Domino Effects within a Chemical Cluster: An Evolutionary Game Approach
Jun Wu1, Hui Yang1, Yuan Cheng2
1
School of Economics and Management, Beijing University of Chemical Technology, Beijing, China
2
School of Mechanical and Electrical Engineering, Beijing University of Chemical Technology, Beijing,
China
Abstract
In a chemical cluster, there are a large number of enterprises, which are adjacent, so that their risk not only
depends on own risk management strategies, but also on those of all others. With this, how to prevent domino
effect is becoming more and more essential. Consider external domino effects, while some enterprises take a
certain level of security investment, there is a certain probability, it can maybe influenced by other enterprises,
which do not make security investments. When a enterprise takes security investment, the probability of
accident within the enterprise will decrease. In this essay, by using security investment model, with
investment utility function, a evolutionary-game model to resolve the action of chemical enterprises,
analyzing what is the evolutionary stable strategy, to maximize social utility.
Key Words: Domino Effect; Evolutionary- game; Utility Function; Chemical Cluster
1
Introduction
The chemical cluster includes hundreds of chemicals, sometimes thousands, which is located adjacent to each
other. Enterprises in the chemical cluster are not only through technology spillovers, logistics advantages, but
also take care of the safety and security requirements through the entire cluster. There are profit opportunities,
economies of scale accompanied by standards of safety and security in the chemical cluster. The average
position of safety and security will reduce with each additional enterprise. Due to technical problems and
safety management, chemical accidents are more frequent, with severity of accidents also tend to increase (F.I.
Khan,1999).
Domino risk' is a term by which the potential for an escalating interaction between groups of chemical
installations in the event of an accident at one of the installations is connoted. The term domino effect thus
denotes a `chain of accidents' (G. Reniers and W. Dullaert, 2009). A domino effect means that the accident
(the so-called domino event) is cascade, in which the consequences of an accident previously was an increase
of one of the following (second), space and time, resulting in a major accident. Thus, the domino effect means
that a major accident on the main installation, induce one or more minor accidents (times). Domino accidents
can be defined as ``a previous accident is increased through spatially and temporally by the following ones,
which cause a cascade of events and became a principal accident" (Delvosalle,1998). Some work has been
focused in developing strategies to evaluate the domino effect not only inside the industrial areas but also to
prevent external effects (Salzano, and Cozzani,2005). Because of the domino effect in the chemical cluster,
the severity of chemical accidents will increase significantly. The large fraction, 89 percent of domino events
are flammable substances, petroleum products, downstream hydrocarbons, and condensed phase explosives
are the substances most commonly involved ( Bahman and Tasneem,2010).
In the book ―Domino effects in the process industries, modelling, prevention and managing" (Reniers and
Cozzan,2013), authors illustrate the characteristics of domino accidents in detail. In some closely related
surveys, the significance of the domino effect in the severity of the major accidents in the chemical cluster is
stressed, but until now, domino accidents do not attract sufficient attention of people.
It is interested to discuss domino effect security investment from a game-theoretic viewpoint, because of the
interaction of enterprises' accident in the chemical cluster, the choice of enterprises with the security
investment strategies is a process of game, the security investment strategy of a enterprise will be impacted by
other enterprises' choices. With game theory, there is a so-called Nash equilibrium for a two- enterprise game
and a evolutionary stable strategy for a n-enterprise game with evolutionary game.
Following section studies the relevance of game theory and evolutionary game which can prevent a domino
effect in the chemical cluster, and to develop research questions. Section 3 mathematically models the
Domino Effect Game. In Section 4 a two-enterprise and n-enterprise example are provided assuming
theoretical figures. Section 5 concludes this article.
2
Research question
In a chemical cluster, the risk of various enterprises is interdependent, each enterprise independently decide
whether to invest, therefore, even if an enterprise take security investments, there is probability that it may
receive the impact of other enterprises. The purpose of this article is discussing the choice of enterprises'
security investment, Nash equilibrium for a two-enterprise game and evolutionary stable strategy for a
n-enterprise game with evolutionary game.
External domino risk is that an enterprise maybe effected by other enterprises in the chemical cluster, these
so-called `negative externalities' are an important characteristic in what we call the ``Domino Effect Game"
(DE Game). Based on Heal and Kunreuther (2007), the DE Game is classified as a game with negative
externalities, which are defined as potential impact that one enterprise can impact on another enterprise.
