esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Fuzzy Kernel Nearest Feature Line Embedding (FKNFLE)
### Classification Results
Ten percent training samples of each class were randomly chosen from 10,249 pixels except for class Oats. Three training samples were randomly chosen from class Oats because of few samples in this data set. The remaining samples were used for testing. The classification error matrix is given in Table 6 in which the overall accuracy and kappa coefficient are 83.85% and 0.826, respectively. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Classes**} & \multicolumn{8}{c}{**Reference Data**} & \multicolumn{8}{c}{**User’s**} \\ \cline{2-11}  & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **Accuracy** \\ \hline
1 & 90.18 & 3.15 & 0 & 0 & 0 & 3.24 & 1.35 & 1.26 & 0.81 & 90.18 \\
2 & 2.31 & 92.50 & 0 & 2.31 & 0 & 1.85 & 0 & 1.01 & 0 & 92.50 \\
3 & 0 & 0 & 90.07 & 2.38 & 1.58 & 0.99 & 2.97 & 0.99 & 0.99 & 90.07 \\
4 & 0 & 1.23 & 2.84 & 90.24 & 1.42 & 1.42 & 1.51 & 1.32 & 0 & 90.24 \\
5 & 0.63 & 1.13 & 0.75 & 1.26 & 91.91 & 0.63 & 1.64 & 0.88 & 1.13 & 91.91 \\
6 & 1.10 & 1.19 & 1.38 & 1.56 & 1.19 & 92.54 & 0.55 & 0.46 & 0 & 92.54 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The classification error matrix for data set Pavia University (in percentage). \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Classes**} & \multicolumn{8}{c}{**Reference Data**} & \multicolumn{8}{c}{**User’s**} \\ \cline{2-11}  & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** & **Accuracy** \\ \hline
1 & 79.20 & 3.43 & 0.28 & 0.35 & 0 & 5.46 & 9.73 & 1.54 & 0 & 0 & 79.20 \\
2 & 5.90 & 81.81 & 0 & 0.12 & 0 & 1.33 & 6.39 & 4.34 & 0 & 0.12 & 81.81 \\
3 & 0 & 0 & 97.49 & 1.46 & 0.21 & 0.42 & 0 & 0.21 & 0.42 & 0.84 & 97.49 \\
4 & 0 & 0 & 0.27 & 96.30 & 0 & 0 & 0 & 0 & 0 & 3.42 & 96.30 \\
5 & 0 & 0 & 0.42 & 0 & 99.58 & 0 & 0 & 0 & 0 & 0 & 99.58 \\
6 & 5.14 & 0.21 & 0.10 & 0.41 & 0 & 88.89 & 4.42 & 0.72 & 0 & 0.10 & 88.89 \\
7 & 10.59 & 5.58 & 0.29 & 0.33 & 0.04 & 9.78 & 69.98 & 3.30 & 0 & 0.12 & 69.98 \\
8 & 1.35 & 4.05 & 1.52 & 0.34 & 0 & 1.69 & 1.85 & 88.53 & 0 & 0.67 & 88.53 \\
9 & 0 & 0 & 3.32 & 0.16 & 0 & 0 & 0 & 0 & 90.83 & 5.69 & 90.83 \\
10 & 0 & 0 & 3.89 & 5.70 & 0 & 0 & 0 & 0.26 & 10.88 & 79.27 & 79.27 \\ Producer’s Accuracy & 77.51 & 86.04 & 90.62 & 91.57 & 99.75 & 82.63 & 75.76 & 89.51 & 88.94 & 87.85 \\ Kappa Coefficient: **0.821** & & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The classification error matrix for data set IPS-10 (in percentage).
# Monitoring Cropland Abandonment in Hilly Areas with Sentinel-1 and Sentinel-2 Timeseries
## 3 Results
### Accuracy Assessment of Annual Land-Cover Maps  
The accuracies of annual land-cover maps were quantified from 2019 to 2021. Firstly, the classification result was validated using the samples obtained by our method. The result  
Figure 5: Spatial distribution map of cropland abandonment, using GF-2 imagery as the background. Abandoned irrigated cropland/abandoned rainfed cropland, intermittent irrigated cropland, intermittent rainfed cropland, and active cropland were the classes considered. (**a**) Spatial distribution map of rules including active cropland, intermittent irrigated cropland, intermittent rainfed cropland, abandoned irrigated cropland, and abandoned rainfed cropland in the study area. (**b**) Partial enlargement of (**a**). (**c**–**f**) Corresponding partial enlargements of the ESA WorldCover 2020 land cover product, the global ESRI 2020 land cover product, the GLC_FCS30 in 2020, and the CLCD in 2020; yellow represents the spatial distribution of cropland.  
