Contrarian effects and echo chamber formation in opinion dynamics

Abstract

The relationship between the topology of a network and specific types of dynamics unfolding in networks constitutes a subject of substantial interest. One type of dynamics that has attracted increasing attention because of its several potential implications is opinion formation. A phenomenon of particular importance, known to take place in opinion formation, is echo chambers' appearance. In the present work, we approach this phenomenon, while emphasizing the influence of contrarian opinions in a multi-opinion scenario. To define the contrarian opinion, we considered the underdog effect, which is the eventual tendency of people to support the less popular option. We also considered an adaptation of the Sznajd dynamics with the possibility of friendship rewiring, performed on several network models. We analyze the relationship between topology and opinion dynamics by considering two measurements: opinion diversity and network modularity. Two specific situations have been addressed: (i) the agents can reconnect only with others sharing the same opinion; and (ii) same as in the previous case, but with the agents reconnecting only within a limited neighborhood. This choice can be justified because, in general, friendship is a transitive property along with subsequent neighborhoods (e.g., two friends of a person tend to know each other). As the main results, we found that the underdog effect, if strong enough, can balance the agents' opinions. On the other hand, this effect decreases the possibilities of echo chamber formation. We also found that the restricted reconnection case reduced the chances of echo chamber formation and led to smaller echo chambers.

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J.Phys.Complex. 2(2021) 025010 (12pp) https://doi.org/10.1088/2632-072X/abe561
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PAPER
Contrarian effects and echo chamber formation in opinion
dynamics
Henrique Ferraz de Arruda, 1,∗Alexandre Benatti1, Filipi Nascimento Silva2,
C´
esar Henrique Comin3and Luciano da Fontoura Costa1
1S˜
ao Carlos Institute of Physics, University of S˜
ao Paulo, S˜
ao Carlos, SP, Brazil
2Indiana University Network Science Institute, Indiana University, Bloomington, Indiana 47408, United States of America
3Department of Computer Science, Federal University of S˜
ao Carlos, S˜
ao Carlos, Brazil
∗Author to whom any correspondence should be addressed.
E-mail: h.f.arruda@gmail.com
Keywords: opinion dynamics, contrarian effects, underdog effect, echo chamber
Abstract
The relationship between the topology of a network and specific types of dynamics unfolding in
networks constitutes a subject of substantial interest. One type of dynamics that has attracted
increasing attention because of its several potential implications is opinion formation. A
phenomenon of particular importance, known to take place in opinion formation, is echo
chambers’ appearance. In the present work, we approach this phenomenon, while emphasizing the
influence of contrarian opinions in a multi-opinion scenario. To define the contrarian opinion, we
considered the underdog effect, which is the eventual tendency of people to support the less
popular option. We also considered an adaptation of the Sznajd dynamics with the possibility of
friendship rewiring, performed on several network models. We analyze the relationship between
topology and opinion dynamics by considering two measurements: opinion diversity and network
modularity. Two specific situations have been addressed: (i) the agents can reconnect only with
others sharing the same opinion; and (ii) same as in the previous case, but with the agents
reconnecting only within a limited neighborhood. This choice can be justified because, in general,
friendship is a transitive property along with subsequent neighborhoods (e.g., two friends of a
person tend to know each other). As the main results, we found that the underdog effect, if strong
enough, can balance the agents’ opinions. On the other hand, this effect decreases the possibilities
of echo chamber formation. We also found that the restricted reconnection case reduced the
chances of echo chamber formation and led to smaller echo chambers.
1. Introduction
The increasing number of online social network users has impacted several aspects of human interactions
and activities, such as votes in elections [1], opinions about products [2], and debates about controversial
subjects [3]. To better understand such phenomena, many aspects of these dynamics have been studied [4,5],
which includes the mechanisms of influence [6]andsocialperception[7]. Part of these studies consider the
dynamics executedon a network structure, in which the nodes and edges represent people and their friendship,
respectively [6,8]. Other approaches also studied time-varying topologies [5,8–14] specific rewiring rules
[15–17], and link prediction [18,19].
As human beings are progressively interconnected, several important phenomena have been identified,
including the formation of echo chambers [8,20–23]. More specifically, people sharing the same ideas tend
to form relatively isolated communities in social networks. One can define echo chambers on networks as
opinions adhered to network communities [24–26]. Because of their importance, echo chambers have been
extensively studied recently [8,20–23].