Domino effects within one enterprise may have devastating effects (i.e., `negative externalities') on the entire
chemical cluster.
Game theory under domino effects is widely considered, in the paper of a game-theoretical approach for
reciprocal security-related prevention investment decisions, Reniers and Soudan (2009) apply
game-theoretical approach offering an indication to enterprises of the win-win circumstances of
security-related prevention and might thereby prove to be very significant in the prevention of incidents
intentionally designed to damage. Enterprises (adjacent chemical enterprises) in the reciprocal security game
may end up by a socio-economic sub-optimal Nash equilibrium (i.e., a win-win situation of strategic decisions)
instead of the unstable collective self-interest equilibrium. However, there is a little attention to the cross-plant
safety-related prevention under the domino effects in chemical cluster. In the paper of a external domino
effects, Reniers et al.(2009) discuss the extent to which game theory is suitable for external safety policy
within a two-company chemical cluster. In the game, there is interdependent between the adjacent enterprises,
the external domino effects game to be a mixed-motive game without a single equilibrium point. When a
sufficiently low cost or deliberate incentive is given, enterprises are willing to cooperate, achieving social
utility maximized.
There are maybe a large number of enterprises in chemical cluster, which are interdependent, so that it is
critical for discussing more than two enterprises. In the paper of domino effects within a chemical cluster,
Reniers et al.(2010) discusses at least three chemical enterprises in the chemical cluster, by a game theoretic
approach, considering whether there is a possibility that by changing the choice of some enterprises, to trigger
the rest of enterprises alter from a socially non-optimal situation to a socially optimal situation.
In this article, our target is forecasting the outcome of the external domino effect prevention, whether
enterprises will choose invest or not. Take two enterprises for example, based on utility function, one
enterprise can be aware of the strategic made by the other enterprise. According to the previously mentioned,
in the real chemical cluster, there are more than two enterprises, so we further discuss n enterprises in
chemical cluster, with evolutionary game, enterprises can change strategy based on other enterprise, whether it
can reach a stable strategy.
Because of the probability of accident occurring is very low, even if taking security investment, the
probability of accident occurring decreases a little, so that many chemical enterprises are not willing to invest,
even worse, one enterprise may be impacted by other enterprise, which may not invest. If enterprises believe
that, whether their neighbour invests or not, the enterprises' strategy to `not invest' is always better than `to
invest', it will not invest. If enterprises believe that, whether their neighbour invests or not, the enterprises'
strategy to `not invest' is always worse than 'to invest', it will invest. There are some situations besides the two
circumstances, which we will discuss in latter.
In this article, our research question is, with static game, under different level of security investment, what is
Nash equilibrium with a two-enterprise game, with dynamic game, whether evolutionary stable strategy with a
n-enterprise game is invest or not, with a limited rationality.
3
Notions on evolutionary game theory
Game theory involves some individual, team or other organization, facing certain environmental conditions,
rules, simultaneously or successively, one or more times, allows the selection to choose from their behavior or
policies, each corresponding achieved the results of the process. The external domino effects game can be
classified as a two-person mixed-motive game of strategy (Kelly,2004 and Barron,2008).
The most classic game model is `martyrdom game', which is characterized with a conflict between individual
self-interest and collective self-interest. A martyrdom game has one Nash equilibrium point. Another
well-known model is the snowdrift game, which has been widely employed to investigate the issues covering
cooperative behavior (Szabó,Szolnoki, Szolnoki). The snowdrift game is based on the action of the co-player:
to cooperate when the other to cooperate and not to cooperate when the other cooperates. Hence, the external
domino effect prevention investment choices made by every individual chemical enterprise might lead to
socio-economic optimal or sub-optimal situations. If security investment has little effect on the probability of
an accident, there will be very few safe investment enterprises. If the utilities are sufficiently high of security
investment (regardless of whether to invest or not in other enterprises, each enterprise will choose to invest) is
a straight forward example of a socio-economic optimal situation. In the two-person mixed-motive game,
which has two equilibriums: both enterprises are not investing and both enterprises are investing, the former is
maybe worse than the latter. However, the strategy of both enterprises to invest is not stable, each enterprise is
tempted to deviate from it (because of the very low probabilities of an external domino effect occurring, with
low possibility to decrease a accident with the security investment).