showed that the overall accuracies ranged from 0.895 to 0.902, with the kappa ranged from 0.851 to 0.862. The F1 scores of irrigated cropland, rainfed cropland, woody vegetation, and herbaceous vegetation ranged from 0.836 to 0.879, 0.759 to 0.8, 0.964 to 0.981, and 0.958 to 0.978, respectively. Then, some field samples were selected to validate the classification results. The results show that the overall accuracy and kappa accuracy ranged from 0.902 to 0.921 and from 0.87 to 0.895, respectively. The F1 score of irrigated cropland, rainfed cropland, woody vegetation, and herbaceous vegetation ranged from 0.863 to 0.902, from 0.781 to 0.813, from 0.971 to 0.990, and from 0.961 to 0.980, respectively (Figure 6). By comparing the classification accuracy of the samples obtained using our method with field samples, the results showed good agreement, thus affirming the reliability of our method in terms of classification accuracy.
## 4 Conclusions  
The kinetic study carried out for the PLA concludes that the three isoconversional kinetic models used in the present work are valid since they present a high correlation coefficient. These isoconversional models can capture the reaction mechanism as the reaction kinetics progress. However, the KAS model was chosen because it has a slightly higher correlation coefficient than the other two models, which also considers the maximum degradation temperature.  
The heating rate directly influences the speed and mechanism that follows the thermal degradation. Regardless of the kinetic model used, at high heating rates, the maximum degradation temperature of the polymer will be higher while the reaction energy (activation energy and enthalpy) and the pre-exponential factor will be lower. The \(\Delta\)G value of PLA at a rate of 5 \({}^{\circ}\)C per minute (170.58 kJ mol\({}^{-1}\)) is slightly lower; therefore, at this heating ramp, the plastic presents the easiest degradation compared to the other tested heating rates. Therefore, with the main kinetic parameters obtained governing the reaction undergone in the pyrolytic reactor, the stability of the PLA thermal degradation can be predicted.  
Conceptualization, P.P.; methodology, M.M. and P.P.; software, M.M. and P.P.; validation M.M., P.P. and D.B.; formal analysis, D.B. and P.P.; investigation, M.M., P.P. and D.B.; resources, M.M., P.P. and D.B.; data curation, M.M., P.P. and D.B.; writing--original draft preparation, P.P.; writing--review and editing, P.P. and J.C.B.; visualization, P.P.; supervision, P.P. and J.C.B.; funding acquisition, P.P. All authors have read and agreed to the published version of the manuscript. This research received no external funding. This research received no external funding. Not applicable. Not applicable.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(\beta\) & E & A & \(\Delta\)H & \(\Delta\)G & \(\Delta\)S \\ (\({}^{\circ}\)C min\({}^{-1}\)) & (kJ mol\({}^{-1}\)) & (s\({}^{-1}\)) & (kJ mol\({}^{-1}\)) & (kJ mol\({}^{-1}\)) & (\(\beta\) mol\({}^{-1}\)) \\ \hline
5 & 145.59 & \(8.958\times 10^{10}\) & 140.54 & 170.58 & \(-\)49.47 \\ \hline
10 & 128.27 & \(2.781\times 10^{9}\) & 123.08 & 172.17 & \(-\)78.57 \\ \hline
15 & 119.44 & \(5.224\times 10^{8}\) & 114.19 & 172.60 & \(-\)92.56 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Thermodynamic properties of PLA at different heating rates.  
Data Availability Statement: Data is contained within this article.  
The authors declare no conflict of interest.
## 4 Mobile Peer-to-Peer Architectures
### Architecture  
While underlays based on (mostly) wired and infrastructure-based systems such as the Internet provide sufficient bandwidth for DHTs even when routing tables have to be maintained constantly due to the changing topology, resources of MANETs as underlay are more limited. Further, as the topology changes more often due to the mobility of nodes in MP2P networks, routing tables have to be maintained more frequently. Due to this, more control traffic is generated in an MP2P network compared to a traditional infrastructure-based P2P network but less bandwidth is available. Therefore, MP2P architectures have to reduce the overhead generated by the routing algorithm and the routing table maintenance. Recently, several approaches were proposed to combine MANETs and P2P networks. The resulting MP2P architectures can be distinguished by the implementation of the P2P algorithm into _layered_, _integrated_ and _cross-layered_ approaches as shown in Figure 6.
