Reinforced communication and social navigation: remember your friends and remember yourself

0.51 MB·English

by  Atieh Mirshahvalad

Reinforced communication and social navigation: remember your friends and
remember yourself
A. Mirshahvalad∗ and M. Rosvall†
Integrated Science Lab, Department of Physics, Ume˚a University, SE-901 87 Ume˚a
(Dated: January 27, 2011)
Insocialsystems,peoplecommunicatewitheachotherandformgroupsbasedontheirinterests.
The pattern of interactions, the network, and the ideas that flow on the network naturally evolve
together. Researchers use simple models to capture the feedback between changing network pat-
ternsandideasonthenetwork,butlittleisunderstoodabouttheroleofpasteventsinthefeedback
process. Hereweintroduceasimpleagent-basedmodeltostudythecouplingbetweenpeoples’ideas
andsocialnetworks,andbetterunderstandtheroleofhistoryindynamicsocialnetworks. Wemea-
1 sure how information about ideas can be recovered from information about network structure and,
1 theotherwayaround,howinformationaboutnetworkstructurecanberecoveredfrominformation
0 about ideas. We find that it is in general easier to recover ideas from the network structure than
2 vice versa.

n
PACSnumbers: 01.20.+x,89.75.Fb,89.65.Ef
a
J

6 I. INTRODUCTION [8, 9], and the continuous relative agreement model by
2 Deffuant et al. [10, 11] all belong to the class of models

We live in the information age; in seconds, news can that study group formation in social systems based on a
]
h spread around the world through the means of modern static underlying structure [11, 12]. But as groups form
p information technology. Still, everyday communication innetworkswithpreexistingheterogenousstructures,one
c- with family, friends, and colleagues plays a major role question remains unanswered: Where do the communi-
o in how information percolates through society. When tiesinreal-worldnetworks[13–15]comefrom? Andmod-
s this private communication is constrained to who talks els that rely on preexisting heterogenous ideas or opin-
s. to whom, information cannot move freely and will not ions [16] leave unanswered the complementary question:
c be shared by everybody. Consequently, the pattern of Wheredidtheideascomefrom? Tounderstandthebasic
i
s interactions, the network, affects who knows what and question of how groups form in social networks, we must
y when. But this network is not static; rather, it changes consider ideas and structure simultaneously.
h
over time and peoples’ current ideas will influence how
p Becauseoftheinteractionbetweenstructureandideas
[ new interactions form. Inevitably, the network and the insociety,weneeddynamicnetworksandtoallowfordy-
ideas that flow through the network are inseparable and namics on the network. Therefore, recent works on the
1
evolvetogether. Moreover,pastevents,storedinpeoples’
v problem of group formation have focused on co-evolving
interest memories and the network structure, also affect
8 networksinwhichpeople’sinteractionsinfluencethenet-
futureevents. However,howthismemoryintegrateswith
4 work structure, and vice versa [17, 18]. For example,
0 social dynamics and what role history plays in the pro- Holme and Newman proposed a model in which a sin-
5 cess is still unclear. For a better understanding, here
gle parameter controls the balance between the two pro-
. we investigate in a simple model how information about
1 cesses: how ideas generate connections and how con-
0 ideasisstoredinthenetworkandhowinformationabout nections generate ideas [19]. They observed a contin-
1 the network is stored in ideas. uos phase transition from a heterogeneous distribution
1 Since we don’t share all our information with every-
of opinions to consensus. Kozma and Barrat gener-
: body, but rather limit most communication to friends
v alized Deffuant’s model to adaptive networks, allowing
i [1], networksprovidegoodtoolsforstudyingsocialorga- agents with similar opinions to communicate and forc-
X
nization [2]. To access remote connections, we must use
ing agents with sufficiently different ideas to cut their
r local information [3], and the remote connections are in
a connections [20]. They showed that adaptive networks
practice established by the flow of information through
facilitate group formation, and that consensus in adap-
the network [4]. In principle, everybody is connected to
tivenetworksishardertoachievethaninstaticnetworks.
everybody in society, but only indirectly [5]. Therefore,
Nardini and Kozma showed that when agents can have
the simplest approach to understanding how ideas form
several opinions at the same time, for example, in the
insocialsystemsistousestaticnetworksandstudyhow
naming game model [21], they more easily form consen-
information flows across those networks. For example,
susinadaptivenetworks[22]. Kumpulaetal.focusedon
the binary Voter model [6, 7], Sznajd’s consensus model
thecouplingbetweenthenetworktopologyandtheinter-
actionintensitybetweenagentsinamodelwithweighted
links [23], thereby highlighting the structural feedback
∗ [email protected] ratherthantheinformationspreadinginsocialnetworks.