One especially interesting situation deserving further investigation regards networks in which agents can
rewire their connections as a consequence of opinion changes [8–13]. In particular, a modified version of
© 2021 The Author(s). Published by IOP Publishing Ltd

J.Phys.Complex. 2(2021) 025010 (12pp) H Ferraz de Arruda et al
the Sznajd model of opinion dynamics was employed [8], considering several network topologies, in order to
study echo chamber formation when agents are allowed to reconnect, after changing their opinion, to other
agents sharing the new opinion. Furthermore, we considered an arbitrary number of opinions, representing
several real scenarios—for example, elections with many distinct candidates, brand and musical preferences,
and among others.
In the present work, we address this problem further with the focus on the effect of contrarian opinions
[1,27–29]. More specifically, when changing their opinion, some people would tend to adopt the position
contrary to the predominant opinion. Because, here, we incorporate many options of opinions, we considered
the less predominant as being the contrarian. This choice can be explained by the underdog effect, which is the
tendency of a part of the public to support the less popular option [30–32]. What would be the effects of this
type of dynamics on the underlying network? Could this contributes to a broader diversity of opinions and/or
promote the echo chamber formation?
Our proposed dynamics is based on a modified version of the Sznajd model [8], called adaptive Sznajd
model (ASM). This dynamics considers that the connections relate not only to friendship but also to possible
interactions with other people. More specifically, in the real world, users of an online social network can have
many friends but typically can communicate effectively only with a small portion of them. To investigate the
effects of the contrarians in this context, we includea new rule that allows the individuals to change their opin-
ions to the contrarian, with a given probability. We also considered the scenario in which the agents reconnect
only within a limited neighborhood, henceforth called context-based reconnection. This type of reconnec-
tion can be understood as a manner to simulate the fact that a person tends to know the friends of his/her
friends [33].
Since echo chambers can be associated with the adherence of opinions to communities, the compari-
son between them can quantify the echo chamber formation. In order to compare the agent’s opinions with
network communities, we employ modularity [34]. More specifically, instead of considering the detected com-
munities, we use the agent’s opinions to calculate this measurement. As a complementary analysis, the opinion
distribution is also quantified concerning its diversity [35], which estimates the effective number of opinions.
Several interesting results have been obtained, including the identification of the significant influence of
the average degree on the formation of the echo chambers, in both considered situations. In addition, the
obtained results were found to exhibit complementary characteristics as far as diversity and modularity are
concerned. In particular, we observed that the modularity tended to vary little in regions of the parameter
space characterized by similar diversity values, and viceversa.Theintensityoftheunderdogeffectcanbe
associated with the balance of the agent’s opinions. More specifically, low and high intensities of underdog
effect can lead the dynamics to echo chamber formation and higher opinion diversity, respectively. Another
interesting finding relates to the verification that the context-based reconnections reduced the chances of echo
chamber formation, which also tended to be smaller. We also observed that, for a given set of parameters, two
types of topologies could be obtained: with or without echo chambers.
This article is organized as follows. We start by presenting a previous related work [8]onwhichthecurrent
approach builds upon, including the description of the modified Sznajd dynamics, the reconnecting schemes,
the definition of diversity and modularity, as well as the adopted network models. The results are then presented
and discussed, and prospects for future studies are suggested.
2. Contrarian-Driven Sznajd model
Before starting the dynamics, each network node, i, is assigned to a categorical opinion, Oi∈N,randomly
distributed with uniform distribution, where Oi∈[0, NO]. The cases Oi=0andOi>0 corresponds to nodes
with null and not-null opinions, respectively. The null opinion means that the individual does not have an
opinion about the subject. For instance, in the case of election opinions, the individuals who do not know the
candidates hold a null opinion about them.
An additional probability, w(0 w1), can also be employed, which corresponds to the probability of
a node randomly changing its opinion. To simplify our analysis, we henceforth adopt w=0.
In order to incorporate the contrarian dynamics, we propose some complementary rules, as presented in
figure 1. Our proposed dynamics simulates the case in which people influenced by their neighbors can adopt
the contrary opinion. Contrarian opinions have been studied by many researchers [1,27–29,36–42]. Here, we
put together the concepts of persuasion, given by the Sznajd model [6], change of friendship, and the contrarian
effect.Inthiscase,twoagentstrytoconvinceanother,which can change its opinion to the contrarian, adopting
the opinion defined according to the underdog effect. An example of the contrarian processing is illustrated
in figure 2.
