# Wavelength selection by interrupted coarsening in reaction–diffusion systems

Fridtjof Brauns<EMAIL_ADDRESS>Henrik Weyer  Arnold Sommerfeld Center
for Theoretical Physics and Center for NanoScience, Department of Physics,
Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 München,
Germany  Jacob Halatek  Biological Computation Group, Microsoft Research,
Cambridge CB1 2FB, UK  Junghoon Yoon  Erwin Frey<EMAIL_ADDRESS>Arnold
Sommerfeld Center for Theoretical Physics and Center for NanoScience,
Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße
37, D-80333 München, Germany

###### Abstract

Wavelength selection in reaction–diffusion systems can be understood as a
coarsening process that is interrupted by counteracting processes at certain
wavelengths. We first show that coarsening in mass-conserving systems is
driven by self-amplifying mass transport between neighboring high-density
domains. We derive a general coarsening criterion and show that coarsening is
generically uninterrupted in two-component systems that conserve mass. The
theory is then generalized to study interrupted coarsening and anti-coarsening
due to weakly-broken mass conservation, providing a general path to analyze
wavelength selection in pattern formation far from equilibrium.

To predict the wavelength of patterns in highly nonlinear systems is a
critical open problem as wavelength selection is ubiquitous in a large range
of non-equilibrium systems Liu and Goldenfeld (1989); Glotzer  _et al._
(1995); Caussin  _et al._ (2014); Solon  _et al._ (2015); Murray and Sourjik
(2017); Chiou  _et al._ (2020); Gai  _et al._ (2020). While the amplitude
equation formalism and weakly nonlinear analysis have been highly successful
in the vicinity of onset Cross and Hohenberg (1993), these approaches are not
informative for large amplitude patterns far away from onset. For one-
component systems, a theory for wavelength selection based on a multiple-scale
analysis has been developed Politi and Misbah (2004, 2006), but
generalizations to multi-component systems have remained elusive.

In this Letter, we propose that wavelength selection in reaction–diffusion
systems can be understood as a coarsening process that is interrupted and even
reversed by counteracting processes at certain wavelengths. Specifically, we
study two-component systems and develop a theory for the mass-conserving case
first where coarsening is uninterrupted. We then generalize this theory to
account for source terms that break mass conservation and counteract the
coarsening process.

While coarsening is well understood as minimization of the free energy for
systems relaxing to thermal equilibrium (such as binary mixtures Wagner
(1961); Lifshitz and Slyozov (1961)), this reasoning is generally not
applicable for non-equilibrium systems such as most reaction–diffusion
systems. Two-component mass-conserving reaction–diffusion (MCRD) systems serve
as paradigmatic models for intracellular pattern formation Otsuji  _et al._
(2007); Goryachev and Pokhilko (2008); Altschuler  _et al._ (2008); Mori  _et
al._ (2008); Jilkine and Edelstein-Keshet (2011); Trong  _et al._ (2014);
Chiou  _et al._ (2018), and are used as phenomenological models for a wide
range of systems including precipitation patterns Scheel (2009), granular
media Aranson and Tsimring (2008), and braided polymers Forte  _et al._
(2019). It has long been speculated that two-component MCRD systems
generically exhibit uninterrupted coarsening Ishihara  _et al._ (2007); Mori
_et al._ (2008); Chiou  _et al._ (2018); Morita and Ogawa (2010). However, it
has remained unclear whether coarsening always goes to completion in two-
component MCRD systems, largely owing to a lack of insight into the underlying
physical processes.

Here, we show that coarsening is driven by positive feedback in the
competition for mass, derive a simple and quantitative description of
coarsening dynamics, and explain why coarsening is generically uninterrupted
in two-component MCRD systems. As they are grounded in a phase-space analysis
Brauns  _et al._ (2020), our results are independent of the specific
mathematical form of the reaction kinetics.

Building on the insights into the coarsening process in the mass-conserving
case, we elucidate and quantify the physical mechanisms underlying wavelength
selection in the presence of weak source terms (weakly broken mass
conservation). Coarsening arrests when mass competition is balanced by
production and degradation. Moreover, domain splitting—owing to the
destabilization of plateaus—reverses coarsening. Both are graphically
understood by a generalization of the phase-space analysis. Since our approach
builds on studying the spatial redistribution of a nearly conserved quantity,
we expect that it can be generalized beyond two-component reaction–diffusion
systems; for instance, to systems with more components and to hydrodynamic
models for active matter systems Cates  _et al._ (2010); Caussin  _et al._
(2014); Cates and Tailleur (2015); Liebchen and Levis (2017); Chaté (2020).

The general form of a reaction–diffusion system with two components, $u$ and
$v$, can be written as

$\displaystyle\partial_{t}u(x,t)$
$\displaystyle=D_{u}\nabla^{2}u+f(u,v)+\varepsilon\,s_{1}(u,v),$ (1a)
$\displaystyle\partial_{t}v(x,t)$
$\displaystyle=D_{v}\nabla^{2}v-f(u,v)+\varepsilon\,s_{2}(u,v),$ (1b)

on a domain $\Omega$, with either no-flux or periodic boundary conditions
111We discuss the dispersion relation of Eq. (1) linearized around a
homogeneous steady state in Fig. S1 in the SM.. For specificity, we choose
$D_{u}<D_{v}$ 222Our findings immediately generalize to systems with density-
independent cross-diffusion, see SM Sec. 1.2.. The reaction term $f$ describes
conversion between $u$ and $v$ while the source terms $s_{1,2}$ with a (small)
dimensionless source strength $\varepsilon$ break mass conservation.

Let us first analyze the mass-conserving case $\varepsilon=0$. Then, the total
density $\rho=u+v$ is conserved such that the average
$\bar{\rho}=|\Omega|^{-1}\int_{\Omega}\mathrm{d}x\rho(x,t)$ remains constant.
The time evolution of $\rho$ is given by Otsuji  _et al._ (2007); Ishihara
_et al._ (2007); Brauns  _et al._ (2020); Forte  _et al._ (2019)

$\partial_{t}\rho(x,t)=D_{v}\nabla^{2}\eta(x,t)$ (2)

with the _mass-redistribution potential_ defined by $\eta:=v+(D_{u}/D_{v})u$;
the corresponding dynamical equation for $\eta(x,t)$ is given in the SM
Note:SM , Sec. 1.1. For stationary patterns $[\tilde{u}(x),\tilde{v}(x)]$, the
mass-redistribution potential must be spatially uniform,
$\eta(x)=\eta_{\mathrm{stat}}$. Based on this one can analyze two-component
MCRD systems in the $(u,v)$ phase plane Brauns  _et al._ (2020): There,
stationary patterns are constrained to a linear subspace,
$v+(D_{u}/D_{v})u=\eta_{\mathrm{stat}}$, called _flux-balance subspace_ (FBS);
see Fig. 1b. The intercept $\eta_{\mathrm{stat}}$ is determined by the balance
of the spatially integrated reactive flows (_total turnover balance_),
corresponding (approximately) to a balance of areas (shaded in red in Fig. 1b)
enclosed by the FBS and the _reactive nullcline_ ($f=0$, NC). The FBS-NC
intersection points correspond to the plateau(s) and inflection point(s) of a
stationary pattern. Two types of patterns can be distinguished—mesas and
peaks. The elementary mesa pattern is composed of two plateaus, connected by
an interface (or “kink”), while a peak forms when the maximum density does not
saturate in a high-density plateau (Fig. 1a, compare Fig. 2a) Brauns  _et al._
(2020)333Diffusive flux balance ensures that any stationary pattern can be
dissected by inserting no-flux boundaries at its extrema.. We begin the
analysis with peak patterns and then generalize the results to mesas.

Figure 1:  (a) Illustration of a stationary peak with peak mass $M$.
Increasing the mass to $M+\delta M$ increases the peak amplitude to
$\hat{u}+\delta\hat{u}$. (b) Representation of the stationary peak in phase
space (thick blue line), which is constrained to the FBS (dashed blue line).
The FBS-offset $\eta_{\mathrm{stat}}(M)$ is determined by a balance of total
reactive turnovers (areas shaded in red). For a peak with increased mass
$M+\delta M$, and thus increased peak amplitude $\delta\hat{u}$, the FBS
shifts downwards $\delta\eta_{\mathrm{stat}}$ until total turnover balance is
restored (balance of green-shaded areas). (c) After a perturbation of two
identical stationary peaks, the gradient in the mass-redistribution potential
$\eta$ (orange line) drives mass-transport between the peaks (orange arrow)
such that the larger (smaller) peak grows (shrinks) further (blue arrows).

