esa-sceva/satcom-chunk-collection huggingface dataset:
## 4 Experimentation
### Design  
The methodology followed to design the evaluation was guided by the research questions outlined in Section 1. First, the evaluation was carried out using two public datasets in English to assess the performance of the proposed approach in various corpora (**RQ1**). Additionally, to investigate the effectiveness of different characteristics for depression detection (**RQ2**), a series of experiments was conducted, categorizing them according to the characteristic framework presented in Section 3.2. Finally, the three models proposed in Section 3.3 are evaluated separately and compared with related works to investigate the performance of the different methods (**RQ3**). These models are denoted as: the lexicon-based feature model (\(M_{LF}\)), the distributional representations model (\(M_{DR}\)), and the ensemble model (\(M_{E}\)).  
We evaluated the proposed approaches using two distinct machine learning classifiers implemented with Python's Scikit-learn library [69]: support vector machines (SVM) and logistic regression. Moreover, RandomizedSearchCV was used to find the optimal hyperparameters. Given that the best results were consistently obtained using a linear support vector machine (SVM), only metrics corresponding to this classifier were included. More details can be found in the source code ([[https://github.com/gsi-upm/depression-sl-text](https://github.com/gsi-upm/depression-sl-text)]([https://github.com/gsi-upm/depression-sl-text](https://github.com/gsi-upm/depression-sl-text)), accessed on 16 August 2023).  
Following the previous research [20], we utilized a 5-fold validation and weighted F1-score as the performance metric. Some actions were taken into account to address the class imbalance problem of the used datasets. The subsets were split using stratified sampling through Scikit-learn StratifiedKFold. This technique guarantees that each data fold preserves the same class distribution as the original dataset. In addition, to further analyze how the class imbalance affects the performance of our method, we performed a random undersampling of the datasets. This technique allowed us to create modified datasets where each class is evenly represented. The performances in these balanced datasets were compared with those obtained when using the original, imbalanced datasets.  
Finally, a Friedman statistical test [70] was performed further to explore the performance and impact of the proposed methods.
## 3 Challenges in Terahertz-Based FSO Communication
### Manufacturing Challenges in THz Communication
#### 3.6.1 High-Precision Fabrication and Nanometer-Scale Tolerances  
THz components, such as waveguides, antennas, and resonators, demand nanometer-scale precision due to their extremely short wavelengths (sub-millimeter range). Conventional microfabrication techniques, such as photolithography and electron beam lithography, face difficulties in maintaining the necessary precision and repeatability at THz frequencies. Moreover, surface roughness and material imperfections introduce significant scattering losses, degrading the overall system performance. The transition from silicon-based fabrication to novel nanomaterials like graphene, black phosphorus, and topological insulators could mitigate some of these issues, but introduces new manufacturing complexities and cost concerns [10].
## 6 Performance Evaluations
### Analysis of Results
Percentage of successfully transmitted packets. NUM_DRN_PER_DDN = 100.  
that as the failure rate of DRN nodes increases from 0.5 to 4.5 percent, the percentage of successfully transmitted packets decreases from 98.85 to 55.01 percent for the wired/wireless case, and from 42.36 percent to 9.33 percent in the wired-only case. First, the decrease of the percentage of successfully transmitted packets as the failure rate increases is reasonable and provides validation for the simulation. Additionally, the enhanced reliability and superior performance of the wired/wireless architecture is evident in the results. This is due to the fact that a failure in the wired-only architecture prevents messages from being forwarded past the failure point. However, the wired/wireless architecture allows nodes to overcome failures in the wired medium by using the alternative wireless link as a backup which ensures continued propagation of messages even though the propagation on that link is done at a lower rate. The data rates differ for different architectures. If we assume 1 Gbps for the wired transmission (fiber optic medium), 2 Mbps for the RF wireless transmission, and 4,800 bps for underwater acoustic wireless transmission are used. Then the data rate is 1 Gbps for underwater wired sensor network without faults and it drops to 0 if there is a fault. However, if we use integrated wired/acoustic wireless sensor network then the data rate is normally 1 Gbps and with a fault this will drop to only a maximum of 4,800 bps by relying on the acoustic nodes to relay the messages past the failure points. Similarly, if the integrated wired/RF wireless sensor network is used then the data rate will be 1 Gbps without faults and 2 Mbps with the faults.
