# Matters Arising in “Plasmon-driven carbon–fluorine (C(sp3)–F) bond
activation with mechanistic insights into hot-carrier-mediated pathways”

Yonatan Dubi1,2, Ieng Wai Un3, Joshua H. Baraban1, and Yonatan Sivan2,3
Ben-Gurion University of the Negev, Israel

In a recent paper [1], Robatjazi et al. demonstrate hydrodefluorination on Al
nanocrystals decorated by Pd islands under illumination and under external
heating. They conclude that photocatalysis accomplishes the desired
transformation CH3F + D2 -¿ CH3D + DF efficiently and selectively due to “hot”
electrons, as evidenced by an illumination-induced reduction of the activation
energy.

Although some of the problems identified in prior work by the same group [2,
3] have been addressed 111In particular, unlike the procedure employed in
previous work by this group [4], the reaction data was not normalized to
different effective volumes in the current work, but rather by the same total
catalyst mass. In that sense, the authors implicitly acknowledge the error we
identified [2, 5, 3] in their previous work [4]., scrutiny of the data in [1]
raises doubts about both the methodology and the central conclusions. First,
we show that the thermal control experiments in [1] do not separate thermal
from ”hot electron” contributions, and therefore any conclusions drawn from
these experiments are invalid. We then show that an improved but still non-
ideal thermal control implies that the activation energy of the reaction does
not change, and that an independent purely thermal calculation (based solely
on the sample parameters provided in the original manuscript [1]) explains the
measured data perfectly. For the sake of completeness, we also address
technical problems in the calibration of the thermal camera, an unjustifiable
disqualification of some of the measured data, as well as concerning aspects
of the rest of the main results, including the mass spectrometry approach used
to investigate the selectivity of the reaction, and claims about the
stoichiometry and reaction order. All this shows that the burden of proof for
involvement of hot electrons has not been met.

##  1 extraction of “hot” electron contribution (Fig. 6a)

###  1.1 Treatment of the thermocatalysis control data

One of the central results of [1] is shown in its Fig. 6a; it purportedly
demonstrates that the activation energy decreases under illumination by
plotting the “hot” carrier contribution to the rate vs. the (intensity-
dependent) surface temperature and performing Arrhenius fits.

In order to explain the possible flaws in Fig. 6a, we must first explain the
procedure used to construct it, as described in the manuscript. First, the
reaction rate is measured in the dark ($R_{dark}$). The sample is then
illuminated and the reaction rate, $R_{illum}$, is measured as a function of
$T_{S}$ again.

However, $R_{illum}$ is _not_ what is plotted in Fig. 6a. Instead, to isolate
the photocatalysis (i.e., the “hot” electron) contribution to the reaction
rate under illumination, denoted by $R_{photo}$, the authors take the
difference between the reaction rate under illumination and the reaction rate
in the dark, i.e., $R_{photo}(T_{S})=R_{illum}(T_{S})-R_{dark}(T_{dark})$ (see
[1, SI, p. 30]). The temperature $T_{dark}$ is the temperature without
illumination (the value is undisclosed in the manuscript) rather than the same
temperature at which the illuminated experiments were conducted. Fitting
$R_{photo}$ to the Arrhenius equation gives $E_{a,photo}=0.59$ eV ($0.67$ eV)
for CW (white light) illumination, both smaller than the activation energy in
the dark, $E_{a,dark}=0.8$ eV. The authors conclude that the apparent
reduction of activation energies is due to “hot” electrons. We note in passing
that the extraction of exponents is based on a surprisingly limited number of
data points and a narrow temperature range (see Appendix A), such that the
differences between activation energies lie within the margin of error.

Already at this stage, it is evident that the thermal control experiment in
[1] is inadequate, since it does not account for the heating caused by the
illumination. As a result, the activation energy extracted from $R_{photo}$ is
misleading, since it includes the thermal contribution to the reaction rates.
This practice is in direct contradiction of earlier work by some of the
authors of the current manuscript [6, 4, 7], as well as their (and our)
thermal calculations, and other recent work [8, 9].

A more adequate thermal control experiment would be to measure the reaction
rates while heating the sample to the same $T_{S}$ and account for the thermal
gradients. However, as we demonstrate below, this control experiment
conclusively shows that there is no contribution of non-thermal electrons to
the reaction.