† [email protected] As they increased the coupling, they observed more and
2
more distinct communities. For all these models, groups II. MODELING COMMUNICATION AND
emerge because people align their ideas with neighbors SOCIAL NAVIGATION
throughcommunicationormovetowardlike-mindedpeo-
ple and away from others in the network. Groups evolve In our previous work, we developed a model for com-
gradually over time, and history will inevitably play an munication and social navigation based on the notion
important role in the dynamics. that people use local interaction to access global infor-
mation. To illustrate how local interactions give ac-
cess to global information, let us consider the example
Theintrinsicmemoryofthesysteminfluencesthefeed- of the Ph.D. student who is looking for a postdoc po-
back between structure and ideas. Past events leave be- sition [17]. During the graduation period, the student’s
hindimprintsinpeoples’currentinterestsandthefriends scientific interest becomes similar to her supervisor’s in-
theyhave,whichwillaffecttheirfuturedecisions. There- terests. When she searches for a postdoc position she
fore, if we want to understand the dynamics of the sys- will, with high probability, go to one of her supervisor’s
tem, we must understand how past experiences are inte- scientific colleagues who themselves have influenced and
grated in the memory of the system. Some of this infor- been influenced by the supervisor. When people navi-
mation is stored in peoples’ interest memories and some gate social networks to get better access to interesting
in the interaction pattern among people. In this way, information, they use information that travels across the
the rich dynamics of social systems are influenced both network, propelled by communication.
by past events stored in the different memories of the Whenpeoplecommunicatewiththeirfriendstogather
system and by the information transfer between those information, they integrate the social system. The more
memories. Here we focus on the latter and ask: To what we communicate, the more up-to-date is our informa-
degree can ideas be recovered from the network struc- tion. But there is another way to get better access to
ture, and, the other way around, to what degree can the up-to-date information: People can navigate their social
interaction pattern be recovered from peoples’ interests? landscape. When we contact a friend’s friend, we short-
cutinformationpathwaysandapproachthesourceofin-
formation. In ref. [17], we showed that reinforced com-
munication and social navigation generate social groups.
To investigate how much people’s ideas can be recov-
Socialgroupsemergebecauseagentsbuildself-organized
ered from the interaction pattern and how much the in-
maps of the network and navigate toward like-minded
teraction pattern can be recovered from people’s ideas,
agents. Theself-organizedmapshelpagentstoaccessin-
we choose an agent-based model framework with agents
formation beyond their nearest neighbors. Here we show
that can store and transmit information. With agents
that we can, in the limit of high communication, use the
that gather information by communicating with each
shortest path as a proxy for the self-organized map and
other and store this information in an interest memory,
simplify the model. In the next section, we describe our
we have shown that global knowledge can emerge from
simplified model framework in detail, and in Appendix
local communication [17]. The interest memory, which
A, we show that our simplified model can capture the
represents the agents’ priorities, naturally brings history
same dynamics as the more complex one.
into the model framework. To illustrate, assume a sce-
nario in which a potential buyer uses his friendship net-
work to look for a good deal on a car. After gathering
informationthroughhisnetwork—thebuyertalkstohis A. Model Definition
car-enthusiastfriend,whotalkstoacardealerfriendwith
theperfectcarinstock—heshowsupatthedealer. But Here we explain the main components of our model
thedealerisnolongerwillingtosellthecarattheagreed to better understand how past events stored in peoples’
price. The buyer’s car-enthusiast friend and the dealer interests and in the network structure, and the informa-
are in conflict, and the car is now reserved for another tion transfer between those memories, influence social
buyer. Obviously, inthisscenariothebuyer’sdecisionto dynamics. Ourmodelhastwomaincomponents: Agents
visit the dealer is based on out-dated information. Over communicateandnavigatetheirsocialnetworktogetac-
time, through repeated local communication events, the cess to information they are interested in. To implement
buyer has built and stored in his memory an interest in communication and social navigation in a simple model,
the dealer. But the interest memory is a reflection of agentshavealistofotheragents’identitiesthatrepresent
past states of the network rather than the current state their interest in other agents and a list of friends with
of the network, and the buyer makes a mistake. From whom they can communicate. When agents communi-
this example, we see that, to better understand the role cate they talk about their interests. That is, the topics
of history in social dynamics, a minimal model need not ofcommunicationarerestrictedtotheagentsthemselves.