## 2 System Modelling
### MCF Model  
The MCF allows the transmission of multiples optical channels in different cores. In this work, only two cores are considered: one serving as the interfering core, i.e., the core that induces the ICXT, and the other acting as the interfered core, i.e., the core impaired by the ICXT. The ICXT induced by the MCF is modeled by the dual polarization discrete changes model (DCM) [18; 19; 20]. Each core operates as a linear single mode fiber (SMF), i.e., it is modulated by the SMF propagation transfer function. The random polarization rotation induced by the fiber birefringence is also included in the transmission model [19].  
To validate the ICXT simulation model, the statistical properties of the in\(-\)phase (I) and quadrature (Q) components of the ICXT obtained by simulation must agree with the theoretical analysis.  
Figure 3 shows the probability density function (PDF) of the in-phase and quadrature components of the ICXT field in both polarizations (\(x\) and \(y\)) directions. The simulation results of the ICXT are obtained with 1000 random phase shifts and for a ICXT level of \(-15\) dB. The ICXT level is the ratio between the mean ICXT power and signal power, at the output of interfered core [6]. A Gaussian PDF obtained from the mean and variance of the simulation results is also shown in Figure 3 as reference. The results of Figure 3 show that the ICXT components are well described by a Gaussian PDF, as predicted theoretically in [18], which validates the ICXT simulation model.
## 5 Framework
### Stage 1: Device Calibration and Estimation of Human Thumb Joint Angles
These values are based on the 3D solid model constraints. \(v_{FE}\) is the voltage reading of the potentiometer associated with the FE motion. The personalization of the device for adjusting the orientation of the pot joint introduces a rotational offset in the FE potentiometer (\(\theta_{p,FE,0}\)). Post\(-\)personalization, the FE potentiometer is rotated until the AA axis is parallel to \(X_{B}\), and the estimated angular displacement is recorded to determine \(\theta_{p,FE,0}\). Then, the corrected angular displacement of the FE potentiometer relative to \(X_{B}\) is evaluated using \(\theta_{pot,FE}=\theta_{p,FE}-\theta_{p,FE,0}\). The AA potentiometer reading is calibrated similarly to the FE one, and its angular displacement is estimated using Equation (4):  
\[\theta_{pot,AA}=\left(\frac{v_{AA}-v_{AA,min}}{\Delta v_{AA}}\right)\Delta \theta_{pot,AA}+\theta_{pot,AA,min} \tag{4}\]  
where \(\Delta\theta_{pot,AA}=(\theta_{pot,AA,max}-\theta_{pot,FE,min})\approx 90^{\circ}\) is the range of motion, \(\theta_{pot,AA,min}=-45^{\circ}\) is the minimum angular displacement measured using a protractor, \(v_{AA}\) is the voltage reading of the potentiometer associated with the AA motion, and \(\Delta v_{AA}=(v_{AA,max}-v_{AA,min})\approx 1.6\) V and \(v_{AA,min}=1.7\) V are its voltage range and minimum voltage reading, respectively. The CMC joint AA motion is estimated from the angular rotation of the AA axis pot joint. The CMC AA joint angle is measured relative to \(X_{FE}\) and is estimated from the rotation of the AA axis potentiometer, \(\theta_{AA}=\theta_{pot,AA}-\theta_{pot,AA,0}\). The \(\theta_{pot,AA,0}\) is the rotational offset introduced during personalization and is equal to the estimated angular displacement of the AA potentiometer when the CMC joint is completely adducted. The flex sensor reading measures the combined flexion of the MCP and IP user joints. The MCP and IP joint motions are assumed to be coupled and actuate at the same rate. Due to this approximation, both the MCP and IP joints reach their limits at the same time, and their respective joint angles can be correlated independently to the flex sensor readings using Equation (5):  
\[\theta_{i}=\left(\frac{v_{f}-v_{f,min}}{v_{f,max}-v_{f,min}}\right)\Delta \theta_{i} \tag{5}\]  
where \(i=(MCP,IP)\), \(\Delta\theta_{i}\) is the respective range of motion, and \(\theta_{i}\) is the estimated angular displacement.
