esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Adaptive Distributed Student's T EKF
### Allan Variance  
As one of the most widely used time-series analysis method, Allan variance is proposed to extract noise from data [6]. In this work, we modify the traditional definition of Allan variance to provide adaptive noise estimation. Starting with the traditional definition of Allan variance, with \(r^{(i)}\), we can obtain that  
\[\sigma_{r^{(i)}}^{2}=\frac{1}{2}E\left(\left(r_{j+1}^{(i)}(t)-r_{j}^{(i)}(t) \right)^{2}\right),i\in[1,N], \tag{4}\]  
where \(j\) is the number of data groups. When the time index is \(t_{0}\), \(N\) is the number of UWB BSs. We can obtain that  
\[\hat{\mathbf{R}}_{t_{0}}^{(i)}=\frac{1}{2(t_{0}-1)}\sum\limits_{j=1}^{N-1} \left[\left(r_{i+1}^{(i)}(\delta)-r_{i}^{(i)}(\delta)\right)^{2}\right],i\in[ 1,N], \tag{5}\]  
where \(N\) is the sum of the data groups. Then, we can modify this equation:  
\[\begin{array}{rcl}\mathbf{\hat{R}}_{\text{t}}^{(i)}&=&\frac{1}{2(t-1)}\sum \limits_{j=2}^{t}\left[\left(r_{j}^{(i)}-r_{j-1}^{(i)}\right)^{2}\right]\\ &=&\frac{1}{2(t-1)}\left\{\sum\limits_{j=2}^{t-1}\left[\left(r_{j}^{(i)}-r_{j -1}^{(i)}\right)^{2}\right]+\left(r_{t}^{(i)}-r_{t-1}^{(i)}\right)^{2}\right\} \\ &=&\frac{t-2}{t-1}\left\{\frac{1}{2(t-1)}\sum\limits_{j=2}^{t}\left[\left(r_{j }^{(i)}-r_{j-1}^{(i)}\right)^{2}\right]\right\}+\frac{1}{2(t-1)}\left(r_{t}^{( i)}-r_{t-1}^{(i)}\right)^{2}\\ &=&\left(1-\frac{1}{t-1}\right)\mathbf{\hat{R}}_{\text{t}-1}^{(i)}+\frac{1}{2( t-1)}\left(r_{t}^{(i)}-r_{t-1}^{(i)}\right)^{2},i\in[1,N],t\geq 2,\end{array} \tag{6}\]  
Thus, we can obtain  
\[\mathbf{\hat{R}}_{\text{t}}^{(i)}=(1-\chi_{t-1})\mathbf{\hat{R}}_{\text{t}-1} ^{(i)}+\frac{1}{2}\chi_{t-1}\Big{(}r_{t}^{(i)}-r_{t-1}^{(i)}\Big{)}^{2},i\in[1, N], \tag{7}\]In this work, we modify Equation (7) as follows:  
\[\hat{\mathbf{R}}_{t}^{(i)}=\left\{\begin{array}{ll}(1-\chi_{t-1})\hat{\mathbf{R }}_{t-1}^{(i)}+\chi_{t-1}\hat{\mathbf{R}}_{\min}^{(i)},&\hat{\mathbf{R}}_{t}^{( i)}<\hat{\mathbf{R}}_{\min}^{(i)}\\ \hat{\mathbf{R}}_{\max}^{(i)},&\hat{\mathbf{R}}_{t}^{(i)}>\hat{\mathbf{R}}_{ \max}^{(i)}\\ (1-\chi_{t-1})\hat{\mathbf{R}}_{t-1}^{(i)}+\frac{1}{2}\chi_{t-1}\Big{(}r_{t}^{ (i)}-r_{t-1}^{(i)}\Big{)}^{2},&\text{otherwise}\end{array}\right. \tag{8}\]  
where \(\hat{\mathbf{R}}_{\max}^{(i)}\) and \(\hat{\mathbf{R}}_{\min}^{(i)}\) represent the defined maximum and minimum values of \(\hat{\mathbf{R}}\), respectively.
# Research on the Influence of Backlash on Mesh Stiffness and the Nonlinear Dynamics of Spur Gears
## 2 Influence of Backlash on Time-Varying Mesh Stiffness
### Influence of Backlash on Stiffness  
The backlash can be obtained by decreasing the thickness of the tooth or by increasing the center distance. Here, only the former situation will be discussed.  