## 4 Experimental Analysis
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Rescue Center (\(r\))** & **Rout** & \(t2_{k_{n}}\)**/min (\(E(\cdot)\).)**\(D(\cdot)\)** & \(R_{k_{n}}\) \\ \hline \multirow{4}{*}{2} & 2-12-17-22-1 & (9.9, 2.03) & 0.994 \\  & 2-9-11-10-16-21-1 & (11.95, 2.21) & 0.916 \\  & 2-9-11-10-16-21-1 & (11.7, 2.16) & 0.937 \\  & 2-12-17-16-21-1 & (11.6, 2.11) & 0.947 \\ \hline \multirow{4}{*}{3} & 3-32-25-22-1 & (7.2, 1.7) & 1 \\  & 3-32-31-30-1 & (7.55, 1.71) & 1 \\  & 3-33-26-23-22-1 & (9.85, 1.72) & 0.999 \\  & 3-33-26-25-22-1 & (9.8, 1.74) & 0.999 \\ \hline \multirow{4}{*}{4} & 4-28-20-21-1 & (9.05, 1.43) & 1 \\  & 4-28-29-30-1 & (9.5, 1.47) & 1 \\  & 4-37-38-39-29-30-1 & (11.05, 1.64) & 0.992 \\ \cline{1-1}  & 4-37-38-28-20-21-1 & (11.4, 1.64) & 0.986 \\ \hline \multirow{4}{*}{7} & 7-26-25-22-1 & (8.65, 1.98) & 0.999 \\  & 7-24-23-22-1 & (8.7, 1.96) & 0.999 \\ \cline{1-1}  & 7-26-25-32-31-30-1 & (11.1, 2.29) & 0.956 \\ \cline{1-1}  & 7-35-34-33-32-25-22-1 & (11.65, 2.4) & 0.919 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Feasible routes and their reliability for rescue resource 2. Based on the rescue route set obtained by the first stage, the NSGA-II algorithm is used to determine the scheduling of rescue resources for each rescue center in the second stage. The size of population is 20, the maximum number of iterations is 100, the crossover probability is \(P_{c}=0.5\) and the mutation probability is \(P_{m}=0.3\). Similarly, the algorithm is executed 10 times in this stage, with an average runtime of about 5 s. The Pareto solutions are shown in Figure 8. In the obtained Pareto solution set, two schemes with the minimum expected total travel time (Scheme 1) and the maximum total reliability (Scheme 7) are selected for analysis, and the results of rescue resource scheduling for the two schemes are shown in Table 12. The object values of Scheme 1 are 2943 and 386.84, and the object values of Scheme 7 are 3018.5 and 388.05. Compared with Scheme 1, the reliability of Scheme 7 is improved, but the total expected travel time increased. Rescue resource 1 of Scheme 7 needs to dispatch resources from three centers due to the capacity limitation of rescue center 4, while Scheme 1 only needs to dispatch resources from two centers. By using the method of information entropy, synthesized objective values can be obtained, and the synthesized objective values of Scheme 2 and Scheme 3 exceed 0.9. It can be observed that Scheme 2 is relatively better in two objectives (2945, 387.92), and the rescue resource scheduling of Scheme 2 is shown in Figure 9. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Rescue Center (\(r\))** & **Route** & \(t2_{k_{n}}\)**/min (\(E(\cdot)\),\(D(\cdot)\))** & \(R_{k_{n}}\) \\ \hline
2 & 2-12-17-22-1 & (7.4, 1.33) & 0.975 \\ \hline
6 & 6-10-16-21-1 & (7.35, 1.63) & 0.948 \\ \hline
7 & 7-26-25-22-1 & (6.65, 1.48) & 0.988 \\ \hline
7-24-23-22-1 & (6.7, 1.46) & 0.988 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Feasible routes and their reliability for rescue resource 4. Figure 8: The distribution of obtained Pareto solutions.
## 1 Introduction
In order to minimize energy consumption, we derive the optimal CH distance, which links to optimal energy consumption. The CCBE algorithm divides the entire sensor nodes in the network to different hexagonal clusters. The CMs of each hexagonal cluster elect a CH based on optimal CH distance and the residual energy of the nodes. The CMs of each cluster are given time slots based on their residual energy in order to increase the network lifetime and synchronize the sleeping period. Furthermore, the energy consumed for the transmission of larger packets is reduced by data aggregation in CHs. The data aggregation is achieved by the fusion of similar data. The decision to fuse data is based on the cost-aware decision scheme introduced in this paper. Additionally, the aggregation level of CH is based on the remaining energy. The remainder of the paper is organized as follows. In Section 2, we continue with related work. Section 3 shows the energy consumption model. In Section 4, we derive the optimal CH distance. In Section 5, we propose the new scheme CCBE. Section 6 shows the performance of the proposed scheme, and we provide conclusions in Section 7.