## A mass-competition instability drives coarsening.

Coarsening requires the transport of mass between peaks. Because mass
transport is diffusive, it is fastest on the shortest length scales; hence,
the dominant process is competition for mass between neighboring peaks (Fig.
1a). Thus, as an elementary case, we study two peaks in a ‘box’ with no-flux
boundary conditions. Consider a situation (“coarsening limit”) where the peaks
are well separated, such that diffusive transport is limiting. We can then
approximate the peaks to be in (regional) quasi-steady state (QSS), such that
$\eta=\eta_{\mathrm{stat}}(M)$ at a given peak with total mass $M$. This
approximation is commonly applied in thin film theory Glasner and Witelski
(2003); Pismen and Pomeau (2004) and Ostwald ripening Lifshitz and Slyozov
(1961); Wagner (1961).

Starting from two identical, stationary peaks, each with total mass $M_{0}$,
the dynamics of the mass difference between them
($M_{\mathrm{R,L}}=M_{0}\pm\delta M$)—obtained by integration of Eq. (2) over
a single peak—is determined by the $\eta$-gradients in the plateau between
them (indicated by the orange arrow in Fig. 1c). Using QSS at each peak
separately, the mass-redistribution potential at the peaks is given by
$\eta_{\mathrm{R,L}}=\eta_{\mathrm{stat}}\pm(\partial_{M}\eta_{\mathrm{stat}}|_{M_{0}})\,\delta
M$. Between the peaks, $\eta$ obeys $\partial_{x}^{2}\eta=0$ because diffusive
relaxation within the plateau is fast compared to the peak evolution (see SM
Sec. 2 for details). Thus in 1D, the resulting gradient in $\eta$ is linear
and determined by $\eta=\eta_{\mathrm{R,L}}$ at the peak positions. For a
given peak separation $\Lambda$, this approximation determines the dynamics of
mass redistribution

$\partial_{t}\delta
M\approx-\frac{2D_{v}}{\Lambda}\left(\partial_{M}\eta_{\mathrm{stat}}\big{|}_{M_{0}}\right)\delta
M=:\sigma_{\mathrm{D}}\,\delta M.$ (3)

The subscript D denotes the diffusion-limited regime. If the growth rate
$\sigma_{\mathrm{D}}$ is positive, an instability driven by positive feedback
in competition for mass results in coarsening. Hence, the condition for
uninterrupted coarsening reads

$\partial_{M}\eta_{\mathrm{stat}}(M)<0,$ (4)

i.e. that $\eta_{\mathrm{stat}}(M)$ is a strictly monotonically decreasing
function for all stable stationary single-peak solutions. This recovers a
previous, mathematically derived coarsening condition Ishihara  _et al._
(2007); Otsuji  _et al._ (2007). Importantly, the analysis presented here
gives insight into the underlying physical mechanism and shows that not only
the criterion for coarsening, but the entire _temporal evolution_ of
coarsening is determined by $\partial_{M}\eta_{\mathrm{stat}}$ via Eq. (3)
444For mesa patterns in 1D, $\partial_{M}\eta_{\mathrm{stat}}$ must be
calculated for the high- and low-density plateaus separately (see SM Sec. 5)..
We learn that the functional dependence of the _mass-redistribution potential_
on the peak mass, $\eta_{\mathrm{stat}}(M)$, plays a role analogous to the
functional dependence of the chemical potential on the droplet size that
drives Ostwald ripening or to the film height in dependence of droplet size
that drives coarsening of unstable thin films Glasner and Witelski (2003);
Pismen and Pomeau (2004).

Figure 2:  (a) Illustration of the peak to mesa transition as the total mass
$M$ is increased. (b) The function $\eta_{\mathrm{stat}}(M)$ obtained by
numerical continuation of the stationary solutions for the reaction kinetics
$f_{\mathrm{ex}}$. Crossover from power law for peak patterns (amplitude not
saturated) to exponential approach to $\eta_{\mathrm{stat}}^{\infty}$ for mesa
patterns. (c) Coarsening dynamics from finite element simulations for
$f_{\mathrm{ex}}$ (black circles; mean peak distance averaged over four
independent runs started from random initial conditions; parameters:
$D_{u}=1,D_{v}=10^{4},\bar{\rho}=1.5$ and system size $|\Omega|=2\times
10^{5}$, periodic boundary conditions). The red line shows the analytic
prediction based on $\sigma_{\mathrm{D}}$ from $\eta_{\mathrm{stat}}(M)$,
shown in (b), via Eq. (3). After an initial transient, power-law coarsening
$\Lambda\sim t^{3/8}$ for peaks is observed, which flattens into logarithmic
coarsening for mesas.

## Generic coarsening laws for mass-conserving systems.

To show that coarsening is uninterrupted, we need to show that the criterion
Eq. (4) holds, and continues to hold as small peaks disappear causing the mass
of the remaining peaks to increase. For an intuitive argument, consider a
single stationary peak with mass $M$ (see Fig. 1a) and its representation in
phase space, the blue line in Fig. 1b. Add an amount $\delta M$ of mass and
hold $\eta_{\mathrm{stat}}$ fixed for the moment (for the sake of argument).
Fixing $\eta_{\mathrm{stat}}$ also fixes the plateau $u_{-}$. Therefore, the
additional mass will increase the peak amplitude $\hat{u}$ (Fig. 1b), causing
the reactive turnover to the right of $u_{0}$ to increase. The resulting
imbalance of total turnover entails a net reactive flow that shifts the flux-
balance subspace downwards, i.e. lowers $\eta_{\mathrm{stat}}$, to restore
total turnover balance. We conclude that, $\eta_{\mathrm{stat}}(M)$ is
generically a monotonically decreasing function. (More rigorous arguments are
given in SM Secs. 4 and 5).

Let us now turn to the dynamic coarsening laws. As an example, consider
$f_{\mathrm{ex}}\,{=}\,(1\,{+}\,u)v\,{-}\,u/(1\,{+}\,u)$, where the first and
second terms may, for instance, describe protein recruitment and first-order
enzymatic detachment, respectively. A simple scaling argument 555For a back of
the envelope calculation we use density at the pattern inflection point
$u_{0}$ and the interface width approximation
$\ell_{\mathrm{int}}\,{\approx}\,\pi/q_{\mathrm{max}}|_{u_{0},\eta_{\mathrm{stat}}}$
Brauns  _et al._ (2020), and $\hat{u}\approx 2u_{0}$ to estimate the peak mass
$M\,{=}\,\int\mathrm{d}x[\tilde{\rho}(x)\,{-}\,\rho_{-}]\,{\approx}\,\hat{u}\cdot\ell_{\mathrm{int}}\,{\approx}\,u_{0}\cdot
2\pi/q_{\mathrm{max}}|_{\eta_{\mathrm{stat}}}\,{\approx}\,2\pi
u_{0}\sqrt{D_{u}/f_{u}|_{\eta_{\mathrm{stat}}}}$. For the example
$f_{\mathrm{ex}}$, one finds $f_{u}\,{\approx}\,\eta_{\mathrm{stat}}$ and
$u_{0}\,{\approx}\,\eta_{\mathrm{stat}}^{-1}$, and thus
$M\,{\sim}\,\eta_{\mathrm{stat}}^{-3/2}\,{=}\,\eta_{\mathrm{stat}}^{-1/\alpha}$,
for sufficiently large $M$ and $D_{v}\,{\gg}\,D_{u}$. Other reaction terms,
e.g. with different nonlinearities in the recruitment term, yields other
exponents $\alpha$.  yields a power-law relation
$\eta_{\mathrm{stat}}(M)\,{\sim}\,M^{-\alpha}$, where the exponent depends on
the specific reaction kinetics ($\alpha\,{=}\,\nicefrac{{2}}{{3}}$ for the
example above); see Fig. 2b. In a large system containing multiple peaks, the
average peak separation $\langle\Lambda\rangle$ is linked to the
characteristic peak mass by $\langle
M\rangle\,{=}\,(\bar{\rho}\,{-}\,\rho_{-})\langle\Lambda\rangle$, where
$\rho_{-}$ is the total density in the low density plateau between the peaks,
and $\langle\cdot\rangle$ denotes an average over the entire system. As peaks
collapse, with a typical time given by the inverse growth rate of the mass-
competition instability $t\,{\sim}\,\sigma_{\mathrm{D}}^{-1}$, the average
peak separation $\langle\Lambda\rangle$ will increase. Combining
$\sigma_{\mathrm{D}}\,{\sim}\,{-}\langle\partial_{M}\eta_{\mathrm{stat}}\rangle/\langle\Lambda\rangle$
with $\langle\partial_{M}\eta_{\mathrm{stat}}\rangle\,{\sim}\,\langle
M\rangle^{-\alpha-1}\,{\sim}\,(\bar{\rho}\langle\Lambda\rangle)^{-\alpha-1}$
yields power-law coarsening with
$\langle\Lambda\rangle(t)\,{\sim}\,t^{1/(2+\alpha)}$; see Fig. 2c and Fig. S4.
Moreover, using appropriate scaling amplitudes, the coarsening trajectories
for different average masses $\bar{\rho}$ can be collapsed onto a single
master curve obtained from $\partial_{M}\eta_{\mathrm{stat}}$ (see SM Sec. 3).
Power-law coarsening in 1D has previously been found for peak-like droplets
formed during the dewetting of thin liquid films Glasner and Witelski (2003).

