
Digital voice assistants (DVAs) are increasingly used to search for health information. However, the quality of information provided by DVAs is not consistent across health conditions. From our knowledge, there have been no studies that evaluated the quality of DVAs in response to diabetes-related queries. The objective of this study was to evaluate the quality of DVAs in relation to queries on diabetes management.
Seventy-four questions were posed to smartphone (Apple Siri, Google Assistant, Samsung Bixby) and non-smartphone DVAs (Amazon Alexa, Sulli the Diabetes Guru, Google Nest Mini, Microsoft Cortana), and their responses were compared to that of Internet Google Search. Questions were categorized under diagnosis, screening, management, treatment and complications of diabetes, and the impacts of COVID-19 on diabetes. The DVAs were evaluated on their technical ability, user-friendliness, reliability, comprehensiveness and accuracy of their responses. Data was analyzed using the Kruskal-Wallis and Wilcoxon rank-sum tests. Intraclass correlation coefficient was used to report inter-rater reliability.
Google Assistant (n = 69/74, 93.2%), Siri and Nest Mini (n = 64/74, 86.5% each) had the highest proportions of successful and relevant responses, in contrast to Cortana (n = 23/74, 31.1%) and Sulli (n = 10/74, 13.5%), which had the lowest successful and relevant responses. Median total scores of the smartphone DVAs (Bixby 75.3%, Google Assistant 73.3%, Siri 72.0%) were comparable to that of Google Search (70.0%, p = 0.034), while median total scores of non-smartphone DVAs (Nest Mini 56.9%, Alexa 52.9%, Cortana 52.5% and Sulli the Diabetes Guru 48.6%) were significantly lower (p < 0.001). Non-smartphone DVAs had much lower median comprehensiveness (16.7% versus 100.0%, p < 0.001) and reliability scores (30.8% versus 61.5%, p < 0.001) compared to Google Search.
Google Assistant, Siri and Bixby were the best-performing DVAs for answering diabetes-related queries. However, the lack of successful and relevant responses by Bixby may frustrate users, especially if they have COVID-19 related queries. All DVAs scored highly for user-friendliness, but can be improved in terms of accuracy, comprehensiveness and reliability. DVA designers are encouraged to consider features related to accuracy, comprehensiveness, reliability and user-friendliness when developing their products, so as to enhance the quality of DVAs for medical purposes, such as diabetes management.
Citation: Joy Qi En Chia, Li Lian Wong, Kevin Yi-Lwern Yap. Quality evaluation of digital voice assistants for diabetes management[J]. AIMS Medical Science, 2023, 10(1): 80-106. doi: 10.3934/medsci.2023008
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Digital voice assistants (DVAs) are increasingly used to search for health information. However, the quality of information provided by DVAs is not consistent across health conditions. From our knowledge, there have been no studies that evaluated the quality of DVAs in response to diabetes-related queries. The objective of this study was to evaluate the quality of DVAs in relation to queries on diabetes management.
Seventy-four questions were posed to smartphone (Apple Siri, Google Assistant, Samsung Bixby) and non-smartphone DVAs (Amazon Alexa, Sulli the Diabetes Guru, Google Nest Mini, Microsoft Cortana), and their responses were compared to that of Internet Google Search. Questions were categorized under diagnosis, screening, management, treatment and complications of diabetes, and the impacts of COVID-19 on diabetes. The DVAs were evaluated on their technical ability, user-friendliness, reliability, comprehensiveness and accuracy of their responses. Data was analyzed using the Kruskal-Wallis and Wilcoxon rank-sum tests. Intraclass correlation coefficient was used to report inter-rater reliability.
Google Assistant (n = 69/74, 93.2%), Siri and Nest Mini (n = 64/74, 86.5% each) had the highest proportions of successful and relevant responses, in contrast to Cortana (n = 23/74, 31.1%) and Sulli (n = 10/74, 13.5%), which had the lowest successful and relevant responses. Median total scores of the smartphone DVAs (Bixby 75.3%, Google Assistant 73.3%, Siri 72.0%) were comparable to that of Google Search (70.0%, p = 0.034), while median total scores of non-smartphone DVAs (Nest Mini 56.9%, Alexa 52.9%, Cortana 52.5% and Sulli the Diabetes Guru 48.6%) were significantly lower (p < 0.001). Non-smartphone DVAs had much lower median comprehensiveness (16.7% versus 100.0%, p < 0.001) and reliability scores (30.8% versus 61.5%, p < 0.001) compared to Google Search.
Google Assistant, Siri and Bixby were the best-performing DVAs for answering diabetes-related queries. However, the lack of successful and relevant responses by Bixby may frustrate users, especially if they have COVID-19 related queries. All DVAs scored highly for user-friendliness, but can be improved in terms of accuracy, comprehensiveness and reliability. DVA designers are encouraged to consider features related to accuracy, comprehensiveness, reliability and user-friendliness when developing their products, so as to enhance the quality of DVAs for medical purposes, such as diabetes management.
