[From CS Fellows]

IEICE Communications Society – GLOBAL NEWSLETTER Vol. 44, No. 4Some Fundamental Concepts
Underlying My Research Activities
Masaki Aida
Tokyo Metropolitan University
1. Introduction
Science & technology and religion are often talked
about as being incompatible, but is that true? It was not
so long ago in the history of humankind that science
separated from religion, furthermore, it was only recent
when technology was systematized as engineering.
Both science & technology and religion are the resultof human efforts to create a “complete system,” and I
think that the structures created by humans all havesomething in common. For example, the formulation ofphysical laws based on the principle of least action thatappears in analytical mechanics seems to be motivatedby the thought that physical laws should be derived
from the first principle. This vision seems to be
conscious of something that governs the laws of theworld. In more detail, the existence of physics itself isbased on the wishful assumption that the laws of theworld are indicative of a beautiful system (which canbe understood by mathematics). We may be able tointerpret this is assuming the existence of God in asense. Interestingly, the wishful assumption of physics
remains undeniable after many measurements andvalidations and is still a force driving human effort.
In science and technology, “facts” that can beverified by experiments are sought after, and appeals to“the way it should be” are supposed to be denied. Ifthese appeals are not adequately suppressed, there is arisk of biased observation that precludes direct
observation of reality and generates incorrectconclusions. However, if there is no intimation of
direction, the individual will be unable to secure guides
to the understanding and systematization of unknown
phenomena. Therefore, some intimations about how toproceed with research are necessary, making balanceessential.
This essay introduces the fundamental concepts
underlying my research activities. These have been
introduced in detail in my Japanese textbooks [1], [2](they are also outlined in [3], [4], respectively), but I
will take the opportunity of this essay to elucidate themin English.
2. How is the Order of Our World Created?
The development of ICT has strengthened the linkage
between users and information network systems. As aresult, user behavior has come to affect the stable
operation of information network systems. For example,
the email generated to exchange New Year greetings is
so large that receiving emails becomes problematic.

Furthermore, the influence of the user's behavior also
affects the behavior of other users via the information
network. For example, when a web page takes too long
to be displayed on a personal computer due tocongestion of the server or the network, the user often
clicks repeatedly. This behavior further loads theinformation network system, which makes it difficultfor other users to display their requests, and therepeated click action propagates to other users.
Following these considerations, it is difficult to think
about the performance and stable operation of
information network systems as a single isolated system,
and it is necessary to enlarge the scope of the target toinclude users' behaviors. Furthermore, considering thatvarious sensors and self-driving cars will soon beconnected to the information network, the entire
information network system will become massive inscale and complexity. It must be emphasized that noone knows all the details of the current state
information of even the current information network
systems. How can we properly operate a system that we
do not know the whole picture? One way is to find asystem that does not know the whole picture but isdeemed to work well, and to draw conclusions about its
mechanism.
The most well-known large-scale and complex
system is our world. The number of components thatform this world and their diversity readily confirm that
it is the ultimate large-scale and complex system. So
why is this ultimate large-scale and complex system,
the world, stable? We believe that the world will still
exist tomorrow and that the sun will rise tomorrow, justas in the past. Even though we know that no past stateis ever repeated precisely at the scale of atoms orelementary particles that make up our world, we
believe that the world is stable. Such orderly behaviorof the world is created through so-called synergistic
effect, self-organization, or the collective phenomenaof fundamental structure. This framework is exciting
and gives useful clues to engineering. The question ofwhere the stability or orderly behavior of the worldcomes from probably corresponds to the following
questions. Assuming that God created the world, what
divine secrets were used at the Creation to yield theorderly behavior of the world? Conversely, even if we
assume that God does not exist, what are thecharacteristics that make us feel that something isbehind the orderly behaviors of the world?
If the characteristics indicative of the order in nature
are known, it should be possible to create a mechanism
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IEICE Communications Society – GLOBAL NEWSLETTER Vol. 44, No. 4

