ーMathematical Exploration of Social Complex Systems ー
Language, Communication, and Financial Markets
We explore the universal properties underlying largescale social
systems through mathematical models derived by computing with big data
obtained from largescale resources. Using these models, we explore
new ways of engineering to aid human social activities.
Analysis of social systems by applying complex systems theory
Empirical properties behind social systems
Mathematical models explaining scaling properties
Methods for measuring long memory and fluctuation
Complexity of social systems
Deep learning/machine learning methods for complex systems
Deep learning models that reproduce the scaling properties
Unsupervised and semisupervised methods
Symbolic approaches for nonsymbolic data
Mathematical informatics across language, financial markets, and communication
Computational linguistics
Mathematics of communication network
Newswire reports and financial market prices
Recent studies
Analysis of largescale social systems by applying complex systems theory
Common scaling properties are known to hold across various largescale
social systems. Using real, largescale data, we study
the nature of these properties and construct a mathematical model that explains
them.
Metrics that characterize kinds of data
Various metrics are considered in terms of whether they characterize different kinds of data.
For example, in the case of natural language, metrics that specify the author, language, or
genre have been studied. One such metric is Yule's K, which is
equivalent to Renyi's secondorder (plugin) entropy. Yule's K computes a value
that does not depend on the data size but only on the data kind.
We explore such metrics among various statistics related to scaling properties
of real data and compare
different kinds of data such as music, programming language sources, and natural language.
Complexity underlying human linguistic sequences
How complex are human linguistic time series such as language, music, and programs?
Consider the number of possibilities for a time series of length n, with a parameter h,
as 2 ^{hn}. For a random binary series consisting of half ones and half zeros,
h=1. For the 26 characters in English, however, the number of possibilities
is not 26 ^{n},
because of various constrains, such as "q" being followed only by "u". Shannon computed that
h=1.3, but the question of acquiring a true h for human language is difficult to
answer and remains unsolved: it is unknown whether h is even positive.
Therefore, we study ways to compute the upper bound of h for various kinds of data, including
music, and programs, in addition to natural language.
Analysis of long memory underlying nonnumerical time series
Real instances of social systems have a bursty character, meaning that
events occur in a clustered manner. For example, the figure on the
right shows how rare events occur over time (the first indicates rarer
events than the second; the second, rarer than the third) in texts.
This clustering phenomenon indicates how the sequence has long memory
and thus exhibits selfsimilarity. We study methods for nonnumerical
time series to quantify the degree of clustering and examine different
selfsimilarity degrees across various systems.
Deep learning/machine learning methods for complex systems
We discuss the potential and limitations of deep learning and other
machine learning techniques with respect to the nature of complex
systems, and we study directions for improvement. Moreover, we explore
unsupervised and semisupervised methods for stateoftheart learning
techniques.
Deep learning and scaling laws
Many difficult problems are now being solved through deep learning techniques, such as
image recognition and machine translation. In these cases, which aspects of real systems
do deep learners capture or ignore? We investigate whether scaling laws
hold for data generated by a deep learner and seek a new way
to evaluate machine learning methods.
For example, the figure on the right shows how
a characterbased long shortterm memory (LSTM) fails to generate a text with long memory that existed
in the original text that it had learned. Similar consideration
applies to financial applications based on deep learning.
Generative models of complex systems
A generative model is a mathematical
formulation that generates a sample similar to
real data. Many such models have been proposed
using machine learning methods including deep
learning. Study of a good model serves to
characterize the nature of a system and also
to understand the potential of machine
learning. We study autoencoders and
adversarial methods, the fundamental
potentials of generative models, to generate a
sample resembling real data.
Extraction of templates from texts
Multiword expressions with slots, or templates , such as
"Starting at __ on __ " or the expression "regard _ as _"
appear frequently in text and also in data from sources such as Twitter.
Automatic extraction of these template expressions is related to grammar inference
and is a challenging problem. We propose to do this by using a binary decision diagram (BDD),
which is mathematically equivalent to a minimal deterministic finitestate automaton (DFA).
We have studied a basic formulation and currently seek a larger application to extract patterns
from social networking service (SNS) data.
Mathematical informatics across language, financial markets, and
communication
We explore common universal properties underlying language, finance,
and communication, through computing with various kinds of largescale
data, and we apply our understanding of those properties to
engineering across domains. For example, we study financial market
analysis by using blogs and other information sources, and we simulate
information spread on a largescale communication network.
Largescale simulation of communication network
After the 2011 earthquake in the Tohoku region of Japan, Twitter
played a crucial role in helping with searching for victims and
locating resources. To study the mathematical nature underlying
information delivery on social media, we crawled the topology and
tweets of an SNS on a very large scale, with over 100 million nodes. On
this gigantic graph, the best mathematical model of communication is
explored via simulation, so that simulated macroscopic statistics,
such as the speed and bounds of information spread, agree with those
of the real data. We also study the best way to visualize such
information spread.
Bitcoin price and Twitter
The bitcoin price crash at the beginning of 2018 was caused by various
social factors. The influence of news wire stories and social media
was especially crucial because of the combination of both credible and
fake information together. We accumulate bitcoin data and analyze the
relation of Twitter data with the bitcoin price. In particular, we
seek to mine Tweets that influence the actual price.
Quantification of structural complexity underlying human linguistic sequences
How grammatically complex are adults' utterances as compared with those of children?
Or, how is a literal text structurally more complex than a Wikipedia source?
One existing, formal way to consider such questions is
through the Chomsky hierarchy, which formulates different complexity levels of grammar
through
constraints put on rewriting rules.
While the hierarchy provides qualitative categorization,
we investigate a new way to quantify structural
complexity by using metrics based on scaling properties.
Moreover, we try to explain the difference, from a complex network perspective.

