esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Spherical Area Coordinates (SACs)
### Planar Area Coordinates  
Let \(P=(\mathbf{v}_{j})_{j=1\dots n}\) be a polygon with vertices \(\mathbf{v}_{j}\). The barycentric coordinates \(\lambda_{i}(\mathbf{v};P)\) of a point \(\mathbf{v}\) are continuous functions that satisfy the following properties for all points \(\mathbf{v}\) inside the polygon.  
1. \(\forall i\quad\lambda_{i}(\mathbf{v};P)>0\) ;
2. \(\sum_{i}\lambda_{i}(\mathbf{v},P)=1\);
3. \(\sum_{i}\lambda_{i}(\mathbf{v},P)\mathbf{v}_{i}=\mathbf{v}\).  
Figure 5 illustrates the idea of barycentric coordinates for the case of planar triangles. Any point \(\mathbf{v}\) on the plane \(\mathbb{E}^{2}\) can be expressed by a linear combination of the vertices of the reference triangle \(\triangle\mathbf{v}_{1}\mathbf{v}_{2}\mathbf{v}_{3}\cdot\mathbf{v}=\lambda_{1}\mathbf{v}_{1}+ \lambda_{2}\mathbf{v}_{2}+\lambda_{3}\mathbf{v}_{3}\) (property 3). The point \(\mathbf{v}\) outside the reference triangle can lead to  
negative coordinates, but this situation is not considered in this paper. Now, the question is, 'What are the continuous functions \(\lambda_{i}(\mathbf{v};P)\) of the barycentric coordinates of point \(\mathbf{v}\)?' In the context of a triangle, barycentric coordinates are also known as area coordinates because the coordinates of \(\mathbf{v}\) with respect to the triangle \(\triangle\mathbf{v}_{1}\mathbf{v}_{2}\mathbf{v}_{3}\) are proportional to the areas of \(S_{\triangle v_{1}\mathbf{v}_{2}\mathbf{v}_{3}}\),\(S_{\triangle v_{1}\mathbf{v}_{3}}\) and \(S_{\triangle v_{1}\mathbf{v}_{2}\mathbf{v}}\). The equations of area coordinates are written as  
\[\lambda_{1}=\frac{S_{\triangle v_{1}\mathbf{v}_{2}\mathbf{v}_{3}}}{S_{\triangle v_{1} \mathbf{v}_{2}\mathbf{v}_{3}}},\quad\lambda_{2}=\frac{S_{\triangle v_{1}\mathbf{v}_{2}\mathbf{ v}_{3}}}{S_{\triangle v_{1}\mathbf{v}_{2}\mathbf{v}_{3}}},\quad\lambda_{3}=\frac{S_{ \triangle v_{1}\mathbf{v}_{2}\mathbf{v}_{1}}}{S_{\triangle v_{1}\mathbf{v}_{2}\mathbf{v}_{3}}}. \tag{1}\]  
So, according to Equation (1), we can easily calculate the area coordinates of points \(v_{1}\), \(v_{2}\), and \(v_{3}\). The area coordinates of \(v_{1}\) are  
\[\lambda_{1}=\frac{S_{\triangle v_{1}\mathbf{v}_{2}\mathbf{v}_{3}}}{S_{\triangle v_{1} \mathbf{v}_{2}\mathbf{v}_{3}}}=1,\quad\lambda_{2}=\frac{S_{\triangle v_{1}\mathbf{v}_{1} \mathbf{v}_{3}}}{S_{\triangle v_{1}\mathbf{v}_{2}\mathbf{v}_{3}}}=0,\quad\lambda_{3}= \frac{S_{\triangle v_{1}\mathbf{v}_{2}\mathbf{v}_{1}}}{S_{\triangle v_{1}\mathbf{v}_{2}\bm {v}_{3}}}=0.\]  
Since the triangles \(\triangle v_{1}\mathbf{v}_{1}\mathbf{v}_{3}\) and \(\triangle v_{1}\mathbf{v}_{2}\mathbf{v}_{1}\) are degenerate, the area of these two triangles is 0. As a result, the area coordinates of \(\mathbf{v}_{1}\) is \(v_{1}(\lambda_{1},\lambda_{2},\lambda_{3})=(1,0,0)\). What is more, the area coordinates of the verties \(\mathbf{v}_{2}\) and \(\mathbf{v}_{3}\) are \(v_{2}(\lambda_{1},\lambda_{2},\lambda_{3})=(0,1,0)\), and \(v_{3}(\lambda_{1},\lambda_{2},\lambda_{3})=(0,0,1)\).
