esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Performance Evaluation
### Outage Probability
Next, substituting (52) into (51), we obtain  
\[\text{B}_{1}\left(u\right)=1+\sum\limits_{m=1}^{M}\left(-1\right)^{m}C_{M}^{ m}\left(1-\text{A}_{2}\right)^{m}\exp\left(-\frac{m\lambda_{\text{SR}}\rho}{ \Delta u}\right). \tag{53}\]  
Differentiating \(\text{B}_{1}\left(u\right)\) with respect to \(u\), yielding  
\[\frac{\partial\text{B}_{1}\left(u\right)}{\partial u}=\sum\limits_{m=1}^{M} \left(-1\right)^{m}C_{M}^{m}\frac{m\lambda_{\text{SR}}\rho}{\Delta}\left(1- \text{A}_{2}\right)^{m}\frac{1}{u^{2}}\exp\left(-\frac{m\lambda_{\text{SR}} \rho}{\Delta u}\right). \tag{54}\]  
Substituting (44) and (54) into (50), and then using ([53], Equation (3.471.9)) for the corresponding integrals, we can obtain  
\[ \begin{array}{ll}\text{OP}_{\text{B-ORS}}&=1+\sum\limits_{t=0}^{K-1}\sum \limits_{m=1}^{M}\left(-1\right)^{m}\frac{2C_{M}^{m}}{t!}\left(\frac{m\lambda_ {\text{BS}}\lambda_{\text{SR}}\rho}{\kappa\Delta}\right)^{\frac{t+1}{2}}\left( 1-\text{A}_{2}\right)^{m}K_{t-1}\left(2\sqrt{\frac{m\lambda_{\text{BS}} \lambda_{\text{SR}}\rho}{\kappa\Delta}}\right)\\ &+\sum\limits_{t=0}^{K-1}\sum\limits_{n=1}^{N}\sum\limits_{m=1}^{M}\left(-1 \right)^{m+n}\frac{2C_{N}^{n}C_{M}^{m}}{t!}\left(\frac{m\lambda_{\text{BS}} \lambda_{\text{SR}}\rho}{\kappa\Delta}\right)^{\frac{t+1}{2}}\left(1-\text{A}_ {2}\right)^{m}\!\left(1+\frac{n\lambda_{\text{SR}}\delta\Delta}{m\lambda_{ \text{SR}}\rho}\right)^{\frac{t-1}{2}}\\ &\times K_{t-1}\left(2\sqrt{\frac{\lambda_{\text{BS}}}{\kappa\Delta}\left(n \lambda_{\text{SP}}\delta\Delta+m\lambda_{\text{SR}}\rho\right)}\right).\end{array}  \tag{55}\]  
Next, substituting (47) into (55), we obtain (48). The derivation of (48) is different from that of (34) and (35) due to the dependence of the end-to-end SNRs. **Lemma 3**. : _When \(1-\tau_{\rm D}^{2}\theta>0\), \({\rm OP_{C-ORS}}\) can be expressed by an exact expression as in (56)_  
\[
# Stabilisation of Soft Clay, Quick Clay and Peat by Industrial By-Products and Biochars
###### Abstract  
The stabilisation of soft soils using the traditional binders cement and quicklime are known to emit large amounts of carbon dioxide. To reduce this carbon footprint, substitutes such as industrial by-products have been thoroughly tested as viable alternatives for soil stabilisation. However, recent research has also shown that biochar from biomass pyrolysis can in some instances have a positive stabilisation effect and even result in a carbon-negative footprint. This paper presents a laboratory study to investigate the stabilisation effect of five industrial by-products and four types of biochar on three natural Norwegian soils: two clays with low and high water contents and one peat with a very high water content. The soils and binders were characterised by their mineralogical and chemical compositions. The biochars had varying stabilisation effects on the clays when combined with cement, with some negative stabilisation effects, whilst the effect was very beneficial in the peat, with a strength increase of up to 80%. The industrial by-products showed opposite results, with beneficial effects in the clays and a strength increase of up to 150%, but negative stabilisation effects in the peat. Correlating the mineralogical and chemical compositions to stabilisation effects was found to be challenging.  