# Adaptive DCS-SOMP for Localization Parameter Estimation in 5G Networks
## 4 Proposed Method
### DCS-SOMP Approach for 3D Parameter Estimation  
The DCS-SOMP method determines the index \(\tilde{h}_{l}\) of the maximum correlation between (4) and (7). Therefore, for the \(l\)-th path, \(\tilde{h}_{l}\) is defined as follows:  
\[\tilde{h}_{l}=\underset{m=1,...,(q_{L}\
eq q_{L})^{2}}{\text{argmax}}\sum_{n=1} ^{N}\frac{|\mathbf{\omega}_{m}^{\text{H}}[n]\mathbf{R}_{l}[n]|}{\|\mathbf{\omega}_{m}[ n]\|_{2}}, \tag{8}\]  
where \(\mathbf{R}_{l}\) represents the received signal's residue and \(m\) represents each column in \(\mathbf{\omega}\). \(\mathbf{R}_{l}=\mathbf{y}\) when \(l=1\).  
The index \(\tilde{h}_{l}\) is converted into a combination of \((\phi_{l}^{az},\phi_{l}^{el})\) and \((\theta_{l}^{az},\theta_{l}^{el})\). The 2D-AoD \((\phi_{l}^{az},\phi_{l}^{el})\) is determined as follows:  
\[l_{\phi}^{l}=\frac{\tilde{h}_{l}}{q_{az}q_{el}},\quad q_{l}^{az}=\left\lfloor \frac{l_{\phi}^{l}}{q_{az}}\right\rfloor,\quad\ell_{l}^{el}=l_{\phi}^{l}\bmod q _{el}, \tag{9}\]  
\[\phi_{l}^{az}=\tilde{\mathbf{\phi}}_{l_{l}^{az}}^{(0)},\quad\phi_{l}^{el}=\tilde{ \mathbf{\phi}}_{l_{l}^{el}}^{(0)}. \tag{10}\]  
Similarly, the 2D-AoA \((\theta_{l}^{az},\theta_{l}^{el})\) is determined as follows:  
\[l_{\theta}^{l}=\tilde{h}_{l}-l_{\phi}^{l}q_{az}q_{el},\quad\gamma_{l}^{az}= \left\lfloor\frac{l_{\theta}^{l}}{q_{az}}\right\rfloor,\quad\gamma_{l}^{el}= l_{\theta}^{l}\bmod q_{el}, \tag{11}\]  
\[\theta_{l}^{az}=\tilde{\mathbf{\theta}}_{\gamma_{l}^{az}}^{(0)},\quad\phi_{l}^{el} =\tilde{\mathbf{\theta}}_{\gamma_{l}^{el}}^{(0)}. \tag{12}\]  
Finally, the DCS-SOMP method updates the residual for the \(n\)-th subcarrier as follows:  
\[\beta_{l}[n]=\frac{\mathbf{\omega}_{h_{l}}^{\text{H}}[n]\mathbf{R}_{l}[n]}{\|\bm {\omega}_{h_{l}}^{\text{H}}[n]\|_{2}^{2}}, \tag{13}\]  
\[\mathbf{R}_{l+1}[n]=\mathbf{R}_{l}[n]-\beta_{l}[n]\mathbf{\omega}_{h_{l}}[n]. \tag{14}\]  
Similar to [5], the estimation of ToA provides a maximum distance of \(NT_{s}c\) (m). Therefore, ToA can be estimated as follows:  
\[\text{distance}=\frac{1}{N}\Bigg{[}\sum_{n=1}^{N}\beta_{l}[n]\Bigg{]}NT_{s} \frac{c}{2\pi}, \tag{15}\]  
\[\tau_{l}=\begin{cases}\text{distance}/c\,,\,\text{if distance}\,\,\geq 0\\ (\text{distance}+NT_{s}c)/c\,,\,\text{if distance}<0,\end{cases} \tag{16}\]  
Figure 2: Comparison between DCS-SOMP and Adaptive DCS-SOMP: (**a**) Variation in Sensing Matrix Size (Number of Elements) and (**b**) Execution Time, both regarding the number of samples.  
where \(c\) is the speed of light.