# Global Dynamics and Implications of an HBV Model with Proliferating Infected Hepatocytes
## 2 Model Development and Dynamics  
We assumed that infected hepatocytes proliferate at a rate less than or equal to the rate of proliferation of healthy hepatocytes. As many other chronic HBV models, we omitted a complex immune response. Therefore, our model has a population of healthy hepatocytes, \(x(t)\), a population of infected hepatocytes, \(y(t)\), and a population of free virions, \(v(t)\),  
\[\frac{dx}{dt} = rx(t)\bigg{(}1-\frac{x(t)+y(t)}{K}\bigg{)}-\frac{\beta v(t)x(t)}{x( t)+y(t)}, \tag{4}\] \[\frac{dy}{dt} = \rho y(t)\bigg{(}1-\frac{(x(t)+y(t)}{K}\bigg{)}+\frac{\beta v(t)x( t)}{x(t)+y(t)}-ay(t),\] (5) \[\frac{dv}{dt} = \gamma y(t)-\mu v(t). \tag{6}\]  
A logistic growth term is also used for the proliferation of healthy and infected hepatocytes with \(r\) and \(\rho\) as the maximum proliferation rates and \(K\) as the carrying capacity. The infection rate is \(\beta\); the death rate of infected hepatocytes is \(a\); the number of free virions produced per infected hepatocyte is \(\gamma\); the death rate of virions is \(\mu\).  
The basic reproduction number, \(R_{0}\), is the same as with all previous models that assume a standard incidence term for infection,  
\[R_{0}=\frac{\beta\gamma}{a\mu}.\]  
The cellular vitality index, \(R^{*}\), first introduced in [PERSON] et al. [36], incorporates the rates of healthy hepatocyte proliferation, infected hepatocyte proliferation, and infected hepatocyte lifespan, and it roughly represents the capacity of the healthy liver to regenerate. For the model (4)-(6),  
\[R^{*}=\frac{r-\rho+a}{a}.\]  
For clarification, \(R_{0}\) has the standard definition, which is the expected number of secondary infections per primary infection in a completely susceptible population. On the other hand, \(R^{*}\) is the point when \(E^{*}\), the chronic infection state with a nonzero healthy hepatocyte population, ceases to exist given that \(R_{0}>1\). Since \(R^{*}\) depends on the proliferation and death rates of hepatocytes and relates to the possible collapse of the system (to the extinction equilibrium), \(R^{*}\) can be thought of as representing the capacity of the healthy liver to regenerate. From this, it can be seen that increasing either the proliferation or lifespan of infected hepatocytes impairs the ability of the infected liver to regenerate, while greater proliferation in healthy hepatocytes is beneficial.  
In the following subsections, we present two different proliferation scenarios that differ in the maximum proliferation rate of infected hepatocytes. In the first of these, we assumed that infected hepatocytes proliferate at the same rate as healthy hepatocytes. In the second, we assumed that hepatocytes proliferate at a non-negligible rate that is nevertheless lower than that of healthy hepatocytes. We assumed nonnegative initial conditions for both models. One can use the methods of [PERSON] et al. [36] to show rigorously that solutions in both models remain bounded and nonnegative.
## 2 Propagation in Dielectric Media
Note that Figure 1b describes the imaginary part \(\varepsilon^{\prime\prime}(f)\) of the atmospheric permittivity is in a logarithmic scale. It seems that the fog effects increased intensely with frequency. Figure 1: (**a**) The real \(\varepsilon^{\prime}(f)\) and (**b**) imaginary \(\varepsilon^{\prime\prime}(f)\) part of dielectric permittivity for different relative humidity \(RH\) (%) and water droplet concentration \(W_{0}\) (g/m\({}^{3}\)) values. Substituting \(\varepsilon^{\prime}(f)\) and \(\varepsilon^{\prime\prime}(f)\) into Equations (8) and (9), we calculated the attenuation coefficient \(\alpha(f)\), the wavenumber \(\beta(f)\), and the resulted frequency dependent incremental part of group delay \(\Delta\tau_{d}(f)\). The attenuation \(20\log(\mathrm{e})\cdot\alpha(f)\) in (dB/km) and the dimensionless measure \(c\cdot\Delta\tau_{d}(f)/d-1\) for different values of relative humidity \(RH\) and water droplet concentration \(W_{0}\) are presented in Figure 2.