soil stabilisation; clay; peat; industrial by-products; biochar; shear strength; stiffness 2023  
3
# Fast Loop Closure Selection Method with Spatiotemporal Consistency for Multi-Robot Map Fusion
## 3 Multi-Robot SLAM
In (3), assume that node \(i\) and node \(j\) belong to the trajectory of robot \(a\), the node \(k\) and node \(l\) belong to robot \(b\). \(t_{i}\) denotes the timestamp related to node \(i\). We further assume that robot poses \(\mathbf{x}_{ij}^{a}\) on a single trajectory are directed in time, where transformations are from past node to current \(\left(t_{j}>t_{i},t_{l}>t_{k}\right)\). The underlying hypothesis of consistency is that the measurements in the selected subset are consistent with each other in the graph, implying that the error is within a certain statistical threshold. Mathematically, for a set \(\mathbf{Z}\) to be pairwise internally consistent, it can be formulated as  
\[c\left(\mathbf{z}_{ik}^{ab},\mathbf{z}_{jl}^{ab}\right)\leq\chi_{a,\delta_{c}} ^{2},\forall\mathbf{z}_{ik}^{ab},\mathbf{z}_{jl}^{ab}\in\mathbf{Z}, \tag{4}\]  
where \(\lVert\cdot\rVert_{\Sigma}\) is the Mahalanobis distance, therefore the threshold follows the chisquared distribution (using the \(\chi^{2}\) threshold with \(\alpha=0.1\)), \(\delta_{c}\) is the degrees of freedom of the graph.
# A New Generation of Fast and Low-Memory Smart Digital/Geometrical Beamforming MIMO Antenna
## 3 Beamforming and Beamsteering
 \tag{13}\]  
and repeat up to the \(n\)th term. \[ \begin{split}\int\limits_{0}^{2\pi}f(\varphi)e^{-i\beta(x_{2} cos\varphi+y_{2}sin\varphi)}d\varphi&=Z_{1}\int\limits_{0}^{2\pi}e^{i \beta[(x_{1}cos\varphi+y_{1}sin\varphi)-(x_{n}cos\varphi+y_{n}sin\varphi)]}d \varphi\\ &\qquad+\ Z_{2}\int\limits_{0}^{2\pi}e^{i\beta[(x_{2}cos\varphi+ y_{2}sin\varphi)-(x_{n}cos\varphi+y_{n}sin\varphi)]}d\varphi+\ldots+Z_{n}\int\limits_{0}^{2 \pi}d\varphi\end{split}  \tag{14}\]  
Finally, \(n\) number of equations can be obtained where \(n\) is equal to the number of dipole elements present in the MIMO antenna. Hence, these equations can be written in the following matrix form:  
\[ \begin{bmatrix}P_{11}&P_{12}&\ldots&P_{1n}\\ P_{21}&P_{22}&\ldots&P_{2n}\\ \ldots&\ldots&\ldots&\ldots\\ P_{n1}&P_{n2}&\ldots&P_{nn}\end{bmatrix}\begin{bmatrix}Z_{1}\\ Z_{2}\\ \ldots\\ Z_{n}\end{bmatrix} = \begin{bmatrix}q_{1}\\ q_{2}\\ \ldots\\ q_{n}\end{bmatrix}  \tag{15}\]  
where  
\[P_{ij}=\int\limits_{0}^{2\pi}e^{i\beta[(x_{j}cos\varphi+y_{j}sin\varphi)-(x_{i} cos\varphi+y_{i}sin\varphi)]}d\varphi \tag{16}\]  
and  
\[q_{i}=\int\limits_{0}^{2\pi}f(\varphi)e^{-i\beta(x_{i}cos\varphi+y_{j}sin\varphi )}d\varphi \tag{17}\]Thus, the optimized coefficients can be obtained from Equation (15), as given below:  
\[ \begin{bmatrix}Z_{1}\\ Z_{2}\\ \ldots\\ Z_{n}\end{bmatrix} = \begin{bmatrix}P_{11}&P_{12}&\ldots&P_{1n}\\ P_{21}&P_{22}&\ldots&P_{2n}\\ \ldots&\ldots&\ldots&\ldots\\ P_{n1}&P_{n2}&\ldots&P_{m}\end{bmatrix} ^{-1} \begin{bmatrix}q_{1}\\ q_{2}\\ \ldots\\ q_{n}\end{bmatrix}  \tag{18}\]  
where the matrix elements \(P_{ij}\) and \(q_{i}\) are numerically calculated. Once the phase delay coefficients are obtained for a selected angle of beamsteering, the electrical field can be evaluated using the expression obtained in Equation (10).