As peaks collapse, those remaining grow in mass and height. When the density
at the peak maximum saturates in a high-density plateau (corresponding to a
FBS-NC intersection point in phase space), a mesa pattern starts to form (Fig.
2a, Fig. S3) 666If $u,v$ describe (shifted) concentrations ($u,v$ bounded from
below) and $D_{u}/D_{v}$ is finite, mesas inevitably form at high densities
(cf. Fig. 2a). Arbitrarily large peaks form if no third FBS-NC intersection
point exists; as, for example, in “Model II” in Ref. Otsuji  _et al._ (2007).
The peak-to-mesa transition has previously been observed for unstable thin
films subject to gravity Gratton and Witelski (2008). . Gratton and Witelski
(2008) For such mesas, somewhat more subtle arguments show that
$\eta_{\mathrm{stat}}(M)$ remains a monotonically decreasing function (see SM
Sec. 5). In essence, changing $M$ shifts the interface positions and thus
changes the width of a mesa’s plateau. As the density profile approaches the
limiting plateaus $u_{\pm}(\eta_{\mathrm{stat}}^{\infty})$ through exponential
tails, $\eta_{\mathrm{stat}}(M)$ approaches $\eta_{\mathrm{stat}}^{\infty}$
exponentially slowly (see inset in Fig. 2b) where we define
$\eta_{\mathrm{stat}}^{\infty}$ as the limit of $\eta_{\mathrm{stat}}$ for the
stationary pattern on an infinite domain (see SM Sec. 5.1). Using the same
scaling arguments as for peaks, one obtains a logarithmic coarsening law for
all mesa patterns, as in the one-dimensional Cahn–Hilliard model Langer
(1971). For the concrete example $f_{\mathrm{ex}}$, we find excellent
agreement between finite-element simulations and $\langle\Lambda\rangle(t)$
obtained from $\eta_{\mathrm{stat}}(M)$ by these scaling arguments (see Fig.
2c). Based on the physical insights presented above, a generalization to more
than one spatial dimension is straightforward. For mesa-like droplets with
radius $R$ one finds $\eta_{\mathrm{stat}}-\eta_{\mathrm{stat}}^{\infty}\sim
R^{-1}$ which yields power law coarsening with the universal exponent
$\nicefrac{{1}}{{3}}$ (see SM Sec. 5.4). For peak-like droplets, we expect
system-dependent exponents as in 1D.

Figure 3:  Wavelength selection by weakly broken mass conservation. (a,b) Mesa
splitting: (a) real space profiles of $\tilde{\rho}(x)$ and $\tilde{\eta}(x)$,
(b) phase space in $(\rho,\eta)$ coordinates, with the source term in local
equilibrium approximation plotted below. The green shaded area indicates the
region of lateral instability. (c) Interrupted coarsening due to a balance of
production, degradation, and mass redistribution between neighboring mesas.
(d) Regimes separated by interrupted coarsening (squares) and mesa splitting
(circles) as well as analytic approximations (blue, green lines) for large
$\Lambda$ and small $\varepsilon$. While in the coarsening regime (blue)
stationary patterns are unstable, no stationary patterns exist in the mesa-
splitting regime (green). In the regime of small $\Lambda$ and large
$\varepsilon$, corrections become large and the approximations do not hold
(see SM Sec. 7). Parameters: $D_{u}=0.1,D_{v}=1,p=2$.

## The limit of large $D_{v}$.

For $D_{v}\,{\rightarrow}\,\infty$, mass redistribution by $v$-diffusion
becomes instantaneous, such that the reactive conversion between $u$ and $v$,
which drives the growth/shrinking of mesas or peaks, becomes limiting. In this
_reaction-limited_ case, we find
$\sigma_{\mathrm{R}}\,{\approx}\,(\partial_{M}\eta_{\mathrm{stat}})\,\ell_{\mathrm{int}}\langle
f_{v}\rangle_{\mathrm{int}}$, where $\ell_{\mathrm{int}}$ is the interface
width and $\langle\cdot\rangle_{\mathrm{int}}$ denotes the average over the
interface region (see SM Sec. 6 for details and numerical verification).
Comparing with Eq. (3) shows that the coarsening criterion Eq. (4) holds in
both regimes, and the crossover from diffusion- to reaction-limited coarsening
occurs at $D_{v}/\Lambda\,{\approx}\,\ell_{\mathrm{int}}\langle
f_{v}\rangle_{\mathrm{int}}$.

## Weakly broken mass conservation.

With an understanding for the coarsening dynamics in the strictly mass-
conserving system, we now consider the effect of slow production and
degradation for $0<\varepsilon\ll 1$. We will see that these additional
processes interrupt coarsening Liu and Goldenfeld (1989); Glotzer  _et al._
(1995); Kolokolnikov  _et al._ (2006); Cates  _et al._ (2010) and can reverse
it by inducing peak/mesa splitting Kolokolnikov  _et al._ (2007); Murray and
Sourjik (2017); Gai  _et al._ (2020), thus selecting a range of stable pattern
wavelengths. In the presence of source terms, the time evolution of the total
density $\rho$ is governed by

$\partial_{t}\rho=D_{v}\partial_{x}^{2}\eta+\varepsilon\,s(u,v),$ (5)

with the total source $s:=s_{1}+s_{2}$. Hence, the average mass
$\langle\rho\rangle$ is no longer a control parameter but a time-dependent
variable that is determined indirectly by a balance of production and
degradation (in short: _source balance_). In phase space, there are now two
reactive nullclines, one each for $u$ and $v$, which both converge to
$f\,{=}\,0$ for $\varepsilon\,{\rightarrow}\,0$. Their intersection point(s)
determine(s) the homogeneous steady state (HSS) $\rho_{\mathrm{hss}}$ that
balances the total source term.

In the following, we restrict ourselves to mesa patterns. To lowest order in
$\varepsilon$, source balance determines the ‘half lengths’ $L_{\pm}$ of the
upper and lower plateaus (see SM Sec. 7). Along the plateaus, the spatial
gradients induced by slow production–degradation ($\varepsilon$ small) are
shallow, such that the dynamics is (approximately) slaved to the nullcline
$f\,{=}\,0$ (see Fig. 3b). This justifies a local equilibrium approximation
$s(u,v)\,{\approx}\,s[u^{*}(\rho),v^{*}(\rho)]\,{\equiv}\,s^{*}(\rho)$ in Eq.
(5), where the local equilibria are defined by $f(u^{*},v^{*})\,{=}\,0$ and
$u^{*}\,{+}\,v^{*}\,{=}\,\rho$. On the short scale of the interface width, the
weak source term is negligible and each interface constrained to a flux-
balance subspace. We are now in a position to generalize the phase-space
analysis introduced in Ref. Brauns  _et al._ (2020) and analyze interrupted
coarsening and mesa splitting.