In the present paper we study the effective conductivity of an
(λ+,λ−)∈[0,+∞[2∗≡[0,+∞[2∖{(0,0)}. |
We note that the limit case of zero conductivity corresponds to a thermal insulator. On the other hand, if the conductivity tends to
We now introduce the geometry of the problem. If
q=(q110⋯00⋱⋯0⋮⋮⋱⋮00⋯qnn), | (1) |
and
Q≡n∏j=1]0,qjj[⊆Rn. | (2) |
The set
˜Q≡]0,1[n,˜q≡In≡(10⋯00⋱⋯0⋮⋮⋱⋮00⋯1). |
Then we take
α∈]0,1[ and a bounded open connected subset Ω of Rn of class C1,α such that Rn∖¯Ω is connected. | (3) |
The symbol '
Sq[qI[ϕ]]≡⋃z∈Zn(qz+qI[ϕ]),Sq[qI[ϕ]]−≡Rn∖¯Sq[qI[ϕ]]. |
The set
With the aim of introducing the definition of the effective conductivity, we first have to introduce a boundary value problem for the Laplace equation. If
{Δu+j=0in Sq[qI[ϕ]],Δu−j=0in Sq[qI[ϕ]]−,u+j(x+qeh)=u+j(x)+δhjqjj∀x∈¯Sq[qI[ϕ]],∀h∈{1,…,n},u−j(x+qeh)=u−j(x)+δhjqjj∀x∈¯Sq[qI[ϕ]]−,∀h∈{1,…,n},λ+∂∂νqI[ϕ]u+j−λ−∂∂νqI[ϕ]u−j=0on ∂qI[ϕ],u+j−u−j=0on ∂qI[ϕ],∫∂qI[ϕ]u+jdσ=0, | (4) |
where
Definition 1.1. Let
λeff[q,ϕ,(λ+,λ−)]≡(λeffij[q,ϕ,(λ+,λ−)])i,j=1,…,n |
is the
λeffij[q,ϕ,(λ+,λ−)]≡1|Q|n{λ+∫qI[ϕ]∂∂xiu+j[q,ϕ,(λ+,λ−)](x)dx+λ−∫Q∖¯qI[ϕ]∂∂xiu−j[q,ϕ,(λ+,λ−)](x)dx}∀i,j∈{1,…,n}. |
Remark 1.2. Under the assumptions of Definition 1.1, by applying the divergence theorem, one can verify that
λeffij[q,ϕ,(λ+,λ−)]=1|Q|n{λ+∫qI[ϕ]Du+i[q,ϕ,(λ+,λ−)](x)⋅Du+j[q,ϕ,(λ+,λ−)](x)dx+λ−∫Q∖¯qI[ϕ]Du−i[q,ϕ,(λ+,λ−)](x)⋅Du−j[q,ϕ,(λ+,λ−)](x)dx}∀i,j∈{1,…,n}. |
Indeed, if we set
˜u+k[q,ϕ,(λ+,λ−)](x)=u+k[q,ϕ,(λ+,λ−)](x)−xk∀x∈¯Sq[qI[ϕ]]˜u−k[q,ϕ,(λ+,λ−)](x)=u−k[q,ϕ,(λ+,λ−)](x)−xk∀x∈¯Sq[qI[ϕ]]−∀k∈{1,…,n}, |
then
1|Q|n{λ+∫qI[ϕ]Du+i[q,ϕ,(λ+,λ−)](x)⋅Du+j[q,ϕ,(λ+,λ−)](x)dx+λ−∫Q∖¯qI[ϕ]Du−i[q,ϕ,(λ+,λ−)](x)⋅Du−j[q,ϕ,(λ+,λ−)](x)dx}=1|Q|n{λ+∫qI[ϕ]Du+j[q,ϕ,(λ+,λ−)](x)⋅D(xi+˜u+i[q,ϕ,(λ+,λ−)](x))dx+λ−∫Q∖¯qI[ϕ]Du−j[q,ϕ,(λ+,λ−)](x)⋅D(xi+˜u−i[q,ϕ,(λ+,λ−)](x))dx}=1|Q|n{λ+∫qI[ϕ]Du+j[q,ϕ,(λ+,λ−)](x)⋅Dxidx+λ+∫qI[ϕ]Du+j[q,ϕ,(λ+,λ−)](x)⋅D˜u+i[q,ϕ,(λ+,λ−)](x)dx+λ−∫Q∖¯qI[ϕ]Du−j[q,ϕ,(λ+,λ−)](x)⋅Dxidx+λ−∫Q∖¯qI[ϕ]Du−j[q,ϕ,(λ+,λ−)](x)⋅D˜u−i[q,ϕ,(λ+,λ−)](x)dx}=1|Q|n{λ+∫qI[ϕ]∂∂xiu+j[q,ϕ,(λ+,λ−)](x)dx+λ+∫qI[ϕ]Du+j[q,ϕ,(λ+,λ−)](x)⋅D˜u+i[q,ϕ,(λ+,λ−)](x)dx+λ−∫Q∖¯qI[ϕ]∂∂xiu−j[q,ϕ,(λ+,λ−)](x)dx+λ−∫Q∖¯qI[ϕ]Du−j[q,ϕ,(λ+,λ−)](x)⋅D˜u−i[q,ϕ,(λ+,λ−)](x)dx}. |
Therefore, in order to conclude that the two definitions are equivalent, we need to show that
λ+∫qI[ϕ]Du+j[q,ϕ,(λ+,λ−)](x)⋅D˜u+i[q,ϕ,(λ+,λ−)](x)dx+λ−∫Q∖¯qI[ϕ]Du−j[q,ϕ,(λ+,λ−)](x)⋅D˜u−i[q,ϕ,(λ+,λ−)](x)dx=0. | (5) |
By an application of the divergence theorem for
∫qI[ϕ]Du+j[q,ϕ,(λ+,λ−)](x)⋅D˜u+i[q,ϕ,(λ+,λ−)](x)dx=∫∂qI[ϕ](∂∂νqI[ϕ]u+j[q,ϕ,(λ+,λ−)](x))˜u+i[q,ϕ,(λ+,λ−)](x)dσx | (6) |
and
∫Q∖¯qI[ϕ]Du−j[q,ϕ,(λ+,λ−)](x)⋅D˜u−i[q,ϕ,(λ+,λ−)](x)dx=∫∂Q(∂∂νQu−j[q,ϕ,(λ+,λ−)](x))˜u−i[q,ϕ,(λ+,λ−)](x)dσx−∫∂qI[ϕ](∂∂νqI[ϕ]u−j[q,ϕ,(λ+,λ−)](x))˜u−i[q,ϕ,(λ+,λ−)](x)dσx. | (7) |
By the periodicity of
∫∂Q(∂∂νQu−j[q,ϕ,(λ+,λ−)](x))˜u−i[q,ϕ,(λ+,λ−)](x)dσx=∫∂Q(∂∂νQxj)˜u−i[q,ϕ,(λ+,λ−)](x)dσx+∫∂Q(∂∂νQ˜u−j[q,ϕ,(λ+,λ−)](x))˜u−i[q,ϕ,(λ+,λ−)](x)dσx=∫∂Q(νQ(x)⋅ej)˜u−i[q,ϕ,(λ+,λ−)](x)dσx+∫∂Q(νQ(x)⋅D˜u−j[q,ϕ,(λ+,λ−)](x))˜u−i[q,ϕ,(λ+,λ−)](x)dσx=0, | (8) |
since contributions on opposite sides of
λ+∫qI[ϕ]Du+j[q,ϕ,(λ+,λ−)](x)⋅D˜u+i[q,ϕ,(λ+,λ−)](x)dx+λ−∫Q∖¯qI[ϕ]Du−j[q,ϕ,(λ+,λ−)](x)⋅D˜u−i[q,ϕ,(λ+,λ−)](x)dx=λ+∫∂qI[ϕ](∂∂νqI[ϕ]u+j[q,ϕ,(λ+,λ−)](x))˜u+i[q,ϕ,(λ+,λ−)](x)dσx−λ−∫∂qI[ϕ](∂∂νqI[ϕ]u−j[q,ϕ,(λ+,λ−)](x))˜u−i[q,ϕ,(λ+,λ−)](x)dσx. | (9) |
Since the validity of (4) implies that
˜u+i[q,ϕ,(λ+,λ−)](x)=˜u−i[q,ϕ,(λ+,λ−)](x)∀x∈∂qI[ϕ] |
and that
λ+∂∂νqI[ϕ]u+j[q,ϕ,(λ+,λ−)](x)−λ−∂∂νqI[ϕ]u−j[q,ϕ,(λ+,λ−)](x)=0∀x∈∂qI[ϕ], |
we then deduce by (9) that (5) holds true.