# Fuzzy Logic-Based Geographic Routing Protocol for Dynamic Wireless Sensor Networks
## 4 Simulation and Complexity Analysis
### Comparison of Network Performance  
To compare the network performances between the FLGR protocol and existing protocols, the QualNet network simulation platform was adopted to construct a simulation environment. The QualNet simulator is the only parallel and message-level network simulation tool, and was developed by Scalable Networks Technologies. It has a faster running speed, higher accuracy, and better extensibility, and is suitable for the development and simulation of wireless sensor networks.  
During simulation, network nodes are randomly distributed in a two-dimensional plane of \(1000\;\mathrm{m}\times 1000\;\mathrm{m}\), where the random waypoint (RWP) movement model is adopted. Every node starts at an initial location and moves toward a randomly chosen destination location with a constant speed, which is randomly chosen in \([0,v_{\mathrm{max}}]\). This process repeats throughout the simulation, and we assumed that the pausing time was equal to zero in Section 4.2. Each node is equipped with a semi-duplex transceiver. The IEEE 802.11 protocol was selected for the physical layer as well as the MAC layer, where the transmission radius of the node was 250 m, and packets arrived to the node according to a Poisson process with \(2 packets/s\); that is, an average of two packets arrived to each node per second. The GPSR, GPSR-AD, LPESGR, and FLGR protocols were adopted for the routing layer. For the GPSR, GPSR-AD, and LPESGR protocols, the GLS algorithm was adopted to obtain the location information of the destination node. According to different maximum speeds of the nodes (10, 15, 20, 25, 30, 35, 40 m/s), the frequencies of the Hello message were set to 1 Hz, 1.5 Hz, 2 Hz, 2.5 Hz, 3 Hz, 3.5 Hz, and 4 Hz respectively. The final data was obtained through the average of 8 trails, and the simulation time of each trail was 10 min. The detailed network parameters are presented in Table 7.
## 4 Design
### Model  
The datasets exhibit characteristics such as a limited number of samples and complex interactions among features. Based on these considerations, MovePerf must satisfy the following constraints. First, the model should effectively handle the limited sample size present in the dataset. Second, it should effectively capture and fully leverage the complex interactions among the features.  
To deal with the interactions between features, the model needs to address both low- and high-order interactions. Considering that high-order interactions often build upon low-order interactions [31], our approach involves using FM to complete low-order interaction information. The order-2 crossover terms of the features are then fed into a component designed to learn high-order interactions. For high-order interactive information learning, we choose the DFNN, which can achieve high accuracy in the case of small samples. Furthermore, we perform preprocessing on the input data by normalizing the maximum values of metric features and converting semantic features into word vector representations.  
Based on the aforementioned considerations, the model of MovePerf is composed of two sub-models, including the FM and DFNN components, as illustrated in Figure 6. The input is the processed features, and the data are transformed and processed through the embedding layer to facilitate more efficient learning and processing by the model. The processed data are then entered into the FM component. FM learns low-order feature interactions and uses the resulting order-2 feature cross-terms as inputs to the DFNN component to capture and learn high-order interactions between the features. The final execution time prediction is obtained by combining the outputs from FM and the DFNN. The calculation is shown in Equation (1).  
\[y=\text{sigmoid}(y_{fm}+y_{dfm}) \tag{1}\]  
where \(y_{fm}\) is the output result of FM and \(y_{dfm}\) is the output result of the DFNN.