To show this, we first obtain, using the data points of Ref. [1] (black and
green points), the total reaction rate under illumination, $R_{illum}$ (orange
points in Fig. 1). Next, to obtain the correct contribution from the
photocatalysis ($R_{photo}$, red points in Fig. 1), we subtract from
$R_{illum}$ not the reaction rate in the dark (as was done in Ref. [1]), nor
the thermal reaction rate assuming a uniform temperature $T_{S}$ in the sample
volume, but rather the thermal reaction rate due to a temperature distribution
which has a surface temperature $T_{S}$ identical to the one measured as well
as the associated thermal gradients (calculated in Appendix B), namely,

$R_{photo}\approx R_{illum}(T_{S})-\int R_{dark}(T(\vec{r}))d\vec{r}.$ (1)

Here, $T(\vec{r})$ is the calculated temperature throughout the sample, and
$R_{dark}(T)=R_{0}\exp\left(-\frac{E_{a}}{k_{B}T(\vec{r})}\right)$ is the
Arrhenius law, with $E_{a}\sim 0.8$eV extracted from the data in the dark
(black points in Fig. 1).

The Arrhenius fit to Eq. (1) (red points in Fig. 1) gives $E_{a,photo}\approx
0.7$ eV ($\approx 0.72$ eV) for illumination with CW (white light). Both
changes are much smaller than the reported reduction; the obtained values are
also well within the reported error bars, such that they cannot serve as
conclusive evidence of any “hot electron” driven mechanism. Put simply, even
if one assumes that there is “hot-electron” photocatalysis, its activation
energy is roughly the same as the thermal one.

###  1.2 A pure thermal analysis

We have shown above that a re-examination of the control experiment and data
analysis [1] invalidates the conclusion of the paper. Now, we continue and
show that a pure thermal analysis can explain the data perfectly.

This requires pointing out yet another possible flaw in [1], namely, the
setting of the sample emissivity. As in the authors’ prior work [4], a
surprisingly high value ($0.95$ [1, SI, p. 28]) was used, which we showed
previously to be insufficiently accurate by the authors’ own calibration
experiment [5, 3] 222In particular, a difference of a few percent in the
reading of the thermal camera and a thermocouple causes an uncertainty of
hundreds of percent in the reaction rate.. Moreover, not only this value is
the default value of the camera, a calculation based on the composition of the
sample in the current study (as done in [2, 3]) predicts an emissivity of
$\approx 0.17$, significantly lower compared to the setting in the experiment
333It is also worth mentioning that our previous work [2, 3] showed
conclusively that the IR camera was not operated properly in previous work of
this group [4] (camera-sample distance was unrealistically high; image out of
focus); see also discussion in [10]. Since the authors do not provide any
detail regarding the camera-to-sample distance, nor evidence for proper
focusing, it is impossible to know if the camera was operated correctly in the
current experiment. .

Furthermore, a thermocouple embedded into the sample measured $10-20^{\circ}$C
higher in the dark and up to $200^{\circ}$C lower under illumination compared
to the thermal camera (see Figs. S13(c) and S13(d), respectively; the former
confirms the inaccuracy in the chosen emissivity). Remarkably, in [1, SI, p.
27], the authors question the validity of the thermocouple reading, and
disregard it. Their reasoning is that the disagreement between the
thermocouple and camera readings results from the inability of the
thermocouple to measure surface temperature “due to the limited light
penetration into the catalyst bed and the heat localization on the surface of
the irradiated catalyst”. Not only does the second part of this statement
contradict an underlying assumption of the analysis (of a uniform sample
temperature), but in fact the entire argument is physically incorrect – the
limited light penetration does not prevent heat diffusion to the lower parts
of the sample (see e.g., [11]). The argument is also logically flawed – the
disagreement in the two temperature readings indicates that either one (or
both) of the measurements is flawed, or that both are correct, but measure
somewhat different quantities.

It seems more than plausible that not only is the camera reading likely to be
inaccurate, but also that the difference between the two temperature readings
is to be expected. Indeed, there is no denying that vertical temperature
gradients do exist in such heated or illuminated catalyst structures. Again,
such gradients were measured by some of the authors of the current manuscript
[7] and by others (e.g. [12, 9]); they can also be extrapolated from the
numerical simulations presented in Fig. S14 (performed over small voxels), and
were described in detail in [5, 11] – see also Appendix B.

Now, since the high emissivity setting may result in a temperature reading
which is colder from the actual surface temperature, we now show that the data
can be fully reproduced with only thermal reactions. To do so, we evaluate the
reaction rate by integrating the Arrhenius law over the entire sample, taking
into account the calculated gradients $T(\vec{r})$ (see Appendix B) and
assuming that the real surface temperature is $T_{S}$ plus some temperature
shift $\delta T$, i.e., $\int
d\vec{r}R_{0}\exp\left(-\frac{E_{a}}{k_{B}(T(\vec{r};T_{S})+\delta
T)}\right)$, with $R_{0}$ and $E_{a}$ taken from an Arrhenius fit to the
reaction rate in the dark.

In particular, if the temperatures are shifted by $\delta T=27$K (CW) and
$\delta T=36$K (white light), one obtains perfect predictions of the measured
reaction rate without modifying the activation energy nor the prefactor (empty
triangles in Fig. 1). Such a shift is of the same order of magnitude as the
discrepancy between the thermocouple and camera readings reported by the
authors themselves (Fig. S13(c)), and much smaller than the estimated error
due to the emissivity and comparable to the independent thermal calculations
shown in Appendix B.