As a consequence, the effective conductivity matrix of Definition 1.1 coincides with the one analyzed by Ammari, Kang, and Touibi [5,p. 121] for a periodic two-phase composite and which can be deduced by classical homogenization theory (see, e.g., Allaire [1], Bensoussan, Lions, and Papanicolaou [6], Jikov, Kozlov, and Oleĭnik [27], Milton [41]). We emphasize that the justification of the expression of the effective conductivity via homogenization theory holds for 'small' values of the periodicity parameters. For further remarks on the definition of effective conductivity we refer to Gluzman, Mityushev, and Nawalaniec [24,§2.2].
The main goal of our paper is to give an answer to the following question:
What can be said on the regularity of the map(q,ϕ,(λ+,λ−))↦λeff[q,ϕ,(λ+,λ−)]? | (10) |
We answer to the above question by proving that for all
Λij:D+n(R)×(C1,α(∂Ω,Rn)∩A˜Q∂Ω)×]−1−ε,1+ε[→R |
such that
λeffij[q,ϕ,(λ+,λ−)]=δijλ−+(λ++λ−)Λij[q,ϕ,λ+−λ−λ++λ−] | (11) |
for all
In particular, in the present paper we follow the strategy of [39] where we have studied the behavior of the longitudinal flow along a periodic array of cylinders upon perturbations of the shape of the cross section of the cylinders and the periodicity structure, when a Newtonian fluid is flowing at low Reynolds numbers around the cylinders. More precisely, we transform the problem into a set of integral equations defined on a fixed domain and depending on the set of variables
Formula (11) implies that the effective conductivity
(q,ϕ,(λ+,λ−))↦λeffij[q,ϕ,(λ+,λ−)] | (12) |
from
λeffij[qδ,ϕδ,(λ+δ,λ−δ)]=∞∑k=0ckδk | (13) |
for
Furthermore, such a high regularity result can be seen as a theoretical justification which guarantees that differential calculus may be used in order to characterize critical periodicity-shape-conductivity triples
As already mentioned, our method is based on integral equations, that are derived by potential theory. However, integral equations could also be deduced by the generalized alternating method of Schwarz (cf. Gluzman, Mityushev, and Nawalaniec [24] and Drygaś, Gluzman, Mityushev, and Nawalaniec [19]), which also allows to produce expansions in the concentration.
Incidentally, we observe that the are several contributions concerning optimization of effective parameters from many different points of view. For example, one can look for optimal lattices without confining to rectangular distributions. In this direction, Kozlov [29] and Mityushev and Rylko [44] have discussed extremal properties of hexagonal lattices of disks. On the other hand, even if, in wide generality, the optimal composite does not exist (cf. Cherkaev [13]), one can discuss the dependence on the shape under some specific restrictions. For example, one could build composites with prescribed effective conductivity as described in Lurie and Cherkaev [38] (see also Gibiansky and Cherkaev [22]). In Rylko [49], the author has studied the influence of perturbations of the shape of the circular inclusion on the macroscopic conductivity properties of 2D dilute composites. Inverse problems concerning the determination of the shape of equally strong holes in elastic structures were considered by Cherepanov [12]. For an experimental work concerning the analysis of particle reinforced composites we mention Kurtyka and Rylko [30]. Also, we mention that one could apply the topological derivative method as in Novotny and Sokołowski [46] for the optimal design of microstructures.
Let
Let
Sq[ΩQ]≡⋃z∈Zn(qz+ΩQ),Sq[ΩQ]−≡Rn∖¯Sq[ΩQ]. |
If
Ckb(¯Sq[ΩQ]−)≡{u∈Ck(¯Sq[ΩQ]−):Dγu is bounded ∀γ∈Nn s. t. |γ|≤k}, |
and we endow
‖u‖Ckb(¯Sq[ΩQ]−)≡∑|γ|≤ksupx∈¯Sq[ΩQ]−|Dγu(x)|∀u∈Ckb(¯Sq[ΩQ]−), |
where
Ck,βb(¯Sq[ΩQ]−)≡{u∈Ck,β(¯Sq[ΩQ]−):Dγu is bounded ∀γ∈Nn s. t. |γ|≤k}, |
and we endow
‖u‖Ck,βb(¯Sq[ΩQ]−)≡∑|γ|≤ksupx∈¯Sq[ΩQ]−|Dγu(x)|+∑|γ|=k|Dγu:¯Sq[ΩQ]−|β∀u∈Ck,βb(¯Sq[ΩQ]−), |
where
Ckq(¯Sq[ΩQ]−)≡{u∈Ckb(¯Sq[ΩQ]−):u is q-periodic}, |
which we regard as a Banach subspace of
Ck,βq(¯Sq[ΩQ]−)≡{u∈Ck,βb(¯Sq[ΩQ]−):u is q-periodic}, |
which we regard as a Banach subspace of
Our method is based on a periodic version of classical potential theory. In order to construct periodic layer potentials, we replace the fundamental solution of the Laplace operator by a
ΔSq,n=∑z∈Znδqz−1|Q|n, |
where
Sq,n(x)=−∑z∈Zn∖{0}1|Q|n4π2|q−1z|2e2πi(q−1z)⋅x |
in the sense of distributions in
We now introduce periodic layer potentials. Let
vq[∂ΩQ,μ](x)≡∫∂ΩQSq,n(x−y)μ(y)dσy∀x∈Rn,wq,∗[∂ΩQ,μ](x)≡∫∂ΩQνΩQ(x)⋅DSq,n(x−y)μ(y)dσy∀x∈∂ΩQ, |
for all
v+q[∂ΩQ,μ]≡vq[∂ΩQ,μ]|¯Sq[ΩQ] v−q[∂ΩQ,μ]≡vq[∂ΩQ,μ]|¯Sq[ΩQ]−. |
We collect in the following theorem some properties of
Theorem 2.1. Let
(i) The map from
(ii) Let
∂∂νΩQv±q[∂ΩQ,μ]=∓12μ+wq,∗[∂ΩQ,μ]on ∂ΩQ. |
Moreover,
∫∂ΩQwq,∗[∂ΩQ,μ]dσ=(12−|ΩQ|n|Q|n)∫∂ΩQμdσ. |
(iii) Let
Δvq[∂ΩQ,μ]=0in Rn∖∂Sq[ΩQ]. |
(iv) The operator
In order to consider shape perturbations of the inclusions of the composite, we introduce a class of diffeomorphisms. Let
A˜Q∂Ω≡{ϕ∈A∂Ω:ϕ(∂Ω)⊆˜Q},A˜Q¯Ω′≡{Φ∈A¯Ω′:Φ(¯Ω′)⊆˜Q}. | (14) |
If
We conclude this section of preliminaries with some results on problem (4). By means of the following proposition, whose proof is of immediate verification, we can transform problem (4) into a
Proposition 2.2. Let
(u+j,u−j)∈C1,αloc(¯Sq[qI[ϕ]])×C1,αloc(¯Sq[qI[ϕ]]−) |
solves problem (4) if and only if the pair
(˜u+j,˜u−j)∈C1,αq(¯Sq[qI[ϕ]])×C1,αq(¯Sq[qI[ϕ]]−) |
delivered by
˜u+j(x)=u+j(x)−xj∀x∈¯Sq[qI[ϕ]],˜u−j(x)=u−j(x)−xj∀x∈¯Sq[qI[ϕ]]−, |
solves
{Δ˜u+j=0in Sq[qI[ϕ]],Δ˜u−j=0in Sq[qI[ϕ]]−,˜u+j(x+qeh)=˜u+j(x)∀x∈¯Sq[qI[ϕ]],∀h∈{1,…,n},˜u−j(x+qeh)=˜u−j(x)∀x∈¯Sq[qI[ϕ]]−,∀h∈{1,…,n},λ+∂∂νqI[ϕ]˜u+j−λ−∂∂νqI[ϕ]˜u−j=(λ–λ+)(νqI[ϕ])jon ∂qI[ϕ],˜u+j−˜u−j=0on ∂qI[ϕ],∫∂qI[ϕ]˜u+jdσ=−∫∂qI[ϕ]yjdσy. | (15) |
Next, we show that problems (4) and (15) admit at most one solution.