## 3 Results and Discussion  
The referring hospital reported 39 patients with diagnosis stroke in the 12-month period from March 2011 to March 2012. In the period from September 2010 to April 2012 (19 months), the VC equipment was only used four times for discussing patients. As the data illustrates, the number of stroke patients is considerably higher than the number of times the professionals collaborate by using VC. To fulfill the national goal of providing more patients with thrombol treatment, and to improve the stroke prognosis, collaborative work is a premise. Every case is considered individually, directed by some norms, which could be discussed in each case. Thromolytic treatment is given under the instruction of a specialist, whose competence the small hospitals do not have. This requires collaborative work between hospitals. How may we understand the contradiction between the need for knowledge-sharing and the reasons for the low frequency of use of VC for discussing stroke patients?  
The experiences of the use of the VC equipment reveal no challenges in the practical use of the technology as a tool _per se_. All the professionals have gone through training. The informants that had used or tested the VC equipment had positive experience and said that it was easy to use. Regarding the technology as a tool in practice, the professionals say:  
_\"All interns have training. We have an introduction course for interns and training in stroke procedures. The use of videoconferencing is a part of it.\" A: Referring hospital._  
_\"I think it has worked fine.\" B: Referring hospital._  
_\"The technology has worked fine; it has not been any...\"_  
_Interviewer: \"It is easy and understandable?\"_  
_\"Yes, yes I think so.\" \"(...) it is quite easy, easy to understand...Yes, it is easy to use. Nothing was problematic regarding the technology.\" C: Specialist hospital._  
It was an overall agreement that it would have been easier to include as a tool in daily services if it had been used more frequently. As the comments illustrate, VC as a tool _per se_ is not the reason for low frequency use for discussing stroke patients.
# Rapid Estimation of Earthquake Magnitude and Source Parameters Using Genetic Algorithms
## 3 Results
### Testing the Okada-GA Inversion Model Using the Observation Data  
The testing in this step aimed to measure the ability of the Okada-GA inversion model to estimate source parameters from the real data of an earthquake. The estimated parameters were the same as those used in the previous stage (i.e., length, width, rake, and slip), in addition to the magnitude \(Mw\) of the earthquake. In this stage, the GA with the best hyperparameter settings and the selected objective function was tested on the real displacement time series data from two earthquake events, i.e., the 2011 Tohoku Oki and 2018 Lombok earthquake events.  
For all experiments carried out in this stage, the difference between the estimated parameters and reference parameters was expressed as the RMSE using the following standard formula:  
\[\text{RMSE}=\sqrt{\frac{1}{N}\cdot\sum_{i=1}^{N}\left(x_{est}^{i}-x_{ref}^{i} \right)^{2}}, \tag{13}\]  
where \(x_{est}^{i}\) is the \(i\)th estimated value, \(x_{ref}^{i}\) is the \(i\)th reference value, and \(N\) is the number of data points.  
The results of the testing for each data event are described in the following sections.
## 3 Membrane Performance Measurements
### Dense Membrane Sample  
The membrane used in this study was produced by dispersing silica nanoparticles in polyurethane [15]. The nanoparticles were dispersed partially and agglomerated to build up passages where water vapor may pass through. As a result, the hydrophilic inorganic ion nanochannels were formed on the hydrophobic polymer base. The synthesized water vapor transport membrane is then joined to perforated polyamide supports by a thermal binding method. Such membranes are not highly sensitive to moisture and have good durability; hence, frequent replacement can be prevented.  
Figure 3 shows a schematic diagram of water vapor transport through the polymer membrane used in our experiments. When hydrophilic particles are placed in the membrane with an optimal concentration of \(\sim\)5 wt% (neither too concentrated nor too dispersed), ion nanochannels are created. In this case, water vapor inside the membrane moves in a molecular state by repeated adsorption and desorption to the surfaces of the hydrophilic particles.  
Figure 3: Schematic diagram of water vapor transport through the polymer membrane used in the experiments.  
Figure 2: Experimental setup of membrane performance test facility (**a**) Schematic diagram (**b**) Side and top view of membrane test cell.  
Figure 4 shows scanning electron microscope (SEM) images of a membrane sample used in this experiment, including the membrane composed of hydrophobic materials, where the partly dispersed silica particles can be seen. In addition, an image of the polyamide support is shown in Figure 4b. Figure 4c shows a cross-sectional SEM image of a membrane sample from which the thickness of the membrane and support were measured just after it was fabricated. The thickness of the hydrophobic membrane was 30 \(\upmu\)m and the support was 40-50 \(\upmu\)m, with an average total thickness of \(\sim\)75 \(\upmu\)m.