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Figure 1. Pseudocode of the proposed survey-driven Sznajd model. The bold text depicts the differences between the
survey-driven Sznajd model and ASM.
Figure 2. Representation of the contrarian-related processing. (a): initial configuration example of nodes iand jand their
respective neighbors. (b): the probabilities of node ito influence its neighbors, in which the highlighted neighbor was convinced
to the opinion of i. In this example, only one neighbor had its opinion changed, but all nodes had the same probability of
adhering to the opinion of i. The underdog effect is illustrated in (c), given that the green node corresponds to the less frequent
opinion. (d): the probabilities of jto convince its neighbors. The highlighted illustrates the change to opinion i.
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In order to study this effect, we considered the ASM and added a rule that incorporates the contrarian
idea, which consists of allowing an agent to have an opinion that is different from the majoritarian. More
specifically, for each iteration, all agents’ opinions are analyzed, and the contrarian opinion is defined as the
less frequent one. Differently from the previous study [8], here we considered the starting number of opinions
as four (this choice is better discussed in section 7.3). Our model incorporates more than two categories of
opinions since, for many real cases, such as political opinion and competitions, it cannot be represented by
binary assumptions.
3. Context-based reconnection
We also investigate a variation of the Contrarian-driven Sznajd model in which the rewirings can be done only
between topologically close agents. We incorporated this new rule in the above-described algorithm. More
specifically, we included a parameter h, which controls the maximum topological distance between iand j,
allowing a change of opinion by i. So, we limit the reconnections to happen only between nodes that are within
a distance lower or equal to h. If there is no possibility of reconnection, the rewiring does not happen. For the
sake of simplicity, here we adopt h=2, which means that the reconnections happen only between the selected
node iand the friends of friends of i.
4. Diversity
To quantify how diverse the opinions are, we employ a respective measurement. There are many possible ways
to define diversity [35]. Here we consider the variation based on information theory [43], which is defined as
follows
D=exp(H), (1)
where His the Shannon entropy, which is defined as
H=−
No

o=0
ρoln(ρo), (2)
where Nois the number of possible opinions and ρois the proportion of the opinion oon network. The value
of diversity, limited within the range 1 DNo+1,canbeunderstoodastheeffectivenumberofstates,
also known as Hill number of order q=1[44,45]. This variation of diversity have been employed to quantify
other opinion-based dynamics [8,46].
5. Modularity
Because diversity only accounts for the variety of opinions, we also consider a measurement regarding the
topology. We employ the modularity [34] that quantifies the tendency of nodes to form communities. These
communities are defined as groups of nodes highly interconnected while being weakly linked to the remaining
network [34].
The adopted modularity measurement is calculated as
Q=1
2m
ij Aij −kikj
2mδ(ci,cj), (3)
where mis the number of edges, Ais the adjacency matrix, and ci,cjare the communities of the nodes iand j,
respectively. The value of modularity gauges the structures of clusters of a network. In this study, we did not
detect communities. Instead, we understand sets of nodes having the same opinion as constituting a respective
community.
6. Network topologies
To account for different network topologies and to incorporate distinct real-based characteristics, we perform
the dynamics considering five different models as follows:
•Watts–Strogatz (WS) [47]: we considered the network created from a 2D toroidal lattice in which the
edges are randomly rewired with probability p=0.1. This network model was originally conceived to
simulate characteristics of real-world social networks. More specifically, the WS model incorporates the
small-world effect while maintaining a high clustering coefficient;
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Figure 3. Comparison between Dand Q, the latter normalized according to the highest value, for a given set of parameters, in
which items (a), (b), and (c) are respective to D, while (d), (e), and (f) relate to Q. The WS network was considered in this
example. The variation of Qfor k=12 is much lower due to the high values of average degrees. Each of the computed points
was calculated for 100 network samples.
•Erd¨
os–R´
enyi [48]: having uniformly random connections with probability p.Thisisasimplisticmodel
also presenting the small world effect and is usually employed as a reference while analyzing the obtained
results;
•Barabási–Albert (BA) [49]: yielding power-law degree distribution. This type of degree distribution is
characteristic of a wide range of real-world networks, including social networks. This model also presents
the small world effect;
•Random geometric graph (GEO) [50]: the positions of the nodes are initially distributed on a 2D surface
and connections between pairs of nodes are drawn according to their proximity. We considered this
topology since it simulates spatial interactions. Thus, the dynamics start with the nodes connected with
spatially close neighbors;
•Stochastic block model (SBM) [51]: we configured the model to account for four well-defined communi-
ties with the same size. The community structure is a characteristic present in many social networks and
is intrinsically related to echo-chamber formation, thus the importance of understanding the proposed
dynamics in such a type of network.