## 4 Experimental Results and Discussion
### Experimental Results and Analysis  
#### 4.4.1 Comparison Experiment  
To verify the effectiveness of the proposed AT-CRF Reader, we conduct comparative experiments on the CMRC2018 and DuReader-checklist datasets to evaluate the overall performance of the model and the ability to deal with unanswerable questions, respectively. We selected and reproduced six state-of-the-art machine reading comprehension models: Bert-base(Chinese), ERNIE, RoBERTa-wwm-ext, ELECTRA, MacBERT-Chinese, and ChineseBERT, and compared them with the AT-CRF Reader to obtain the final results.  
The experimental results on the overall performance of the models on the CMRC2018 dataset are shown in Table 4. It can be seen from the results that the AT-CRF Reader in this paper has an EM value of 65.52%, and an F1 score of 87.51%. Compared with the Bert-base(Chinese), ERNIE, RoBERTa-wwm-ext, ELECTRA, and MacBERT-Chinese, the EM values are increased by 4.45%, 2.61%, 1.65%, 1.09%, and 0.18%, and the F1 scores are increased by 2.65%, 0.99%, 1.15%, 0.78%, and 0.67%, respectively. In addition, the AT-CRF Reader proposed in this paper has almost the same performance as the ChineseBERT proposed in the 2021 ACL Conference, which confirms that the model proposed in this paper has certain performance advantages.  
The experimental results of the performance of unanswerable questions on the DuReader-checklist dataset are shown in Table 5. The results show that the AT-CRF Reader achieves an EM value of 74.45%, and an F1 score of 87.39% on this dataset. Compared with Bert-base(Chinese), ERNIE, RoBERTa-wwm-ext, ELECTRA, and MacBERT-Chinese, the EM values are increased by 3.88%, 2.97%, 1.34% 0.63%, and 0.49%, and the F1 scores are increased by 2.68%, 1.62%, 0.81%, 0.56%, and 0.25%, respectively. In addition, the performance of the AT-CRF Reader proposed in this paper is basically the same as that of the ChineseBERT proposed in the 2021 ACL Conference, which shows that this model can not only predict correct answers, but also has a better response ability for unanswerable questions.  
\begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Setting Value** \\ \hline Epoch & 3 \\ Batch size & 32 \\ Learning-rate & \(3\times 10^{-5}\) \\ Dropout & 0.01 \\ Max A tokens & 50 \\ Max-seq-length & 512 \\ \hline \end{tabular}
\end{table}
Table 3: Training parameters.
# Sub-Band Backdoor Attack in Remote Sensing Imagery
## 8 Results of Sub-Band Backdoor Attack
### Results of Defense Mechanisms against Sub-band BadNets  
#### 8.2.1 Fine-Pruning  
Experiment results showed that fine-pruning techniques could not remove the backdoor for both cases, where the trigger was embedded in either important bands or less important bands. This showed that traditional blind backdoor removal techniques are not useful in removing sub-band backdoor triggers in remote sensing datasets. Again, we do not show all the failed cases here to save space.
# Special Issue on \"Advances in Organic Corrosion Inhibitors and Protective Coatings\"
## 3 Corrosion Protective Coatings  
In general, three different types of coatings exist for corrosion protection of metal alloys. Barrier coatings prevent the aggressive elements from coming together with the substrate to onset the corrosion process. Inhibitive coatings actively block the electrochemical reaction from happening by interfering with the electrolytes needed to start the corrosion process. Sacrificial coatings are a type of metal coatings that become more oxidated than the metal surface they protect. Three articles and one review based on corrosion protective coatings were published in this Special Issue. In the work of [PERSON] et al. [8], smooth coatings of TiNb and TiNb were deposited on 316L stainless steel by magnetron sputtering in order both to improve the corrosion resistance and the electronic conductivity of bipolar plates for proton exchange membrane fuel cells.  