The evolutionary game theory is the combination of game theory and dynamic evolution (Maynard, Selten). It
is an extension of the game, is based on limited rationality, multiple game players with fast learning ability,
continue to adjust its strategy, ultimately achieving evolutionary stable strategy. It focuses on the dynamic
equilibrium, not to emphasize the static equilibrium and comparative static equilibrium, which differs from
game theory. Evolutionary game theory has been widely applied in cooperative behavior (Jiang Guoyin,Hu
Bin, Zhou Min, Luo Jianfeng) and strategy selection problem (Tan Jiayin, Zhang Junjun, Han Xiao). The
evolutionary stable strategy (ESS) is the primary content of the evolutionary game model, it describes the
dynamic convergence process to the steady state. The replicator dynamic equations describe the steady state of
the evolutionary game (Hofbauer and Sigmund, 1998).
In the external domino effects game, each enterprise has two choices: invest or not invest. Based on the
relation of utility with invest or not, each enterprise makes a strategy. Due to limited rationality, not all
enterprises can achieve surefire strategy, with fast learning ability, each enterprise adjust itself based on others,
eventually all of the enterprises to adopt the same strategy, that is, evolutionary stable strategy. The
evolutionary stable strategy has two results, invest or not invest. Whether to invest or not, it will maximize
social benefits.
4
The domino effects game model
Consider two adjacent enterprises in our domino effects game, they adopt a measure with security investment,
the level of investment is considered ai or 0, which represents investing in external domino effects prevention
and not investing in external domino effects prevention, respectively.
Let the element pi , j represent the probability that an accident which took place in enterprise i will give rise
to a security accident in enterprise j (in other words, pi , j is the possibility of an external domino effect,
which took place in enterprise j caused by enterprise i ). If i = j , then the element means the possibility for
an internal domino effect in enterprise i . Every enterprise can decide either to invest in external domino
effect prevention or not. If an external domino accident happens, the loss of enterprise i equals u s . If
external domino effect prevention investments are made in enterprise i , the possibility for an internal
domino effect in enterprise i is ( pi ,i  rai ) , for r represents the impact factor of investment level for an
internal domino effect, the same is true for enterprise j .
If enterprise i invests in external domino effects prevention measures (originated at the own enterprise i ),
and enterprise j does not invest in external domino effects prevention measures (originated at the own
enterprise j), then enterprise i incurs the expected loss of an accident from (i) an accident originated within
the own enterprise (i.e., ( pi ,i  rai )u s ), conditioned on there being no accident from enterprise j onto
enterprise i (i.e., times 1  p j ,i p j , j ), plus (ii) the expected loss from an accident from enterprise j onto
enterprise i (i.e., p j ,i p j , j u s ), conditioned on there being no accident initiated within the own enterprise (i.e.,
times 1  ( pi ,i  rai ) ). An analogous loss can be made for enterprise i not investing and enterprise j
investing. If enterprise i and enterprise j don’t invest, then enterprise i has an expected loss from (i) an
accident originated within the own enterprise (i.e., pi ,i u s ), conditioned on there being no accident in
enterprise i caused by enterprise j (i.e., times 1  p j ,i p j , j ), plus (ii) the expected loss from an accident
from enterprise j onto enterprise i (i.e., p j ,i p j , j u s ), conditioned on there being no accident originated
within the own enterprise (i.e., times 1  p j ,i p j , j ). The conditions illustrate the fact that the chemical
equipment can only explode or be destroyed once and that the internal and external accidents do not initiate
simultaneously.
Assume that competition in the business enterprise only consider the cost of profits brought price competition.
Security investment utility function is:
(1)
ui (ai , a j )=xi (ai , a j )  yi (ai , a j )  vi (ai )
Where xi (ai , a j ) is enterprise i in competition with other enterprises, because the cost of security
investment allows enterprises to bring profits relative changes in external competitive conditions change, and
the impact on the enterprise's overall utility value; yi (ai , a j ) is security investment in this process, which is
the economic entities utility value of i caused by the level of investment for enterprises i , j ; vi (ai ) is a
security investment cost of enterprise i , and vi (ai )  0 .