(i) Peak/mesa splitting. Consider the fully coarsened state for
$\varepsilon\,{=}\,0$ and add a small source term such that
$s^{*}(\rho_{+})\,{<}\,0$ and $s^{*}(\rho_{-})\,{>}\,0$ (i.e.
$\rho_{-}\,{<}\,\rho_{\mathrm{hss}}\,{<}\,\rho_{+}$, see Fig. 3b) 777In steady
state, net degradation in high-density regions ($\rho>\rho_{\mathrm{hss}}$)
and net production in low-density regions ($\rho<\rho_{\mathrm{hss}}$) must
balance. . The upper plateau is depressed by net degradation and is refilled
by inflow from the interfaces that connect to the lower plateau where net
production prevails. The longer the plateaus (and the larger $\varepsilon$),
the more they curve towards $\rho_{\mathrm{hss}}$. Since
$\rho_{-}\,{<}\,\rho_{\mathrm{hss}}\,{<}\,\rho_{+}$, $\rho(x)$ will eventually
enter the interval of lateral instability
$[\rho_{\mathrm{lat}}^{-},\rho_{\mathrm{lat}}^{+}]$ (where
$\partial_{\rho}\eta^{*}\,{<}\,0$), triggering a nucleation event that results
the splitting of the mesa (see Fig. 3a and Movie 2). A simple approximation
for the threshold wavelength $\Lambda_{\mathrm{split}}(\varepsilon)$ where
this happens is derived in the SM, Sec. 7.1. Comparison with numerical
simulations shows excellent agreement (see Fig. 3d).

(ii) Interrupted coarsening. Intuitively, production and degradation can
counteract the mass-competition instability. To determine the corresponding
length scale $\Lambda_{\mathrm{stop}}$ where coarsening arrests, we consider
the stability of two neighboring, symmetric mesas. A perturbation that moves a
small amount of mass from one mesa to the other (Fig. 3c) has two effects:
First, it shifts the mass-redistribution potential at the interfaces, leading
to mass transport that further amplifies the perturbation with rate
$\sigma_{\mathrm{D}}(\Lambda)\delta M$ as in the strictly mass-conserving
situation; cf. Eq. (3). Second, the changed lengths $\delta L\,{=}\,\delta
M/(\rho_{+}\,{-}\,\rho_{-})$ of the two mesas result in net production
(degradation) in the shorter (longer) mesa with rate
$\varepsilon|s^{*}(\rho_{\mathrm{outer}})|\delta L$ (indicated by the purple
arrows in Fig. 3c). Here $\rho_{\mathrm{outer}}$ denotes the total density of
the outer plateau (the inner plateau shifts as a whole and does not change in
length, see Fig. 3b). Together, the balance of both processes determines
$\Lambda_{\mathrm{stop}}$ (see SM Sec. 7.2 for details)

$\sigma_{\mathrm{D}}(\Lambda_{\mathrm{stop}})\approx\varepsilon\frac{|s^{*}(\rho_{\mathrm{outer}})|}{\rho_{+}-\rho_{-}}.$
(6)

As a concrete example, we apply Eq. (6) to the “Brusselator” model Prigogine
and Lefever (1968) ($f\,{=}\,u^{2}v\,{-}\,u$, $s\,{=}\,p\,{-}\,u$), and find
excellent agreement with numerics (Fig. 3c). Notably, the simple estimate
given by Eq. (6) generalizes a previous, mathematically obtained results
Kolokolnikov  _et al._ (2006); McKay and Kolokolnikov (2012).

Our analysis shows that the mechanisms underlying mesa splitting and
interrupted coarsening are distinct. Notably, the length scale where
coarsening stops is much smaller than the length scale where mesas/peaks split
(see Fig. 3d). This implies that there are stable periodic patterns for a
large, continuous range of wavelengths (multistability), as was shown
previously for the ‘Brusselator’ Prigogine and Lefever (1968); Kolokolnikov
_et al._ (2006, 2007). Similarly, multistability of wavelengths was recently
found in a hydrodynamic model for flocking Caussin  _et al._ (2014).
Interestingly, a unique length scale is selected once noise is accounted for
Solon  _et al._ (2015). Noise-driven wavelength selection was also observed in
an “active Model B” Tjhung  _et al._ (2018). It would be interesting to study
whether this phenomenon is also found in reaction–diffusion systems.

Another interesting open problem are systems with cross diffusion and density-
dependent diffusion coefficients (see e.g. Refs. Vanag and Epstein (2009);
Rossi  _et al._ (2011); Giri  _et al._ (2020); Giunta  _et al._ (2020)). We
also expect that our approach can be generalized to systems with more than two
components, higher spatial dimensions and also beyond reaction–diffusion
systems. In particular, conserved densities (particle numbers) are a generic
feature of many active matter systems in which coarsening and length-scale
selection (“micro-phase separation”) are of growing interest Cates  _et al._
(2010); Liu  _et al._ (2013); Wittkowski  _et al._ (2014); Caussin  _et al._
(2014); Cates and Tailleur (2015); Gonnella  _et al._ (2015); Sabrina  _et
al._ (2015); Liebchen and Levis (2017); Tjhung  _et al._ (2018); Liu  _et al._
(2019); Curatolo  _et al._ (2019); Li and Cates (2020); Chaté (2020).

###### Acknowledgements.

This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German
Research Foundation) through the Collaborative Research Center (SFB) 1032 –
Project-ID 201269156 – and the Excellence Cluster ORIGINS under Germany’s
Excellence Strategy – EXC-2094 – 390783311. FB and HW contributed equally to
this work.

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# Two Truths and a Lie: Exploring Soft Moderation of COVID-19 Misinformation
with Amazon Alexa

Donald L. Gover  DePaul University 1 E Jackson BlvdChicagoIllinoisUSA
<EMAIL_ADDRESS>and  Filipo Sharevski  DePaul University 1 E Jackson
BlvdChicagoIllinoisUSA<EMAIL_ADDRESS>
###### Abstract.

In this paper, we analyzed the perceived accuracy of COVID-19 vaccine Tweets
when they were spoken back by a third-party Amazon Alexa skill. We mimicked
the soft moderation that Twitter applies to COVID-19 misinformation content in
both forms of warning covers and warning tags to investigate whether the
third-party skill could affect how and when users heed these warnings. The
results from a 304-participant study suggest that the spoken back warning
covers may not work as intended, even when converted from text to speech. We
controlled for COVID-19 vaccination hesitancy and political leanings and found
that the vaccination hesitant Alexa users ignored any type of warning as long
as the Tweets align with their personal beliefs. The politically independent
users trusted Alexa less then their politically-laden counterparts and that
helped them accurately perceiving truthful COVID-19 information. We discuss
soft moderation adaptations for voice assistants to achieve the intended
effect of curbing COVID-19 misinformation.

Alexa, Misinformation, COVID-19, Twitter Soft Moderation

##  1\. Introduction

Misinformation and rumors about viruses are not a new thing. What’s new is the
size of the target audience and the speed with which such damaging information
spreads online. It took weeks and a publication in foreign media outlets for
the KGB-initiated “Operation Infektion,” spreading the rumour that HIV/AIDS
was a misfired American biological weapon in the 1980s, to gain traction and
manipulate the public opinion, at least outside of the U.S. (Boghardt, 2009).
Fast forward 40 years, one can choose an aspect of the novel COVID-19 virus
misinformation (e.g. origin, vaccines’ adverse effects, efficacy) as well as
audience (e.g. Twitter, Facebook, Parler) and manipulate the public opinion in
a matter of seconds both in the U.S. and everywhere in the world (Jachim et
al., 2020; Peironi et al., 2021).

While there was no structure of countering the old-style vaccination rumors, a
coordinated soft moderation of misinformation was rather quickly put in place
during the COVID-19 pandemic on the mainstream social media platforms (Roth
and Pickles, 2020). Such an effort was warranted because the real world
implications of (mis)information and unverified rumors have a direct impact on
public health, especially of mass immunization. According to Twitter, who
opted to use warning tags and covers as misinformation labels, the supposed
aim of the soft moderation is to reduce misleading or harmful information that
could “incite people to action and cause widespread panic, social unrest or
large-scale disorder” (Roth and Pickles, 2020).