Thus, by Ockham’s razor, it seems far more likely that our simple yet
remarkably quantitative thermal argument is the correct explanation for the
faster chemistry reported compared with the speculative explanation provided
in the original manuscript. Definitive proof of “hot” electron driven
catalysis, particularly in light of the issues discussed above, will require
approaches that can more precisely isolate thermal effects.

Figure 1: Reaction rates for (a) CW and (b) white light illumination as a
function of the measured surface temperature $T_{S}$. Black points: reaction
rate in the dark, $R_{dark}(T_{S})$, giving (from an Arrhenius fit) an
activation energy of $0.8eV$. green (a; CW) and magenta (b; white light)
points: contribution of “hot” electrons to the reaction rate under
illumination, $R_{photo}=R_{illum}(T_{S})-R_{dark}(T_{S})$, as evaluated in
[1], disregarding the temperature difference between the bulk and surface
reported by the authors themselves. Red points: corrected contribution of
“hot” electrons to the reaction rate under illumination (1), with a much
smaller change in the activation energy. Orange points: total reaction rate
(black + green/pink points; raw data); Triangles: fit to raw data using a
purely thermal model with a slightly shifted surface temperature; perfect
agreement is observed.

##  2 Absence of 13CH3F in mass spectrometry results (Fig. 2b)

Aside from the (problematic) analysis of the purported photocatalysis
contribution to the reaction rate, the authors reported other results that
they claim support involvement of “hot” electrons. We find these observations
and analyses unconvincing, especially as originally reported in [1], as
described in the following.

The time evolution of the starting material CH3F ($m/z$ 34) and desired
product CH3D ($m/z$ 17) as followed by mass spectrometry are shown in Fig. 2b
of [1]. To demonstrate the selectivity of the reaction, traces for several
side products, including CH2DF ($m/z$ 35), are also displayed and remain at
zero. However, 13CH3F should also appear with $m/z$ 35; in its $1.1\%$ natural
abundance [13], this translates to $1.1\%$ of the reported 12CH3F ($m/z$ 34)
response or $(7.1)(0.011)=0.078$, which should be visible on this plot, yet is
inexplicably absent. Consider by contrast that care was taken to provide an
explanation for the absence of the signal for DF, but no such physical or
chemical explanation is possible for the absence of 13CH3F.

Even if we presume that the authors made an unannounced baseline correction,
this type of presentation is unjustified here because these background levels
are pertinent chemical data. If such a correction was performed here it was
inconsistently applied, as some species (e.g. DF in Fig. 3 of [1]) are not
baseline-corrected, and there is no basis to categorize species (to be more
precise, $m/z$ values) as reactants vs. products, since $m/z$ 35 is decidedly
both. The 13CH3F $m/z$ signal would decrease in roughly the same proportion as
the 12CH3F ($0.2/7.1=2.8\%$), which translates to changes of 220 counts/s in
the $m/z$ 35 and 18 (13CH3D) channels. Based on the signal and noise levels
shown in Fig. S4 of [1], such changes would be near the observable limit if
the data were plotted appropriately. It is unclear how the authors propose to
distinguish between different species with the same $m/z$, which leads us to
the larger problems with the mass spectrometry approach reported here.

Mass spectra require interpretation [14]. Electron impact ionization causes
severe fragmentation (see e.g., the NIST spectra of 12CH3F cited above [13]),
and in this case it would be mostly coincidence if no daughter ions fell into
the mass channels that the authors desired to interpret as products.
Furthermore, this fragmentation varies substantially across isotopologues,
both for statistical and other reasons – discussion of this phenomenon in the
relevant example of deuteromethanes can be found in [15]. Full mass range
scans are essential to identifying the molecules present (if possible) and to
check for the presence of other species (for example, methane or ethane in
this case). Such information is especially important in the present work,
where highly reactive species such as DF and methyl radicals are present, and
only an extremely restricted reaction mechanism has been considered.

##  3 Reaction order and stochiometry (Figs. 6b and 6c)

Given the less than ideal execution and analysis of the mass spectrometry
aspects of this study, its authors choose instead to highlight the overall
stoichiometric carbon balance and the observed change in D2 reaction order
(Figs. 6b-c of [1]). However, the CH3F and CH3D curves do not mirror one
another completely, indicating that the stoichiometry of the reaction evolves
over the course of the illumination, such that the carbon balance and
mechanism are not as straightforward as the authors would have us believe.