Therefore, take enterprise i for example, take xi (ai , a j )  wi ai a j , wi reflects the change of enterprise i
because of security investment, with respect to enterprise j , its symbols keep (a j  ai ) the same, reflecting
the overall utility contribution of xi for enterprise i . Based on the experience, we can know that, ai has a
negative impact on competitive conditions, a j to have a positive impact on competitive conditions; the
increase in security investments will bring increased cost.
yi (ai , a j )  [1  ( pi ,i  rai )]u c  ( pi ,i  rai )u s [1  p j ,i ( p j , j  ra j )]  [1  ( pi ,i  rai )]u s p j ,i ( p j , j  ra j )
c
u is the normal production benefit without security incidents;
(2)
u s is the loss of enterprise security incidents ;
1
vi (ai , a j )  bi ai  cai2
2
(3)
Then, after security investments, the utility of the enterprise i is:
1
ui (ai , a j )  wi ai a j  [1  ( pi ,i  rai )]u c  ( pi ,i  rai )u s [1  p j ,i ( p j , j  ra j )]  [1  ( pi ,i  rai )]u s p j ,i ( p j , j  ra j )  bi ai  cai2
2
(4)
For there is no enterprise for security investments, it can be obtained with 0 instead of ai , that is:
xi (ai , a j )  zi ai  z j a j
(5)
For enterprise i , ai has a negative impact, while a j has a positive effect, so that, zi <0, z j > 0.
To research whether it is possible in the n-enterprise case study for obtaining a socio-economic optimal
situation of both enterprises investing in external domino effect prevention, we have to establish
two-enterprise matrix with the utility.
Table 1: the utility matrix of the game
Enterprise2
a
0
Enterprise1
a
u1 (a, a) ,
u2 (a, a)
u1 (a, 0) ,
u2 (a, o)
0
u1 (0, a) ,
u2 (0, a)
u1 (0, 0) ,
u2 (0, 0)
Assuming enterprises 1 and 2 are two identical enterprises, it can be seen: w = 0, so that pi , j  p j ,i  t ,
z1   z2  z , respectively, the utility function:
u1 (0,0)  u2 (0,0)  (1  p)u c  pu s (1  tp)  tpu s (1  p)
1
u1 (a,0)  u2 (0, a)  za  [1  ( p  ra)]u c  ( p  ra)u s (1  tp)  tpu s [1  ( p  ra)]  ba  ca 2
2
u1 (0, a)  u2 (a, o)   za  (1  p)u c  pu s [1  t ( p  ra)]  t ( p  ra)(1  p)u s
1
u1 (a, a)  u2 (a, a)  [1  ( p  ra)]u c  ( p  ra)u s [1  t ( p  ra)]  t ( p  ra)u s [1  ( p  ra)]  ba  ca 2
2
4.1
A two-player game
We consider the static state selection of enterprises’ investment strategy in the chemical cluster, assuming
there are two identical chemical enterprises, to analysis the Nash equilibrium.
4.1.1
Scenario 1
u1 (0,0)  u1 (a, a)  u1 (0, a)
From it , we can get：
1
1
a  [ z  ru c  ru s (1  2tp)  b] / ( c  2tr 2u s ) a  [ru c  ru s (1  t  4tp)  b] / ( c  2tr 2u s )
2
2
The model is a prisoner's dilemma game, with a stable equilibrium: (0, 0), when investing in the other, the
player's strategy is not to invest, so the both players tend not to invest, and ultimately reach a stable
equilibrium (0, 0). If both of enterprises take strategy of not investment, the utility of enterprise is u1 (0, 0) , if
one enterprise deviates from this equilibrium, it is not stable. The equilibrium (a, a) is better than the Nash
Equilibrium, but it is unstable as enterprises plan to deviate from it.
4.1.2
Scenario 2
u1 (0, a)  u1 (a, a)
u1 (a,0)  u1 (0,0)
From it , we can get：
1
1
[ z  ru c  ru s (1  2tp)  b] / ( c)  a  [ z  ru c  ru s (1  2tp)  b] / [ c  2tr 2u s ]
2
2
It shows a coordination game with two stable equilibria, (0, 0) and (a, a) . This is a mixed-motive game of
strategies and there is no dominant strategy in the game. If both players take security investment, the risk of
external domino effects will reduce. In this case, the cluster reaches an optimal socio-economic situation. In
scenario 2, equilibrium (a, a) utility is higher for each player than equilibrium (0, 0). The characteristic of
this method is not perfect, but complete information, and based on completely rationality, both players will
choose a strategic of safe investment. The game is no longer a martyrdom game and the socio-economic
optimum is reached. If based on limited rationality, both players will not choose a strategic of safe investment,
the game is a martyrdom game and is not to reach the socio-economic optimum.