# Assessment of Energy Use and Photovoltaic Energy Potential in Saudi Arabian Governmental Schools
## 4 Results and Discussions  
### Electricity Consumption and Indicators  
Equation (1) calculates the monthly electricity consumption of three schools in Buraidah City in the Qassim region: school 1, school 2, and school 3. Table 2 shows that the maximum electric energy consumption is in August and September due to air conditioning, while consumption is low in the summer months due to the summer vacation and in some months due to not using AC. Electrical energy consumption indicators were calculated per unit area and person using Equations (2) and (3). Table 3 shows the annual energy consumption and EUI per unit area and person CPC in the schools under study. Values 22-48 and 337-630 were obtained for EUI and CPC, respectively. It is noted that the EUI in these schools is consistent with what was published by [PERSON] and [PERSON] [4]. In contrast, these values are considered low compared to those published in university buildings, as shown in [PERSON] and [PERSON] [37] and [PERSON] and [PERSON] [46]. Schools' low electricity consumption indicators can be mitigated by the summer vacation, limited daily working hours, and fewer devices used than university buildings.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Month** & **School 1 (kWh/Month)** & **School 2 (kWh/Month)** & **School 3 (kWh/Month)** \\ \hline
1 & 6069 & 17,046 & 9359 \\ \hline
2 & 5758 & 10,289 & 7157 \\ \hline
3 & 4980 & 14,281 & 2753 \\ \hline
4 & 6640 & 17,813 & 2753 \\ \hline
5 & 4254 & 30,252 & 23,672 \\ \hline
6 & 4669 & 18,274 & 6056 \\ \hline
7 & 4358 & 6450 & 6606 \\ \hline
8 & 12,139 & 54,361 & 34,682 \\ \hline
9 & 14,836 & 57,126 & 48,445 \\ \hline
10 & 10,998 & 8446 & 7707 \\ \hline
11 & 5810 & 20,577 & 3303 \\ \hline
12 & 3891 & 22,343 & 12,111 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Monthly electric energy consumption of the investigated schools.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Annual Electrical Energy Consumption (\&Wh)** & **EUI** & **CPC** \\  & **(kWh/m2)** & **(kWh/Capita)** \\ \hline School 1 & 84,402 & 22 & 630 \\ \hline School 2 & 277,259 & 37 & 417 \\ \hline School 3 & 164,603 & 48 & 337 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Annual electrical energy consumption indicators.
## 3 Results
### Impact of Factors on the LUEmax
#### 3.2.2 Impact of Factors on the LUEmax Across Different Climate Types  
Geodetector's factor detector was employed to assess the influence of ten factors on the LUEmax in different climates. The results show the explanatory power of each factor on the spatial differentiation of LUEmax (Figure 7). The variability of the LUEmax image factors was significant for different climates.  
In tropical climates, both P and VPD strongly influence LUEmax, suggesting that these two factors are the primary controllers of LUEmax in tropical regions. In dry climates, the degrees of influence of all factors are relatively low. This may be due to the limited water in arid areas, which leads to minor impacts of other factors. In temperate climates, the main influencing factor of LUEmax is LSWI, followed by TA. This is related to this region's relative water demand and climate change characteristics. In continental climates, LUEmax is mainly affected by the LAI, while the influences of other factors are rather limited. In polar and alpine climates, the TS and TA responses are significant, and the influence of EVI cannot be ignored either, although the overall impact is relatively small.  
Figure 6: The explanatory power of the interaction between factors across different vegetation types. (The darker the color, the stronger the importance of the variable).  
The interaction detector assessed the explanatory power of factor interactions in LUEmax spatial variation across different climate types (Figure 8). Within different climate types, the interaction of two factors had a greater influence on LUEmax's spatial variation than either factor alone.  
Figure 8: The explanatory power of the interactions between factors across different climate types. (The darker the color, the stronger the importance of the variable).  
Figure 7: The q values of the factors across different climate types.  
These results demonstrate the substantial differences in the interaction relationships and influence degrees among environmental factors across different climate types. These differences reflect the impacts of the specific environmental conditions in each climate zone on the LUEmax.