for creating order in a system by recreating it in anengineering system, even if there is no one who
understands the state information of the entire system.
In other words, it is a prospective attempt to create anengineering system that replicates the order assumed toindicate the presence of God.
Of course, we cannot create a complete answer withregard to these characteristics since the natural
mechanisms are not completely understood. However,since our purpose is not to understand nature but tocreate engineering systems that replicate its
characteristics, we should assess our current
understandings in terms of their usefulness in systems
engineering. My current research activities consider thefollowing two characteristics.
 Action through a medium (Local interaction)
In physical systems, there are two concepts that
describe the interactions that can occur between
two objects in spatially different locations; action
at a distance and action through a medium (local
interaction). The former yields a model in which
two widely-separated objects interact directly. The
latter does not permit the existence of directinteraction between widely-separated objects; itassumes that interaction occurs only between
spatially adjacent objects, and the effect ofinteraction is incrementally exchanged between
the objects. Modern physics supports the actionthrough-a-medium concept, so interaction occurs
locally. In such a model, space is filled withphysical quantities at all points (which forms afield), and any variation in the physical quantity ata point propagates through the field at a finite
speed.
 Renormalizability (Reducing the degrees of
freedom in dynamics)
When attempting to observe a massive
aggregation of extremely small objects thatinteract in complex ways, we can more easily
comprehend the aggregate (or system) byreducing either the temporal or spatial resolution(or both), i.e., coarse-graining the system. In therenormalization theory, complex systems areunderstood by observing changes in ameasurable attribute identified by the coarsegrain transformation. The coarse graintransformation of observations is called
renormalization. We consider a system thatexhibits large (or infinite) degrees of freedom at
the microscopic scale. If the system is welldescribed by small (or finite) degrees of freedom
at the macroscopic (measurable) scale throughrenormalization,thesystemiscalledrenormalizable.
In the action-through-a-medium concept, an object
interacts only with its neighbors, at any instant. In theworld of action at a distance, changes in or by an object
instantly influence all places, including the end of theuniverse, and conversely, the changes of any object,regardless of its location, instantly influence the object.
6

In this situation, the components of reality areassociated with each other very strongly, which might
limit the flexibility of the world. Therefore, the actionthrough-a-medium concept appears to be a key
characteristic in producing stable systems while also
ensuring the freedom of local action.
Even if we do not fully comprehend the attributes of
micro-components such as atoms or we do notunderstand the complete mechanisms of nature, we canadmire the orderly behavior of the world. This meansthat even if there are huge degrees of freedom when theworld is observed at the micro-scale, almost all degrees
of freedom are missing at the macro-scale of humanperception, and only a small number of macroparameters are needed to describe the world. Thisconfirms the renormalizability of the world.
Based on these ideas, my research activities havebeen considering a hierarchical model based on
temporal and spatial scales as a framework for
information network control technologies. At eachlayer, the hierarchical model considers local
interactions on the temporal and spatial scales thatcharacterize the layer. The rules that describe local
interactions are described by a partial differential
equation, and the resulting overall system state is thesolution of the partial differential equation. In otherwords, a macro-scale state is realized as a solution of apartial differential equation by the micro-scale action
rule given as a local interaction. What kind of effectoccursbetweendifferent
layersinvolves
renormalization from the perspective of how coarsegrained the observations are.
3. User Dynamics and Relativistic Quantum
Mechanics
Imagine if there is any object in the world that does
not interact with others, can it be said that it reallyexists? Since it does not interact with light, it does notreflect light and is therefore invisible. Since it escapes
gravity, it must have no mass, and of course, it escapes
the sense of touch. Even if such a thing exists, isn't it
the same as not existing? From that point of view, it
can be seen that real existence is a concept based oninteraction with others. Then, what are the uniqueproperties possessed by objects that actually exist? For
example, attributes of the object itself, such as its color
being red, are recognized only when there is anotherobject that permits comparison, so it is also a conceptthat is based on mutual relationships. The real objects
themselves and their interrelationships are inseparable,
and they together make up this world. In therelationship between the characteristics of the “object”
itself that really exists and the “environment” createdby the interaction with others, we can recognize that
their boundaries are ambiguous. If we consider thiswhole and inseparable world as a network, our world isthe network itself.
A network that represents the relationship between
people through an information network is called an
online social network (OSN). Due to the rapid

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IEICE Communications Society – GLOBAL NEWSLETTER Vol. 44, No. 4

development and spread of ICT in recent years,
communication between people has been dramatically
activated, and the ability to transmit information
generated by individuals has been strengthened; thishas greatly stimulated the activities of users in OSNs.
Therefore, understanding user dynamics in OSNs havebecome a significant issue. In my research activities,
the oscillation model was proposed to describe the user
dynamics in OSN; it is formulated as a wave equationon the network. In research on wired networks, thefirst-order differential equations with respect to time,such as Markov chains, are often used, but secondorder differential equations with respect to time, suchas the wave equation, are rarely used. The reasons why
my research uses the wave equation for modeling user
dynamics are as follows. The strength of the user's
activity influences the strength of the activity of otherusers via the OSN, but the influence does not spread
instantaneously, rather it propagates across the OSN ata finite speed. The wave equation describes thecharacteristics of propagation in a medium at a finite
velocity. For example, consider a function that
expresses the effect of influence propagation amongusers. If the effect propagates at a finite speed, then thetrigonometricfunctionsyieldedby
Fouriertransformation also move at the same speed. With
regard to the trigonometric function at each frequency,
if the movement is observed at a fixed point, it appears
to be oscillating. In other words, behind thephenomenon of propagation at a finite velocity, astructure that instantiates wave propagation isnecessary. The oscillation model was introduced for apurely theoretical reason following this background,but the oscillation energy is related to node centrality, aconcept often used in conventional network analysis.
For example, under the condition of uniform OSN use,
if all link weights are one, the oscillation energy of anode represents its degree centrality, and if the linkweight is the amount of traffic passing through the link,
the oscillation energy of the node represents its
betweenness centrality. Furthermore, oscillation energy
may diverge depending on the structure of the network,
which is considered to represent the situations in which
the intensity of user dynamics activity diverges, such as
the flaming phenomenon.
The oscillation model enables us to understand therelationship between user dynamics and network
structure. Thus, the oscillation model has the potential
to yield countermeasures to explosive user dynamics,
including flaming, such as altering the network
structure. In this situation, don't you want to understand the causal relationship between the kind of OSN
structure and the type of user dynamics evidenced by
the structure? The wave equation that describes user
dynamics is a second-order differential equation withrespect to time. Note that the first-order differential
equation with respect to time is essential here as it can
explicitly describe the causal relationship between the
network structure and user dynamics. Of course, its
solution must describe propagation at a finite velocity

