esa-sceva/satcom-chunk-collection huggingface dataset:
# Experimental Study on the Surface Properties of Nanoalumina-Filled Epoxy Resin Nanocomposites
## 2 Materials and Experimental Procedures  
### Raw Materials  
The used EP polymeric matrix was a 2-[[4-[2-[4-(Oxiran-2-ylmethoxy)phenyl]propan-2-yl]phenoxyyl]moixrane (D.E.R.tm 332) based on bisphenol A diglycidyl ether (DGEBA, also known as BADGE). This thermosetting EP presents uniform performance, low viscosity, low chloride content, and light color. Two curing agents were used to obtain two different thermosetting EP systems: bis(4-aminophen)methane (DDM), and 3-dodec-2-enyloxolane-2,5-dione (DDSA) + 8-methyl-3a,4,7,7a-tetrahydro-4,7-methano-2-benzofuran-1,3-dione (MNA). For the EP cured with DDSA+MNA, the catalyst \(N\),\(N\)-dimethyl-1-phenylmethanamine (BDMA) was applied during the curing reaction. All the raw chemicals were purchased from Sigma-Aldrich Co.  
The alumina NPs, with 99.99% purity, were purchased from NanoshellTM LLC. The NPs are of irregular shape and present an average size less than 100 nm. The specific surface area of the NPs is of \(\sim\) 20 m\({}^{2}\)/g. Figure 2a shows a micrograph of the as-received NPs obtained using electron scanning microscopy (SEM), using a FEI Quanta 400 FEG E SEM microscope. Figure 2b shows a graph of the NP size distribution, as given by the supplier. The as-received alumina NPs incorporated a surface pretreatment (functionalized NPs) with a silane agent (3-Aminopropyl) triethoxysilane (APTES) to ensure high dispersion into the EP polymeric matrix.
# Application of Blockchain Technology in Emergency Management Systems: A Bibliometric Analysis
## 5 Discussion
### Future Directions  
Building upon the bibliometric analysis presented in this study, several promising avenues for future research can be identified. These directions aim to address gaps, enhance theoretical understanding, and accelerate practical implementation:  
1. Interdisciplinary integration and technological convergence: Future research should focus on the synergies between blockchain and other cutting-edge technologies such as artificial intelligence, IoT, and next-generation communication networks (5G/6G). Exploring how these technologies can collectively enhance data analytics, predictive modeling, real-time monitoring, and automated response mechanisms in emergency scenarios is crucial.
2. Scalability and interoperability solutions: Addressing scalability challenges and ensuring interoperability between different blockchain platforms and legacy systems are essential for widespread adoption. Future studies should investigate the feasibility of layer-2 scaling solutions, cross-chain protocols, and standardized data formats to enable seamless data exchange and collaboration across diverse emergency management stakeholders. Additionally, exploring how interoperability between different platform types (public, private, and consortium blockchains) can optimize coordination and resource allocation during crises will be a critical area of research.
3. Regulatory and governance frameworks: Further research is needed to examine the regulatory landscape surrounding blockchain adoption in emergency management, including issues of data privacy, security, liability, and compliance. Developing clear guidelines and governance frameworks will be critical for fostering trust and encouraging public-private partnerships.
4. Real-world pilot implementations: Despite the theoretical potential of blockchain technology, there is a lack of real-world pilot implementations and comprehensive case studies in emergency management settings. Future research should prioritize the design, deployment, and evaluation of blockchain-based solutions in diverse emergency contexts such as natural disasters, public health crises, and humanitarian relief operations.
5. Social and ethical considerations: As blockchain technology becomes more integrated into emergency management systems, it is important to address the social and ethical implications, including issues of digital inclusion, data bias, algorithmic transparency, and the potential for unintended consequences. Future research should explore these dimensions to ensure that blockchain solutions are equitable, responsible, and aligned with societal values.
6. Global collaboration and knowledge sharing: The bibliometric analysis revealed limited global collaboration in blockchain research for emergency management. Future initiatives should promote international collaboration, knowledge sharing, and capacity building, particularly in developing countries, in order to foster a more inclusive and coordinated approach to leveraging blockchain technology for humanitarian purposes.