## 3 Results
### Absorption and Emission Properties
These values are larger than those obtained for other silicate and phosphate glasses, the bandwidth of which ranges from 30-40 nm for silicate and 46 nm for phosphate glasses, respectively [33]. This feature is highly significant since broadband amplifiers and tunable lasers require large bandwidth. \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{548 nm (\({}^{4}\)S\({}_{92}\)) (\(\lambda_{\textbf{exc}}\) = 488 nm)} & 660 nm (\({}^{4}\)F\({}_{92}\)) (\(\lambda_{\textbf{exc}}\) = 488 nm) & 1528 nm (\({}^{4}\)I\({}_{13/2}\)) (\(\lambda_{\textbf{exc}}\) = 800 nm) \\ \hline Er1 & 3.60 \(\pm\) 0.11 \(\mu\)s & 3.06 \(\pm\) 0.09 \(\mu\)s & 4.91 \(\pm\) 0.12 ms \\ Er4 & 3.20 \(\pm\) 0.07 \(\mu\)s & 3.17 \(\pm\) 0.03 \(\mu\)s & 3.01 \(\pm\) 0.06 ms \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Lifetimes at room temperature of the \({}^{4}\)S\({}_{3/2}\) and \({}^{4}\)F\({}_{9/2}\) levels obtained under excitation at 488 nm and \({}^{4}\)I\({}_{13/2}\) levels obtained under excitation at 800 nm. Figure 3: Experimental decays of the \({}^{4}\)S\({}_{3/2}\) and \({}^{4}\)F\({}_{9/2}\) levels of the Er-doped aluminosilicate glasses with 1 wt% under excitation at 488 nm. Figure 2: Room temperature emission spectra of the Er-doped aluminosilicate glasses with 1 wt% and 4 wt% under excitation at 488 nm. In addition to the bandwidth, the stimulated emission cross-section, \(\sigma_{em}\), is another important parameter that provides information about the optical amplification. This parameter was estimated from the absorption spectra by using the McCumber approach [34], in which the absorption and emission cross-section are related according to  
\[\sigma_{em}(v)=\sigma_{abs}(v)exp\bigg{[}\frac{\varepsilon-hv}{KT}\bigg{]}, \tag{2}\]  
where \(\sigma_{em}\) and \(\sigma_{abs}\) are the stimulated emission and absorption cross-section, respectively, \(v\) is the photon frequency, \(h\) is the Planck constant, \(K\) is the Boltzmann constant, and \(\varepsilon\) is the net free energy required to excite one Er\({}^{3+}\) ion from states \({}^{4}\)I\({}_{15/2}\) to \({}^{4}\)I\({}_{13/2}\) at temperature \(T\). The absorption cross-section was experimentally obtained and \(\varepsilon\) was determined by using the simplified procedure provided by Miniscalco [35]. The maximum emission cross-sections were found to be 3.51 \(\times\) 10\({}^{-21}\) cm\({}^{2}\) and 4.19 \(\times\) 10\({}^{-21}\) cm\({}^{2}\) at 1530 nm for the samples doped with 1 wt% and 4 wt% of Er\({}_{2}\)O\({}_{3}\), respectively. These values were similar to those found in other aluminosilicate glasses [32]. As an example, Figure 5 shows the absorption and emission cross-section for the sample doped with 4 wt% of Er\({}_{2}\)O\({}_{3}\). Figure 4: Emission spectra of the \({}^{4}\)I\({}_{13/2}\)\(\rightarrow\)\({}^{4}\)I\({}_{15/2}\) transition for Er-doped aluminosilicate glasses with 1 wt% and 4 wt% under excitation at 802 nm. Figure 5: Absorption and emission cross-section for the aluminosilicate glass doped with 4 wt% of Er\({}_{2}\)O\({}_{3}\).
# Multiband Frequency Tuneable Antennas for Selection Combining Strategy in White Space Applications
## 5 Antenna Diversity System  
By applying antenna diversity techniques, the performance of mobile communication systems could be greatly enhanced. The envelope correlation coefficient (ECC) is the main parameter that characterizes the effect of correlation between two antennas. On the basis of [22], the ECC was determined using the far-field pattern data as shown in (1).  
\[\rho_{ECC}=-\frac{\iint\!\!\int_{4\pi}E_{1}(\theta,\phi)\times E_{2}^{*}(\theta, \phi)d\Omega}{\sqrt{\iint\!\!\int_{4\pi}E_{1}(\theta,\phi)\times E_{1}^{*}( \theta,\phi)d\Omega\times\iint\!\!\int_{4\pi}E_{2}(\theta,\phi)\times E_{2}^{*} (\theta,\phi)d\Omega}} \tag{1}\]  
where \(E_{1}\) and \(E_{2}\) are the radiation patterns in the far field of Antennas 1 and 2 at different angles of \(\theta\) and \(\phi\). This ECC value was calculated using the Scilab code, and the results are shown in Table 3. The value obtained at 700 MHz was relatively small, about 0.0481, while at 470 MHz, it was more significant, about 0.475. It can be explained by the fact that the wavelength at 470 MHz is longer than that of 700 MHz; therefore, the coupling between antennas at low frequencies is greater than that at high frequencies. Therefore, the mutual influence increases more. However, all of these values were less than 0.5; hence, a reduction in signal fading and a higher level of diversity gain could be achieved.