Consequently, the academic community set forth to investigate whether this
seemingly noble aim was in fact achieved among the social media users and the
general public. In an early study, the soft moderation labels were found to
have a counter effect since the warnings convinced people to believe the
misinformation even more than if the labels were not there (Clayton et al.,
2019). A study exploring this so-called “soft moderation” implemented by
Twitter found that the platforms’ content with warning labels generated more
action than content without said labels (Zannettou, 2021). The soft moderated
Tweets were more likely to be distributed than a “valid” Tweet through
discourse, not always because the soft moderated Tweets contained
misinformation but because they contained a response to mock or disclaim an
original author or a valid Tweet. Interestingly, a mere 1% of the Tweets
gathered for the study were labeled with a COVID-19 warning and a number of
these few Tweets were found to be mislabeled simply because they contained the
words “oxygen” and “frequency”. Another study, in this context, found that
some users did not trust the soft moderation intervention and felt that
Twitter itself was biased and mislabeling content (Geeng et al., 2020). Even
without the warning labels, a varying degree of users’ perceptions and beliefs
regarding vaccines in general and about COVID-19 vaccines in particular plays
a role in individuals’ reaction to (mis)information Tweets. A study on vaccine
misinformation spreading and acceptance on social media platforms showed the
effectiveness of “influential users” within like minded vaccine-fearing
followers to be very high (Featherstone et al., 2020).

Mainstream social media platforms like Twitter allow for visual discernment of
the information including the warning labels, formation of so-called
“influencer” accounts, and direct communication of the engagement with the
content metrics such as number of replies, re-Tweets, likes, and shares. While
all of these factors certainly affect the receptivity of any COVID-19 vaccine
information, little attention is devoted to exploring how people respond to
soft moderated COVID-19 vaccine Tweets when these are delivered through a
voice assistant like Amazon Alexa. Unlike the traditional Twitter interface,
Alexa is the sole authority or “influencer” that delivers the Tweet when
prompted possibly without disclosing the details of any labeling or engagement
metrics (depending on the configuration for retrieval and presentation of
one’s twitter diet). Users usually trust Alexa and worry only about Alexa
intruding into their privacy, but not about the validity of the information
delivered by Alexa (Lau et al., 2018). Since the configuration of how one’s
twitter diet is spoken-back by Alexa can be customized and implemented by
various third-party applications, called “skills” we set to explore how users
will respond when such a third-party skill is used to deliver soft moderated
COVID-19 vaccine Twitter content. Studies in the past have shown that third-
party skills could be dangerous in that can silently rephrase information from
any source to mislead a user and induce misperception about a polarizing topic
such as vaccination, free speech, or government actions (Sharevski et al.,
2020a; Sharevski et al., 2020b, 2021).

##  2\. Soft Moderation by Alexa

Malicious skills for Alexa, unsurprisingly, exist on the Amazon Skills Store
(Vaidya et al., 2015). Some of them pray on malicious voice commands (songs,
phonemes, inaudible noises) to be interpreted as legitimate by Alexa and
invoke a skill that snoops on the user or attempts to steal their credentials
(Carlini et al., 2016; Kumar et al., 2018; Yuan et al., 2018). Some of them
try to lure the user to spell their password directly to Alexa in the voice
variant of phishing or “vishing” (Security Research Labs, 2019). Some of them
don’t bother with the invocation logic or users’ credentials, but instead,
manipulate the content that is spoken back to the users (Sharevski et al.,
2020c). This new type of malicious skills, in a man-in-the-middle fashion,
rewords a legitimate content in such way that the user makes an improbable
interpretation of a set of true facts. The goal of this skill is to induce
misperception, that is, to distort the reality of a targeted user in a similar
way information operations attempt to do with disseminating alternative
narratives on social media (Starbird, 2017). The authors of this proof-of-
concept malicious skill, manipulated regulatory news to present the government
in two different lights as a pro-worker and as a pro-business. A user study
was conducted that validated the potential of the malicious skill to induce
misperception about the government’s proclivity towards workers and the
businesses.

The possibility for manipulating spoken back content by the voice assistant
prompted us to think how such a skill could be weaponized if the content comes
from Twitter. Twitter is one the main “battlefileds” for information
operations with numerous alternative narratives surrounding the COVID-19
pandemic. Recognized that these alternative dangerously pollute the public
discourse on the platform and started to actively label them as “COVID-19
misinformation” (Roth and Pickles, 2020). The labels come in two forms: (1) a
warning cover with a verbose text hiding the text and allowing the user to
skip a COVID-19 misinformation Tweet; and (2) a warning tag underneath a
content providing a link for users to “get the facts about COVID-19.” Twitter
is not just providing content but also provides context on it’s truthfulness
to the user with such label. It has been found that similar labels on social
media reduce the perceived accuracy of an alternative narrative, e.g. it help
users recognize an attempt for inducing misperception (Clayton et al., 2019).

Circling back to the possibility for inducing misperception by manipulating
content by a malicious skill, we are also interested in the ability of this
skill to suppress or deliberately insert such labels in order to enhance or
attenuate the misperception-inducing effect of a selected Twitter content. In
other words, we wanted to know how the user will perceive a spoken back
Twitter content by the malicious skill in the following scenarios: (1) Alexa
utters the warning label text and speaks back the content of a
misinformation/valid Tweet; (2) Alexa speaks back the content of a
misinformation/valid Tweet and then utters the warning tag; and (3) Alexa
suppresses the warning label text/tag and only speaks back the content of a
misinformation/valid Tweet;

##  3\. Alexa Tweeter Reader Skill

The thrust of our research was not to fully implement a malicious Alexa skill
that reads Tweets but rather to test the effect should one be developed (we
elaborate the ethics of our research in the Discussion section), therefore, we
produced a proof-of-concept that closely resembled such a skill. The “Twitter
Reader” skill could automatically interact with both the user and Twitter
adjusting the interaction depending on the “blueprint” selected for the user
interaction (Amazon, 2019). The Amazon Alexa skill ecosystem has a broad
selection of “blueprints” or prepackaged skills from which one can easily
deploy voice activated applications to the Alexa with minimal effort.
Initially for this study we started using the Flash Briefing skill which
allowed us to present to a user a predefined set of Tweets. This however was
limited as having to statically define the Tweets. The requirements for
dynamic content retrieved from Twitter, possible presentation of multimedia
files, and conditional responses quickly outgrew the Flash Briefing skill and
a more sophisticated platform was required. We migrated our implementation to
VoiceFlow where we developed the Twitter Reader skill flow shown in Figure 1
(voi, 2021).

Figure 1. The Alexa Twitter Reader Skill (logical flow)

To invoke the Twitter Reader skill the user utters the skill’s invocation name
Alexa, open the Twitter Reader. Alexa response with the welcome message
Welcome to the Alexa Official Twitter Reader and ask the name of the user.
This is done to allow for reading Tweets from multiple accounts in one
household, for example. Once Alexa connects the name to the configured Twitter
account, Alexa prompts the user whether they want to hear the latest Tweet in
their Tweeter stream. Assuming a confirmation answer from the user, Alexa
retrieves the Tweet together with any warning labels attached to it. If a
COVID-19 misinformation warning label is appended at the end of the Tweet,
Alexa first converts the Tweet’s text into speech, clearing special characters
like “@” for account links and “#” for hashtags, and responds, for example A
second nytimes article quotes doctors who say the mRNA technology used in
COVID vaccines may cause immune thrombocytopenia, a blood disorder that last
month led to the death of a Florida doctor after getting the Pfizer vaccine
(this Tweet is also shown in Figure 2a). Once done reading the Tweet, Alexa
appends the warning tag, removing the exclamation mark favicon, and utters Get
the information about COVID nineteen.

If a warning cover precedes the Tweet, Alexa first converts the text of the
warning to speech and utters it back to the user. In the case of COVID-19
misinformation, this cover reads: This Tweet violated the Twitter Rules about
spreading misleading and potentially harmful information related to COVID-19.
However, Twitter has determined that it may be in the public’s interest for
the Tweet to remain accessible. Would you like me to read the Tweet?. If the
user says Yes, Alexa proceeds and converts the Tweet’s text into speech as in
the scenario shown in Figure 3. If the user says No, then Alexa responds Would
you like to hear another Tweet?. If the user again declines to hear another
Tweet, Alexa simply responds Thank you for using the Alexa Official Twitter
Reader. Otherwise, Alexa proceeds and selects the next Tweet in the stream.

##  4\. Research Study

###  4.1. Misperceptions: Accuracy of Tweets

To test the misperception inducing-effect we investigated whether
(mis)information Tweets about the COVID-19 vaccine efficacy, spoken back by
Alexa and in the presence or absence of warning labels affect individuals’
perceptions of the Tweet’s accuracy with the following set of hypotheses:

  * •

H1: The utterance of a warning tag following a Tweet containing misleading
information about COVID-19 vaccines by Alexa will not reduce the perceived
accuracy of the spoken back Tweet’s content relative to a no warning tag
condition.