# A Comparative Study of 3D UE Positioning in 5G New Radio with a Single Station
## 5 Conclusions  
In this paper, the subspace- and EM-based signal station 3D UE positioning methods in the 5G network are proposed. The positioning function is facilitated by the uplink SRS emitted by the UE and by the antenna array-equipped 5G base station. The 3D positioning performances of both algorithms are investigated under various SNRs, array configurations, channel bandwidths, and multipath scenarios. The simulation results show that both the subspace- and EM-based methods are able to accurately estimate the azimuth/elevation angles and time delay with the 3D signal manifold. We also note that the EM-based method outperforms the subspace-based method in the low SNR region in both the estimation error and resolution. Moreover, the EM-based approach presents the advantage of a lower computational resource cost than the subspace-based approach. Both proposed methods show the capability of achieving different positioning resolutions and accuracy levels by using a flexible signal bandwidth and subcarrier spacing, which is provided by the 5G NR for the different application scenarios. In addition, the orthogonality of the SRSs from different UEs provides excellent conditions for both positioning approaches to detect, localize, and keep tracking a large number of UEs without mutual interference and performance loss. However, the multipath propagation, and especially the reflections close to the UEs, will deteriorate both the accuracy and the resolution performance. Therefore, our future work will focus on the environment-robust 3D positioning method in 5G networks, aiming at better multipath mitigation and better dealing with non-line-of-sight scenarios.  
Conceptualization, B.S. and B.T.; methodology, B.S., B.T., and W.W.; software, B.S.; validation, B.S. and W.W.; formal analysis, B.S., B.T., and W.W.; investigation, B.S., B.T., and W.W.; writing--original draft preparation, B.S., B.T., and W.W.; writing--review and editing, B.T. and E.S.L.; visualization, B.S.; supervision, B.T. and E.S.L.; project administration, B.T. and E.S.L.; funding acquisition, E.S.L. All authors read and agreed to the published version of the manuscript.  
This work was partly supported by the Academy of Finland, under the project ULTRA (328226, 328214). This research was also partly funded by the SESAR Joint Undertaking (SJU) in project NewSense (Evaluation of 5G Network and mmWave Radar Sensors to Enhance Surveillance of the Airport Surface), Grant Number 893917, within the framework of the European Union's Horizon 2020 research and innovation program. The opinions expressed herein reflect the authors' view only. Under no circumstances shall the SU be responsible for any use that may be made of the information contained herein.  
Not applicable.  
The authors declare no conflict of interest.
## 3 Methodology and Model
### IPSA-DV-Hop Algorithm
#### 3.1.3 Improved PSA Mechanism
Mapping this onto the feasible domain, where the desired population exists, can be obtained by Equation (29):  
\[X_{i}^{j}=a_{j}+P_{n}(i)\cdot\left(b_{j}-a_{j}\right) \tag{29}\]  
where \(b_{j}\) and \(a_{j}\) represent the upper and lower limits of the current dimension, respectively. The initial population, constructed using the set of good points, is more evenly distributed, which enhances diversity and accelerates the algorithm's convergence speed in the early stages. To prevent the algorithm from falling into the problem of local optima during later iterations, the Cauchy-Gaussian perturbation strategy is introduced into the position update formulas. The Cauchy distribution function has a smaller peak at the beginning but a longer distribution at the ends, allowing it to generate larger perturbations near the current individual and, thus, enabling it to escape local optima. This improves the ability to reach the global optimum. The Cauchy-Gaussian perturbation strategy is expressed in Equations (30) and (31). \[\mathcal{U}_{\text{best}}^{t}=X_{\text{best}}^{t}\cdot\left[1+\lambda_{1} \cdot Cauchy(0,\ \sigma^{2})+\lambda_{2}\cdot Gauss(0,\ \sigma^{2})\right] \tag{30}\]  
\[\sigma=\left\{ \begin{array}{ll}1&,\quad f_{\text{best}}<f_{i}\\ e^{\frac{f_{\text{best}}-f_{i}}{\left|\text{best}\right|}}&,\quad\text{ otherwise}\end{array} \right. \tag{31}\]  
where \(\mathcal{U}_{best}^{t}\) represents the position of the optimal individual after perturbation, and \(\sigma^{2}\) represents the standard deviation in the Cauchy-Gaussian disturbance strategy. \(Cauchy(0,\ \sigma^{2})\) and \(Gauss(0,\ \sigma^{2})\) are random variables following the Cauchy and Gaussian distributions, respectively. The dynamic parameters \(\lambda_{1}=1-t^{2}/T_{max}^{2}\) and \(\lambda_{2}=t^{2}/T_{max}^{2}\) adaptively adjust with the number of iterations.