# A Location Routing Problem with Time Windows Consideration: A Metaheuristics Approach
## 2 Materials and Methods
### Problem Description
\]  
Objective function:  
\[\text{minz}=\sum_{i\in I}O_{i}y_{i}+\sum_{i\in V}\sum_{j\in V}\sum_{k\in K}c_ {ij}x_{ijk}+\sum_{k\in K}\sum_{i\in I}\sum_{j\in J}F_{i}x_{ijk} \tag{1}\]  
subject to  
\[\sum_{k\in K}\sum_{i\in V}x_{ijk}=1 \forall j\in J \tag{2}\] \[\sum_{j\in I}\sum_{i\in V}x_{ijk}d_{j}\leq Q \forall k\in K\] (3) \[\sum_{j\in I}d_{i}f_{ij}\leq W_{i}y_{i} \forall i\in I\] (4) \[\sum_{j\in V}x_{ijk}-\sum_{j\in V}x_{ijk}=0 \forall i\in V,k\in K\] (5) \[\sum_{i\in I}\sum_{j\in I}x_{ijk}\leq 1 \forall k\in K \tag{6}\]\[\sum_{i\in S}\sum_{j\in S}x_{ijk}\leq|S|-1\qquad\forall S\subseteq J,k\in K \tag{7}\] \[\sum_{u\in I}x_{ilk}-\sum_{u\in V\{j\}}x_{ujk}\leq 1+f_{ij}\qquad \forall i\in I,j\in J,k\in K\] (8) \[\sum_{i\in V}\sum_{j\in V}t_{ij}x_{ijk}+\sum_{i\in V}(\delta_{i}+w _{i})\sum_{j\in V}x_{ijk}\leq B_{k}\qquad\forall k\in K\] (9) \[\sum_{k\in K}\sum_{i\in V}x_{ijk}\Big{(}a_{ik}+t_{ij}+\delta_{i}+w _{i}\Big{)}\leq a_{jk}\qquad\forall j\in J\] (10) \[\sum_{k\in K}\sum_{i\in V}x_{ijk}=1 \forall j\in J \tag{2}\]0 (11) \[\sum_{k\in K}\sum_{i\in V}x_{ijk}=1 \forall j\in J \tag{2}\]1 (12) \[\sum_{k\in K}\sum_{i\in V}x_{ijk}=1 \forall j\in J \tag{2}\]2 (13) \[\sum_{k\in K}\sum_{i\in V}x_{ijk}=1 \forall j\in J \tag{2}\]3 (14) \[\sum_{k\in K}\sum_{i\in V}x_{ijk}=1 \forall j\in J \tag{2}\]4  
Equation (1) stipulates the objective function of this problem which is to minimize total cost for depot opening cost and distribution cost. Constraint (2) ensures that each customer belongs to exactly one route. Constraints (3) and (4) are capacity constraints for the route and depot while Constraints (5) and (6) guarantee that the route starts and ends in the same depot. Constraint (7) is a sub-tour elimination constraint. The sub-tour elimination constraint is used to ensure the connectedness of solutions. The sub-tour elimination constraint being used is based on the one presented in [PERSON] et al. [3]. The subset S represents a sub-tour that constructs the solution for the problem. Thus, Constraint (7) imposes the connectivity of the sub-tour at each vehicle based on the cardinality of each subtour. Constraint (8) guarantees a customer is assigned to a depot if there is a route connecting them. The next constraints explain time window constraints. Constraint (9) is the maximum travel time constraint and Constraints (10)-(12) ensure the relations between arrival time, departure time, and service time with regard to a customer's time window. Finally, Constraints (13)-(15) provide details on the binary variables that were incorporated into the formulation.
## 2 BiCA-LSTM-Informer Framework
### Bidirectional Cross-Attention Fusion  
To achieve deep feature-level interaction between the BiLSTM and Informer branches, a bidirectional cross-attention fusion module (BiCA) [12; 13; 14] is introduced. This module fully exploits the complementary nature of local dependency features and global con textual features, thereby enhancing the richness and discriminative power of the final feature representation.  
Cross-attention enables cross-branch information exchange by using one set of features as the query and another as the key and value. Let \(H^{\text{local}}\in\mathbb{R}^{T\times d}\) denote the local feature representation encoded by BiLSTM, and let \(H^{\text{global}}\in\mathbb{R}^{T\times d}\) represent the global feature representation extracted by Informer. The bidirectional cross-attention mechanism is defined as follows:  
Local-to-global cross-attention:  
\[\tilde{H}^{\text{local-global}}=\text{softmax}\left(\frac{H_{\text{local}}W_ {Q}(H_{\text{global}}W_{K})^{\top}}{\sqrt{d}}\right)H_{\text{global}}W_{V} \tag{10}\]  
Global-to-local cross-attention:  
\[\tilde{H}^{\text{global}\rightarrow\text{local}}=\text{softmax}\left(\frac{H_ {\text{global}}W_{Q}^{\prime}(H_{\text{local}}W_{K}^{\prime})^{\top}}{\sqrt{d} }\right)H_{\text{local}}W_{V}^{\prime} \tag{11}\]  
Here, \(W_{Q},W_{K},W_{V},W_{Q}^{\prime},W_{K}^{\prime},W_{V}^{\prime}\) are learnable linear transformation matrices, and \(d\) denotes the feature dimension.  