Proposition 2.3. Let
(i) Problem (4) has at most one solution in
(ii) Problem (15) has at most one solution in
Proof. By the equivalence of problems (4) and (15) of Proposition 2.2, it suffices to prove statement (ⅱ), which we now consider. By the linearity of the problem, it clearly suffices to show that if
{Δ˜u+j=0in Sq[qI[ϕ]],Δ˜u−j=0in Sq[qI[ϕ]]−,˜u+j(x+qeh)=˜u+j(x)∀x∈¯Sq[qI[ϕ]],∀h∈{1,…,n},˜u−j(x+qeh)=˜u−j(x)∀x∈¯Sq[qI[ϕ]]−,∀h∈{1,…,n},λ+∂∂νqI[ϕ]˜u+j−λ−∂∂νqI[ϕ]˜u−j=0on ∂qI[ϕ],˜u+j−˜u−j=0on ∂qI[ϕ],∫∂qI[ϕ]˜u+jdσ=0, | (16) |
then
Let
∂∂νqI[ϕ]˜u−j=0on ∂qI[ϕ]. |
Accordingly, the divergence theorem implies that
0≤∫Q∖¯qI[ϕ]|D˜u−j(y)|2dy=∫∂Q˜u−j(y)∂∂νQ˜u−j(y)dσy−∫∂qI[ϕ]˜u−j(y)∂∂νqI[ϕ]˜u−j(y)dσy=0. |
Indeed, by the
∫∂Q˜u−j(y)∂∂νQ˜u−j(y)dσy=0. |
Then, there exists
Next we consider the case
∂∂νqI[ϕ]˜u+j=0on ∂qI[ϕ]. |
By the uniqueness of the solution of the interior Neumann problem up to constants, there exists
In this section, we convert problem (4) into an equivalent integral equation. As done in [39] for the longitudinal flow along a periodic array of cylinders, we do so by representing the solution in terms of single layer potentials, whose densities solve certain integral equations. Therefore, we first start with the following proposition regarding the invertibility of an integral operator that will appear in such integral formulation of problem (4).
Proposition 3.1. Let
Kγ[μ]=12μ−γwq,∗[∂qI[ϕ],μ]on ∂qI[ϕ],∀μ∈C0,α(∂qI[ϕ]). |
Then the following statements hold.
(i)
(ii)
Proof. We first consider statement (ⅰ). If
γ=γ+−γ−γ++γ−. |
Accordingly, we have to consider only the limit cases
K1[μ]=12μ−wq,∗[∂qI[ϕ],μ]=0on ∂qI[ϕ]. |
The jump formula for the normal derivative of the single layer potential of Theorem 2.1 (ⅱ) implies that
μ=∂∂νqI[ϕ]v−q[∂qI[ϕ],μ]−∂∂νqI[ϕ]v+q[∂qI[ϕ],μ]=0on ∂qI[ϕ]. |
Next, we consider the case
K−1[μ]=12μ+wq,∗[∂qI[ϕ],μ]=0on ∂qI[ϕ]. |
The jump formula for the normal derivative of the single layer potential of Theorem 2.1 (ⅱ) implies that
μ=∂∂νqI[ϕ]v−q[∂qI[ϕ],μ]−∂∂νqI[ϕ]v+q[∂qI[ϕ],μ]=0on ∂qI[ϕ]. |
Next, we consider statement (ⅱ). The Fredholm alternative theorem and the compactness of
Kγ[μ]=12μ−γwq,∗[∂qI[ϕ],μ]=0, | (17) |
then
0=∫∂qI[ϕ]Kγ[μ]dσ={12−γ(12−|qI[ϕ]||Q|)}∫∂qI[ϕ]μdσ. |
A straightforward computation shows that
We are now ready to show that problem (4) can be reformulated in terms of an integral equation which admits a unique solution.
Theorem 3.2. Let
(u+j[q,ϕ,(λ+,λ−)],u−j[q,ϕ,(λ+,λ−)])∈C1,αloc(¯Sq[qI[ϕ]])×C1,αloc(¯Sq[qI[ϕ]]−). |
Moreover
u+j[q,ϕ,(λ+,λ−)](x)=v+q[∂qI[ϕ],μj](x)−−∫∂qI[ϕ]v+q[∂qI[ϕ],μj](y)dσy−−∫∂qI[ϕ]yjdσy+xj∀x∈¯Sq[qI[ϕ]],u−j[q,ϕ,(λ+,λ−)](x)=v−q[∂qI[ϕ],μj](x)−−∫∂qI[ϕ]v−q[∂qI[ϕ],μj](y)dσy−−∫∂qI[ϕ]yjdσy+xj∀x∈¯Sq[qI[ϕ]]−, | (18) |
where
12μj−λ+−λ−λ++λ−wq,∗[∂qI[ϕ],μj]=λ+−λ−λ++λ−(νqI[ϕ])jon ∂qI[ϕ]. | (19) |
Proof. We first note that, by Proposition 2.3 (ⅱ), problem (4) has at most one solution in
(νqI[ϕ])j∈C0,α(∂qI[ϕ])0, |
Proposition 3.1 (ⅰ) implies that there exists a unique solution
λ+(−12μj+wq,∗[∂qI[ϕ],μj])−λ−(12μj+wq,∗[∂qI[ϕ],μj])=(λ–λ+)(νqI[ϕ])jon ∂qI[ϕ],v+q[∂qI[ϕ],μj]−−∫∂qI[ϕ]v+q[∂qI[ϕ],μj]dσ−v−q[∂qI[ϕ],μj]+−∫∂qI[ϕ]v−q[∂qI[ϕ],μj]dσ=0on ∂qI[ϕ]. |
Accordingly, the properties of the single layer potential (see Theorem 2.1) together with Proposition 2.2 imply that the pair of functions defined by (18) solves problem (4).