so that it must also be a solution to the original wave
equation. If the equations that satisfy both requirements
are created, the OSN structure will not be conserved,
and problems will arise in which all users all over theworld will be directly linked to each other. Therefore,
in addition to the above requirements, we must find an
equation that completely conserves the OSN link
structure. The literature [5] (also [1] in Japanese) has
succeeded in giving a fundamental equation thatsatisfies all of the above requirements. Interestingly
enough, the fundamental equations of user dynamics
thus obtained have the same structure as the Diracequation that appears in relativistic quantum mechanics.
Here, relativistic quantum mechanics is a fundamental
theory of physics that combines special relativity andquantum mechanics and is the starting point of
quantum field theory. From this, the user dynamics aredescribed by the wave function that is quantized by the
anticommutation relations yielded by fermionic fields.
Note that the research did not artificially apply theequations of physics to describe user dynamics. The
fundamental equation of user dynamics is naturally
obtained from the goal of explicitly describing thecausal relationship of the network structure andconservation of the OSN link structure. Quantum
theory often details a mysterious world that differsfrom the real world, such as Schrödinger's cat, often
mentioned in public awareness books. However, thefindings obtained from the fundamental equations ofuser dynamics suggest that the framework of quantum
theory is not unique to the microscopic world, butinstead is inherent in the description of causal
relationships.
In quantum theory, there are several mathematicallyequivalent formulations, depending on the temporalchanges in the linear operator and/or the state vector
appearing in the equation. The formulation in which
the linear operator evolves with time is called theHeisenberg picture, the formulation in which the statevector changes over time is called the Schrödinger
picture, and the formulation in which both change overtime is called the interaction picture. In the fundamental
equation of user dynamics, the linear operator is amatrix that represents the network structure, and thestate vector is the state of the user. Therefore, the time
evolution of the linear operator is the change of therelation between the users, that is, the environmentchanges and the time evolution of the state vector is thetime change of the user's state. Since there are multiple
mathematically equivalent expressions depending on
which one changes over time, it can be recognized that
there are various views on whether the user's state is hisor her personality or is created from the environment.
As stated at the beginning of this section, this meansthat the user and the environment are inseparable.
4. Conclusions
This essay has introduced some of the concepts I
have become aware of in my daily research activities.
Although these are rarely stated explicitly in research7

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IEICE Communications Society – GLOBAL NEWSLETTER Vol. 44, No. 4

publications, they are the ideas that have become theguiding principles for my research activities. I do notknow if they will help others, but if you are interested,feel free to contact me at any time. I hope that we candiscuss related topics together.
5. Acknowledgments
I would like to thank Ms. Kozue Kamikura at Tokyo
Metropolitan University for her comments andimpression on my draft manuscript.
6. References[1] M. Aida, Distributed Control and Hierarchical
Structure in Information Networks, Corona
Publishing Co. Ltd., 2015. (Japanese)ISBN 978-4-339-02803-4

8[2] M. Aida, Introduction to Network Dynamics,
Morikita Publishing Co. Ltd., 2020. (Japanese)ISBN 978-4-627-85511-3[3] M. Aida, “Using a renormalization group to create
ideal hierarchical network architecture with timescale dependency,” IEICE Transactions on
Communications, vol. E95-B, no. 5, pp. 14881500, May 2012.
[4] M. Aida, C. Takano, and M. Murata, “Oscillation
model for describing network dynamics caused byasymmetric node interaction,” IEICE Transactions
on Communications, vol. E101-B, no. 1, pp. 123136, Jan. 2018.
[5] M. Aida, C. Takano and M. Ogura, “On thefundamental equation of user dynamics and thestructure of online social networks,” proc. NetSciX 2020: Sixth International Winter School andConference on Network Science, pp. 155-170,
Springer, 2020.
ISBN 978-3-030-38965-9