The bidirectional interaction structure enables both branches to dynamically absorb each other's salient information while preserving their respective modeling characteristics, effectively bridging the gap in modeling granularity. After bidirectional attention computation, the resulting feature representations are concatenated and linearly fused to produce the integrated output:  
\[H^{\text{fusion}}=\text{ReLU}\left(\left[\tilde{H}^{\text{local-glob}};\tilde{H }^{\text{global-local}}\right]W_{f}+b_{f}\right) \tag{12}\]  
where \(W_{f}\) and \(b_{f}\) are the learnable weight matrix and bias term for the fusion operation.  
The ReLU activation function introduces nonlinearity, further enhancing the sparsity and discriminative capability of the feature representation. While BiLSTM excels at capturing short-term local dynamics, Informer is particularly effective in modeling long-term global trends. The cross-attention mechanism enables their complementary integration by dynamically allocating attention weights based on the current temporal context, improving the model's sensitivity to critical time steps. Compared to simple concatenation or weighted averaging, bidirectional cross-attention allows fine-grained control over information flow at the feature level, reducing information contamination. Additionally, the internal use of low-rank matrix operations ensures that the overall computational complexity remains within acceptable limits.
# Antigate Melt-Electrowritten Biodegradable Mesh Implants for Enhanced Pelvic Organ Prolapse Repair
## 3 Results
### Differential Scanning Calorimetry  
To gain deeper insight into the influence of HT on PCL, particularly regarding its crystallinity and potential structural changes, a DSC test was performed to analyze the thermal properties of the material.  
The addition of HT progressively alters the thermal behavior of PCL, as seen in the broadening and shifting of the melting peaks (Figure 9A). These changes suggest that HT modifies the crystallization process, leading to finer or more heterogeneous crystalline domains. The peak area analysis further supports this (Figure 9B), showing that lower HT concentrations (0.03 wt% and 0.06 wt%) reduce crystallinity, while 0.1 wt% HT results in a peak area comparable to the control samples.  
The curve for 0.1 wt% HT reveals differences when compared to the other concentrations, possibly highlighting optimal stability and crystallinity, which corresponds with improved mechanical properties. This implies that 0.1 wt% HT might act as a threshold concentration where HT exerts the most substantial influence on the thermal and crystalline characteristics of the polymer without oversaturating or disrupting its structure. This suggests that it may function as a nucleating agent, facilitating the development of uniform or enhanced crystalline regions.  
Despite these alterations, the melting temperatures across all samples remain consistent, indicating that HT does not compromise the polymer's thermal stability, which is essential for biomedical applications. Furthermore, the broadening of melting peaks at higher HT concentrations suggests a range of crystalline and amorphous areas, likely contributing to increased tensile strength and stiffness. These results illustrate that HT can be used to optimize the thermal and mechanical properties of PCL meshes, making them suitable for applications such as POP repair.  
Figure 9: (**A**) DSC curves of the PCL meshes with varying concentrations of HT (0.03 wt%, 0.06 wt%, and 0.1 wt%) and the control (pure PCL), showing the effect of HT incorporation on thermal transitions. (**B**) Peak area of each curve of the DSC tests performed on the PCL meshes.
## 2 ROV Modeling
### ROV Dynamic Model  
In [PERSON]'s theory [27], ROV dynamics consist of a rigid body force, hydrodynamic force, and water surface static force:  
\[\begin{split}& M\dot{V}+C_{RB}(V)V+C_{A}(V)V+...\\ & D_{NL}(V)V+D_{L}(V)V+g(\eta)+g_{r}=\tau+\tau_{env},\end{split} \tag{5}\]  