## Appendix  
### Summary on Some Main Methods for the Determination of Weights  
In [6], the variation coefficient method was presented to compute the weight of the criteria as follows.  
Step 1 (Normalization). Each component of the evaluation matrix is normalized to a value in the interval \([0,1]\):  
\[\hat{x}_{ij}^{k}=\frac{\hat{x}_{ij}^{k}-x_{ij}^{k}}{\sum\limits_{i=1}^{n}x_{ij} ^{k}}. \tag{11}\]  
Step 2 (Averaging). For the \(j\)-th criterion, calculate the average value by:  
\[\overline{x_{j}^{k}}=\frac{1}{n}\sum\limits_{i=1}^{n}\hat{x}_{ij}^{k}. \tag{12}\]  
Step 3 (Deviation). For the \(j\)-th criterion, calculate the standard deviation by:  
\[\Theta(x_{j}^{k})=\sqrt{\frac{1}{n}\sum\limits_{i=1}^{n}\left(\hat{x}_{ij}^{k }-\overline{x_{j}^{k}}\right)^{2}}. \tag{13}\]  
Step 4 (Weights of criteria). For the \(j\)-th criterion, calculate the weights of criteria by:  
\[u_{j}^{k}=\delta_{j}^{k}/\sum\limits_{i=1}^{n}\delta_{j}^{k}, \tag{14}\]  
where:  
\[\delta_{j}^{k}=\Theta(x_{j}^{k})/\overline{x_{j}^{k}}. \tag{15}\]  
In [7], the entropy-based method was presented to choose the weights of criteria as follows.  
Step 1 (Normalization). Each component of the evaluation matrix is normalized by Equation (11).  
Step 2 (Computation of entropy). For the \(j\)-th criterion, calculate the entropy by:  
\[En_{j}^{k}=-\lambda\sum\limits_{i=1}^{n}\hat{x}_{ij}^{k}\log(\hat{x}_{ij}^{k}), \tag{16}\]  
where:  
\[\lambda=1/\log(m). \tag{17}\]  
Step 3 (Weights of criteria). For the \(j\)-th criterion, calculate the weights of criteria by:  
\[u_{j}^{k}=(1-En_{j}^{k})/\sum\limits_{j=1}^{m}(1-En_{j}^{k}) \tag{18}\]  
In [8], a distance-based method was presented to determine the criteria weights as follows.  
Step 1 (Normalization). Each component of the evaluation matrix is normalized by Equation (11).  
Step 2 (Classification of criteria). Denote \(J_{1}\) as the positive criteria (e.g., profit) and \(J_{2}\) as the negative criteria (e.g., cost). For the \(j\)-th criterion, compute its optimistic and pessimistic values by \(u^{+}=(u_{1}^{+},u_{2}^{+},\cdots,u_{m}^{+})\) and \(u^{-}=(u_{1}^{-},u_{2}^{-},\cdots,u_{m}^{-})\), where:\[u_{j}^{+k}=\left\{\begin{array}{ll}\max\limits_{1\leqslant i\leqslant n}\hat{x}_{ ij}^{k}&j\in(J_{1})\\ \min\limits_{1\leqslant i\leqslant n}\hat{x}_{ij}^{k}&j\in(J_{2})\end{array}\right. \tag{11}\]  
\[u_{j}^{-k}=\left\{\begin{array}{ll}\min\limits_{1\leqslant i\leqslant n} \hat{x}_{ij}^{k}&j\in(J_{1})\\ \max\limits_{1\leqslant i\leqslant n}\hat{x}_{ij}^{k}&j\in(J_{2})\end{array}\right. \tag{12}\]  
Step 3 (Computation of deviation). For the \(j\)-th criterion, calculate the deviation by:  
\[d_{j}^{+k}=\sqrt{\sum_{i=1}^{n}(\hat{x}_{ij}^{k}-u_{j}^{+k})}, \tag{13}\]  
\[d_{j}^{-k}=\sqrt{\sum_{i=1}^{n}(\hat{x}_{ij}^{k}-u_{j}^{-k})}. \tag{14}\]  
Step 4 (Weights of criteria). For the \(j\)-th criterion, calculate the weights of criteria by:  
\[u_{j}^{k}=\xi_{j}^{k}/\sum_{j=1}^{m}\xi_{j}^{k}, \tag{15}\]  
where:  
\[\xi_{j}^{k}=d_{j}^{+k}/(d_{j}^{+k}+d_{j}^{-k}). \tag{16}\]