According to ISO/TR 10064-2-1996, the value of minimum backlash can be expressed as  
\[b_{min} = \frac{2(0.06+0.0005a\ +\ 0.03m)}{3} \tag{19}\]  
where \(a\) is the center distance.  
In this paper, three cases will be discussed, i.e., Case 1: \(b\ =\ \ 0\); Case 2: \(b\ =\ \ b_{min}\); Case 3: \(b\ =\ \ 2b_{min}\).  
The parameters of an example gear pair are listed in Table 2.  
According to the above-mentioned mesh stiffness model, the single-tooth-pair mesh stiffness and time-varying mesh stiffness can be calculated, as shown in Figures 3 and 4.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Properties** & **Symbol** & **Value (Unit)** \\ \hline Young’s modulus & E & 206 (GPa) \\ Poisson’s ratio & \(v\) & 0.3 \\ Pressure angle & \(a\) & 20\({}^{\circ}\) \\ Width of teeth & \(L\) & 20 (mm) \\ Number of teeth & \(N_{1}/N_{2}\) & 45/45 \\ Module & \(m\) & 3 \\ Radius of the inner & \(r_{int}\) & 25 (mm) \\ hub & \(r_{int}\) & 25 (mm) \\ Addendum & \(h_{a}^{*}\) & 1 \\ coefficient & \(c^{*}\) & 0.25 \\ Clearance coefficient & \(c^{*}\) & 1.7358 \\ Contact ratio & \(\varepsilon\) & 1.7358 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The parameters of the example gear pair.  
By introducing a stiffness coefficient \(\eta\),  
\[\eta = \frac{K_{b}(t)}{K_{b}=0(t)} \tag{20}\]  
where \(K_{b}(t)\) is the single-tooth-pair mesh stiffness for different values of backlash, a better view can be obtained to present the effect of backlash on stiffness, as shown in Figure 5.  
Figure 4: The time-varying mesh stiffness.  
Figure 5: \(\eta\) for the different values of backlash.  
Figure 3: The single-tooth-pair mesh stiffness.  
Compared to Case 1, Case 2 and Case 3 shows an obvious reduction in single stiffness and mesh stiffness according to Figure 5. Moreover, the reduction is not proportionate. Compared with Case 1, the rate of decline for Case 2 and Case 3 shows a trend of decreasing first and then increasing in a mesh cycle from coming into the mesh to going out of the mesh.
## 3 Test Results and Analysis
### Effect of Biopolymer on Compressive Strength
#### 3.1.2 Elastic Modulus  
This study evaluates the impact of biopolymers on the stiffness of GRS using the elastic modulus (E-value) [36], the tangent modulus corresponding to half of the peak strength is used, as shown in Figure 9. The trend in the E-value of biopolymer-treated soil follows a pattern similar to that of UCS but with different growth rates. In the short-term curing stage, the E-value of XG-treated soil initially decreases, then increases, and subsequently decreases again, always remaining lower than that of untreated GRS. However, as the curing time increases, the E-value of XG-treated soil first increases and then decreases, always remaining higher than that of untreated soil. This indicates that long-term curing significantly enhances the stiffness of soil treated with XG. Specifically, soil treated with 1.5% XG shows the most significant enhancement in stiffness. The E-value of XG-treated soil clearly demonstrates time dependence on GRS. For LBG and GG treatments, the E-value of the soil is generally higher than that of untreated GRS and gradually increases with curing time. Soil treated with 1.5% LBG exhibits the highest stiffness, while GG at a 2% content shows the most substantial effect. Overall, among the three biopolymers, GG-treated soil demonstrates the highest stiffness.  
Figure 8: UCS of biopolymer-treated soil at different curing times: (**a**) XG; (**b**) LBG; and (**c**) GG.