The system inertia matrix \(M\in R^{4\times 4},M=M_{RB}+M_{A}\), composed of the rigid-body and added mass matrices,  
\[M_{RB}=\begin{bmatrix}m&0&0&0\\ 0&m&0&0\\ 0&0&m&0\\ 0&0&0&I_{z}\end{bmatrix},M_{A}=\begin{bmatrix}-X_{\dot{u}}&0&0&0\\ 0&-Y_{\dot{v}}&0&0\\ 0&0&-Z_{\dot{v}}&0\\ 0&0&0&-N_{r}\end{bmatrix}, \tag{6}\]  
The Coriolis-centripetal matrix \(C(V)\in R^{4\times 4}\), \(C(V)=C_{RB}(V)+C_{A}(V)\) is composed of the rigid-body and added mass effects:  
\[C_{RB}(V)=\begin{bmatrix}0&0&0&-mv\\ 0&0&0&mu\\ 0&0&m&0\\ mv&-mu&0&0\end{bmatrix},C_{A}(V)=\begin{bmatrix}0&0&0&Y_{\dot{v}}\upsilon\\ 0&0&0&-X_{\dot{u}}u\\ 0&0&0&0\\ -Y_{\dot{v}}\upsilon&X_{\dot{u}}u&0&-N_{r}\end{bmatrix}, \tag{7}\]  
The damping matrix \(D(V)\in R^{4\times 4},D(V)=D_{L}+D_{NL}(V)\) is composed of the linear and nonlinear hydrodynamic damping:  
\[D_{L}=\begin{bmatrix}-X_{u}&0&0&0\\ 0&-Y_{v}&0&0\\ 0&0&-Z_{uv}&0\\ 0&0&0&-N_{r}\end{bmatrix}, \tag{8}\]  
\[D_{L}=\begin{bmatrix}-X_{|u|u}|u|&0&0&0\\ 0&-Y_{|v|v}|v|&0&0\\ 0&0&-Z_{|v|w}|w|&0\\ 0&0&0&-N_{|r|r}|r|\end{bmatrix}, \tag{9}\]  
\(g(\eta)\) and \(g(0)\) are the restoring forces that try to bring the system to its natural equilibrium; it is implemented as  
\[g(\eta)=\begin{bmatrix}0\\ 0\\ -(W-B)\\ 0\end{bmatrix}, \tag{10}\]  
where \(W\) and \(B\) are, respectively, buoyancy and gravity.  
For the ROV, \(\tau\) gives propulsion. There are only four different motions, surge, sway, heave, and yaw, because the ROV is attached to an anchor chain; hence, \(\tau\in R^{4\times 1},\tau=[\tau_{x}\ \tau_{y}\ \tau_{z}\ \tau_{y}]\)  
The ROV is exposed to environmental disturbance forces and moments in the water throughout the diving process, which are made up of secondary wave forces, ocean currents, and wind forces. The bias model \(\dot{b}\) is  
\[b=F_{b}+w_{b}, \tag{11}\]  
where \(w_{b}\) is a zero mean Gaussian white noise vector, and \(F_{b}\) is a environmental disturbance matrix.
## 2 Materials and Methods
### Air Resistance  
The second parameter is the air resistance of a device (Ra, in Pa\({}^{0.5}\) min L\({}^{-1}\)). It links the pressure drop generated (\(\Delta\)P\({}_{\mathrm{a}}\), in Pa) by a device for a given airflow rate (Q\({}_{\mathrm{a}}\), in L min\({}^{-1}\)). The type of experiments carried was also performed using medical inhalators [16,17] or classical cigarettes [18]. Air resistance is determined using Equation (3).  
\[R_{\mathrm{a}}=\frac{\sqrt{\Delta\mathrm{P}_{\mathrm{a}}}}{Q_{\mathrm{a}}} \tag{3}\]  
To obtain this value for each device, many airflow rates should be generated, and the corresponding pressure drops collected. To do so, a differential pressure sensor is used to measure the pressure drop at the drip tip when an airflow is generated using a mass flow regulator and a pump (Figure 7) as it is perceived during inhalation.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**AWG Diameter** & 26 & 27 & 28 & 29 & 30 & 31 & 32 & 33 & 34 & 35 & 36 & 37 & 38 \\ \hline
**mm Diameter** & 0.41 & 0.36 & 0.32 & 0.29 & 0.26 & 0.23 & 0.20 & 0.18 & 0.16 & 0.14 & 0.13 & 0.11 & 0.10 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Correspondence between the diameter in AWG and in mm.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Metal** & Kanthal A & Kanthal A1 & SS 316L & SS 904L & Nichrome \\ \hline \(\rho_{\mathrm{w}}\)**(10\({}^{-6}\)\(\Omega\) m)** & 1.39 [12] & 1.45 [12] & 0.74 [13] & 0.95 [13] & 1.08 [14] \\ \hline \hline \end{tabular}
\end{table}
Table 3: Electric resistivity of the wire metals reported in Table 2.  
Pressure drop are measured using an airflow rate between 1 L min\({}^{-1}\) (standard vaping regimen) and 10 L min\({}^{-1}\) (direct lungs vaping regimen) by step of 1 L min\({}^{1}\). A calibration experiment is firstly carried without connecting an e-cig (or atomiser). Then, the air resistance of the empty setup is obtained. It is finally subtracted from the other values measured when a device is connected.