# A Forward\(-\)Backward Splitting Equivalent Source Method Based on S\(-\)Difference
## 2 Forward-Backward Equivalent Source Method Based on S\(-\)Difference
### Forward and Backward Splitting (FBS) Regularization Method for \(S-\)Difference  
The forward and backward splitting algorithm was initially applied in the domain of image restoration. In this section, we modify the regularization parameter in the FBS algorithm and introduce an \(s-\)difference adjustment strategy to solve the objective function under the norm constraint. This modification was aimed at improving the accuracy of the algorithm.  
In the reconstruction process of image restoration and other practical applications, the \(l_{0}\) non\(-\)convex regularization of the norm has more advantages than the \(l_{1}\) norm; therefore, we introduce the \(l_{0}\) constraint problem, expressed as:  
\[\min_{x}\phi(x)subject\quad to\left\|x\right\|_{0}\leq s \tag{4}\]  
Firstly, we represent the \(l_{0}\) constraint problem as the difference between the function \(R(x)\) and the corresponding \(s\) truncation function \(R(x^{s})\),where \(x^{s}\) is the best S-term approximation of \(x\). Then, the regularization of S\(-\)difference \(R(x)-R(x^{s})\) type is used to solve the unconstrained lowest slide problem. Finally, the closed-form solution is derived from the proximal operator of \(R(x)-R(x^{s})\) and common \(R(x^{s})\).  
The \(l_{0}\) constraint problem is expressed as the difference of convex functions as follows:  
\[\left\|x\right\|_{0}\leq s\Leftrightarrow\left\|x\right\|_{1}-\left\|x\right\| _{s}=0 \tag{5}\]  
where \(s\in\left\{1,2,\ldots,N\right\},\left\|x\right\|_{s}\) represents the sum of the absolute values of the first s larger elements in the vector, also known as the maximum \(s-\)norm (or CVaR\(-\)norm) [19].  
\[\left\|x\right\|_{s}:=\left|x_{\pi_{x}(1)}\right|+\left|x_{\pi_{x}(2)}\right| +\cdots+\left|x_{\pi_{x}(s)}\right| \tag{6}\]  
where \(\left|x_{\pi_{x}(1)}\right|\geq\) the absolute value of the I th largest element in the vector \(x\in R^{N}\), so \(\left|x_{\pi_{x}(1)}\right|\geq\left|x_{\pi_{x}(2)}\right|\geq\cdots\geq\left| x_{\pi_{x}(N)}\right|\). Define its set \(\Gamma_{x}^{s}=\left\{\pi_{x}(1),\pi_{x}(2),\ldots,\pi_{x}(s)\right\}\), and \(\Gamma_{x}^{1}\subseteq\Gamma_{x}^{2}\subseteq\cdots\subseteq\Gamma_{x}^{N}\).  
Define its set difference by using \(\centerdot\centerdot\), \(\centerdot\), \(\Gamma_{x}^{N}\backslash\Gamma_{x}^{s}=\left\{\pi_{x}(s+1),\pi_{x}(s+2), \ldots,\pi_{x}(N)\right\}\).  
Let \(x^{s}\) be defined as the best S\(-\)term approximation of the vector x. By using the \(x_{\pi_{x}(i)}\) definition, we have:  
\[x_{i}^{s}=\left\{\begin{array}{l}x_{i},\quad if\quad i\in\Gamma_{x}^{s}\\ 0,\quad if\quad i\in\Gamma_{x}^{N}\backslash\Gamma_{x}^{s}\end{array}\right. \tag{7}\]
## 3 Methodology and Data Collection
### Traffic Data
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**ID** & **Name** & **Road Section** & **Year** &
\begin{tabular}{c} **Transport** \\ **Corridor** \\ \end{tabular} & \multicolumn{6}{c}{**Average Age/Type of Vehicle**} \\ \cline{4-10}