## 2 Methodology
### Improved Weighted Extreme Learning Machine (IWELM)
The computation is reduced by removing the calculation of the generalized inverse matrix from the iterative process. ```
1:Initialize:\(\delta{=}10^{-6},\quad\beta_{1}=0.9,\quad\beta_{2}=0.999,\quad T_{2}=20,\quad \mathbf{Y}=\mathbf{I}\mathbf{W}\) and \(\boldsymbol{b}\) are given randomly \(\boldsymbol{\beta}=\mathbf{H}^{\intercal}\boldsymbol{r},\quad\eta{=}\| \mathbf{H}\boldsymbol{\beta}-\mathbf{r}\|^{2}\)
2:Begin:
3:while\(\eta_{0}<\eta\)do
4:\(\kappa=1,\quad t_{1}=0\)
5:while\(\kappa>10^{-3}\)&\(t_{1}<T_{1}\)do (LM)
6:\(\mathbf{J}=\left[\left(\frac{\partial\xi_{1}}{\partial\mathbf{Y}}\right)^{T}, \left(\frac{\partial\xi_{2}}{\partial\mathbf{Y}}\right)^{T},\ldots\ldots\left( \frac{\partial\xi_{n}}{\partial\mathbf{Y}}\right)^{T}\right]^{T},\quad\Delta \mathbf{Y}=-\left(\mathbf{J}^{T}\mathbf{J}+\lambda I\right)\mathbf{J}^{T} \left(H\boldsymbol{\beta}-r\right)\)
7:\(\mathbf{Y}^{\prime}{=}\mathbf{Y}+\Delta\mathbf{Y},\quad\boldsymbol{\beta}^{ \prime}{=}\left(I/C+\mathbf{H}^{T}\mathbf{H}\right)^{-1}\mathbf{H}^{T}r\)
8:if\(\eta<\|\mathbf{H}\boldsymbol{\beta}^{\prime}-r\|\)then
9:\(\kappa{=}\|\boldsymbol{\beta}^{\prime}-\boldsymbol{\beta}\|/\|\boldsymbol{ \beta}\|,\quad\eta\leftarrow\|\mathbf{H}\boldsymbol{\beta}^{\prime}-r\|\)
10:\(\boldsymbol{\beta}\leftarrow\boldsymbol{\beta}^{\prime},\quad\mathbf{Y} \leftarrow^{\prime},\quad\lambda\leftarrow\lambda/10\)
11:else
12:\(\lambda\gets 10\lambda,\quad t_{1}\gets t_{1}+1\)
13:endif
14:endwhile
15:\(t_{2}=0,\quad\boldsymbol{u}_{0}=0,\quad\boldsymbol{v}_{0}=0\)
16:while\(t_{2}<T_{2}\)do (Adam)
17:\(\boldsymbol{g}_{t_{2}}=\partial\eta/\partial\left(\mathbf{W},\boldsymbol{b} \right)\), \(t_{2}\gets t_{2}+1\), \(\quad\boldsymbol{u}_{t_{2}}=\frac{\beta_{1}}{1-\beta_{1}^{2}}\boldsymbol{u}_{t _{2}-1}+\frac{1-\beta_{1}}{1-\beta_{1}^{2}}\boldsymbol{g}_{t_{2}}\)
18:\(\boldsymbol{v}_{t_{2}}=\frac{\beta_{2}}{1-\beta_{2}^{2}}\boldsymbol{v}_{t_{2}- 1}+\frac{1-\beta_{2}}{1-\beta_{2}^{2}}\boldsymbol{g}_{t_{2}}\otimes \boldsymbol{g}_{t_{2}},\quad\left(\mathbf{W},\boldsymbol{b}\right)\leftarrow \left(\mathbf{W},\boldsymbol{b}\right)+0.001\cdot\frac{\boldsymbol{u}_{t_{2}}} {\sqrt{\boldsymbol{v}_{t_{2}}^{2}+\varepsilon}}\)
19:endwhile
20:endwhile
21:Return\(\mathbf{Y},\mathbf{W},\boldsymbol{b},\boldsymbol{\beta}\)
```  
**Algorithm 1** Switch from LM to Adam.