contain more than the network and the agents’ interest We run the system with N = 100 agents and L =
memory. Therefore, in the next section we present a 200 links, and give each agent a an interest memory of
i
minimal version of the agent-based model presented in size M . In principle, the agents’ memories can vary in
i
ref. [17]. size, but for simplicity, we set the memory size to the
3
system size. That is, each agent a stores M =N agent our simulations at R = 0.5 if we do not mention other-
i i
indices in an array that represents the interest memory. wise.
The number of times a specific agent occurs in the array In detail, in each time step, with probability 1−R we
reflects the relative interest in that agent. do L communication events as follows (see Fig. 1(a)):
When two agents communicate, one of the agents
1. We pick two agents. A random agent a with at
choosesatopicfromitsinterestmemoryandbothagents i
least one link picks one of her friends a propor-
updatetheirinterestmemoriessothattheybecomemore j
tional to her interest in a .
interested in the topic and also in each other (Fig. 1(a)). j
In our previous model, the agents stored the age of the
2. Wepickthetopic. Agenta ora ,chosenrandomly,
i j
informationtheyreceivedandwhoprovidedtheinforma-
picksthetopica proportionaltoherinterestina .
k k
tion. When agents knew who provided the most recent
information about a specific agent, they knew who to 3. We let them exchange information. Agents a and
i
talk to to access information about this agent. To sim- a replacestworandomelementsintheirmemories
j
plifythemodel, hereweusetheshortestpathasaproxy with the other agent’s identity and the topic a .
k
fortheself-organizedmap. InAppendixA,weshowthat
With probability R, we do 1 social navigation step as
we can recover the same dynamics as long as communi-
follows (see Fig. 1(b)):
cation dominates over social navigation. To shortcut the
information pathways for better access to information,
1. Wepickoneagentandhertarget. Arandomagent
agents can navigate their social network and establish
a pickstargeta proportionaltoherinterestina .
i k k
connections to their friends’ friends (see Fig. 1(b)).
2. We calculate the information route. Agent a is
l
(a) (b) agent a ’s friend’s friend on the shortest path be-
i
tween agent a and a .
k i
3. We rewire. Agent a adds a link to agent a and a
i l
i i random agent loses one link.
TherewiringratioRcontrolsthetwo-wayinformation
transfer between the interest memory and the network
j j structure. The other parameter we use is the external
k k
noise probability P . The external noise captures the
l noise
conceptthatreal-worldcommunicationisnotalwaysper-
fect,butisalwaysinfluencedbyexternalfactors(TV,ra-
FIG. 1. Modeling communication and social navigation. dio, the Internet, etc). We implement the external noise
(a) Communication: A random agent a selects one of her with probability P by adding a random agent to an
i noise
neighbors a proportional to her interest in a . In the same agent’s interest memory instead of the current topic. As
j j
fashion, one of the two agents selects agent ak from her in- we demonstrate in Appendix A, external noise plays the
terest memory. When agent ai and aj communicate, they same role as memory size in our previous model [17]: At
increase their interest in each other and also in agent a .
k high noise, the system forms a centralized system with
(b)Socialnavigation: Arandomagenta selectsanagenta
i k hubs, and at low noise, the system self-organizes a mod-
proportionaltoherinterestina ,andfindsherfriend’sfriend
k ular structure both in interest and network structure. In
a on the shortest path between a and a . Agent a forms a
l k i i our analysis below, we set the noise level to 1 percent,
link to a and shortens her distance to a . To keep the num-
l k
which generates modular structures.
ber of links fixed in the network, a random agent loses one
random link.