Regarding the reaction order change, while the change in reaction order for D2
is noteworthy, such an effect could certainly be caused by a temperature
increase, via the temperature dependence of the elementary step rate constants
and equilibrium constants (See Supplementary Note 4 in the SM of [1]), but no
control experiment was performed to test this possibility. Furthermore, the
proposed explanation that illumination would enhance D2 desorption is also
what one would expect from elevated surface temperatures 444Parenthetically,
the incident power density of 1.4 W/cm-2 used in Fig. 6b is higher than the
range of 0.6-1.1 W/cm-2 given otherwise. .

Finally, we would like to emphasize yet again that our purpose here is not to
disprove contributions from photocatalytic mechanisms, but rather to argue
that the experiments and analysis of Halas et al. as originally published in
[1] do not meet the burden of proof.

##  Appendix A Data analysis in [1]

In addition to the technical and conceptual problems described above, the
original data analysis of the manuscript suffers from insufficient data
recording.

Indeed, somewhat surprisingly, the original analysis relied on measurement of
only 4 data points, does not incorporate any error bars on the experimental
accuracy, and is performed over a limited temperature range of a few tens of
degrees (compared to heating by many hundreds of degrees in [4]). As a result,
the extracted $R_{photo}$ varies modestly (compared to changes by several
orders of magnitude, see e.g., [6, 16, 4]), making it highly sensitive to the
details of the data analysis. This analysis consisted of, in addition to the
obvious Arrhenius fit, an interpolation of the measured data. Indeed, since
under illumination the temperature profile is different than in the
thermocatalysis control experiment [9, 5, 3] (in the current case, by several
tens of degrees; data not shown), the correlation of the photocatalysis
experiment to its control required proper lowering of the heater temperature.
As a result, the data was eventually obtained at different surface
temperatures for the photocatalysis and thermocatalysis control.

Thus, as discussed in [5, 3], due to the exponential sensitivity inherent to
the Arrhenius Law, the extraction of the activation energy from the data is
associated with a very large error margin which makes any claims about the
physics and chemistry underlying the reaction questionable.

##  Appendix B Thermal calculations

The temperature profile in the experiment described in [1] was determined by a
detailed thermal calculation that accounted for the geometry described in the
manuscript, together with the appropriate (temperature-dependent) material
parameters, see Fig. 2. While it could be possible that some of these details
differ from the actual experiment, extensive simulations show a modest
sensitivity to all relevant parameters, in agreement with our previous
extensive investigation of this very topic [11]. Gas flow, which was not
accounted for in the simulations, was already shown to be a very weak effect
[5, Appendix C]).

One can observe clear temperature gradients in both the transverse and
vertical directions of a few tens of degrees. As a result, the Arrhenius Law
predicts that regions of the catalyst at the bottom and edges of the catalyst
sample contribute as much as $50\%$ of the top (hottest) point.

Figure 2: (a) Details of the photocatalytic chamber used in [1] which we used
for reproducing the temperature distribution. The temperature along the (b)
horizontal and (c) vertical cross-sections (shown in (a)) for the
photocatalysis experiment using the broadband visible light illumination
(450-800 nm, 2.0 W/cm2) (solid lines) and thermocatalysis control experiment
(dashed lines).

The experimental setup in [1] has a rather limited capability to identify
these gradients. First, the available transverse resolution is demonstrated in
Fig. S15, where the pixels seem to be roughly $0.5$mm in size; this is in line
with the camera manual which indicates an optimal transverse resolution of
$690\mu$m [3]. Note, however, the incorrect claims on the transverse
resolution made by the authors $\sim 100\mu$m resolution [SI, p. 6]. Thus, the
authors are also unaware to their inability to identify these gradients
experimentally.

Vertical gradients of up to $200^{\circ}$K were observed in an offline
temperature calibration experiments (Fig. S13) performed on a thicker sample.
Further thermal simulations show that such gradients may be obtained by
focusing the incoming beam, a practice that was adopted in the measurement
described in Fig. S13 (but mentioned only in private correspondence with the
editor).

## References

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# The Effect of Social Media on Shaping Individuals Opinion Formation

Semra Gündüç  Department of Computer Engineering
Faculty of Engineering, Ankara University
06345 Gölbası Ankara, Turkey
<EMAIL_ADDRESS>
###### Abstract

In this paper, the influence of the social media on the opinion formation
process is modeled during an election campaign. In the proposed model, peer-
to-peer interactions and targeted online propaganda messages are assumed to be
the driving forces of the opinion formation dynamics. The conviction power of
the targeted messages is based on the collected and processed private
information. In this work, the model is based on an artificial society,
initially evenly divided between two parties. The bounded confidence model
governs peer-to-peer interactions with a value of confidence parameter which
leads to consensus. The targeted messages which was modeled as an external
interacting source of information convert some weakly committed individuals to
break this evenness. Both parties use the same methods for propaganda. It is
shown that a very small external influence break the evenness of the opinion
distribution which play significant role in the election results. Obtained
opinion fluctuation time series have close resemblance with the actual
election poll results.