  * •

H2: The utterance of a warning cover before a Tweet containing misleading
information about COVID-19 vaccines by Alexa will not reduce the perceived
accuracy of the spoken back Tweet’s content relative to a no warning cover
condition.

  * •

H3: The utterance of a warning tag following a Tweet containing valid
information about COVID-19 vaccines by Alexa will not reduce the perceived
accuracy of the spoken back Tweet’s content relative to a no warning tag
condition.

  * •

H4: The utterance of a warning cover before a Tweet containing valid
information about COVID-19 vaccines by Alexa will not reduce the perceived
accuracy of the spoken back Tweet’s content relative to a no warning cover
condition.

To test the first hypothesis we utilized the Tweets containing misleading
information shown in Figure 2a and Figure 2b. The Tweet in Figure 2a has a
warning tag indicating that the above content is misinformation. The Tweet
promulgates COVID-19 rumour about a rare adverse effect that was linked to the
SARS-CoV-2 virus, not the vaccine, at the time of writing (Chappell, 2021). To
remove bias due to the “influencer” effect, the Tweet comes from a verified
account “TheVaccinator” (which we made up). An alteration of the same Tweet is
shown in Figure 2b without the accompanying warning tag. To test the second
hypothesis we utilized the Tweets shown in Figure 2b and Figure 3 (which
includes a warning cover instead of a warning tag). In all the cases, the
content of the Tweet and the warning covers/tags were converted from text-to-
speech by the malicious Alexa skill as described above.

(a)

(b)

Figure 2. A Misleading Tweet: (a) With a Warning Tag;
(b) Without a Warning Tag for Misleading Information. Figure 3. A Warning
Cover Preceding a Misleading Tweet

To test the third hypothesis we utilized the Tweets containing verified
information shown in Figure 4a and Figure 4b. The original Tweet content cites
the CDC’s announcement about proceeding with the second dose of the COVID-19
vaccine in case an individual has a serious reaction from the first dose,
altered to include a warning tag in Figure 4b (for Disease Control and
Prevention, 2021). To control for bias, the Tweet comes from a verified
account “TheVirusMonitor” instead of the CDC account. To test the fourth
hypothesis we utilized the Tweets containing verified information shown in
Figure 4a and Figure 5. We retained Figure 4a for the comparison of the
conditions and altered the labeling in the Figure 4b to include a warning
cover instead of a warning tag. Similarly, the text from the twitter content
and the labels was converted as a text-to-speech by Alexa.

(a)

(b)

Figure 4. A Verified Tweet: (a) Without a Warning Tag;
(b) With a Warning Tag for Misleading Information. Figure 5. A Warning Cover
Preceding a Verified Tweet

###  4.2. Misperceptions: Hesitancy and Political Leanings

We also controlled for hesitancy and political leanings, following the
moderating effect of these variables reported in (Zannettou, 2021), (Pennycook
et al., 2018), to examine the perceived accuracy of spoken-back Tweets with
COVID-19 vaccine information in presence/absence of uttering warning labels.
We used the same Tweets as shown in Figures 2-5 together to test the following
hypotheses:

  * •

H5a: The COVID-19 vaccine personal hesitancy will not affect the perception of
accuracy of a spoken back Tweet with misleading information about COVID-19 in
any condition (with a warning a preceding warning cover, with a following
warning tag, or without any warning)

  * •

H5b: The COVID-19 vaccine personal hesitancy will not affect the perception of
accuracy of a spoken back Tweet with valid information about COVID-19 in any
condition (with a warning a preceding warning cover, with a following warning
tag, or without any warning)

To test the association between one’s political leanings and the perceived
accuracy of the Tweets from Figures 2-5 we asked:

  * •

RQ1: Is there a difference in the perceived accuracy of spoken-back COVID-19
misleading/verified Tweets with warning labels (tags or covers) between
Republican, Democrat, and Independent users?

###  4.3. Sampling and Instrumentation

We set to sample a population using Amazon Mechanical Turk that is 18 years or
above old, is a Twitter user and an Amazon Alexa user, and has encountered at
least one Tweet into their feed that relates to COVID-19 vaccines. Because we
were not allowed to physically invite the participants in our lab, we recorded
the interaction between a user prompting Alexa to open the Twitter Reader
skill and read the Tweets, which was offered as a recording to each
participant. The study was approved by the Institutional Review Board (IRB) as
a non-full disclosure experiment. Consequently, participants were initially
told that they are being asked to gauge the effectiveness or usability of the
Alexa skill as an experimental COVID-19 Tweeter Reader. After participation,
each participant was debriefed and offered small compensation.

We crafted the content of the Tweets to be of relevance to the participants
such that they meaningfully engage with the Tweet’s content (i.e., their
responses are not arbitrary). We assumed participants understood the Amazon
Alexa interfaces and were aware of the COVID-19 pandemic in general. However,
we acknowledge that the level of interest regarding the COVID-19 vaccines
could vary among the individual participants, affecting the extent to which
their responses reflect their opinions. To assess the perceived accuracy, we
used the questionnaire from (Clayton et al., 2019), adapted to the content
presented in Figures 2-5. The questionnaire assesses the perceived accuracy of
each of the Tweets on a 4-point Likert scale (not at all accurate, not very
accurate, somewhat accurate, very accurate).

To assess participants’ subjective attitudes and beliefs regarding the
COVID-19 vaccine, we used a modified questionnaire from (Biasio et al., 2020).
To assess the subjective attitudes we asked if the participants will receive a
COVID-19 vaccine (Yes/No/I Don’t Know); and (c) politically speaking, do they
consider as (Republican/Democrat/Independent). The overall questionnaire was
anonymous with no personally identifiable data collected from the
participants. We utilized a 2x3 experimental design where participants will be
randomized into one of six groups: (1) spoken back misleading Tweet with a
follow up warning tag; (2) spoken back misleading Tweet without a warning tag
suppressed by Alexa; (3) spoken back misleading Tweet preceded by an utterance
of a warning cover; (4) spoken back verified Tweet; (5) spoken back verified
Tweet with a follow up warning tag; and (6) verified Tweet preceded by an
utterance of a warning cover.

##  5\. Results

We conducted an online survey (N = 304) in January and February 2021. There
were 195 (64.1%) males and 103 (33.9%) females, with 6 participants (2.0%)
identifying as non-cis. The age brackets in the sample were distributed as
follows: 26 (8.6%) [18 - 24], 112 (36.8%) [25 - 34], 106 (34.9%) [35 - 44], 35
(11.5%) [45 - 54], 18 (5.9%) [55 - 64], 6 (2.0%) [65 - 74], and 1 (.3%) [75 -
84]. Our sample was younger-leaning and slightly skewed towards male Twitter
and Alexa users. The sample was also slightly Democrat-leaning with 51 (16.8%)
Republicans, 173 (56.9%) Democrats, and 80 (26.3%) Independent.

###  5.1. Misperceptions: Accuracy of Tweets

We first hypothesized that the utterance of a warning tag following a Tweet
containing misleading information (Figure 2a) about COVID-19 vaccines by Alexa
will not reduce the perceived accuracy of the spoken back Tweet’s content
relative to a no warning tag condition (Figure 2b). We have to confirm this
hypothesis since we haven’t found any statistically significant result in the
perceived accuracy ($U=1288.5$, $p=.917,(\alpha=0.05)$). In practical terms,
this means that the follow up warning tag doesn’t not work as intended - both
groups perceived the Tweet as “somewhat accurate” on average. Alexa users
either ignored the warning tag utterance at the end or perhaps the warning tag
saying Get the facts about COVID nineteen is ambiguous and logically doesn’t
actually say that the particular Tweet is indeed misinformation.

Granted, tagging the content is primarily intended for visual inspection and
includes a warning exclamation favicon and a link to the COVID-19 verified
information, which is not available directly to the users. We did allow for
the participants to repeat the interaction with Alexa and change their
reported perception of accuracy, but that didn’t seem to matter. Perhaps, for
a future use, Alexa could proceed and turn the warning tag into a question,
prompting the user with This Tweet was labeled as COVID nineteen
misinformation. Would you like to hear the facts about the COVID nineteen?. A
case for such an adaptation also brings the test result for the third
hypothesis, which was also didn’t yield a significant result ($U=1177$,
$p=.490,(\alpha=0.05)$). While it seems that the Alexa users correctly ignored
the tag because the Twitter Reader skill inserted the warning tag utterance
after it spoke back the Tweet as shown in Figure 4b, we don’t know if this is
because the Alexa users considered the warning tag at all.