Whenagentscommunicate,theyadapttheirmemories III. RESULTS AND DISCUSSION
tothecurrentnetwork,andwhentheynavigatethesocial
network, they seek new friends to meet their current in- Reinforcedfeedbackbetweeninterestmemoryandnet-
terests. Wecontroltheratiobetweencommunicationand work structure generates modular networks. We always
social navigation with the rewiring parameter R. When initiate the system randomly and run the game of com-
R = 0, the agents only communicate and the interests munication and social navigation for a long time before
fluctuate around a steady state that depends on the net- analyzingtheoutcome. Figure2(a)showsatypicalmod-
work configuration. Conversely, when R =1, the agents ularoutcomeattimet ,wheneverylinkhasbeenrewired
1
onlyrewireandthenetworkfluctuatesaroundaconfigu- hundredsoftimes. Figures2(b)and(c)showthesystem
ration that depends on the state of the agents’ interests. at time t , when every link on average has been rewired
2
In this paper, we study intermediate values of R, which one more time. In Fig. 2(b) we have continued the pro-
generateever-changingdynamicstructures. Wescalethe cesswithfeedback,andnotonlydoesthenetworkremain
communication-to-navigation ratio such that L commu- modular, but agents also preserve their neighborhoods.
nication events correspond to 1 navigation step and run In contrast, Fig. 2(c) shows the outcome when we turn
4
off the feedback at time t and agents no longer base with feedback because the current network structure af-
1
their interests on communication with their friends. As fectstheinterestdynamicsandthecurrentinterestmem-
aresult,thenetworkloosesallmodularfeatures;without ories affect the network dynamics. They are two differ-
feedback, agents do not preserve their neighborhoods. ent memories about the state of the system connected
bythefeedback. Becauseagentsgatherinformationover
time, their memories do not reflect a specific network
configuration, but rather they reflect the configurations
(b) of networks of the recent past. To quantify how well
the interest memory reflects past networks, in the inset
of Fig. 3(a) we show the Hamming distance of memory
betweenagivenpointintimeatequilibriumandtheref-
erencepointoutofequilibrium. Toreachequilibrium,we
(a)
stop rewiring and let the agents communicate for a long
time.
The negative values from a few time steps before the
reference time mean that the current interest memory
(c) in fact better captures the system of the recent past
thanthecurrentstate. Naturally,thefeedbackalsoslows
down the network dynamics. Figure 3(b) shows that the
network evolves more slowly toward the reference point
with feedback than without.
InterestMemory NetworkStructure
1 1
e e
c c
FstIrGuc.tu2.re gFeeneedrabtaecskmboetdwuelaernninettweroersktsminemwohriychanadgenntestwporrek- gdistan00..68 0.12 Equilibrium gdistan00..68
sfoerrmveetdheairmnoeidguhlbaorrnheotowdosr.k(aa)tWtimithefte1e.db(abc)kC,tohnetiangueinntgshwaivthe ammin0.4 00..00048 ammin0.4 withoutfeedback
feedback, the agents have preserved their neighborhoods at H0.2 (a) H0.2 (b)
withfeedback
time t , when every link on average has been rewired one -50 -25 0.0
2 0 0
more time. (c) Continuing without feedback, the agents can- −400 −300 −200 −100 0 −400 −300 −200 −100 0
not preserve their neighborhoods and the modular structure Time Time
breaks down.
FIG. 3. Feedback between interest memory and network
structure slow down the dynamics of the system. (a) The
Feedbackbetweeninterestmemoryandnetworkstruc-
Hamming distance of the agents’ interest memories between
ture makes all the difference when the system evolves agiventimeandthereferencetimeatt=0,withandwithout
over time. With feedback, we see slow dynamics be- feedback. The inset shows the Hamming distance at equilib-
cause agents gradually adapt themselves to the changes rium (infinite communication) relative to the reference time
inthesystemwithoutforgettingtheirpastknowledgeall out of equilibrium. (b) The dynamics of the network struc-
at once. In contrast, without feedback, agents quickly ture with and without feedback. In one time unit, all links
adjust themselves to the changes in the system and for- have been rewired once on average.
get their previous picture of the system. In Fig. 3, we
quantify the rate of change with and without feedback Becauseofthefeedbackbetweenmemoryandnetwork,
between the interest memory and the network structure. every agent is affected both by her neighbors and by her
To measure memory and network distance between a own interest memory. To better understand how much
given point in time and the reference point t = 0, we information is stored in the interest memory and how
tried several metrics and selected the Hamming distance muchisstoredinthenetworkstructure,wemeasurehow
for its simplicity. The Hamming distance for interest much one can be recovered from the other if one of them
memory measures the number of substitutions required is scrambled.