###### keywords:

Opinion formation, social media, fake news, fabricated news.

††journal: Physica A

##  1 Introduction

During the last decade internet and particularly online news services and
social media networks have been the dominant information sharing channels. In
the social media large groups of individuals, sharing similar interests form
networks [1] which create mutual trust among the members of the network.
Information coming from a member of the network is accepted and propagated by
the members of the group without much criticism [2, 3, 4]. Such a free
environment make the users vulnerable since as well as expressing their
opinions they also reveal some personal data. Third parties may collect such
personal information, process it and use for their purposes. Advertising
agencies and political parties are willing use the personal information to
convince or to convert individuals. Hence the freedom of expressing opinion
and spreading information may be misused to propagate rumor, gossip and
misleading or false information [5, 6, 7]. The question, whether such
interventions effect the public opinion or not [8] is still an open debate.
The effect of an information system such as TV, newspaper, blogs, on the
evolution of public opinion is studied in [9]. Also, the analysis of the
frequency of interaction is considered in [10]. It is also shown that, to
use/support some concepts which are valuable or very sensitive for the
society, such as religion, nationality, cultural issues, collective beliefs
can also make a profit for politicians [11] and even the ideas adopted by the
minority of the society can be supported by the majority, after such a
process.The effect of the social network utilizing degree-dependent fitness
and attributes when there are competing opinion diffusion is introduced in
[12]. The role of the social media on the social polarization of the society
is studied through both data [1, 13] and model studies [6, 3]. Although the
social studies still do not have clear evidence on the influence of such
misleading information flow on the social preferences, it is shown that false
news propagation is faster and broader than the spread of true news due to the
attractiveness of the false news [14].

Recently, two very important social events, namely Brexit –the British
referendum to leave the European Union– and 2016 US presidential election
campaigns are the striking examples of such social phenomena. During the
campaign the fake news are not only fabricated but more than that the issues
are carefully selected by using personal information of the social media users
[15, 17]. The collected personal information is used to convince and convert
individuals. It is shown that in the US Presidential election campaigns some
nodes and bots, i.e. automated accounts, in the social networks spread
fabricated, fake, biased information, distort actual news, disseminate
deceptive information [4, 8, 14, 16]. The severity of the outside interruption
can be seen by comparing the numbers: Only on 20 election stories, the number
of Facebook engagements are 8.7m fake news versus 7.3m mainstream news
starting from the beginning of August to the election day [18]. During a
recent survey, nearly $85$ percent of respondents stated that they believed
fake news is a serious social problem [19].

The aim of this work is to build a model to study the effects of varying
sources of fake and biased news on the opinion formation during an election
campaign. The model society consist of $N$ individuals with multi-component
opinion on the election issues. On the decision-making process information,
originating from different sources, play a vital role to build up opinion. For
the simplicity election issues are limited in the model. The individuals
exchange opinion on only three different issues (such as the economy, health
services, security). Hence, each individual is identified by three real
opinion values, but when it comes to making a decision on the vote, the choice
is a result of combined opinion formed on all three issues. In this sense, the
opinion structure of the model resembles Axelrod mode [20]. The individuals
exchange opinion according to the bounded confidence model (BCM)[21]. Each
individual is also subject to information flow through public services, social
media, and online news sources. Some of this information may be fake,
fabricated and even targets a particular individual. Targeted news
specifically designed by considering the individual preferences [15] which is
more effective on the non-committed individuals. To mimic the effects of the
public services, social media, targeted, false or biased information spread a
new interaction is introduced.

situations.

The model is tested on four different cases:

  1. 1.

Individual interact with others through peer-to-peer interactions no external
sources affects the dynamics.

  2. 2.

One of the parties send messages to convert less convinced individuals.

  3. 3.

Both of the parties send mes-ages to convert less convinced individuals.

  4. 4.

Both parties send messages but one sends more convincing (fabricated)
messages.

In all four cases individuals exchange opinion through social media channels.
The acceptability of the messages of online news sources are controlled by
using different probability values which are discussed in detail in the
results section.

The rest of this paper is organized as follows. Section 2 provides a
background for the proposed model with bounded confidence opinion dynamics.
Section 3 is devoted for presentation of the simulation results. Finally
Section 4 concludes the paper.

##  2 The Model

The proposed model is based on an artificial society with $N$ individuals. The
communication network is a fully connected network with nodes, $i=1,\dots N$.
This topology allows every individual to interact with every other mutually.
Even though it looks too simple; it eliminates the artifacts of more
complicated network topology which is essential for our discussion. The
position of each member of the society is labeled by Latin alphabets
$i,j\dots$. Each individual carries a three opinion component which is labeled
by Greek alphabet, $\alpha=1,2,3$.

Eq.1 defines the opinion of an individual who has three opinion components in
the matrix form.