# Analysis of Earth Pressure Variation for Partial Displacement of Retaining Wall
## 2 Materials and Testing Procedures
### Test Procedures  
The sand was filled and compacted in layers with a height of 10 cm each time. During filling, the relative compactness of each layer was controlled to be 0.75. According to the Standard for Geotechnical Testing Method (GB/T 50123-2019), the compactness of sand \(D_{\mathrm{r}}\) is controlled by the relative density, as shown in Equation (1).  
\[D_{\mathrm{r}}=\frac{\rho_{\mathrm{dmax}}(\rho_{\mathrm{d}}-\rho_{\mathrm{dmin }})}{\rho_{\mathrm{d}}(\rho_{\mathrm{dmax}}-\rho_{\mathrm{dmin}})} \tag{1}\]  
where \(\rho_{\mathrm{dmax}}\) is the maximum dry density of sand; \(\rho_{\mathrm{dmin}}\) is the minimum dry density; and \(\rho_{\mathrm{d}}\) is the actual dry density of the soil. By equating \(D_{\mathrm{r}}\) in Equation (1) to 0.75, the actual dry density of the sand can be calculated (\(\rho_{\mathrm{dmax}}\) and \(\rho_{\mathrm{dmin}}\) are shown in Table 1). Accompanied with the already-known volume of each filling, thus the relative compactness of each layer can be controlled by the mass of sand in each filling.  
The sand around the stress detectors was tamped with a rubber hammer to minimize the impact on the stress detectors. To control the movement precisely, the displacement was applied by rotating the levers. A diagram of multi-stage movement in three displacement modes is shown in Figure 5. The trap-door could move outward by rotating the lever and rotating the lever; one lap could achieve a 0.5 mm distance of the trap-door. Therefore, the distance can be controlled by the number of rotating laps. Thereby, rotating the top lever and fixing the bottom lever corresponded to the RB mode and rotating the bottom lever and fixing the upper lever achieved RT mode. Rotating both the top lever and bottom lever for the same laps could realize T mode. Regarding the movement level as \(N\), the \(N\)-level displacement amount can be referred to as \(\Delta=N\times 0.5\,\mathrm{(mm)}\) with every 0.5 mm increment.  
After each movement step of the movable plates, the earth pressure was measured by the Donghua monitor software shown in Figure 3 when the number of stress detectors was stabilized. All the test conditions are listed in Table 2 and the experiment process is shown in Figure 6.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Test Condition** & **Width of Trap-Door (cm)** & **Movement Mode** & **Filler Height (cm)** & \(N\)**-Level Distance (mm)** \\ \hline
1–3 & 10 & T, RT, RB & 50 & \(0.5\times N\) \\
4–6 & 20 & T, RT, RB & 50 & \(0.5\times N\) \\
7–9 & 30 & T, RT, RB & 50 & \(0.5\times N\) \\
10–12 & 40 & T, RT, RB & 50 & \(0.5\times N\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Test condition of the horizontal trap-door test.  
Figure 5: Diagram of multi-stage loading in three displacement modes: (**a**) T mode, (**b**) RT mode, (**c**) RB mode.
## 3 Simulation Results and Discussion
### Global Learning Rate  
Global learning rate \(\eta\) is another important parameter for the RMS-Prop algorithm. The simulated DOP and PER at different global learning rates are shown in Figure 4a,b, with \(\delta\)u = 0.06 and cost function of J\({}_{3}\). The optimal value for the global learning rate is 0.6 according to the curve figures. On the one hand, when \(\eta\) is smaller than 0.6, the convergence speed is relatively slow. On the other hand, when \(\eta\) is larger than 0.6, the convergence of PER degenerates severely, which converges fast in the first few steps while beginning to fluctuate around a relatively small value not long after the algorithm works.  
Figure 4: Convergence curves for different global learning rates: (**a**) DOP curves; (**b**) PER curves.  
Figure 3: Convergence curves for different perturbation amplitudes: (**a**) DOP curves; (**b**) PER curves.  
According to the above analysis, the optimal combination of parameters for the RMS-Prop algorithm is concluded. The PER of the output laser is the optimal cost function for the algorithm. When the amplitude of random perturbation is 0.06 and the global learning rate is 0.6, the control effect of polarization is optimal, which means the DOP converges very close to 1 and the PER reaches an extremely high value at a high speed.