**Station** & & & & **B** & **C2** & **C3** & **T3S2** & **T3S3** & **T3S2R4** \\ \hline
274 & El Cerrito & Queretaro-San Luis Potosi & 2011 & 1 & 6.5 & 8.1 & 13.1 & 8.1 & 9.2 & 6.1 \\
257 & Samalayuca III & El Sueoc-Ciudad Juíarez & 2010 & 2 & 8.1 & 7.6 & 13.1 & 10 & 11.9 & 7.6 \\ \hline
249 & Las Viguitas & Hermosillo-Nogales & 2010 & 3* & 6.3 & 8.1 & 14.7 & 13.1 & 13.4 & 8.7 \\ \hline
259 & El Valiente &
\begin{tabular}{c} Ciudad \\ Obregón-Hermosillo \\ \end{tabular} & 2010 & 3* & 7 & 8.4 & 12.7 & 10.2 & 12.2 & 6.9 \\ \hline
229 & PC Cuyutlan & Armeria-Manzanillo & 2009 & 4 & 6.9 & 7.7 & 9.3 & 7.3 & 6.4 & 4.8 \\ \hline
154 & Canal SARH & Córdoba-Veracruz (cuota) & 2002 & 5 & 7.3 & 10.1 & 8.6 & 8.6 & 4.9 & 5.6 \\ \hline
279 & Vega de & Poza Rica-Veracruz & 2011 & 6 & 6.8 & 9.4 & 16.4 & 9.3 & 9.3 & 3.6 \\ \hline
271 & Los Tamarindos & Coatzacoolos-Salina Cruz & 2011 & 7 & 10.7 & 11.1 & 12.7 & 12.1 & 11 & 6.9 \\ \hline
264 & Tabasquillo & Villa Hermosa-Cd. & 2010 & 8 & 6.4 & 7.5 & 9.7 & 8.3 & 8.9 & 6 \\ \hline
283 & Baclar &
\begin{tabular}{c} Reforma Agaria-Puerto \\ Juíarez \\ \end{tabular} & 2011 & 9 & 9 & 9 & 13.2 & 10.3 & 14.4 & 6.5 \\ \hline
228 & San Felipe & Playa Azul-Manzanillo & 2009 & 10 & 10 & 10.3 & 18.4 & 11 & 12.4 & 14.3 \\ \hline
205 & La Rosa & Saltillo-Torreón & 2006 & 11 & 8.3 & 8.3 & 12.1 & 10.1 & 10.5 & 8.7 \\ \hline
245 & Popotla & Tijuana-Ensenada & 2010 & 12 & 14.5 & 12.5 & 13 & 16.3 & 15 & 8.1 \\ \hline
237 & Cuapiaxtla & Amozoc-Perote & 2009 & 13 & 8.5 & 10.5 & 15.6 & 8.3 & 10.8 & 5.6 \\ \hline
292 & Palo Blanco & Cuernavaca-Acapulco & 2012 & 14 & 6.5 & 8.7 & 12.9 & 9.2 & 9.1 & 6.2 \\ \hline
292 & Palo Blanco & Cuernavaca-Acapulco & 2011 & 15 & 6.5 & 8.7 & 12.9 & 9.2 & 9.1 & 6.2 \\ \hline
268 & Zacatal & Coatzacoolos-Salina Cruz & 2011 & 16 & 10.6 & 10.09 & 17.7 & 13.4 & 15 & 7.1 \\ \hline \end{tabular} Source: Own elaboration based on Mexican Institute of Transportation (2002, 2009, 2010, 2011) [44].  
\end{table} 
Table 2: Average age of the vehicle fleet.
## 5 Results and Discussion
Although the output power is low, the production process of the STMC is simple and the production cost is low, which eliminates the complicated pre-taper process used in the production of mode selection couplers. In addition, the commercial Corning SMF-28e is used to design and manufacture the STMC, so as to avoid the complicated design and production process of 1 \(\upmu\)m band TMFs, which has great engineering application potential. By adjusting PC3, CVBs with a torus intensity pattern distribution can be obtained, and TM\({}_{01}\) and TE\({}_{01}\) modes can be distinguished by rotating the polarizer. The mode intensity distribution of TM\({}_{01}\) and TE\({}_{01}\) modes was obtained using a CCD camera (DataRay, WinCamD-LCM). The results are shown in Figure 10. The purity of TM\({}_{01}\) and TE\({}_{01}\) modes was measured to be 97.18% and 97.07%, respectively. We can conclude that the STMC achieves a high-quality TM\({}_{01}\) or TE\({}_{01}\) mode output, and the output mode is tunable.