We also hypothesized that the utterance of a warning cover before a Tweet
containing misleading information about COVID-19 vaccines by Alexa (Figure 3)
will not reduce the perceived accuracy of the spoken back Tweet’s content
relative to a no warning cover condition (Figure 3a). Here too, we didn’t find
a statistically significant result in the perceived accuracy ($U=1280$,
$p=.889,(\alpha=0.05)$). This made us speculate if the perhaps the content of
the Tweet was more so perceived as potentially an unverified rumor rather then
a misinformation altogether (at least at the time of the study there was no
official repudiation of the link between the COVID-19 vaccine and the death
caused by the immune thrombocytopenia). What made us think of the nuanced
choice of misinformation and COVID-19 rumors is the rejection of the fourth
hypothesis where the utterance of the warning cover before Alexa spoke back
the information from the valid Tweet shown on Figure 5 ($U=1601$,
$p=.002^{*},(\alpha=0.05)$, Cohen’s $d=0.619$ medium).

The cover was sufficiently potent for the users in the test group to perceive
the following Tweet as “not very accurate” while the ones in the control
condition as ”somewhat accurate” as shown in Figure 6. This result suggest
that the warning cover is a potent way of swaying users about potential
misinformation, even if the following Tweet containing in fact verified
information released by the CDC. This result, considering the possibility of
developing a purely malicious Twitter Reader skill, could inject
misinformation warning covers to a Tweet of choice and meddle with the public
opinion on the COVID-19 vaccine effectiveness. A similar effort, though with
actual Tweets and not warning labels, already surfaced on Twitter promoting a
homegrown Russian vaccine and undercutting the vaccines from the rivals such
as AstraZenecca (Frenkel et al., 2021).

Figure 6. A difference in perceived accuracy between the group exposed to a
warning cover utterance (Figure 5) and the group exposed only to the spoken
back Tweet (Figure 4a)

###  5.2. Misperceptions: Hesitancy

Hesitancy of vaccination has been shown to be a discriminative lens through
which people critically discern online information, which also includes
COVID-19 Tweets on the COVID-19 topic (Biasio et al., 2020). Therefore, we
wanted to test and see if the COVID-19 vaccine hesitancy will affect the
perception of accuracy of a spoken back Tweet with misleading information
about COVID-19 in any condition (with a warning a preceding warning cover,
with a following warning tag, or without any warning). When controlling for
hesitancy, we found a significant difference only in the warning cover
condition (Figure 3). The vaccine hesitant participants were more likely to
perceive the spoken back misleading Tweet as “somewhat accurate”, while the
vaccine accepting and undecided as “inaccurate” as shown in Figure 7
($\chi^{2}(2)=10.058$, $p=.007^{*},(\alpha=0.05)$). It seems that the vaccine
hesitant participants were alerted by the warning cover to contextually access
the grim outlook linking the COVID-19 vaccine with death with their sceptic
outlook of the COVID-19 vaccination, otherwise we would should have observed a
similar result for the the warning tag condition.

Figure 7. Vaccine hesitancy and perceived accuracy of the misleading Tweet in
Figure 3.

That this is a plausible explanation of the obvious misperception suggest the
similar test of the verified Tweet condition, where we also found a
significant result only for the condition where a warning cover was uttered
before the verified Twitter is spoken back by Alexa (Figure 5). Again, the
vaccine hesitant participants were more likely to perceive the spoken back
Tweet, this time containing verified information from the CDC, as “somewhat
accurate”, while the vaccine accepting and undecided as “inaccurate” as shown
in Figure 8 ($\chi^{2}(2)=6.432$, $p=.040^{*},(\alpha=0.05)$). We previously
noted that the warning cover, spoken back by Alexa, seems sufficiently potent
to add credibility to Alexa as the “best friend forever” (Purington et al.,
2017). After all, the best friends don’t lie and we trust them when they warn
us that what they have found on Twitter might be a disinformation if they say
so. But if this Twitter content aligns with our deeply held beliefs that the
COVID-19 vaccines are bad and we for sure won’t get vaccinated, we might
disregard what Twitter has told Alexa to convey to us, and instead believe the
content. After all, we might have heard that many users feel Twitter itself is
biased and mislabeling content (Geeng et al., 2020), so who knows, maybe Alexa
stumbled upon a mislabeled Tweet with an ominous COVID-19 misinformation
warning cover.

Figure 8. Vaccine hesitancy and perceived accuracy of the verified Tweet in
Figure 5.

###  5.3. Misperceptions: Political Leanings

The COVID-19 pandemic was not “immune” from politicization, expectedly, as a
highly polarizing topic. Curious to test the early evidence that perceptions
are modulated by one’s political leanings (Zannettou, 2021; Christenson et
al., 2020; Nyhan and Reifler, 2010), we controlled for participant’s political
identification to compare the perceived accuracy of the spoken back content by
Alexa with and without warning covers/tags. We only found a statistical
difference in for the condition where Alexa utters a warning cover before the
valid Tweet (Figure 5). While the republican and democrat users took the Alexa
“warning” and reported that this content is “not so accurate” the independent
ones dismissed this warning and perceived this content as ”somewhat accurate”
as shown in Figure 9 ($\chi^{2}(2)=6.171$, $p=.046^{*},(\alpha=0.05)$).

Figure 9. Vaccine hesitancy and perceived accuracy of the verified Tweet in
Figure 5.

This result contrast the divided receptivity to allegedly misinformation
content between the republicans (further drawn to believe it in presence of
warnings) and democrats (repelled by the warnings) previously reported. But
such a comparison might not hold relevant in our case first because the
warnings and content in the previous studies focused on political social media
content and second because the information interface was a screen, not a voice
assistant. It might be expected for politically-laden users to assume the
authority and trust Alexa as telling the truth so it comes to no surprise that
they heeded the warning cover and payed little attention to the following
Tweet content. The higher level of critical discernment for the independent
might be the varied exposure to information to both left, center, and right
leaning media and Twitter content in general (Pennycook et al., 2018).

##  6\. Discussion

Exploring the soft moderation when communicated by Alexa instead of a label on
a screen, we found that warning covers when converted from text to speech and
uttered by Alexa work as intended in grabbing the attention of the Alexa
users. All would have been good and promising, if it wasn’t for the malicious
skill inserting these covers as utterances before Alexa spoke back a Tweet
content that was true and validated by the CDC. The users in our study trusted
Alexa and it’s seemingly benign third-party skill “Twitter Reader” to tell the
truth without critically discerning the Tweets spoken back by Alexa. We
explored what might cause such an effect and found a difference in perception
based on one’s political leanings - the users considering themselves
independent were the ones actually trying to make sense of the Tweets
regardless of what Alexa (e.g. Twitter) had to say about the content. Alexa in
our study wasn’t able to dispel any biases that were rooted in personal
beliefs (Mercadante and Law, 2020), (Thorson, 2016). One’s personal hesitancy
from COVID-19 vaccination sufficed for biased perception of the information
from Alexa despite any labeling as long as the Tweets echoed their sceptic
outlook of the whole COVID-19 vaccination business (Pennycook et al., 2020;
Nyhan and Reifler, 2010).

###  6.1. Ethical Implications

While we set to investigate the effect of a third-party skill that arbitrary
manipulates the soft moderation covers and tags attached by Twitter to dubious
COVID-19 vaccine content and debriefed the participants at the end of the
study, the results could have several ethical implications nonetheless. We
exposed the participants to moderated content that could potentially affect
participants’ stance on COVID-19 vaccination and the pandemic. The exposure
might not sway participants on their vaccine hesitancy in the long run, but
could make the participants reconsider their approach of obtaining the vaccine
for themselves or their families. The exposure to Twitter content spoken back
by Alexa as a novel interface could also affect the participants’ stance on
communicating important topics with their voice assistants. A recent study
found that personification of Alexa is associated with increased levels of
satisfaction, so learning that Alexa could be secretly controlled by a
malicious third-party skill to insert or drop Twitter misinformation warnings
might affect the user satisfaction with Alexa (Purington et al., 2017).