In all the above cases, the parameters were chosen to yield the same expected average degree, k.Forall
these adopted networks, we considered the number of nodes as being approximately 1000. Furthermore, we
employed three different average degrees (k=4, 8, 12). However, in the case of the GEO model, we consid-
ered only k=8, 12 since it is difficult to achieve a single connected component with a lower average degree.
More information regarding several of the adopted network models can be found in [52].
7. Results and discussion
In this section, we present the results according to two respective subsections considering the no-reconnection
constraint and context-based reconnections. In both cases, we analyze the diversity and modularity of the
opinions.
7.1. No-reconnection constraint
First, we analyzed the diversity (D) behavior in terms of the reconnection probability (q) and contrarian prob-
ability (g) for all considered topologies and three average degrees (k=4, 8, 12). For most of the dynamics,
we executed 1000000 iterations, except for GEO, which was performed 100 million (for average degree 8) and
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Figure 4. PCA projection of D, by employing the same set of parameters as figure 3. It is possible to observe groups of samples
(identified by ellipses), according to k.
25 million (for average degree 12). These numbers of iterations were chosen to allow the dynamics to reach
a steady state. Furthermore, we repeated each experiment 100 times. For all of the considered topologies, we
calculated the average values of Dby varying qand g. An example regarding the WS network is shown in
figures 3(a)–(c), in which well-defined regions can be observed. For almost all network models, the results
were found to be similar. The lower diversity values were observed for lower values of qand g. Interestingly,
even when we consider q=0 (no reconnections), some values of glead the dynamics to converge to high val-
ues of opinion diversity, D. In other words, we verified that the employed parameter configuration strongly
affects the measurement of diversity (D).
Inordertobetterunderstandthevariationofthediversity with the parameters, we flattened the obtained
values of Dand calculated the respective principal component analysis (PCA) projection [53,54](seefigure4).
More specifically, for each network type, we compute a matrix of Dsimilar to the results shown in figure 3.
Also, we flattened the obtained values of Dand, by considering these vectors, we obtained the PCA projection.
An interesting result concerns the separation of the cases into three regions in terms of the average degree,
identified by respective ellipses in figure 4. For the two highest values of average degree, the samples were
found to be more tightly clustered. Furthermore, for k=4, the group is more widely scattered. This result
suggests that the average degree plays a particularly important role in defining the characteristics of the opinion
dynamics in the considered cases.
Next, we analyzed how the opinions modularity (Q) changes according to the model parameters. Because
average degrees can influence the network modularity [55], for all of the matrices, we divide the values by the
highest average value. This procedure was not employed to Dbecause, in this case, the obtained result is related
to the effective number of opinions. We compute Qfor all network variations, and for k=4, 8, 12 using the
same set of parameters we employed in the previous case. Figures 3(d)–(f ) illustrate examples of Qfor WS
networks, in which well-defined regions can also be found. For the highest of the considered values of gand q,
high values of Qwere obtained, except for k=12. It means that there is a possibility to have echo chambers.
The other parameter configurations led to networks without well-defined communities. Similar results were
also observed for the other models. For higher average degrees, Qtends to be lower for all possibilities of
parameters (gand q). Another critical aspect involved in interpreting the Qmeasurement is setting the limit
of detection [56].Forexample,inthecasesinwhichD>4, there are disconnected nodes that have a null
opinion.
Now, we proceed to discuss the results obtained for diversity and modularity in an integrated way. The
modularity analysis reveals a pattern not evidenced by the diversity analysis (see figure 3). For the highest values
of diversity D, the modularity Qwas found to be more sensitive to parameter variations. More specifically,
while Dis found to measure almost always similar values in this region, Qdisplays a broader variation. In
a complementary fashion, for the lowest values of modularity, the diversity was found to be more sensitive
(as can be seen in figure 3). In general, both measurements are equally important to describe the presented
dynamics behavior. Furthermore, the formation of the echo chamber can happen only for high values of Dand
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Figure 5. Some examples of the resulting networks for given parameters. The heatmap represents Qvalues (normalized to have
maximum value equals to one) obtained after the execution of our dynamics. Here, we employ the BA network, for k=4.
Interestingly, for q=0.40 and g=0.02 more than one type of network organization can be obtained. The node colors in the
network visualizations represent the opinions. Each of the computed points was calculated for 100 network samples. The network
visualizations were created using the software implemented in [57].