Let the probability of the use of investment strategies is p A , the probability of not use investment strategies
is 1  p A , whether the other’s strategy is investment or not, the utility is Identical.
pAu1 (a, a)  (1  p)u1 (a,0)  pAu1 (0, a)  (1  p)u1 (0,0)
1
From it, we can draw: pA  [ ca  (b  z )  ru c  ru s (1  2tp)] / (2tr 2 au s )
2
When the probability of a enterprise to adopt investment strategy is p A , the two sides cannot change the
game by a single random probability distribution of their own to change their expectations of utility, so the
mixed strategy combination is stable.
4.1.3
Scenario 3
u1 (0, a)  u1 (a, a)
u1 (0,0)  u1 (a,0)
1
2
From it , we can get： a  [ z  ru c  ru s (1  2tp)  b] / ( c)
It shows a game with one stable equilibria (a, a) , whether or not to invest in each other, because of
u1 (0,0)  u1 (a,0) , the player will choose to invest, it will contribute to the other take security investment,
eventually reach a stable equilibrium (a, a) , based on the utility, both players would not choose to deviate
from it, so it is a stable strategy.
4.1.4
Scenario 4
u1 (0,0)  u1 (a,0)  u1 (a, a)  u1 (0, a)
From it , we can get：
1
a  [ z  ru c  ru s (1  2tp)  b] / ( c)
2
1
a  [ z  ru c  ru s (1  2tp)  b] / ( c  2tr 2u s )
2
It shows a snowdrift game with two stable equilibria, (a, 0) and (0, a) . Because of u1 (0,0)  u1 (a,0) ,
when there is no one to invest, the other investment utility will be greater than not investment;
u1 (a, a)  u1 (0, a) , when one to invest, the other’s investment utility will be lower than not investment. So
the best strategy depends on the other side of the game, if the other’s choice is investment, the best strategy is
not to invest in game; if the other’s choice is not investment, the best strategy is to invest.
4.2
A n-player game
We consider the dynamics selection process of enterprises’ investment strategy in the chemical cluster,
assuming there are n identical chemical enterprises in the chemical cluster, the proportion of use security
investment strategy is x , the proportion of not use security investment strategy is (1  x) , the expected
utility of the two strategies were u1x and u2 x ;
u1x  xu(a, a)  (1  x)u(a,0)
u2 x  xu(0, a)  (1  x)u(0,0)
Average utility of enterprises：
u  xu1x  (1  x)u2 x
The replicator dynamic equation of enterprises, with not use security investment strategy
F ( x) 
dx
1
 x(u1x  u)  x(1  x)[ za  ba  ca 2  rau c  rau s (1  2tp)  2 xr 2a 2tu s ]
dt
2
The replicator dynamic has three stable points:
1
x  0, x  1, x  [ ca  (b  z )  ru c  ru s (1  2tp)] / (2tr 2au s )  q
2
4.2.1
Scenario 1
1
2
q>1, solving equation, it can be drawn: a  [ z  ru c  ru s (1  2tp)  b] / ( c  2tr 2u s )
The game model
has two stable points x = 0, x = 1, replicator dynamic phase diagram as shown in figure 1:
Figure 1: replicator dynamic phase diagram
As can be seen from the figure, x = 0 is the game's evolutionary stable strategy, x = 1, x = q is not the
game's evolutionary stable strategy.
According to the replicator dynamic phase diagram can be seen that when the initial x-fall interval is (0, 1),
the replicator dynamics will tend to zero, all enterprises would choose to invest in the game.
It can be seen that when the level of investment is bigger than a fixed value, the limited degree of rationality
enterprises with fast learning ability, will gradually adjust their investment strategies according to the adjacent
enterprises' strategy until all enterprises don't take the security investment, achieving evolutionary stable
strategy.