## 3 Problem Formulation
### Realization  
In the realization step, the complex-valued variables are converted to the real-valued version. For example, the realization of \(\mathbf{\bar{s}}\) takes the real part of \(\mathbf{\bar{s}}\) in one column vector and the complex part in another vector and then stacks the column vectors together to give \(\mathbf{\bar{s}}_{r}\). The realization of \(\mathbf{\bar{s}}_{r}\), \(\mathbf{\overline{x}}_{r}\), \(\mathbf{\overline{A}}_{r}(\Theta)\), and \(\mathbf{\overline{A}}_{r}\Big{(}\widehat{\Theta}\Big{)}\) is given as  
\[\begin{split}\mathbf{\bar{s}}_{r}&=\begin{bmatrix} \Re\{\mathbf{\bar{s}}\}\\ \Im\{\mathbf{\bar{s}}\}\end{bmatrix}\\ \mathbf{\bar{x}}_{r}&=\begin{bmatrix}\Re\{\mathbf{\bar{x}}\}\\ \Im\{\mathbf{\bar{x}}\}\end{bmatrix}\\ \mathbf{\overline{A}}_{r}(\Theta)&=\begin{bmatrix}\Re\{\mathbf{\overline{A}}( \Theta)\}&-\Im\{\mathbf{\overline{A}}(\Theta)\}\\ \Im\{\mathbf{\overline{A}}(\Theta)\}&\Re\{\mathbf{\overline{A}}(\Theta)\} \end{bmatrix}\\ \mathbf{\overline{A}}_{r}\Big{(}\widehat{\Theta}\Big{)}&=\begin{bmatrix}\Re\{ \mathbf{\overline{A}}\Big{(}\widehat{\Theta}\Big{)}\}&-\Im\{\mathbf{\overline{A} }\Big{(}\widehat{\Theta}\Big{)}\}\\ \Im\{\mathbf{\overline{A}}\Big{(}\widehat{\Theta}\Big{)}\}&\Re\{\mathbf{ \overline{A}}\Big{(}\widehat{\Theta}\Big{)}\}\end{bmatrix}\end{split} \tag{13}\]  
In terms of vectorized real-valued variables, the CM constraint is given by  
\[\mathbf{\bar{s}}_{r}^{T}\mathbf{E}_{i}\mathbf{\bar{s}}_{r}=1,i=1,2,\cdots,2 MN \tag{14}\]  
where  
\[\mathbf{E}_{i}(m,n)=\left\{\begin{array}{ll}1&:\ m=n=i\\ 1&:\ m=n=i+MN\\ 0&:\ otherwise\end{array}\right. \tag{15}\]and \(0\leq m,n,i\leq 2 MN\). At the end of the realization step, the problem Equation (12) can be expressed as  
\[\underset{\mathbf{\bar{g}}_{r}}{\text{minimize}} \mathbf{\bar{s}}_{r}^{T}\mathbf{\bar{A}}_{r}\left(\widetilde{\Theta }\right)\mathbf{\bar{A}}_{r}^{T}\left(\widetilde{\Theta}\right)\mathbf{s}_{r}\] (16) subject to \[\mathbf{\bar{A}}_{r}^{T}(\mathbf{\bar{0}})\mathbf{\bar{s}}_{r}= \mathbf{\bar{x}}_{r}\] \[\mathbf{\bar{s}}_{r}^{T}\mathbf{E}_{i}\mathbf{\bar{s}}_{r}=1,i= 1,2,\cdots,MN.\]  
The optimization problem in Equation (16) can be solved to obtain \(\mathbf{\bar{s}}_{r-opt}\), which is the vectorized and real-valued version of \(\mathbf{S}_{opt}\). So, the reverse operation, i.e.,  
\[\mathbf{S}_{opt}=mtx\left(\mathbf{\bar{s}}_{r1-opt}+i\cdot\mathbf{\bar{s}}_{ r2-opt}\right) \tag{17}\]  
can be performed to obtain \(\mathbf{S}_{opt}\), where \(\mathbf{\bar{s}}_{r1-opt}\) contains the first \(MN\) elements, the real part, and \(\mathbf{\bar{s}}_{r2-opt}\) contains the other \(MN\) elements, the imaginary part.