# Development of a Motorized Hospital Bed with Swerve Drive Modules for Holonomic Mobility
## 2 Designs and Methods  
### Mechanical Design  
The prototype of the proposed motorized hospital bed in this study was developed based on a common off-the-shelf hospital bed. Achieving holonomic mobility can be realized by incorporating omni wheels, mecanum wheels, or a swerve drive module. Omni and mecanum wheels are popular options in many robot competitions, whereas the swerve drive is mostly found in the industries of autonomous guided vehicles. The swerve drive was adopted in this project because it would require minimum modifications to existing hospital beds. In addition, to incorporate omni or mecanum wheels, they have to be placed in a certain fashion, i.e., circular or symmetrical, to make sure that their kinematic requirements are met. In contrast, the swerve drive is more flexible in this regard due to its additional steering motor, which enables wheels to rotate in any direction. Second, the swerve drive bears the closest resemblance to the general casters found in off-the-shelf hospital beds.  
The proposed general design of the swerve drive module is shown in Figure 1a, and its major parts are shown in Figure 1b. This swerve drive module is used to replace casters to realize the whole conversion of usual hospital beds to motorized ones (Figure 1c).  
Figure 1: (**a**) Swerve drive module; (**b**) Exploded view of the swerve drive module showing its major parts; and (**c**) Concept of the modification of usual hospital beds into motorized ones by adding the swerve drive module.  
Two motors were used for each swerve drive module: one for steering and the other for propulsion. The target load the prototype could handle was set to 100 kg, therefore the choices of the propulsion motor and gear system were crucial. For steering, a DC motor (PG36 600 rpm from Brontoseno Electric) was used. The gear ratio between the steering motor, sensor, and steering mechanism was 30:18:18. For propulsion, a DC motor (PG45 500 rpm), a timing belt, and a pulley were used (i.e., HTD 5M 32 teeth in the propulsion motor and HTD 5M 60 teeth in the shaft). Most parts of the swerve drive module, including the spacers, mountings, and plates, were 3D printed using PLA. Additionally, the material used for the shaft was stainless steel, whereas aluminum, nylon, and silicon rubber were used for the hub, rim, and traction surface area of the wheels, respectively.
# A Self-Powered UHF Passive Tag for Biomedical Temperature Monitoring
## 2 Architecture of Proposed Self-Powered Passive Tag
### Low Frequency (LF) Section
#### 2.1.1 PTC Temperature Sensor  
The proposed PTC ring oscillator is presented in Figure 2. It uses five Flipped Voltage Follower (FVF) cells (\(m_{1}-m_{3},m_{p_{1}}\)) which are biased by some current mirrors (\(m_{n_{1}}\),\(m_{p_{1}}\)) and uses the \(V_{I_{P}}\) voltage to generate a PTAT \(I_{P}\) current; a single FVF cell is colored blue where \(i_{i}\) is its input current and \(i_{o}\) is its output current. The gate terminal of all \(m_{3}\) transistors is connected to the \(V_{REF}\) temperature-compensated reference voltage. Transistors \(m_{4}\) and \(m_{p_{1}}\) are used to obtain the output voltage \(v_{osc}\). All transistors operate in the subthreshold region, reducing the power consumption.  
Based on the Barkhausen criterion, the oscillation frequency \(\omega_{osc}\) of a ring oscillator and the minimum open-loop gain \(A_{min}\) to sustain such oscillation are given by Equation (7), where \(N\) is the number of FVF cells and \(\omega_{p}\) is the dominant  
Figure 2: Block diagram of the proposed ring oscillator.  
\[\omega_{osc}=\omega_{p}\cdot tan\bigg{(}\frac{180^{\circ}}{N}\bigg{)}\ \ \,\ \ \ A_{min}\geq\sqrt{1+\bigg{[}tan\bigg{(}\frac{180^{\circ}}{N}\bigg{)}\bigg{]}^{2}} \tag{7}\]  
By considering Equation (7), the pole location of the FVF must be known. To this end, the small-signal model of the FVF cell must be derived. The small-signal model is drawn in Figure 3, where \(C_{i}=C_{db_{1}}+C_{dg_{1}}+C_{sb_{2}}+C_{gs_{3}}\) and \(C_{a}=C_{gd_{1}}+C_{gs_{1}}+C_{gs_{2}}+C_{gd_{2}}+C_{gd_{3}}+C_{dB_{3}}+C_{gd_{ 2}}+C_{gd_{1}}+C_{gd_{1}}+C_{gd_{p1}}\). After solving the small-signal model for \(i_{o}/i_{i}\) and assuming \(g_{m_{o}}r_{o_{n}}\gg 1\), the transfer function of the FVF is shown in Equation (8).  