The previous theorem provides an integral equation formulation of problem (4) and a representation formula for its solution. We conclude this section by writing the effective conductivity in a form which makes use of the density
∫qI[ϕ]∂∂xiu+j[q,ϕ,(λ+,λ−)](x)dx=∫∂qI[ϕ]u+j[q,ϕ,(λ+,λ−)](y)(νqI[ϕ](y))idσy=∫∂qI[ϕ](v+q[∂qI[ϕ],μj](y)−−∫∂qI[ϕ]v+q[∂qI[ϕ],μj](z)dσz−−∫∂qI[ϕ]zjdσz+yj)(νqI[ϕ](y))idσy=∫∂qI[ϕ]v+q[∂qI[ϕ],μj](y)(νqI[ϕ](y))idσy−∫∂qI[ϕ](νqI[ϕ](y))idσy−∫∂qI[ϕ]v+q[∂qI[ϕ],μj](z)dσz−∫∂qI[ϕ](νqI[ϕ](y))idσy−∫∂qI[ϕ]zjdσz+δij|qI[ϕ]|n. |
Similarly, we have
∫Q∖¯qI[ϕ]∂∂xiu−j[q,ϕ,(λ+,λ−)](x)dx=∫∂Qu−j[q,ϕ,(λ+,λ−)](y)(νQ(y))idσy−∫∂qI[ϕ]u−j[q,ϕ,(λ+,λ−)](y)(νqI[ϕ](y))idσy=δij|Q|n−∫∂qI[ϕ]v−q[∂qI[ϕ],μj](y)(νqI[ϕ](y))idσy+∫∂qI[ϕ](νqI[ϕ](y))idσy−∫∂qI[ϕ]v−q[∂qI[ϕ],μj](z)dσz+∫∂qI[ϕ](νqI[ϕ](y))idσy−∫∂qI[ϕ]zjdσz−δij|qI[ϕ]|n. |
Indeed
∫∂Q(v−q[∂qI[ϕ],μj](y)−−∫∂qI[ϕ]v−q[∂qI[ϕ],μj](z)dσz−−∫∂qI[ϕ]zjdσz+yj)(νQ(y))idσy=∫∂Qyj(νQ(y))idσy=δij|Q|n. |
Moreover, by the divergence theorem, we have
∫∂qI[ϕ](νqI[ϕ](y))idσy=0∀i∈{1,…,n}. |
Accordingly, by the continuity of the single layer potential, we have that
λeffij[q,ϕ,(λ+,λ−)]=1|Q|n{λ+∫qI[ϕ]∂∂xiu+j[q,ϕ,(λ+,λ−)](x)dx+λ−∫Q∖¯qI[ϕ]∂∂xiu−j[q,ϕ,(λ+,λ−)](x)dx}=1|Q|n{δijλ−|Q|n+(λ+−λ−)(∫∂qI[ϕ]vq[∂qI[ϕ],μj](y)(νqI[ϕ](y))idσy−∫∂qI[ϕ](νqI[ϕ](y))idσy−∫∂qI[ϕ]vq[∂qI[ϕ],μj](z)dσz−∫∂qI[ϕ](νqI[ϕ](y))idσy−∫∂qI[ϕ]zjdσz+δij|qI[ϕ]|n)}=δijλ−+(λ++λ−){1|Q|n(λ+−λ−)(λ++λ−)(∫∂qI[ϕ]vq[∂qI[ϕ],μj](y)(νqI[ϕ](y))idσy+δij|qI[ϕ]|n)}. | (20) |
Thanks to Theorem 3.2, the study of problem (4) can be reduced to the study of the boundary integral equation (19). Therefore, our first step in order to study the dependence of the solution of problem (4) upon the triple
Before starting with this plan, we note that equation (19) is defined on the
Lemma 4.1. Let
12θj(t)−λ+−λ−λ++λ−∫qϕ(∂Ω)DSq,n(qϕ(t)−s)⋅νqI[ϕ](qϕ(t))(θj∘ϕ(−1))(q−1s)dσs=λ+−λ−λ++λ−(νqI[ϕ](qϕ(t)))j∀t∈∂Ω, | (21) |
if and only if the function
μj(x)=(θj∘ϕ(−1))(q−1x)∀x∈∂qI[ϕ] | (22) |
solves equation (19). Moreover, equation (21) has a unique solution in
Proof. The equivalence of equation (21) in the unknown
Inspired by Lemma 4.1, for all
Mj:D+n(R)×(C1,α(∂Ω,Rn)∩A˜Q∂Ω)×]−2,2[×C0,α(∂Ω)→C0,α(∂Ω) |
by setting
Mj[q,ϕ,γ,θ](t)≡12θ(t)−γ∫qϕ(∂Ω)DSq,n(qϕ(t)−s)⋅νqI[ϕ](qϕ(t))(θ∘ϕ(−1))(q−1s)dσs−γ(νqI[ϕ](qϕ(t)))j∀t∈∂Ω, | (23) |
for all
Mj[q,ϕ,λ+−λ−λ++λ−,θ]=0 on ∂Ω. | (24) |
Our aim is to recover the regularity of the solution
Lemma 4.2. Let
(i) The map from
V[q,ϕ,θ](t)≡∫qϕ(∂Ω)Sq,n(qϕ(t)−s)(θ∘ϕ(−1))(q−1s)dσs∀t∈∂Ω, |
is real analytic.
(ii) The map from
is real analytic.
Next, we state the following technical lemma about the real analyticity upon the diffeomorphism
Lemma 4.3. Let
(i) For each
Moreover, the map
(ii) The map from
We are now ready to prove that the solutions of (24) depend real analytically upon the triple 'periodicity-shape-contrast'. We do so by means of the following.
Proposition 4.4. Let
(i) For each
and we denote such a function by
(ii) There exist
to
Proof. The proof of statement (ⅰ) is a straightforward modification of the proof of Lemma 4.1. Indeed, it suffices to replace
Next we turn to consider statement (ⅱ). As a first step we have to study the regularity of the map
for all
In this section we prove our main result that answers to question (10) on the behavior of the effective conductivity upon the triple 'periodicity-shape-conductivity'. To this aim, we exploit the representation formula in (20) of the effective conductivity and the analyticity result of Proposition 4.4.
Theorem 5.1. Let
(25) |
for all
Proof. Let
for all
for all
clearly
Then, by taking into account that the pointwise product in Schauder spaces is bilinear and continuous, and that the integral in Schauder spaces is linear and continuous, Lemma 4.3 implies that the map from
In the present paper we considered the effective conductivity of a two or three dimensional periodic two-phase composite material. The composite is obtained by introducing into a homogeneous matrix a periodic set of inclusions of a large class of sufficiently smooth shapes. We proved a regularity result for the effective conductivity of such a composite upon perturbations of the periodicity structure, of the shape of the inclusions, and of the conductivities of each material. Namely, we showed the real analytic dependence of the effective conductivity as a functional acting between suitable Banach spaces.
