You will be presented with the full text of a science research paper. Please write an abstract for this paper. Your response should include the abstract and no additional text.

Paper text:
our aim here is to study the results of competition of two types of contact processes ( cp ) @xcite in the watts - strogatz network .
the idea is as follows .
the network nodes are assumed to be in one of two states , say s and d. one of cp is the voter dynamics @xcite , where a randomly selected s node changes the state of one of his neighbor from d to s. the other cp is the unifying step of the sznajd dynamics @xcite , where a randomly selected pair of neighboring nodes , once both d , change the state of all their neighbors from s to d. + in a recent text @xcite , a similar competition has been investigated on the watts - strogatz ( ws ) and the erds - rnyi ( er ) networks . also there , one process of activating nodes has been ruled by the voter dynamics , and the other was triggered by a pair of mutually connected nodes .
the difference between that approach and the present work is that in paper @xcite a node was activated by a pair of d nodes only if it was a nearest neighbor of both nodes of the pair . on the contrary , in the sznajd dynamics used here all neighbors of each member of the d pair
are activated @xcite .
we note that the third model of this family is the bootstrap percolation , where nodes of the activating pair are not necessary neighbors of each other @xcite ; the latter model is not investigated here .
+ our motivation is as follows . in @xcite ,
the clustering coefficient @xmath0 was used as a control parameter . in ws , @xmath0
was controlled by rewiring , while in er , it was controlled by adding new links , along the method proposed by holme and kim @xcite .
the results of @xcite indicate , that in ws , tuning of @xmath0 can lead to switching the d process off and on .
namely , the d process is blocked if the clustering coefficient is below some critical value .
this effect is a consequence of the model assumption , that both nodes of the activating pair must be neighbors of the activated node .
the density of triangles is controlled by @xmath0 .
if the triangles in the network are rare , the d process is stopped . to check this conclusion
, we are going to investigate the same process with the sznajd dynamics , where triangles are not necessary .
consequently , the clustering coefficient @xmath0 should be less important . + it is worth to add that the competing cp s enables a more precise measurement of intensity of the investigated process by its comparison with the voter dynamics . in a finite network , in particular a small - world network ,
the process can reach the whole lattice in a few steps . to switch another process on allows to find their mutual intensity when both processes balance each other . in @xcite ,
the voter process was more intense and therefore it was applied with probability @xmath1 , while the d process was applied with probability 1 . here
the situation is opposite ; the sznajd dynamics is applied with the probability @xmath1 , and the voter dynamics with the probability 1 .
we look for the values of @xmath2 where the stationary percentage of both kinds of nodes is 50 - 50 .
fifty ws networks of @xmath3=1000 nodes and degree @xmath4 are prepared by gradual rewiring of randomly selected links , and they are stored when their clustering coefficient @xmath0 is in the range @xmath5 .
the demanded @xmath6 are from 0.5 down to 0.1 .
next we select randomly a given percentage of nodes and assign them to be in the state s ; other nodes are in the state d. + the simulation is performed as follows .
a node is selected randomly ; if it is in the state s , we check all its neighbors .
if there is a node d , it is converted to be s. if the randomly selected node is in the state d , we continue with the probability @xmath1 : namely , we check all his neighbors . if there is a node d , all its neighbors and all the neighbors of the initially selected node ( which appeared to be d ) are converted to be d. having done this , we select another node and continue . the change is done immediately .
+ in each time step , @xmath3 nodes are selected .
there is 2500 time steps .
the results are averaged over 50 networks , except in the case @xmath7 , when there is only one network and the simulation is run 50 times .
the influence of the clustering coefficient @xmath0 on the population of s nodes is most apparent in the range of small initial population of these nodes , then the results to be shown here are obtained in this range . also , their dependence on the initial state is visible there .
+ in figs . 1 and 2 we show the time dependence of the population of s nodes for two values of the clustering coefficient @xmath0 , 0.1 and 0.5 .
we observe that for @xmath0=0.1 ( fig.1 ) the time of simulation is long enough to get the stationary state .
although we have not obtained this state for @xmath0=0.5 ( fig .
2 ) , the results clearly show that in the latter case the relatively large probability @xmath1 of the d process is not enough to reduce the population of s nodes as strongly , as it is found for @xmath0=0.1 .
namely , while @xmath1=0.27 is enough to eliminate s nodes for @xmath0=0.1 , we find that for @xmath0=0.5 s nodes still prevail for @xmath1=0.38 .
+ the results on the population of s nodes after 2500 time steps are shown in figs . 3 and 4 for different values of @xmath0 and two different values of the initial population of s nodes , 0.1 and 0.25 .
the results show how the fall of the observed population of s nodes with the probability @xmath1 depend on the clustering coefficient @xmath0 .
clearly , the larger @xmath0 , the stronger is the process s , as larger values of @xmath1 are necessary to damp the population of s nodes .
+ from these results , we can evaluate the probability @xmath2 when the calculated population of s nodes is 0.5 after 2500 time steps . as shown in fig .
5 , the initial population of s nodes does not change these results qualitatively . in both cases ,
the observed probability @xmath2 increases with @xmath0 from about 0.26 to about 0.4 in the investigated range of @xmath0 .