## 2 Results and Discussion
### MazEF
#### 2.2.2 MazEF (II)-RHH-MazF Composite
MazEF (II) of _G. thermodenitrificans_ NG80-2  
The gene with the locus tag GTNG_0207 codes for a putative MazF toxin (Table 1). The aa sequence of the putative toxin is identical to MazF toxins in the three other _Geobacillus_ strains mentioned above (Table S1; global alignment in Figure S3a). The gene with the locus tag GTNG_0206, which is upstream of GTNG_0207 and potentially sharing its operon, codes for a putative RHH domain-harboring antitoxin (Table 1). The aa sequence of the antitoxin is highly similar (~98%) to the antioxins of the three other _Geobacillus_ strains mentioned above. The antitoxin-coding gene, GTNG_0206, has been annotated as coding for a hypothetical protein in both genome records of the strain (Table S1). The results of our analysis, however, highlighted the identity of this protein as a putative RHH domain-harboring antitoxin (Table 2). Overall, the MazEF TA family is harbored by all the four _Geobacillus_ strains, but three of the strains have two pairs of two different composites; the RHH-MazF and the MazE-MazF, while the fourth one (i.e., _G. thermodenitrificans_ NG80-2) has only one pair of the RHH-MazF composite (Table 1 and Table S1). As can be concluded from the gene order and aa sequences, each composite is highly conserved among the analyzed strains (Figures S2 and S3). However, the two composites are diverse (Figures S2 and S3). The antitoxins of the two different composites have different conserved domains, RHH and MazE (Table 1). While the toxin in each composite has a MazF domain, the two composites have two different MazF sequences. The MazF toxins are diverse within one MazF protein family [72]. The MazEF protein pairs of the two composites may coordinate their activity to help the strain adapt to stress [73].
# Several Tree-Based Solutions for Predicting Flyrock Distance Due to Mine Blasting
## 4 Modeling Procedure
### XGBoost  
Although RF is renowned as a powerful prediction tool, it has some drawbacks. The main defect of RF is that if it initially makes a mistake in all trees, the algorithm will repeat this mistake in its next iterations. To this end, ensemble methods such as XGBoost and AdaBoost are developed to address the problems by their nature and to learn from the mistakes of trees to overcome the shortcomings and improve the results considerably.  
In this section, the XGBoost model was developed in order to determine flyrock distance. For learning a full tree, Scikit-learn and XGBoost Python packages were used. To develop an XGBoost model, hyperparameters should be considered as the main factors during model development. These parameters are the number of features, the number of trees, the maximum depth of trees, whether to bootstrap, how many samples should be left in a node before the split, and how many samples should remain in the leaf node at the end. Generally, to reduce the probability of overfitting, it is necessary to avoid complexity by increasing the values of hyperparameters. Moreover, accompanied by performance maximization, it is important to consider parameter tuning to prevent overtraining and generating too complex models. After a trial and error procedure, the optimal values for XGBoost were acquired. Table 7 displays the optimum XGBoost parameters for predicting flyrock caused by mine blasting.  
One of the drawbacks of XGBoost is the inconsistency between the speed of trees' generation and the learning from them. This inconsistency causes newly generated trees to receive less importance than older ones. To overcome this drawback, [PERSON] and [PERSON] [95] introduced the DART booster for XGBoost. In this study, the DART booster was applied, and it was found that, compared to other boosting algorithms, its performance is better. Figure 8 shows some of the estimators that were developed by XGBoost for flyrock prediction.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Range** & **Value** \\ \hline Criterion & [Entropy, Gini] & Entropy \\ Estimators number & [50, 100, 200, 300] & 200 \\ Bootstrap & [True, False] & True \\ Max depth & [3, 4, 5, 6, 7] & 4 \\ Max features & [sqrt, log2] & Sqrt \\ OOB score & [True, False] & True \\ \hline \hline \end{tabular}
\end{table}
Table 6: RF Hyperparameters for estimating flyrock.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Range** & **Value** \\ \hline learning rate (eta) & [0.1, 0.2, 0.3, 0.5, 1, 1.5, 2, 3] & 0.3 \\ number of estimators & [50, 100, 200, 300] & 100 \\ max depth & [2, 3, 4, 5, 6] & 3 \\ gamma & [0.0001, 0.001, 0.01, 0.1,0.5, 1] & 0.001 \\ min child weight & [0.2, 0.5, 0.8, 0.9, 1, 1.5, 2] & 0.9 \\ max delta step & [0.2, 0.5, 0.8, 0.9, 1, 1.5, 2] & 0.9 \\ booster & [gbtree, gblinear, DART] & DART \\ \hline \hline \end{tabular}
\end{table}
Table 7: Optimum XGBoost algorithm parameters for flyrock prediction.  