to change an agent’s interest memory from one state Beforescramblingtheinterestmemoriesorthenetwork
into another, averaged over all agents and normalized structure, we run the dynamics at the default rewiring
by dividing by the maximum number of substitutions. rate R = 0.5. At the reference time t = 0, we scramble
Similarly, the Hamming distance for the network struc- the memories by reshuffling the interest memories be-
ture measures the number of substitutions necessary to tweentheagentsorbyreshufflingthefriendsbetweenthe
change an agent’s interest memory from one state into agents. After scrambling the system, we continue with
another, averaged and normalized in the same way. different rewiring ratios to quantify how well the sys-
Figure 3(a) shows that the system evolves much more tem recovers. If, after scrambling the interest memories,
slowly with feedback than without toward a reference agents stop rewiring and only communicate with each
point at time t = 0. The system evolves more slowly other (R = 0), they recover their interest memories to
5
the equilibrium state after a few time steps. Figure 4(a)
0.6 Networkstructure
shows that the smallest rewiring rate prevents recovery
Interestmemory
to the equilibrium state. While the agents communicate
to recover their interests, the social navigation based on 0.5
their new interests makes them gradually diverge from e
c
the unperturbed case. The agents cannot fully recover an 0.4
st
before the network has already changed too much. di
g
n
mi 0.3
InterestMemory,R=0.1 NetworkStructure,R=0.99
m
1 1 Ha
ce ce 0.2
an0.8 an0.8
dist0.6 dist0.6
ng ng 0.1
mi0.4 mi0.4
m m
a a
H0.2 H0.2
(a) Scrambledmemory (b) Scrambledstructure 0
0 Unperturbed 0 Unperturbed 0 0.2 0.4 0.6 0.8 1
−100 −50 0 50 100 150 200 −100 −50 0 50 100 150 200
Rewiringratio(R)
Time Time
FIG. 4. System information is stored both in the agent’s FIG. 5. System recovery after scrambling depends on the
memory and in network structure. (a) Interest memory evo- rewiring ratio. Low communication is necessary for network
lution, R=0.1. (b) Network evolution, R=0.99 structure recovery, and a low rewiring rate is necessary for
interest memory recovery.
To quantify how much information the interest mem-
ories can store about the network structure, we quantify
how well the network can be recovered from the interest One may suggest that expanding the size of the inter-
memory. Figure4(b)showshowthenetworkevolvesover est memories would enhance recovery, but when we ran
time. When we scramble the network at the reference the simulations with memories twice as big, the results
time t = 0, we see a sharp jump in the Hamming dis- were the opposite. With bigger memories, the agents
tanceofthenetworkbecauseagentslosetheiroldfriends can remember longer, but the memories are also less up-
and attach to random new agents. In this case, if agents to-date. At any given time, the memories are farther
stop communicating and only rewire, they reach equilib- from equilibrium and recovery to the present network
rium after a few time steps. But Fig. 4(b) shows that 1 decreases. In contrast to memory recovery, the network
percent communication is enough to break the recovery. recoveryisbetterwhenagentshavelargermemories, be-
The agents find new interests while searching for their cause the agents lose their old friends in favor of new
old friends and they forget their old friends. Therefore, interests at a lower rate.
thenetworkdynamicsdivergefromtheunperturbedcase
and recovery decreases.
To better understand how the feedback affects recov-
ery at different rewiring rates, we measured the recovery
IV. CONCLUSIONS
for R between 0 and 1. Figure 5 shows the results. Very
littlecommunicationisenoughtosignificantlyreducethe
network recovery, because agents gradually forget their Inthispaperwehaveintroducedasimpleagent-based
old friends when they communicate with new neighbors model to quantify and better understand the reinforced
while searching for their old friends. An agent’s typical feedback between changing network patterns and ideas
distancetoagentsofinterestbeforeandafterscrambling thatgeneratessocialgroups. Wehavedemonstratedthat
was 2.6 and 8.4, respectively, which means that after history plays an important role in generating and pre-
scrambling,agentsareroughly3timesfartherawayfrom serving groups in the system. In the communication and
their interests. It is a long way back to the old friends, socialnavigationmodel,wehavestudiedtheinformation
and when agents communicate, they add new topics to transferbetweentheinterestmemoriesofagentsandthe
their interest memories. Consequently, the agents lose network structure. To quantify how much information
interest in their old friends before they come back and about the agents’ ideas is stored in the network struc-
network recovery declines. Interest memory is easier to ture and, the other way around, how much information
recover,becausetheroutebackismoredirectinthesim- aboutthenetworkstructureisstoredintheagents’ideas,
pler space of the interest memory than in the more com- we measured how well agents in the model could recover
plex configuration space of the network structure. But information stored in ideas versus information stored in
inthesamewayasfornetworkrecovery,assoonasthere the network. We conclude that the network structure
is information transfer between the network and the in- contains more information about the agents’ ideas than
terest memories, the recovery declines. the other way around.