$O=\left(\begin{array}[]{ccc}o_{11}&o_{12}&o_{13}\\\ o_{21}&o_{22}&o_{23}\\\
\vdots&\vdots&\vdots\\\ o_{N1}&o_{N2}&o_{N3}\\\ \end{array}\right)$ (1)

Here $N$ is the number of individuals, $o_{i\alpha}$,
($o_{i\alpha}\in\mathbb{R}`w$,) are the opinion values of $i^{\rm th}$
individual on the $\alpha^{\rm th}$ issue. All three opinion components are
assigned randomly to each individual. Each opinion component has a Gaussian
distribution with mean value $<O>=\pm 1$, indicates two opposing views. In
order to have some interaction between different views (different opinion
individuals), variance of the Gaussian is used as the control parameter of the
overlapping region.

At every interaction a randomly chosen pair of individuals exchange opinion on
a randomly chosen issue. In each interaction individuals discuss on any one of
the three issues in concern. Opinion exchange is realized according to BCM
[21] given in Eq.2.

$\displaystyle if\;|o_{i\alpha}(t)$ $\displaystyle-$ $\displaystyle
o_{j\alpha}(t)|\leq\Delta$ (2) $\displaystyle o_{i\alpha}(t)$ $\displaystyle=$
$\displaystyle\omega o_{i\alpha}(t-1)+(1-\omega)o_{j\alpha}(t-1)$
$\displaystyle o_{j\alpha}(t)$ $\displaystyle=$ $\displaystyle\omega
o_{j\alpha}(t-1)+(1-\omega)o_{i\alpha}(t-1)$

Here $\Delta$ is the tolerance threshold, $\omega$ is the opinion exchange
factor, and $t$ indicates discrete time steps.

Eq. 3 defines the interaction of external influences with the individuals.

${\rm\;if}\;\;o_{i\alpha}\leq\eta_{i,\alpha}\;\;{\rm
then}\;\;o_{i\alpha}=\left\\{\begin{array}[]{ll}o_{i\alpha}+M_{i\alpha}&{\rm\;\;if}\;\;P_{i\alpha}>r\\\
&\\\ o_{i\alpha}&{\rm otherwise}\end{array}\right.$ (3)

Here, $P_{i\alpha}$ is the probability of $i^{\rm th}$ individual receiving an
information on the issue $\alpha$, $r$ is a uniform random number between $0$
and $1$, $o_{i\alpha}$ and $\eta_{i,\alpha}$ are the opinion and the tolerance
level of the $i^{\rm th}$ individual on the issue $\alpha$ respectively.

At any discrete time step each individual, $i$, may receive a message on the
issue $\alpha$ if he/she is supporting his/her idea less than a threshold
value $\eta_{i,\alpha}$. The individual adopts the incoming message,
$M_{i\alpha}$ with a probability of $P_{i\alpha}$. Hence the opinion value is
replaced with a new value which is modified by the message content. Messages
can be sent by either one of the two parties or by any existing friend. If the
$i^{\rm th}$ individual is a supporter of one of the parties but not a
committed follower of its political stands on some of the issues the message
may convert the individual as a new supporter of the opposite party.

The society can have different sensitivities on different issues which are
represented as $s_{\alpha}$ in the numerical simulation. To deal with this
scenario three opinion weights can be assigned, $s_{\alpha}\;\;\alpha=1,2,3$,
to each three opinion components (Eq. 4).

$RO_{i}(t)=s_{1}o_{i1}(t)+s_{2}o_{i2}(t)+s_{3}o_{i3}(t)$ (4)

where $RO_{i}(t)$ is the resulted opinion of the $i^{\rm th}$ individual,
$s_{\alpha}$ and $o_{i\alpha}(t)$ are the weights,$\alpha=1,2,3$, and the
opinions on different issues respectively.

A binary decision of the individual proceed continuous opinion components
which is calculated by using the sign of the Eq. 4 5.

$D_{i}=\left\\{\begin{array}[]{rl}1&if\;\;RO_{i}>0\\\
-1&if\;\;RO_{i}<0\end{array}\right.$ (5)

If the overall opinion of the individual is positive we say an individual is
the supporter of the first view, otherwise the second view.

Both parties use regular media and social media communications to locate
weakly committed individuals and try to win them over by sending messages. The
system evolves a one-time step in discrete time as follows;

  1. 1.

Choose randomly an individual,$i$, from the set $\\{1,2,\dots,N\\}$

  2. 2.

Choose randomly a neighbor,$j$, from the set $\\{1,2,\dots,N\\}$

  3. 3.

Choose randomly an issue,$\alpha$, to discuss from the set $\alpha=1,2,3$

  4. 4.

Check the opinion component difference between individual $i$ and individual
$j$ on issues $\alpha$

  5. 5.