Q.Inotherwords,Ddescribes the effective number of opinions, and Qis a quantification of the community
organization.
Figure 5illustrates the resulting topologies when starting with BA networks. More specifically, we present a
heatmap of Qvalues and some respective examples of the resulting networks. In the well-defined region with
Qnext to zero, the dynamics converge to a single opinion (see figure 5(a)). Figures 5(b) and (c) were obtained
in regions with intermediate values of Q. In this case, the communities are not well-defined. Even so, in both
cases, there is a high level of diversity, indicated by the visualization colors. Networks with distinct commu-
nities were obtained for large qand g—see figures 5(d) and (e). Thus, larger reconnection and contrarian
probabilities further the formation of echo chambers. The network shown in figure 5(e) has communities that
are disconnected among themselves. For some configurations, both behaviors, with and without community
structure, can be found for the same parameter configurations (see figures 5(f) and (g)). The value displayed in
the matrix means an average, where for figure 5(f), Qis much higher than for figures 5(g), in which Qis found
to be near to zero. Figures 5(f) and (g). Interestingly, this situation was also identified for another opinion
dynamics (ASM), reported in [8].
The observed results can be explained from a more practical point of view. The pattern of reconnection of
individuals is decisive to lead the dynamics to consensus (see figure 5(a)). Comparing the cases in figures 5(d)
and (e), both represent social scenarios in which there are tendencies to have segregated groups of individuals
with distinct opinions. However, in panel (e), the groups are separated, while in panel (d), there is information
exchange between the groups. In this case, contrarians’ presence leads the dynamics to connect the different
groups, allowing information exchange. This effect can be intensified by using other parameter combinations,
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J.Phys.Complex. 2(2021) 025010 (12pp) H Ferraz de Arruda et al
Figure 6. Comparison between Dand Q, the latter normalized according to the highest value, for a given set of parameters, in which
panels (a), (b), and (c) are respective to D, while (d), (e), and (f) relate to Q. Here, we considered SBM networks and the context-based
reconnection dynamics (h=2).
Figure 7. Visualizations of resultant topologies when starting with GEO networks (k=8). The employed dynamics is based on the
context-based reconnection (h=2). Each of the computed points was calculated for 100 network samples.These network visualizations
were created using the software implemented in [57].
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Figure 8. Dobtained for BA networks (with k=4), with varied numbers of opinions.
asshowninfigures5(b) and (c). There are also ambiguous outcomes (see figures 5(f) and (g)), corresponding
to a situation in which it is much more challenging to interpret the results.
7.2. Context-based reconnection
In this subsection, we explore the effects of the proposed dynamics when the interactions are restricted. This
constraint simulates the fact that people tend to become a friend of a friend (h=2). In this case, we considered
only the SBM and GEO networks because these networks have higher diameters than the other considered
models. So, the effect of the context-based reconnection is more visible.
By considering the diversity (D), the results were found to be similar to the no-rewiring constraint dynamics
(see figures 6(a)–(c)). However, the regions with lower values of Dare found only for smaller regions defined
by specific combinations of parameters. Also, comparing with the previous model, the modularity values were
foundtobedifferent.Inthiscase,theregioninwhichQtendstozeroisconsiderablyampler.
Figure 7shows some possible resulting topologies when starting with GEO networks (k=8). Figure 7(a)
illustrates an example for q=0 (no reconnections are allowed), characterized by high value of Dand low value
of Q. The opinions were found to define relatively small groups. In the case of figure 7(b), there is also a wide
range of opinions, but with the formation of echo chambers. Furthermore, nodes from completely separated
communities can have the same opinion. Figure 7(c) shows another possibility of resulting network with high
value of Dand low value of Q. As in the previous result, isolated nodes can also be found. In summary, by
considering this restriction (h=2), we found that it is much easier to have parameters that give rise to high
diversity. However, high modularity is observed only within a more restricted region defined by gand q.
7.3. Varied numbers of opinions
In this subsection, we compare the execution of the dynamics by varying the number of opinions, NO(2,3,4,5,
and 6 opinions). Here, we considered a single network topology, which is the same topology we considered in
figure 5. More specifically, we employ BA networks with k=4. Figures 8and 9illustrate the obtained results
of Dand Q, respectively. All in all, the results are found to be similar. For all of the tested cases, the number
of both scenarios, of a single or NOopinions, were found. Additionally, the measured values of Qmean that
the dynamics drove to have both types of topology, with or without communities. In the case of D,thesetof
parameters that give rise to the lowest values (figure 8) are ordered in increasing order according to NO. Similar
results were found for Q(figure 9), where NOis also related to the sets of parameters that result in networks
without communities.