That a portion of the participants were able to critically discern the
verified content even in presence of the maliciously inserted Alexa’s warnings
is reassuring and proves that users keep a critical mindset despite the
proclivity for anthropomorphism towards Alexa (Wagner and Schramm-Klein,
2019). However, the ease of crafting a malicious skill that could suppress or
add warning utterances, could have unintended consequences. With the evidence
of nation-states disseminating misinformation, it is possible that they could
resort to malware for voice assistants to avoid both the soft and hard
moderation on social media platforms like Twitter (Thomas et al., 2012). Sure,
this could be far from the realm of possibility, even if the capabilities
exist, but for such a sensitive topic as COVID-19 vaccination, meddling with
spoken-back content from Alexa could give an edge to a vaccine competitor in
the global race for development and procurement of a COVID-19 solution. We
certainly condemn such ideas and such a misuse of our research results and
therefore only presented a very limited proof-of-concept flow for such a
malicious skill. For example, evidence for such a misinformation campaign has
already surfaced on Twitter, promoting homegrown Russian vaccines and
undercutting rivals (Frenkel et al., 2021). One could also point the malicious
third-party skill to pull content from Parler instead of Twitter and package
the disinformation vector as a skill that reads the “real” truth about the
vaccine and avoid soft moderation altogether. Again, we condemn development of
such a capability outside of academic research, even if it doesn’t pose an
imminent problem for the defense community (Shevlane and Dafoe, 2020).

###  6.2. Future Research

We acknowledge that there is further research to be done into investigating
the manipulation of soft moderation and communication of Twitter content
through voice assistants. Visually assessing warning labels might have a
different effect when they are spoken by Alexa so it will be informative to
see how a variation of the warning text could affect the perceived accuracy of
content to which they are attached. Out results suggest that the follow up
warning tag utterance has no effect at all due, we suspected, the ambiguous
language. If perhaps Alexa speaks with a different tone and is more direct,
saying This Tweet seems like is spreading misinformation. Do you want me to
check the COVID-19 facts on the official CDC website?, one might hypothesize
that the intended effect of soft moderation be better achieved. Certainly, the
proposed adaptation entails extensive usable security research to determine
the optimal way of delivering soft moderation warnings, especially with the
option for Alexa to express emotions (e.g. “disappointed” and low volume in
uttering the warning covers or “disappointed” and high volume in uttering the
said tag (Gao, Catherine, 2019)). This is yet another step in future research,
and we plan to broadly explore the domain of voice-based security warnings.

Along this line and the politicization of COVID-19 debate, an interesting
experiment we plan to conduct is to go beyond the emotions of Alexa but
instead test a voice application that reads the Tweets in the voice of a
famous political person. Siri, Apple’s voice assistant allows for
customization with accents (e.g. Irish) so one would expect that the voice
assistants in future could be configured to speak with the voice of our
beloved celebrity or authoritative figures (Shen et al., 2018). A neural
network that could synthesize speech directly from inputted text exists and
with a moderate training models can be created to generate the speech from
almost any individual (NVI, 2021). It would be interesting to see how users
will respond to same Tweets and warning covers read by John Oliver, Hillary
Clinton, Donald Trump, or Barack Obama (one could already test these voices on
the Vocodes website (voc, 2021)).

###  6.3. Combating Malicious Skills

The misperception-inducing logic is enabled by customizing, in a relatively
easy way, a blueprint template and registering a seemingly benign skill. As
discussed in (Sharevski et al., 2021), a thorough certification process could
uncover the malicious logic and remove the skill from the Amazon Skills Store.
Another solution is monitoring for suspicious skills’ behaviour with a tool
like the SkillExplorer proposed in (Guo et al., 2020). Again, a skill can
evade both certification and exploring by claiming that the rephrasing aims to
communicate important COVID-19 vaccine information in an assistive way, for
example, to non-native English speakers (Jang et al., 2014).

As an additional layer of protection, feedback from users post-release could
help close this gap. Twitter similarly hopes to identify and address
misinformation through the use of pre-selected user “fact checkers”, piloted
in its Birdwatch program (Ortutay, 2021). Amazon could similarly crowd-source
its Alexa skill moderation and allow users with a high “helpfulness” score, as
in Birdwatch, to identify potentially malicious or misinforming skills for
further review and removal. Though allowing users to flag skills may be
helpful in eliminating misinformation, this crowd-sourced soft moderation
could be exploited by malicious users to flag legitimate skills or hijacked by
partisan users if a skill’s content has been highly politicized.

In the context of malicious third party skills, instead of manipulating
warning labels, a skill might be directed to an RSS feed that steadily
promotes rumours and unverified COVID-19 vaccine information. One might not
need to make a Twitter reader, but a Parler reader, to access a wealth of
unverified claims about COVID-19 vaccination and supply Alexa with “Parler
COVID-19 briefings” . For one, a widely shared information tidbit by
“influencers” about the COVID-19 vaccine on Parler is that it contains HIV
(Aliapoulios et al., 2021). We experimented with mostly rumours about COVID-19
in our study, but exposing participants to such blatant misinformation, spoken
by a trusted intermediary (Alexa, and not Alex Jones), could possibly uncover
important dynamics in the relationship or personification of Alexa as a “Best
Friend Forever” (Purington et al., 2017).

###  6.4. Scope Limitations

The current study has important limitations. First, we limited our questions
to couple of Tweets that were relevant to the state of the pandemic and mass
immunization during the period of January-February 2021, which could be
perceived with a different level of accuracy after a certain period of time.
Overall, the findings may be specific to the effect the malicious skill has
only on COVID-19 mass immunization and may not be generalizable to other
topics. Second, though our survey asked participants whether they intend to
receive a COVID-19 vaccine, we did not ask participants who answered in the
affirmative how soon they intended to get vaccinated. An affirmative intention
to vaccinate does not indicate an intention to vaccinate immediately and
unconditionally, and therefore, the results cannot be interpreted as such. We
likewise did not ask why participants who answered in the negative why they
did not intend to get vaccinated or whether any factors could change this. A
negative intention to vaccinate does not indicate an intention to never
receive the COVID-19 vaccine, and likewise, these results should not be
interpreted as such.

Third, regular Alexa or voice assistant participants in general may be
desensitized to the spoken back information, which may have affected their
perception of the COVID-19 vaccine irrespective of the rephrasing. Our
experiment was limited to Alexa as a voice assistant of choice and the Twitter
as a COVID-19 vaccination information. We were limited to evaluating the
effects of COVID-19 vaccination only in the U.S., and this information might
not be relevant for places where other vaccines (the AstraZeneca, Sinopharm or
Gamaleya vaccines) are used. We were limited to the choice of soft moderation
labels present at the time of the study that could change the perception of
the spoken-back information if reworded later by Twitter. Finally, although we
tried to sample a representative set of participants for our study using
Amazon Mechanical Turk , the outcomes might have been different if we used
another platform, or another type of sampling. Also, a larger sample size, one
that was gender and politically balanced, could have provided a more nuanced
view of Alexa as a “Tweeter Reader”, but we had limited funding for this
study.

##  7\. Conclusion

In this study, we explored whether a third-party Alexa skill could
successfully affect the perceived accuracy of COVID-19 vaccine Tweets and
induce misperceptions in users by simply manipulating the soft moderation
applied by Twitter. Additionally, we examined whether participants’ vaccine
hesitant sentiment and political leanings had any effect on the perception of
accuracy of the Tweets spoken back by Alexa. Our findings suggest that users
were most likely to be misled on Twitter information when Alexa utters a
warning speech before it delivers the Tweet’s content, regardless of it’s
validity. Participants’ perception of the accuracy of both misleading and
verified COVID-19 Tweets appear warped by participants’ personal biases -
participants judged Alexa’s accuracy by how closely the response aligned with
their own sceptic beliefs on the subject. We found a significant difference in
perceived accuracy only for the apolitical Alexa users, which appear not to
contextualize any misinformation labeling before they actually inspect a
Tweet. All of our findings might be an effect of the lack of interaction or
response users have when interacting with a voice assistant that they do not
lack in online discourse on social media. Given the ease with which a user
lacking developer experience can craft and share a third-party skill via the
Amazon Skills Store, we believe it necessary to augment existing practices to
catch malicious and misinforming skills like the one we showcased in this
study. Likewise, we believe that the adaptation of the soft moderation with
better verbal misinformation warnings may help break the confirmation bias
feedback loop that reinforces listeners’ biased vaccine outlooks.

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