\[FT(s)=\frac{i_{o}}{i_{i}}=\frac{g_{m_{2}}}{g_{m_{1}}}\cdot\frac{1}{\frac{C_{i}C _{a}}{\delta n_{1}g_{m_{3}}}s^{2}+\frac{C_{a}}{g_{m_{1}}}s+1} \tag{8}\]  
Based on the dominant pole system approximation, Equation (8) leads to a DC current gain \(A_{i}=g_{m_{2}}/g_{m_{1}}\) and a dominant pole location at \(\omega_{p}=-g_{m_{1}}/C_{a}\). By substituting \(\omega_{p}\) into Equation (7), the oscillation frequency and the minimum open-loop gain that sustain the oscillation of the proposed ring oscillator are defined in Equation (9). The last expression for \(w_{osc}\) was obtained from Equation (2).  
\[\omega_{osc}=0.726\frac{g_{m_{1}}}{C_{a}}=\frac{0.726I_{D_{1}}}{\eta V_{T}C_{ a}}\ \ \,\ \ \ A_{min}\geq 1.24 \tag{9}\]
## 3 Demand Forecasting Models and Power Theft Detection Strategy
### Long Short Term Memory Model  
The LSTM is a sort of RNN that is capable of remembering information for a significantly long period of time. In contrast to basic neural networks, where each node is characterized by a single activation function, each node in LSTM is employed as a memory cell that may store other information. LSTMs, in particular, have their own cell state, an input gate, an output gate and a forget gate. The cell remembers values over arbitrary time intervals, and the three gates regulate the flow of information into and out of the cell. These characteristic allow LSTMs address the problem of disappearing gradients from prior time-steps [23; 24; 25]. In our application, there are three LSTM layers, each with 40 units, a _tanh_ activation function, and a drop out value of 0.15. The input sequence length is defined as 20.  
**Step 1:**: Create testing and training datasets with the train_test_split function. Here, we divided it into 70% training dataset, 30% testing dataset.
**Step 2:**: Build the linear regression model using long short term memory model with predefined parameters for the training dataset.
**Step 3:**: Forecast the consumption values for the testing dataset.
**Step 4:**: Plot the actual and forecasted values of the testing dataset.
**Step 5:**: Calculate MSE, MAE, and RMSE.
# Effects of Nanoparticles on Algae: Adsorption, Distribution, Ecotoxicity and Fate
## 4 Ecotoxic Effects of NPs on Algae
### Effect of NPs on the Photosynthesis System
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Nanoparticles** & **Diameter (nm)** & **Tested Algae** & **Toxic Effects** & **References** \\ \hline \multirow{4}{*}{Silver (Ag)} & \multirow{4}{*}{20–50} & _Chlamydomonas reinhardtii_ & EC\({}_{50}\): 9.9 \(\mu\)g/L (96 h) & \multirow{4}{*}{[19; 25]} \\  & & _Feinhardtii_ & Affecting photosynthesis, inhibition in cell growth & & \\  & & _Pseudokirchneriella_ & & & \\  & & _subcapitata_ & & & \\ \hline \multirow{4}{*}{Copper oxide (CuO)} & \multirow{4}{*}{30–40} & _Chlamydomonas reinhardtii_ & EC\({}_{50}\): 45.7 mg/L (72 h) & \multirow{4}{*}{[47; 51]} \\  & & _Chloella pyrenoidosa_ & & & \\ \hline \multirow{4}{*}{Titanium oxide (TiO\({}_{2}\))} & \multirow{4}{*}{20–35} & _Pseudokirchneriella_ & EC\({}_{50}\): 10–26 mg/L (72 h) & \multirow{4}{*}{[15; 73]} \\  & & _subcapitata_ & Decrease in chlorophyll a and & \\  & & _Desmodesmus_ & soluble protein content, accumulation of lipid & \\  & & _subpicatus_ & hydroperoxide & \\ \hline \multirow{4}{*}{Zinc oxide (ZnO)} & \multirow{4}{*}{20–30} & _Pseudokirchneriella_ & EC\({}_{50}\): 0.5–1.5 mg/L (96 h) & \multirow{4}{*}{[20; 73; 75]} \\  & & _subcapitata_ & Inhibition in cell growth, destruction of cell antioxidant & \\  & & _subiquus_ & capacity & \\ \hline \multirow{4}{*}{Quantum dots (QDs)} & \multirow{4}{*}{1–10} & _Chlamydomonas reinhardtii_ & EC\({}_{50}\) < 5 mg/L (72 h) & \multirow{4}{*}{[76; 77]} \\  & & _Feinhardtii_ & Cell aggregation, lipid peroxidation & \\ \hline \multirow{4}{*}{\begin{tabular}{c} Fullerene (C\({}_{60}\)) \\ \end{tabular} } & \multirow{4}{*}{\textless{200}} & _Scenedesmus_ & \multirow{4}{*}{Increase in cell death, affecting photosynthetic and respiratory processes in cytosol} & \multirow{4}{*}{[27; 39]} \\  & & _Chlamydomonas reinhardtii_ & & \\ \hline \multirow{4}{*}{\
\begin{tabular}{c} Single-walled \\ carbon nanotubes (SWCNT) \\ \end{tabular} } & \multirow{4}{*}{\textless{2}} & _Pseudokirchneriella_ & \multirow{4}{*}{EC\({}_{50}\): 22.6 mg/L (96 h) & \multirow{4}{*}{[27; 78]} \\  & & _Scenedesmus_ & Inhibition in cell growth & \\  & & _obliquus_ & & \\ \hline \multirow{4}{*}{
\begin{tabular}{c} Multiwalled \\ carbon nanotubes (MWCNT) \\ \end{tabular} } & \multirow{4}{*}{10–20} & _Scenedesmus_ & \multirow{4}{*}{EC\({}_{50}\): 15.5 mg/L (96 h) & \multirow{4}{*}{[27; 34]} \\  & & _Desmodesmus_ & Decrease in cell viability & \\ \cline{1-1}  & & _subpicatus_ & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Toxic effects of nanoparticles on algae.
# Parallel Extreme Learning Machines Based on Frequency Multiplexing
## 3 Principle of Operation
### Definitions  
We denote by \"single operation mode\" a configuration in which the \(N_{S}\) different combs are treated as parts of the same neuron layers, hence a single ELM is executed. In this case, for each data sample supplied to the network, we define by \(\mathbf{u}\) the set of input features, by \(\mathbf{I}^{\text{out}}\) the set of hidden neuron measurements, and by \(\hat{\mathbf{y}}\) the target output. The network output is obtained through the multiplication of hidden neuron measurements by output weights. We define by \(\mathbf{W}\) the set of output weights and by \(\mathbf{y}^{\text{out}}=\mathbf{W}\cdot\mathbf{I}^{\text{out}}\) the network output. Weights are chosen to minimize the squared error \((\mathbf{y}^{\text{out}}-\hat{\mathbf{y}})^{2}\). \(\mathbf{u}\) and \(\mathbf{I}^{\text{out}}\) are row vectors composed of as many elements as lines in all the \(N_{S}\) combs; depending on the dimension of the output of the specific task, \(\mathbf{y}^{\text{out}}\) and \(\hat{\mathbf{y}}\) are scalar or row vectors, while \(\mathbf{W}\) is a column vector or a matrix.  
We denote by \"parallel operations mode\" a configuration in which the \(N_{S}\) different combs are treated as independent neuron layers and constitutes \(N_{S}\) independent ELMs. Definitions are similar to the ones presented above, but now account for the presence of multiple ELMs. Everywhere in this paragraph, \(j\in[1,\ N_{S}]\). We define by \(\mathbf{u}^{i}\) the set of input features of the \(j\)-th ELM, by \(\mathbf{I}^{\text{out}\cdot j}\) the set of hidden neuron measurements of the \(j\)-th ELM, and by \(\hat{\mathbf{y}}^{i}\) the target output of the \(j\)-th ELM. The output of the \(j\)-th ELM is defined by \(\mathbf{y}^{\text{out}\cdot j}=\mathbf{W}^{j}\cdot\mathbf{I}^{\text{out}\cdot j}\), where \(\mathbf{W}^{j}\) is the the set of optimal output weights for the \(j\)-th ELM, again obtained by minimizing the squared error \((\mathbf{y}^{\text{out}\cdot j}-\hat{\mathbf{y}}^{j})^{2}\).