The consequences of our result are twofold. First, this high regularity result represents a theoretical justification to guarante that differential calculus may be used in order to characterize critical periodicity-shape-conductivity triples
for
Both the authors are members of the 'Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni' (GNAMPA) of the 'Istituto Nazionale di Alta Matematica' (INdAM) and acknowledge the support of the Project BIRD191739/19 'Sensitivity analysis of partial differential equations in the mathematical theory of electromagnetism' of the University of Padova. P.M. acknowledges the support of the grant 'Challenges in Asymptotic and Shape Analysis - CASA' of the Ca' Foscari University of Venice. The authors wish to thank the anonymous referees for many valuable comments that have improved the presentation of the paper.
[1] | Kinsella B, Mutchler A (2018) Voice assistant consumer adoption report. Voicebot.AI . Available from: https://voicebot.ai/wp-content/uploads/2018/11/voice-assistant-consumer-adoption-report-2018-voicebot.pdf. |
[2] | National Public Media, Edison Research.The Smart Audio Report. National Public Media (2020) . Available from: https://www.nationalpublicmedia.com/insights/reports/smart-audio-report/. |
[3] | Laricchia F (2022) Number of voice assistants in use worldwide from 2019 to 2024 (in billions). Statista . Available from: https://www.statista.com/statistics/973815/worldwide-digital-voice-assistant-in-use/. |
[4] | Laricchia F (2022) Factors surrounding preference of voice assistants over websites and applications, worldwide, as of 2017. Statista . Available from: https://www.statista.com/statistics/801980/worldwide-preference-voice-assistant-websites-app/. |
[5] | Kinsella B, Mutchler A (2019) Voice assistant consumer adoption in healthcare. Voicebot.AI . Available from: https://voicebot.ai/wp-content/uploads/2019/10/voice_assistant_consumer_adoption_in_healthcare_report_voicebot.pdf. |
[6] |
Ferrand J, Hockensmith R, Houghton RF, et al. (2020) Evaluating smart assistant responses for accuracy and misinformation regarding human papillomavirus vaccination: Content analysis study. J Med Internet Res 22: e19018. https://doi.org/10.2196/19018 ![]() |
[7] |
Alagha EC, Helbing RR (2019) Evaluating the quality of voice assistants' responses to consumer health questions about vaccines: An exploratory comparison of Alexa, Google Assistant and Siri. BMJ Health Care Inform 26: e100075. https://doi.org/10.1136/bmjhci-2019-100075 ![]() |
[8] |
Goh ASY, Wong LL, Yap KYL (2021) Evaluation of COVID-19 information provided by digital voice assistants. Int J Digit Health 1: 3. https://doi.org/10.29337/ijdh.25 ![]() |
[9] |
Kocaballi AB, Quiroz JC, Rezazadegan D, et al. (2020) Responses of conversational agents to health and lifestyle prompts: investigation of appropriateness and presentation structures. J Med Internet Res 22: e15823. https://doi.org/10.2196/15823 ![]() |
[10] |
Miner AS, Milstein A, Schueller S, et al. (2016) Smartphone-based conversational agents and responses to questions about mental health, interpersonal violence, and physical health. JAMA Intern Med 176: 619-625. https://doi.org/10.1001/jamainternmed.2016.0400 ![]() |
[11] |
Bickmore TW, Trinh H, Olafsson S, et al. (2018) Patient and consumer safety risks when using conversational assistants for medical information: An observational study of Siri, Alexa, and Google Assistant. J Med Internet Res 20: e11510. https://doi.org/10.2196/11510 ![]() |
[12] |
Bérubé C, Schachner T, Keller R, et al. (2021) Voice-based conversational agents for the prevention and management of chronic and mental health conditions: Systematic literature review. J Med Internet Res 23: e25933. https://doi.org/10.2196/25933 ![]() |
[13] | World Health Organization.Global report on diabetes. World Health Organization (2016) . Available from: https://www.who.int/publications/i/item/9789241565257. |
[14] | World Health Organization.New WHO Global Compact to speed up action to tackle diabetes. World Health Organization (2021) . Available from: https://www.who.int/news/item/14-04-2021-new-who-global-compact-to-speed-up-action-to-tackle-diabetes. |
[15] |
Ow Yong LM, Koe LWP (2021) War on diabetes in Singapore: A policy analysis. Health Res Policy Syst 19: 15. https://doi.org/10.1186/s12961-021-00678-1 ![]() |
[16] | Amazon. Alexa developer document—Design your skill. Amazon, (n.d.). Available from: https://developer.amazon.com/en-US/docs/alexa/design/design-your-skill.html. |
[17] | Google DevelopersIntegrate with Google Assistant. Google, (n.d.). Available from: https://developers.google.com/assistant. |
[18] | Martineau P (2019) Alexa, What's my blood-sugar level?. Wired . Available from: https://www.wired.com/story/alexa-whats-my-blood-sugar-level/. |
[19] | One DropAlexa skills: One Drop. Amazon, (n.d.). Available from: https://www.amazon.com/One-Drop/dp/B072QDCSQH. |
[20] | DataMysticAlexa skills: My Sugar by Jade Diabetes. Amazon, (n.d.). Available from: https://www.amazon.com/My-Sugar-by-Jade-Diabetes/dp/B0874717X2/ref=sr_1_3?dchild=1&keywords=diabetes&qid=1627894652&s=digital-skills&sr=1-3. |
[21] | Epad IncGoogle Assistant: Diabetes Tips. Google, (n.d.). Available from: https://assistant.google.com/services/a/uid/00000063a0945bf1?hl=en-US. |
[22] | Epad InccGoogle Assistant: Diabetes Checkup. Google, (n.d.). Available from: https://assistant.google.com/services/a/uid/000000e2388921d2?hl=en-US. |
[23] | DietLabsGoogle Assistant: Well With Diabetes. Google, (n.d.). Available from: https://assistant.google.com/services/a/uid/0000000a181531b7?hl=en-US. |
[24] | RocheAlexa skills: Sulli the Diabetes Guru. Amazon, (n.d.). Available from: https://www.amazon.com/Roche-Sulli-the-Diabetes-Guru/dp/B08BLTFY75. |
[25] | eHealth Support NetworksAlexa skills: My Diabetes Lifestyle. Amazon, (n.d.). Available from: https://www.amazon.com/eHealth-Support-Networks-Diabetes-Lifestyle/dp/B08V8DGL69/ref=sr_1_1?dchild=1&keywords=diabetes&qid=1625367230&s=digital-skills&sr=1-1. |
[26] | Heifner M Sulli The Diabetes Guru: Your diabetes voice assistant (2020). Available from: https://beyondtype2.org/sulli-the-diabetes-guru/. |
[27] |
Schachner T, Keller R, Wangenheim FV (2020) Artificial intelligence-based conversational agents for chronic conditions: Systematic literature review. J Med Internet Res 22: e20701. https://doi.org/10.2196/20701 ![]() |
[28] |