In the study by [PERSON] et al. [9], poly(phenylene methylene)-based coatings were developed for corrosion protection of aluminum alloy AA2024. These copolymer-based coatings contained n-octyloxy side chains and their anti-corrosion behavior was estimated via several electrochemical methods. The obtained results revealed that these coatings exhibited good corrosion protection of the metal surface towards a sodium chloride solution. Thin multifunctional coatings of cerium oxide nanoparticles with anti-reflective properties were developed onto glass and silicon substrates by [PERSON] et al. [10]. These coatings could be used as an intermediate layer between air and substrates for providing anti-reflection features. Finally, in the review paper of [PERSON] et al. [11], the advances and challenges of corrosion and topology detection of grounding grid are discussed. This paper presents the research status of grounding corrosion and topological detection in detail and introduces the basic principles, research difficulties and existing problems of the methods such as the electromagnetic field method, electric network method, ultrasonic detection method, electrochemical method and electromagnetic imaging method.
# Recirculated Wave Undulators for Compact FELs
## 7 Coherent Synchrotron Radiation  
To take into account for the Coherent Synchrotron Radiation (CSR) emitted in the magnetic chicane and to which extent this affects the longitudinal electron beam dynamics, the longitudinal phase-space density at the exit of the magnetic chicane must be expressed with a correction term:  
\[\rho(\psi,\delta;t)=\rho(\psi-\Delta\psi,\delta-\Delta\delta;0)=\rho\bigg{(} \psi-\frac{2\pi}{\lambda_{0}}R_{56}\delta_{0},\delta-\kappa\delta_{0};0\bigg{)} \tag{28}\]  
which is different than Equation (11) because of the factor \(\kappa\) which explains the relative energy losses due to the emission of CSR. The synchrotron radiation spectrum at low frequencies is proportional to the \(\omega^{1/3}\) where \(\omega\) is the angular frequency of the photons. The total CSR energy \(E_{CSR}\) emitted by a bunch with gaussian envelope over one full circle is calculated as:  
\[E_{CSR}=\frac{N_{e}^{2}e^{2}}{4\pi\epsilon_{0}c}\int e^{-\omega^{2}\tau_{e}^{2 }}\bigg{(}\frac{\omega R}{c}\bigg{)}^{1/3}d\omega=\Gamma\bigg{(}\frac{2}{3} \bigg{)}\frac{N_{e}^{2}e^{2}}{8\pi\epsilon_{0}c\tau_{e}}\bigg{(}\frac{R}{c\tau _{e}}\bigg{)}^{1/3} \tag{29}\]  
where \(\Gamma(x)\) is the Gamma function, \(\tau_{e}\) is the rms electron bunch length, \(N_{e}\) is the number of electrons in the bunch and \(R\) is the bending radius. The total beam energy is calculated as \(E_{beam}=N_{e}\tau_{e}mc^{2}\). The CSR correction is therefore found to be:  
\[\kappa=\frac{E_{CSR}}{E_{beam}}=\frac{4\theta}{2\pi}\Gamma\bigg{(}\frac{2}{3} \bigg{)}\frac{N_{e}e^{2}}{8\pi\epsilon_{0}c\tau_{e}mc^{3}}\bigg{(}\frac{R}{c \tau_{e}}\bigg{)}^{1/3} \tag{30}\]  
where the factor \(4\theta/2\pi\) takes into account for the fact that the CSR emitted in the four bending magnets composing the chicane corresponds to a total bending angle which is smaller than the full circle. For a better evaluation of the \(\kappa\) parameter the microbunching should be taken into account beyond the bunch envelope (in this case gaussian), nevertheless this is not relevant for the design considered here since the critical energy of the synchrotron radiation spectrum falls in a range of frequencies much lower than the microbunching frequency.
## 1 Introduction
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**References** & **Concrete Type** & **25 \({}^{\circ}\)C** & **100 \({}^{\circ}\)C** & **250 \({}^{\circ}\)C** & **300 \({}^{\circ}\)C** & **500 \({}^{\circ}\)C** & **600 \({}^{\circ}\)C** & **750 \({}^{\circ}\)C** & **900 \({}^{\circ}\)C** & **1000 \({}^{\circ}\)C** \\ \hline
[10] & PCC with fly ash & \begin{tabular}{c} \(\blacksquare\) \\ 40 \\ \end{tabular} & - & \begin{tabular}{c} \(\blacksquare\) \\ 38 \\ \end{tabular} & - & \
\begin{tabular}{c} \(\blacksquare\) \\ 37 \\ \end{tabular} & - &
\begin{tabular}{c} \(\blacksquare\) \\ 15 \\ \end{tabular} & - & - \\ \hline
[11] & PCC & \
\begin{tabular}{c} \(\blacksquare\) \\ 79 \\ \end{tabular} & - & - &
\begin{tabular}{c} \(\blacksquare\) \\ 85 \\ \end{tabular} & 45 & - & - & - & - \\ \hline \hline \end{tabular} SS: Sodium silicate SH: Sodium hydroxide.  