Figure 8: _Cont._
# Anomaly Detection in Microservice-Based Systems
## 3 Model and Results
### Evaluating Classifier Performance
Among these metrics, recall stood out with the highest average of 98%, indicating that the model could accurately identify a high percentage of anomalies. In contrast, FPR had the lowest average value of 0.01%, indicating that the model had a low false-positive rate. The validation results suggest that the model performed well in detecting anomalies. The high recall value indicates that the model effectively identified most anomalies, while the low FPR value indicates that the model produced few false positives. These results support the use of the model in anomaly detection applications. Figure 5: Comparison of confusion matrices of the model with the dataset with application-level and service-level anomalies. (**a**) Confusion matrix for the application-level anomaly dataset. (**b**) Confusion matrix for the service-level anomaly dataset. Figure 5b displays the confusion matrix for the average of the 10 dataset runs with service-level anomalies. The values of TP, TN, FP, and FN were 198.4, 202.9, 4, and 9.7, respectively. These values correspond to 48% TP, 49% TN, 1% FP, and 9.7% FN. These results suggest that the model was able to classify the majority of the data points effectively. The high percentages of TP and TN indicate that the model had good overall performance in identifying both positive and negative cases. The low percentages of FP and FN indicate that the model had low rates of misclassifying data points. These results support the use of the model in detecting application-level anomalies. The standard deviation of the ten runs concerning the mean was between 0.01 and 0.02 for all the evaluated metrics. Precision had the largest variability with a value of 0.02, while recall had the smallest one with 0. These results suggest that the model's performance was relatively consistent across the ten runs for all the metrics, except for precision which showed greater dispersion. The low standard deviation in recall suggests that the model was able to consistently identify a high percentage of TP in each run. However, the higher standard deviation in precision indicates that the model's ability to avoid false positives may have been less consistent. These insights into the model's standard deviation can help understand its strengths and weaknesses and can inform further improvements and refinements to the model. Among the 10 runs evaluated, the highest F1-score value was obtained in run ten. The hyperparameters used in this run were: the activation function tanh, an L2 penalty parameter of 0.001, a network architecture composed of two layers with 100 and 50 neurons, respectively, an initial learning rate of 0.001, and the Adam for weight optimization. These results suggest that the combination of hyperparameters used in run ten was particularly effective in achieving a high F1-score. Further analysis could be conducted to understand the impact of each individual hyperparameter on the model's performance. These findings highlight the importance of tuning hyperparameters in machine learning models to achieve optimal performance.
## 4 Experimental Validation
### Results and Discussion
#### 4.4.1 Pollen Grain Microscopy  
In Tables 2 and 3, we present the results of our experiments on the pollen grain microscopy dataset. The results obtained with the models trained only from manually labeled data are provided as a baseline but also because they reflect the level of error affecting the pseudo-labels. They indicate that the random ferns method performs significantly better than the CNN method when only one annotated image is available. However, as the annotated data increase, the CNN method overcomes the random ferns. Specifically, when using 50 annotated images, the CNN achieves a foreground IoU result of 81.6%, surpassing random ferns, which achieves 79.2%. The pixel accuracy is also comparable, with values of 97.4% for CNN and 97.5% for random ferns. When using random ferns and CNN as pseudo-label generators, even with only one annotated image, the CNN*_0.50 yields an IoU result of 80.0%, outperforming random ferns, which achieves 74.7%. The experimental results clearly indicate that leveraging unlabeled data through pseudo-labels enhances CNN* model quality compared to a model (either random ferns or CNN) trained solely on manually labeled samples. Interestingly, Tables 2 and 3 also demonstrate that CNN*_(0.45,0.55) consistently outperforms CNN*_0.45, CNN*_0.50, and CNN*_0.55, indicating that increasing the diversity of pseudo-labels is beneficial. Additionally, Figure 3 illustrates the predictions of various methods on the pollen test set. The models depicted in the figure are trained using only a single labeled image. Through the comparison between the predictions and the ground truth, it is observed that employing a fixed threshold to generate pseudo-labels causes a bias in training [10], resulting in inferior predictions compared to using a varying threshold.