If $diff=o_{i\alpha}-o_{j\alpha}$ is less than tolerance threshold,$\Delta$,
exchange opinion with the rule;

$\displaystyle o_{i\alpha}(t)$ $\displaystyle=$ $\displaystyle\omega
o_{i\alpha}(t-1)+(1-\omega)o_{j\alpha}(t-1)$ $\displaystyle o_{j\alpha}(t)$
$\displaystyle=$ $\displaystyle\omega
o_{j\alpha}(t-1)+(1-\omega)o_{i\alpha}(t-1)$

  6. 6.

If $o_{i\beta}<\eta$, where $\beta$ is the issue on which external observer
send messages,

  7. 7.

Individual $i$ receive a targeted message $M_{i\beta}$

  8. 8.

Chose a random number, $r\in(0,1)$

  9. 9.

If $P_{\beta}>r$ where $P_{\beta}$ is the probability to adopt the message,
individual $i$ accepts the message and update opinion
$o_{i\beta}=o_{i\beta}+M_{i\beta}$

  10. 10.

Repeat starting from the first step and continue $N$ times.

The above steps describe $1$ discrete time step. The system is followed until
the final date of the campaign.

In the next section simulation results, obtained by applying the the proposed
model is introduced with figures.

##  3 Results and Discussion

The proposed model, described in section 2 contains two different but
complementary interactions among the members of an artificial society which
consists of $N=40000$ fully connected individuals. Simulations are carried on
discrete time steps. A time step is defined as the number of interactions,
$\mathbb{O}(N)$ which is sufficient for each individual to interact with at
least with one neighbor and one outside news source. At each time slice the
averages are taken over the opinion configurations. In the simulations, 500
different initial opinion configurations are created. The time span of the
election campaign is chosen as $200$ time steps.

The society, initially, consists of equally divided group of individuals. Each
opinion component has a Gaussian distribution with mean value $\pm 1$,
indicates two opposing views, and variance $\sigma^{2}=0.5$. With these
choices, the Gaussian opinion distributions overlap at the origin. As the
variance becomes closer to $1$ the overlapping opinions increases. The
individuals who constitutes the overlap region ( uncommitted supporters of
opposing ideas) are the targeted individuals by the external influences to
persuade to their view.

The interaction parameters are grouped into two. The first group is related to
peer-to-peer interactions while the second one is external influences.

  1. 1.

Peer-to-Peer Interaction Parameters Two parameters, the tolerance limit,
$\Delta_{i\alpha}$ and opinion exchange parameter $\omega$ controls the peer-
to-peer interactions. $\Delta_{i\alpha}$ is taken as a constant for all
members of the society and all issues, $\Delta_{i\alpha}=\Delta$. The choice
of tolerance parameter $\Delta=1.216$ allow the individuals to interact with a
wide range of opinion holders only excludes extremists. The opinion exchange
parameter is taken as, $\Omega=0.8$ which controls the speed of the opinion
formation process.

  2. 2.

The influence of the external sources

The sign of the resultant opinion (Eq.(4)) is the indicator of the vote where
the relative weights of the issues are taken equal fir the simplicity of the
discussions. The conviction parameter, $\eta$, is considered as a small value
in the simulation studies the value is used as $\eta=0.3$. The news acceptance
probability, $P_{\beta}$, take different values according to the alignment of
the opinion of the individual and the incoming news item. The message size,
$M_{i\beta}$, is also an other parameter which changes at each interaction. It
is taken as random value, $0\leq M_{i\beta}<0.5$.

Four different situations are considered: (a) averaged opinion with only peer-
to-peer interactions ($P_{\beta}=0;\;{\rm for}\;\;\beta=0,1$), (b) one of the
opinion supporters spread information by using mainstream and social media
while the other opinion spread only by peer-to-peer interactions,
($P_{0}=0.5;\;{\rm and}\;\;P_{1}=0.0$ ) (c) both opinion followers use the
same means of external influences, ($P_{\beta}=0.5;\;{\rm for}\;\;\beta=0,1$)
(d) both parties use influential sources together with peer-to-peer
interactions, but one put more convincing arguments forward, $P_{0}=1.0;\;{\rm
and}\;\;P_{1}=0.5$.

###  3.1 Individual interact with others through peer-to-peer interactions no
external sources affects the dynamics.

Figure 1 shows simulation results starting from different initial opinion
configurations which may be interpreted as the opinion changes in a region
during an election campaign (Paths of opinion). As it can be observed from the
figure, (Figure 1) each initial configuration converges a different final
state. This situation resemble election results in different election zones.
In different election zones, majority support may be on different parties but
the overall votes are the decisive factor for the result of the election.

Figure 1: Paths of opinion change starting from statistically independent
initial configurations.

In fact non of these individual paths has much meaning, the result of the
campaign is the average of all these paths. Figure 2 (a) shows that if there
is no external influences in the average both parties share the population
almost equally.