\end{table} 
Table 1: _Cont._to fly ash-based geopolymers could improve setting time [24]. In their study, [PERSON] and [PERSON] examined the effects of steel fiber and blast furnace slag content on the fresh and hardened properties of self-compacting fly ash-based geopolymer concrete. Blast furnace slag was reinforced into geopolymer concrete at 0%, 25%, 50%, 75%, and 100% by weight. They found that the increase in the proportion of blast furnace slag had a negative effect on the properties of fresh concrete, but it significantly increased the compressive strength [25]. [PERSON] and [PERSON] tried to achieve the best compressive strength in their study by using different proportions of blast furnace slag and fly ash. The results show that reducing the proportion of blast furnace slag and substituting fly ash causes a decrease in compressive strength [26]. Fly ash is a pozzolanic material formed by coal combustion and is widely found in nature [27; 28]. [PERSON], [PERSON], and [PERSON] found that different fly ash specimens cured at 85 \({}^{\circ}\)C for 24 h had compressive strengths between 35 and 40 MPa. However, by adding glass water to the NaOH activator in fly ash-based geopolymer concrete, the compressive strength reached approximately 90 MPa [29]. The alkaline liquids used in this study are sodium silicate (Na\({}_{2}\)SiO\({}_{3}\)) and sodium hydroxide (NaOH). In their study, [PERSON] and his colleagues found that the high-temperature resistance of geopolymer concrete increased as the amount of sodium silicate increased [30]. Several studies have been conducted on the behavior of PCC, and geopolymer concrete under high temperatures. However, there is a noticeable gap in research on the high-temperature behavior of ceramic fiber-added concrete. The objective of this study is to improve the mechanical performance of concrete against high temperatures by incorporating ceramic fibers, which dissolve upon contact with liquid, into the concrete. This study explores the behavior of ceramic fiber and geopolymer concrete under high temperatures and presents noteworthy findings to the literature.
# Research on Agricultural Product Price Prediction Based on Improved PSO-GA
## Appendix A
### Gated Recirculation Units (GRUs)  
Gated recurrent units comprise a variant of LSTM that is also used to process sequence data. It simplifies the structure by combining the forgetting and input gates of the LSTM into a single update gate and by combining the unit state and hidden state. GRUs are particularly suited to processing and predicting time-series data, such as stock prices, natural language processing (including text generation and machine translation), and speech recognition.  
The relevant formulae for GRUs are as follows:  
1. Renewal gates: \(\mathsf{z}_{\mathsf{t}}=\sigma(\mathsf{W}_{\mathsf{z}}\cdot[\mathsf{h}_{ \mathsf{t}-1},\mathsf{x}_{\mathsf{t}}]+\mathsf{b}_{\mathsf{z}})\)  
2. Reset door: \(\mathsf{r}_{\mathsf{t}}=\sigma(\mathsf{W}_{\mathsf{r}}\cdot[\mathsf{h}_{ \mathsf{t}-1},\mathsf{x}_{\mathsf{t}}]+\mathsf{b}_{\mathsf{r}})\)  
3. Candidates for hidden status: \(\mathsf{h}_{\mathsf{t}}=\tanh(\mathsf{W}\cdot[\mathsf{r}_{\mathsf{t}}\;*\; \mathsf{h}_{\mathsf{t}-1},\mathsf{x}_{\mathsf{t}}]+\mathsf{b})\)  
4. Hidden states: \(\mathsf{h}_{\mathsf{t}}=(1-\mathsf{z}_{\mathsf{t}})\;*\;\mathsf{h}_{\mathsf{t }-1}+\mathsf{z}_{\mathsf{t}}\;*\;\widetilde{\mathsf{h}}_{\mathsf{t}}\) where \(\sigma\) is the sigmoid function, \(\mathsf{b}\) is the hyperbolic tangent function, \(\tanh\) is the hyperbolic tangent function, \(\mathsf{W}\) and \(\mathsf{b}\) are the weights and bias, \(\mathsf{h}\) is the hidden state, and \(\mathsf{x}\) is the input.