4.2.2
Scenario 2
0<q<1, solving equation, it can be drawn:
1
1
[ z  ru c  ru s (1  2tp)  b] / ( c)  a  [ z  ru c  ru s (1  2tp)  b] / [ c  2tr 2u s ]
2
2
The game model has three stable points x = 0, x = 1, x = q , replicator dynamic phase diagram as shown
in figure 2:
Figure 2: replicator dynamic phase diagram
As can be seen from the figure, x = 0, x = 1 is the game's evolutionary stable strategy, x = q is not the
game's evolutionary stable strategy.
According to the replicator dynamic phase diagram, it can be seen that when the initial x-fall interval is (0,
q ), the replicator dynamics will tend to zero, all game players will not choose to invest; When the initial
x-fall interval is ( q , 1) , the replicator dynamics will tend to 1, all enterprises will choose to invest in the
game.
We can know that when the level of investment in a given interval, the number of enterprises choose the
investment strategy will affect the investment decisions of other enterprises in the limited degree of rationality,
enterprises with fast learning ability, according to the adjacent enterprises’ strategy to gradually adjust their
investment strategies until all enterprises take security investments or not, to achieve evolutionary stable
strategy, social maximized.
4.2.3
Scenario 3
1
2
q<0, solving equation, it can be drawn: a  [ z  ru c  ru s (1  2tp)  b] / ( c)
The game model has two stable points x = 0, x = 1, replicator dynamic phase diagram as shown in figure
3:
Figure 3: replicator dynamic phase diagram
As can be seen from the figure, x = 1 is the game's evolutionary stable strategy, x = 0, x = q is not the
game's evolutionary stable strategy.
According to the replicator dynamic phase diagram, we can draw it that when the initial x-fall interval is (0, 1),
the replicator dynamics will tend to 1, all game players will choose not to invest.
It shows that when the level of investment is lower than a fixed value, the effectiveness of security investment
will be more than the utility without security investment in a limited degree of rationality, enterprises with fast
learning ability, according to the adjacent enterprises' strategy gradually adjust their investment strategy until
all enterprises do invest, to make evolutionary stable strategy, social maximized.
From these scenarios, we can draw some conclusion:
(1) When the level of investment a is less than a fixed value, as long as there are enterprises investing, which
will encourage other enterprises to adjust their investment strategies until all enterprises take security
investments, that is evolutionary stable strategy, social utility reached maximum.
(2) When the level of investment is between a range, if the proportion of not investment enterprises is more
than evolutionary stable point, will encourage other enterprises to invest, until all enterprises to invest. If the
proportion of not investment enterprise is less than evolutionary stable point, will encourage other enterprises
not to invest, until all enterprises not to invest.
(3) When the level of investment a is more than a fixed value, as long as there are enterprises not investing,
which will encourage other enterprises to adjust their investment strategies until all enterprises don't take safe
investments, that is evolutionary stable strategy, social utility reached maximum.
4.3
Comparation
From the above comparison of static and dynamic game, we can know that, static game is a manifestation
form of the dynamic game. With the static game, two enterprises make a choice simultaneously, the focus of
study is a Nash equilibrium; with the dynamic game, it is a dynamic process of selection of enterprises'
strategies, the game will reach a evolutionary stable strategy accompanied by continuous learning. The
substance of both are identical, the result is also the same.
5
Conclusion
This paper discussed whether game theory is appropriate to security investment based on external domino
effects within a two-enterprise game and a n-company game in chemical cluster. The risk of enterprises'
accidents are interdependent, the utility of security investment can be depicted a strategic game. We suppose
all the enterprise are identical, there are a certain percentage of enterprises have chosen to invest, because of
interdependence, they constantly adjust strategies until reach the evolutionary stable strategy.
In the article, we apply utility function to represent gains, which is composed by three parts, based on it, each
enterprise choose whether to invest. Enterprises do hope to obtain a stable equilibrium, while they do not
automatically tend towards a socio-economic optimum. The article firstly discusses two enterprises with game
theory, then discusses n enterprises with evolutionary game. With different level of security investment, the
evolutionary stable strategies are various.
Based on this, enterprises can take a security investment, which is not only in favor for itself, but also other
enterprises in the chemical cluster. Security investment of the external domino effects may result in higher
utility and lower probability of accident in the chemical cluster.
The proposed approach will be conducted to further refine and to research more complex real-life problems in
future studies.
Acknowledgement
This study is supported by the NSFC (71072157, 71372195) and Fundamental Research Funds for the Central
Universities (ZZ1317).
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