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Figure 9. Normalized version of Qobtained for BA networks, with k=4, witch varied numbers of opinions.
8. Conclusions
Several studies have addressed the topic of opinion formation, and in particular, echo chamber formation
in social networks. In the present work, we approached the problem of echo chamber formation in several
types of complex networks, as modeled by a modified Sznajd model. In particular, we focused attention on
the effects of contrarian opinions by considering a time-varying topology. More specifically, we incorporate
the underdog effect, and multiple opinion possibilities. Furthermore, two strategies have been tested, which
include: (i) the agents can be reconnected only with others sharing the same opinion, and (ii) the agents also
can be reconnected only with other that share the same opinion, but within a limited neighborhood.
Several interesting results have been obtained and discussed. Regarding the analysis based on diversity and
modularity, the obtained results were found to exhibit complementary characteristics. More specifically, we
found that some regions of the parameter space are characterized by a gradual variation of diversity while dis-
playing very similar modularities, and vice versa. For specific parameter configurations, two types of topologies
can be observed: with or without the presence of echo chambers. In addition, by considering both types of
dynamics, the contrarians, conducted by the underdog effect, play an important role in the resultant topology
and dynamics. In the case of high contrarian probability, g, the effective number of opinions tends to be high.
However, when low values of gare employed, less well-defined communities are found. In other words, the
underdog effect can contribute to an increase in the heterogeneity of opinions. In our result, this effect can as
well balance the group sizes.
Moreover, one of the factors that strongly influences the dynamics was found to be the average degree,
which is particularly determinant on the formation of the echo chambers. This result means that the average
number of friends plays an important role in the dynamics. In the case of the context-based reconnections, it
reduced the chances of echo chamber formation, which also tended to be smaller. By considering the number
of opinions, we found that this parameter did not strongly affect the steady-state of the dynamics. However,
the formed echo chambers reflect the number of opinions. Observe also that in this work, it was decided not to
analyze our dynamics analytically because our model is particularly intricate as a consequence of many possible
parameter configurations.
Answering the question presented in the introduction, in general, the contrarian parameter, g,tendstolead
the dynamics to outcomes with high values of opinions diversity. More specifically, for higher network average
degrees, without considering the underdog effect, the diversity tends to be close to one. In conclusion, higher
values of this parameter help promoting diversity of opinions with no echo chamber formation.
The findings reported in this article motivate several further investigations. In particular, it would be inter-
esting to study the effect of the spontaneous opinion changes. One possibility is to consider different types
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of rewiring dynamics. For instance, one could consider probabilistic rewiring mechanisms in order to mit-
igate or strengthen the echo chamber formation. Taking into account that there is an abrupt change when
switching between non-reconnection constraint and context-based reconnections configurations, intermediate
scenarios can be proposed. For instance, a smooth rewiring probability function based on the topological dis-
tance between nodes can be considered. In this case, we expect the dynamics to converge to a broader range of
states. Also, continuous variables could be adopted in order to characterize opinions. Another possibility is to
consider weighted and/or directed complex networks.
Acknowledgments
Henrique F de Arruda acknowledges FAPESP for sponsorship (Grant No. 2018/10489-0 and No.
2019/16223-5). Alexandre Benatti thanks Coordenaç˜
ao de Aperfeiçoamento de Pessoal de Nível
Superior—Brasil (CAPES)—Finance Code 001. Luciano da F Costa thanks CNPq (Grant No. 307085/2018-0)
and NAP-PRP-USP for sponsorship. C´
esar H Comin thanks FAPESP (Grant Number 18/09125-4) for
sponsorship. This work has been supported also by FAPESP Grants No. 11/50761-2 and No. 2015/22308-2.
Data availability statement
No new data were created or analysed in this study.
ORCID iDs
Henrique Ferraz de Arruda https://orcid.org/0000-0002-4325-6888
Alexandre Benatti https://orcid.org/0000-0002-7419-4712
Filipi Nascimento Silva https://orcid.org/0000-0002-9151-6517
C´
esar Henrique Comin https://orcid.org/0000-0003-1207-4982
Luciano da Fontoura Costa https://orcid.org/0000-0001-5203-4366
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