6
40 20 100 100 1
s
Kmax123000 (a) (cid:52)/(cid:52)r11055 (b) Typicalmodulesize: 24680000 (c) Socialhorizon 257505 (d) nnlgolcoablal Hammingdistance0.5 (e) IWnsihdoeleclnuesttwerork
0 0 0 0 0
1 10 100 1000 1 10 100 1000 1 10 100 1000 1 10 100 1000 1 10 100 1000
η η η η η
FIG. 6. Reinforced communication and social navigation generate social groups. Network modularity depends on noise
probability. As a function of η = 1 , the panels illustrate (a) the maximum degree in the network, (b) the abundance of
Pnoise
triangles, (c) typical module size, (d) social horizon, and (e) Hamming distance-based measure ∆.
Appendix A: Validating the minimal model number of agents that an agent talks about,
(cid:28) (cid:29)
N
Here we show that, as long as communication dom- n = , (A2)
local <m2(j)>/<m (j)>
inates over social navigation, we can capture the same i i
dynamicsinourminimalmodelasinourpreviousmodel
and n is the typical number of agents whom agents
global
[17]. Both models of communication and social naviga-
talk about in the entire system,
tion show how feedback between interest memories and
network structure generates social groups. In the mini- (cid:28) N2 (cid:29)
malmodel,weusetheshortestpathsasaproxyforcom- nglobal = <m2(j)>/<m(j)> . (A3)
munication pathways and the external noise corresponds
to the memory size η of the previous model [17]. Figure 6(d) shows that, with decreasing noise level,
In Fig. 6(a)-(d), we investigate the same four system n decreases as the agents focus more on a few
local
characteristics as in ref. [17] and show that the results agents in more modular networks. As in the previous
agree. The first three panels of the figure measure the model, n remains fairly constant, which means that
global
structuralpropertiesofthenetwork. Panel(a)showsthe no agents are forgotten. The conclusion gained from
maximum degree against the inverse noise probability, Figs. 6(a)-(d), is that the minimal model presented in
and panel (b) shows the abundance of triangles relative this paper can capture the same feedback dynamics as
to random counterparts of the network. To quantify the the more complex model in ref. [17].
modularity of the networks, we partitioned the networks Because it is interesting to capture the entanglement
[24] into modules of sizes {s } and measured the typical betweenthenetworkstructureandtheinterestmemories,
l
module size s, defined as the average module size that a finally we investigate how much we can learn about the
randomly selected agent is part of, interestmemorybylookingatthenetworkstructure. We
definetheaverageHammingdistanceofmemory∆asthe
(cid:10)s2(cid:11) necessarynumberofeditsbetweentwoagents’memories,
s= l . (A1) normalized by the maximum possible number of edits,
(cid:104)s (cid:105)
l
(cid:28) (cid:29)
# edits
Figure 6(c) shows that the typical module size decreases ∆= i→j . (A4)
max # possible edits
as the external noise decreases. When the external noise
decreases, the agents reinforce their interests in their Figure 6(e) shows, with decreased external noise to the
friends and do not navigate away from their neighbor- right,theHammingdistanceofmemory∆averagedover
hoods. Insmallerandsmallergroups,thedensityoflinks agents in the same module or in the entire network. For
increases and the links form many triangles. The maxi- modularnetworkswithlownoise,twoagentsinthesame
mumdegreedecreaseswithgroupsize,becausethegroup modulesharehalftheirinterestsandalmostnothingwith
size limits the number of friends an agent can have. agents in other modules.
Thetransformationprocessfromacentralizednetwork
toamodularnetworkisalsoreflectedintheagents’inter-
est memories. To measure how the interest memory re- ACKNOWLEDGMENTS
vealsthistransformation,wemeasuredn ,thetypical
local
number of agents that occupy an agent’s interest mem- We are grateful to Kim Sneppen and Deborah Kolp
ory, and nglobal, the total number of agents who receive for many valuable suggestions. MR was supported by
attention from others [17]. That is, nlocal is the typical the Swedish Research Council grant 2009-5344.
7
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