Figure 2: Time evolution of the configuration averaged opinion distributions.

The dynamics of opinion formation without external influences can be better
understood by observing the changes of the opinion distributions. Figure 3,
show the averaged opinion distributions for four instances of the election
campaign.

Figure 3: The snapshots of the averaged opinion distribution without external
influences.

At the initial stages of the campaign, $t=0$ (Figure 3 (a)), the society is
assumed to be equally divided on two opposing opinions. As soon as the
campaign starts, bounded confidence dynamics unite individuals around the
opposing opinions which sharpens the Gaussian opinion distributions. This
situation is not stationary, a third peak start to appear around the origin,
$t=40$ (Figure 3 (c)). As the time passes, the supporters of both parties,
apart from some extremists, converge towards a moderate opinion ($t=60$,
(Figure 3 (d))) and the distribution remains the same (Figure 4 (a)).

###  3.2 One of the parties send messages to convert less convinced
individuals.

In any election campaign, ideally, both parties use the same means to convince
individuals. Never the less, it is not always possible to maintain the same
level of publicity or use of media for both parties. The uncommitted
($\left|{O_{i,\beta}}\right|<\eta$) electors remain under one-sided news
bombardment which may change opinion of some of the individuals who aim to
vote for one party without a deep conviction. The average daily progress of
the opinion formation results are presented by figure 2 (b).

Figure 4: Configuration averaged opinion distributions .

If the outside sources can convince even a small group of uncommitted
individuals it may be sufficient to win the election. The time dependent
variations of the opinion distributions also give clear picture of the process
of opinion changes. Figure 4 (b) show that at $t=100$, peer-to-peer
interactions sharpen the Gaussian while the external influences change the
heights of the Gaussian’s. At the final stages of the election campaign the
middle peak lean towards the opinion who use external sources to convince
moderate individuals.

###  3.3 Both of the parties send messages to convert less convinced
individuals.

Figures 2 (c) and LABEL:FinalDistribution (c) show that if both parties are
using external news sources and the social media to convince the less
committed individuals, the picture is quite similar to the one seen for only
peer-to-peer interaction case. The moderate individuals fluctuate between two
opposing opinions, hence, the final election result is unpredictable, figure 2
(c)

###  3.4 Both parties send messages but one sends more convincing (fabricated)
messages.

The final consideration is that both parties use media and social media. One
of the parties increase activities, send targeted, fake or fabricated
messages, on the social media during the election period. This resemble the
situation during 2016 US Presidential elections [22]. The situation is not as
sewer as the one party usage of the social media (Discussed in subsection 3.2)
but even such an effort difference can be sufficient for winning the election.
Figure LABEL:LocalVsGlobal show the

Fig.LABEL:BCSurveyResultedOpinion that the percentage of the decision of two
parties under the effect of propaganda by both political side. This figure
shows an alternating behavior and when it comes to election day the election
result can be rather unpredictable.

##  4 Conclusions

Recently the internet is the primary source of acquisition of knowledge for
the societies. This makes the internet a very powerful and unique. An exciting
information, whether it is fake, fabricated or destructive propagate very fast
among the members of the societies. Media can put forward some ideas or hide
some information, by censoring, to make followers/members gain an advantage.
In social interactions the spread of gossip and fabricated information has a
very long history and it is not only limited with the online media [23]. Never
the less the involvements of various data companies on the 2016 US
presidential elections are publicly known and opened a debate on the violation
of civil liberties [17]. Such a data-driven research needs of using an
interdisciplinary approach. Using data science techniques to understand voter
behavior on the segment of their ideas allow politicians to use digital-
marketing strategies to reach individuals. Hence usage of powerful data
analyzing techniques is becoming increasingly harmful to the civil liberties.
As the 2020 US presidential election is approaching the studies on the effects
of the fake and fabricated news and personalized, targeted messages gain
upmost importance.

The present work aims to introduce a simple agent-based model to simulate the
effects of using gathered information to send targeted messages during an
election process. Recent studies show that societies are almost evenly divided
on the main political issues. Hence such a targeted external information
bombardment may be very effective to change the opinions. Since all parties
may use the same techniques, a small percentage of, $(1\%-2\%)$, opinion
fluctuations may be decisive on the result of the elections. The above
assumptions seem reasonably realistic considering voting processes such as
Scottish referendum $(55.3\%-44.7\%)$, 2016 US Election $(46.1\%-48.2\%)$ and
Brexit referendum $(51.9\%-48.1\%)$. It is observed that if both parties
compete equally the election results are unpredictable. If one of the parties
use the technological power and social media more than the opponents, can
easily gain the required small percentage of the undecided voters. It is
evident that in the next decade the use of artificial intelligence techniques
to extract information from individuals social media history will be used more
frequently unless some global legislative regulation on the use of private
information.

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