and evening rush patterns, and changes in people flows during the COVID-19 pandemic. Research on this data includes the following.

      1. Research on People Flows Patterns in City Areas
        By dividing city areas into 1 km meshes and calculating the average flow within each mesh, observing the basin of people flows is possible. Based on the data, we analyze and mathematically model how the shape and distribution of the basin change in the morning, afternoon, and evening.
        Scientific Reports 2020
      2. Research on Modeling People Flows in City Areas Using an Electric Circuit Model
        We can calculate the spatial distribution of currents at each time by regarding a moving person as a charged particle. Assuming a hypothetical electric circuit model that describes this current distribution, changes in people flows are expressed in terms of changes in electric potential.
        Scientific Report 2022
      3. Research on the Gravity Model of People Flows
        The gravity model characterizing the flows of people between cities (The people flows are proportional to the product of the city population and inversely proportional to the power-law of distance.) has long been known. We are also working on extending the model to apply to the people flows inside cities.
      4. Estimation of the Number of COVID-19 Infected People Based on GPS Data
        Since infectious diseases are spread through contact between people, we can quantitatively evaluate the possibility of infection by estimating the density of people from GPS data. This makes it possible to predict infections in city areas.
        Scientific Reports 2022

      5. All phenomena dealing with vast amounts of high-frequency data are also the subject of research.

checkResearch on Transportation Systems in Autonomous Distributed Systems

The Internet is a vast autonomous distributed system that transports information electronically. In such a vast system, it has been found that fluctuations such as the power spectrum following 1/f are observed in the density fluctuations of packets when measuring the information flow. Behind such a phenomenon, we have elucidated that a dynamic phase transition occurs between the congested and non-congested phases, with the flow of packets per unit time as the control parameter. Furthermore, we have elucidated the Internet protocols in detail and shown that the most efficient transport in the system is achieved at the critical point (critical point control).

Suppose the Internet is the world's largest artificially created information transportation system; in that case, our brain is a system that processes information at high speed and on a large scale, which is truly a miracle created by nature. Although we are beginning to understand the characteristics of neurons in detail, we have only just started to understand the advanced functions of the brain, such as thinking and feeling, created by the complex network of neurons. The research on functions arising from such biological information systems is a field that is expected to develop further with the deepening of our understanding of complex systems science.

  1. Research on the Congestion Phenomena of the Internet
  2. Research on Life Information Systems