+    = 0.1 .
the probability @xmath1 is from 0.2 to 0.27 with step 0.01 , in ascending order from the top to the bottom of the graph.,width=472 ]    = 0.5 .
the probability @xmath1 is from 0.20 to 0.38 with step 0.02 , in ascending order from the top to the bottom of the graph.,width=472 ]     for the ws network ( 10 percent of all 1000 nodes are initially s - nodes ) for different clustering coefficient @xmath0= 0.1 , 0.2 , 0.3 , 0.4 and 0.5 ( curves from left to right , respectively),width=472 ]     for the ws network ( 25 percent of all 1000 nodes are initially s - nodes ) for different clustering coefficient @xmath0= 0.1 , 0.2 , 0.3 , 0.4 and 0.5 ( curves from left to right , respectively),width=472 ]     against the clustering coefficient @xmath0 for the ws network for different initial s - nodes participations equal to 10 percent ( bottom curve ) and 25 percent ( top curve).,width=472 ]
the results indicate , that the s process is relatively more active for ws networks with large clustering coefficient @xmath0 . in particular , for the case
when the initial amount of s nodes is 0.1 , the critical value @xmath2 is about 0.38 for @xmath7 , but only 0.25 for @xmath8 . when the initial amount of nodes is 0.25 , the same numbers for @xmath2 are 0.40 and 0.28 .
this means , that in clusterized networks , a larger probability of the d process is necessary to balance the s process , than for the case when the clustering is small . +
this result is opposite to the one obtained in our previous calculations @xcite , where the activation of d nodes was possible only if a node was simultaneously a nearest neighbor of both nodes of the activating pair of d nodes .
this detail appears to be the cause of the observed different role of the clustering coefficient .
while it seems natural that in our case the variation of @xmath0 is simply not relevant , the reversed influence of the clustering calls for an interpretation .
+ to accomplish this , let us compare two limit cases : the ws network without rewiring , where the clustering coefficient is maximal , and the bethe lattice . for the mean degree @xmath9=4 , as assumed here , the respective values of @xmath0 are 0.5 and 0.0 .
although in our case the ws network with large amount of rewiring is not equivalent to the bethe lattice , it is anyway close to an erds - rnyi network , which could be approximated by a regular tree . for the purpose of our explanation , it is important only that in both cases the clustering coefficient is small .
let us consider the simplified case of the velocity of spread of the d phase from a pair of neighbours , with the s process switched off and all nodes are simultaneously updated . in the ws network
, this velocity is constant : for @xmath10=4 , two nodes are switched from s to d at each step . on the contrary , in the bethe lattice with the same degree the number of nodes switched from s to d along one tree branch is multiplied by @xmath11 at each time step .
we should add that for the process investigated in @xcite , the above multiplication does not occur ; in trees the d process considered there does not work at all .
+ the list of applications of the sznajd model in politics and economy can be found in @xcite .
here we add that the comparison of the results presented here and of those in @xcite reveals that a subtle modification of the mechanism seriously alters the intensity of the sznajd dynamics in clusterized networks . in the literature on the sznajd model ,
often we find a reference to the threshold effect introduced to sociology by granovetter @xcite . in this effect , people are inclined to imitate the others behaviour if more than a given number of persons behave in a given way .
this means , that the imitators see all the imitated persons , and not only one .
accordingly , this sociological effect is described more accurately by the model described in @xcite or even by the bootstrap percolation , than by the sznajd dynamics .
the calculations were performed in the ack cyfronet , cracow , grants no .
mnisw/ ibm_bc_hs21/agh/070/2010 and mnisw / sgi3700/ agh/070/2010 .
this work was partially supported from the agh ust project no .
10.10.220.01 .
99 j. marro and r. dickman , _ nonequilibrium phase transitions in lattice models _ , cambridge up , cambridge 2002 .
t. m. liggett , _ interacting particle systems _ , springer - verlag , new york 1985
. k. sznajd - weron and j. sznajd , _ opinion evolution in closed community _ , int .
j. modern phys .
c 11 , 1157 ( 2000 ) .
k. sznajd - weron , _ sznajd model and its applications _ , acta phys . pol .
b 36 , 85 ( 2005 ) .
m. rybak and k. kuakowski , _ competing contact processes on homogeneous networks with tunable clusterization _ , int . j. mod
c 24 , 1350012 ( 2013 ) .
j. adler , _ bootstrap percolation _ , physica a 171 , 453 ( 1991 ) .
g. j. baxter , s. n. dorogovtsev , a. v. goltsev and j. f. f. mendes , _ bootstrap percolation on complex networks _ , phys .
e 82 , 011103 ( 2010 ) .
p. holme and b. j. kim , _ growing scale - free networks with tunable clustering _ ,
e 65 , 026107 ( 2002 ) .
a. maka , k. malarz and k. kuakowski , _ clusterization , frustration and collectivity in random networks _ , int .
j. modern phys .
c 18 , 1772 ( 2007 ) .
m. granovetter , _ threshold model of collective behavior _ , amer .
j. of sociology 83 , 1420 ( 1978 ) .
g. marwell and p.
oliver , _ the critical mass in collective action _
, cambridge up , cambridge 1993 .
we investigate the watts - strogatz network with the clustering coefficient @xmath0 dependent on the rewiring probability . the network is an area of two opposite contact processes , where nodes can be in two states , s or d. one of the processes 
 is governed by the sznajd dynamics : if there are two connected nodes in d - state  all their neighbors become d with probability @xmath1 . for the opposite process it is sufficient to have only one neighbor in state s ; this transition occurs with probability 1 . 
 the concentration of s - nodes changes abruptly at given value of the probability @xmath1 . 
 the result is that for small @xmath1 , in clusterized networks the activation of s nodes prevails . 
 this result is explained by a comparison of two limit cases : the watts - strogatz network without rewiring , where @xmath0=0.5 , and the bethe lattice where @xmath0=0 .