Sezgin E, Militello LK, Huang Y, et al. (2020) A scoping review of patient-facing, behavioral health interventions with voice assistant technology targeting self-management and healthy lifestyle behaviors. Transl Behav Med 10: 606-628. https://doi.org/10.1093/tbm/ibz141 ![]() |
[29] | Cheng A, Raghavaraju V, Kanugo J, et al. (2018) Development and evaluation of a healthy coping voice interface application using the Google home for elderly patients with type 2 diabetes. 2018—15th IEEE Annual Consumer Communications and Networking Conference (CCNC) . https://doi.org/10.1109/CCNC.2018.8319283 |
[30] |
Akturk HK, Snell-Bergeon JK, Shah VN (2021) Continuous glucose monitor with Siri integration improves glycemic control in legally blind patients with diabetes. Diabetes Technol Ther 23: 81-83. https://doi.org/10.1089/dia.2020.0320 ![]() |
[31] | Maharjan B, Li J, Kong J, et al. (2019) Alexa, what should I eat?: A personalized virtual nutrition coach for native American diabetes patients using Amazon's smart speaker technology. 2019—IEEE International Conference on E-Health Networking, Application and Services, (HealthCom) . https://doi.org/10.1109/HealthCom46333.2019.9009613 |
[32] | Statista Research Department.Worldwide desktop market share of leading search engines from January 2010 to July 2022. Statista (2022) . Available from: https://www.statista.com/statistics/216573/worldwide-market-share-of-search-engines/. |
[33] |
Yap KYL, Raaj S, Chan A (2010) OncoRx-IQ: A tool for quality assessment of online anticancer drug interactions. Int J Qual Health Care 22: 93-106. https://doi.org/10.1093/intqhc/mzq004 ![]() |
[34] | Health On The Net (HON) Foundation.HONcode certification. Health On The Net (2020) . Available from: https://myhon.ch/en/certification.html. |
[35] | Charnock D (1998) The DISCERN Handbook: Quality criteria for consumer health information on treatment choices. Abingdon, Oxon: Radcliffe Medical Press 55 pp. Available from: https://a-f-r.org/wp-content/uploads/sites/3/2016/01/1998-Radcliffe-Medical-Press-Quality-criteria-for-consumer-health-information-on-treatment-choices.pdf. |
[36] |
Charnock D, Shepperd S, Needham G, et al. (1999) DISCERN: An instrument for judging the quality of written consumer health information on treatment choices. J Epidemiol Community Health 53: 105-111. https://doi.org/10.1136/jech.53.2.105 ![]() |
[37] |
Robillard JM, Jun JH, Lai JA, et al. (2018) The QUEST for quality online health information: validation of a short quantitative tool. BMC Med Inform Decis Mak 18: 87. https://doi.org/10.1186/s12911-018-0668-9 ![]() |
[38] |
Shoemaker SJ, Wolf MS, Brach C (2014) Development of the Patient Education Materials Assessment Tool (PEMAT): A new measure of understandability and actionability for print and audiovisual patient information. Patient Educ Couns 96: 395-403. https://doi.org/10.1016/j.pec.2014.05.027 ![]() |
[39] | Shoemaker SJ, Wolf MS, Brach C The Patient Education Materials Assessment Tool (PEMAT) and User's Guide (2013). Available from: https://www.ahrq.gov/health-literacy/patient-education/pemat.html |
[40] | National Library of Medicine.Evaluating Internet Health Information Tutorial. MedlinePlus (2020) . Available from: https://medlineplus.gov/webeval/intro1.html. |
[41] | Tan RY, Pua AE, Wong LL, et al. (2021) Assessing the quality of COVID-19 vaccine videos on video-sharing platforms. Explor Res Clin Soc Pharm 2: 100035. https://doi.org/10.1016/j.rcsop.2021.100035 |
[42] | Ministry of Health Singapore.Your Diabetes Questions Answered. HealthHub (2020) . Available from: https://www.healthhub.sg/live-healthy/1392/your-diabetes-questions-answered. |
[43] | American Diabetes Association.Frequently Asked Questions: COVID-19 and Diabetes—How COVID-19 impacts people with diabetes. American Diabetes Association . Available from: https://www.diabetes.org/coronavirus-covid-19/how-coronavirus-impacts-people-with-diabetes. |
[44] | GoogleFAQ about Google Trends data—Trends Help. Available from: https://support.google.com/trends/answer/4365533?hl=en&ref_topic=6248052. |
[45] | AnswerThePublicSearch listening tool for market, customer & content research. Available from: https://answerthepublic.com/. |
[46] | American Diabetes AssociationAmerican Diabetes Association—Connected for Life. Available from: https://diabetes.org/. |
[47] | Centers for Disease Control and Prevention.Diabetes. Centers for Disease Control and Prevention (2021) . Available from: https://www.cdc.gov/diabetes/index.html. |
[48] | National Institute of Diabetes and Digestive and Kidney Diseases.Diabetes. National Institute of Diabetes and Digestive and Kidney diseases (NIDDK) . Available from: https://www.niddk.nih.gov/health-information/diabetes. |
[49] | Cleveland Clinic.Diabetes: An overview. Cleveland Clinic (2021) . Available from: https://my.clevelandclinic.org/health/diseases/7104-diabetes-mellitus-an-overview. |
[50] | US Food and Drug Administration.Food and Drug Administration homepage. US FDA . Available from: https://www.fda.gov/. |
[51] | Diabetes UK.Diabetes UK—Know diabetes. Fight diabetes. Diabetes UK . Available from: https://www.diabetes.org.uk/. |
[52] | UK National Health Service.Diabetes—NHS. National Health Service . Available from: https://www.nhs.uk/conditions/diabetes/. |
[53] | Victoria State GovernmentBetter Health Channel—Diabetes. Available from: https://www.betterhealth.vic.gov.au/health/conditionsandtreatments/diabetes. |
[54] | Diabetes AustraliaDiabetes Australia homepage. Available from: https://www.diabetesaustralia.com.au/. |
[55] | Ministry of Health SingaporeHealthHub Health Services. Available from: https://www.healthhub.sg/. |
[56] | National University Health System.National University Hospital: Home. National University Hospital . Available from: https://www.nuh.com.sg/Pages/Home.aspx. |
[57] | Royal Australian College of General Practitioners, Diabetes Australia.Management of type 2 diabetes: A handbook for general practice. Royal Australian College of General Practitioners (2020) . Available from: https://www.diabetesaustralia.com.au/wp-content/uploads/Available-here.pdf. |
[58] | Ministry of Health Singapore.Diabetes Mellitus—MOH Clinical Practice Guidelines 1/2014. Ministry of Health (2014) . Available from: https://www.moh.gov.sg/docs/librariesprovider4/guidelines/cpg_diabetes-mellitus-booklet---jul-2014.pdf. |
[59] | Diabetes Care.Introduction: Standards of Medical Care in Diabetes—2021. Diabetes Care (2021) . Available from: https://care.diabetesjournals.org/content/44/Supplement_1. |
[60] | National Institute for Health and Care Excellence.Type 1 diabetes in adults: Diagnosis and management—NICE guideline. National Institute for Health and Care Excellence (2021) . Available from: https://www.nice.org.uk/guidance/ng17. |
[61] |
Cosentino F, Grant PJ, Aboyans V, et al. (2020) 2019 ESC Guidelines on diabetes, pre-diabetes, and cardiovascular diseases developed in collaboration with the EASD: The Task Force for diabetes, pre-diabetes, and cardiovascular diseases of the European Society of Cardiology (ESC) and the European Association for the Study of Diabetes (EASD). Eur Heart J 41: 255-323. https://doi.org/10.1093/eurheartj/ehz486 ![]() |
[62] | American Diabetes Association.6. Glycemic targets: Standards of medical care in diabetes—2021. Diabetes Care (2021) 44: S73-S84. https://doi.org/10.2337/dc21-S006 |
[63] | American Diabetes Association.Myths about Diabetes. American Diabetes Association . Available from: https://www.diabetes.org/diabetes-risk/prediabetes/myths-about-diabetes. |
[64] | Centers for Disease Control and Prevention.Flu & people with diabetes. Centers for Disease Control and Prevention (2022) . Available from: https://www.cdc.gov/flu/highrisk/diabetes.htm. |
[65] | Rahmatizadeh S, Valizadeh-Haghi S (2018) Evaluating the trustworthiness of consumer-oriented health websites on diabetes. Libr Philos Pract, 1786. |
[66] |
Keselman A, Arnott Smith C, Murcko AC, et al. (2019) Evaluating the quality of health information in a changing digital ecosystem. J Med Internet Res 21: e11129. https://doi.org/10.2196/11129 ![]() |
[67] | National Library of MedicineMedlinePlus evaluating internet health information: A tutorial National Library of Medicine (2018). Available from: https://medlineplus.gov/webeval/EvaluatingInternetHealthInformationTutorial.pdf. |
[68] |
Smith DA (2020) Situating Wikipedia as a health information resource in various contexts: A scoping review. PLoS One 15: e0228786. https://doi.org/10.1371/journal.pone.0228786 ![]() |
[69] | Google Developers.Policies for actions on Google. Google Developers . Available from: https://developers.google.com/assistant/console/policies/general-policies. |
[70] | Amazon.com Inc.Alexa developer documentation: Policy requirements. Amazon . Available from: https://developer.amazon.com/en-US/docs/alexa/custom-skills/policy-testing-for-an-alexa-skill.html. |
[71] |
Savitha S, Hirsch IB (2014) Personalized diabetes management: Moving from algorithmic to individualized therapy. Diabetes Spectrum 27: 87-91. https://doi.org/10.2337/diaspect.27.2.87 ![]() |
[72] | Patel N 6 timely SEO strategies and resources for voice search. Available from: https://neilpatel.com/blog/seo-for-voice-search/. |
[73] |
Shafiee G, Mohajeri-Tehrani M, Pajouhi M, et al. (2012) The importance of hypoglycemia in diabetic patients. J Diabetes Metab Disord 11: 17. https://doi.org/10.1186/2251-6581-11-17 ![]() |
[74] | Diabetes.co.uk.Hypoglycemia (low blood glucose levels). Diabetes.co.uk (2022) . Available from: https://www.diabetes.co.uk/Diabetes-and-Hypoglycaemia.html#:~:text=Diabetes%20UK%20recommend%20that%20you,a%20non%2Ddiet%20soft%20drink. |
[75] | Centers for Disease Control and Prevention.How to treat low blood sugar (Hypoglycemia). Centers for Disease Control and Prevention (2021) . Available from: https://www.cdc.gov/diabetes/basics/low-blood-sugar-treatment.html. |
[76] | Amazon.com Inc.What is natural language understanding?. Amazon . Available from: https://developer.amazon.com/en-US/alexa/alexa-skills-kit/nlu. |
[77] | Kinsella B (2019) Voice assistant demographic data—Young consumers more likely to own smart speakers while over 60 bias toward Alexa and Siri. Voicebot.ai . Available from: https://voicebot.ai/2019/06/21/voice-assistant-demographic-data-young-consumers-more-likely-to-own-smart-speakers-while-over-60-bias-toward-alexa-and-siri/. |
[78] | Cherney K, Wood K (2022) Age of onset for type 2 diabetes: Know your risk. Healthline . Available from: https://www.healthline.com/health/type-2-diabetes-age-of-onset#age-at-diagnosis. |
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1. | Wojciech Nawalaniec, Katarzyna Necka, Vladimir Mityushev, Effective Conductivity of Densely Packed Disks and Energy of Graphs, 2020, 8, 2227-7390, 2161, 10.3390/math8122161 | |
2. | Matteo Dalla Riva, Paolo Luzzini, Paolo Musolino, Multi-parameter analysis of the obstacle scattering problem, 2022, 38, 0266-5611, 055004, 10.1088/1361-6420/ac5eea | |
3. | Matteo Dalla Riva, Massimo Lanza de Cristoforis, Paolo Musolino, 2021, Chapter 13, 978-3-030-76258-2, 513, 10.1007/978-3-030-76259-9_13 | |
4. | Matteo Dalla Riva, Riccardo Molinarolo, Paolo Musolino, Existence results for a nonlinear nonautonomous transmission problem via domain perturbation, 2022, 152, 0308-2105, 1451, 10.1017/prm.2021.60 | |
5. | Yu. V. Obnosov, Analytical Evaluation of the Effective Electric Resistivity and Hall Coefficient in the Rectangular and Triangular Checkerboard Composites, 2022, 43, 1995-0802, 2989, 10.1134/S1995080222130352 | |
6. | Vladimir Mityushev, Dmytro Nosov, Ryszard Wojnar, 2022, 9780323905435, 63, 10.1016/B978-0-32-390543-5.00008-6 | |
7. | Matteo Dalla Riva, Paolo Luzzini, Paolo Musolino, Roman Pukhtaievych, 2022, 9780323905435, 271, 10.1016/B978-0-32-390543-5.00019-0 | |
8. | Matteo Dalla Riva, Paolo Luzzini, Paolo Musolino, Shape analyticity and singular perturbations for layer potential operators, 2022, 56, 2822-7840, 1889, 10.1051/m2an/2022057 | |
9. | Natalia Rylko, Pawel Kurtyka, Olesia Afanasieva, Simon Gluzman, Ewa Olejnik, Anna Wojcik, Wojciech Maziarz, Windows Washing method of multiscale analysis of the in-situ nano-composites, 2022, 176, 00207225, 103699, 10.1016/j.ijengsci.2022.103699 | |
10. | Matteo Dalla Riva, Paolo Luzzini, Paolo Musolino, 2023, Chapter 20, 978-3-031-36374-0, 271, 10.1007/978-3-031-36375-7_20 | |
11. | Riccardo Molinarolo, Existence result for a nonlinear mixed boundary value problem for the heat equation, 2025, 543, 0022247X, 128878, 10.1016/j.jmaa.2024.128878 | |
12. | Natalia Rylko, Michał Stawiarz, Pawel Kurtyka, Vladimir Mityushev, Study of anisotropy in polydispersed 2D micro and nano-composites by Elbow and K-Means clustering methods, 2024, 276, 13596454, 120116, 10.1016/j.actamat.2024.120116 |