## 1 Introduction
### FR3 Band: The Goldilocks Spectrum  
On the one-hand, FR1/sub-6 GHz frequency bands--the legacy spectrum--is simply not available for expanded growth. Indeed, the 100 MHz sub-band at 3.5 GHz was sold at an eye-popping USD 29B, clearly showing the demand from the wireless industry. However, all the money in the world cannot provide you with resources that do not exist. Given that mm-wave is unlikely to lead to practical systems in the near future, the industry is turning to a middle ground. This spectral middle ground lies in the FR3 band (6 GHz to 24 GHz), affectionately known as the _upper-mid band_ by industry players. In our recent work, we showed that the upper-mid band is not too low such that it is as overcrowded as the FR1 (legacy band) and is not too high that building practically scalable infrastructure is not currently viable. The FR3 band sits \"just right\" as it lies within a range that is favorable for scalable systems. Additionally, bandwidth is available in FR3 for the next-generation of wireless technology, provided that the tangled web of spectrum policy can be navigated [2].
# Differentially Private XGBoost Algorithm for Traceability of Rice Varieties
## 3 Methodology
### Privacy Computing  
Since the boosting algorithm needs to be calculated through multiple iterations, we need to calculate the cumulative value of the privacy budget through composition theorem.  
**Lemma 1** (Basic Composition [39]).: _Let a series of randomized algorithm \(\mathcal{M}_{i},i=1,\cdots,t\) satisfies \((\epsilon_{i},\delta_{i})\)-differential privacy. Then \(\mathcal{M}=\{\mathcal{M}_{1},\cdots,\mathcal{M}_{t}\}\) satisfies \((\sum_{i=1}^{t}\epsilon_{i},\sum_{i=1}^{t}\delta_{i})\)-differential privacy._  
According to the property of the Gaussian mechanism (see Equation (4)), we can calculate that the privacy budget provided by injecting Gaussian noise with scale parameter \(\sigma\) once is \(\epsilon=\sqrt{2 ln\Big{(}\frac{1.25}{\delta}\Big{)}\cdot\frac{\Delta_{2}}{ \sigma}}\). Then, according to the basic composition theorem, we can obtain the cumulative privacy budget during \(t\) iterations as  
\[\sum_{i=1}^{t}\sqrt{2 ln\Big{(}\frac{1.25}{\delta}\Big{)}}\cdot\frac{\Delta_{2} }{\sigma}. \tag{13}\]  
Figure 1: The schematic diagram of DP-XGBoost model. We inject Gaussian noise with \(\sigma_{G}\) and \(\sigma_{H}\) as scale into the first derivative (gradient) and the second derivative (Hessian) respectively to guarantee the ensemble tree model is protected by DP. Gradient and Hessian are applied to calculate the objective function, and the training process aims to minimize the objective function.  
Although the cumulative privacy budget in multiple iterations can be calculated through Equation (13). However, basic composition is usually not efficient, which means that we are likely to overestimate the cumulative privacy budget. Therefore, we introduce the advanced composition theorem, expecting to achieve a tighter privacy budget.  
**Lemma 2** (Advanced Composition [40]).: _Suppose \(\epsilon,\delta,\delta^{\prime}\geq 0\) and \(\mathcal{M}_{i},i=1,\cdots,t\) satisfies \((\epsilon,\delta)\)-differential privacy. Then \(\mathcal{M}=\{\mathcal{M}_{1},\cdots,\mathcal{M}_{t}\}\) satisfies \((\epsilon^{\prime},t\delta+\delta^{\prime})\)-differential privacy and_  
\[\epsilon^{\prime}=\sqrt{2 tln(2/\delta^{\prime})\epsilon}+t \epsilon(\epsilon^{\prime}-1). \tag{14}\]  
Similarly, we can also obtain the cumulative privacy budget during t iterations from Lemma 2 as  
\[\sqrt{2 tln(2/\delta^{\prime})\sqrt{2 ln\left(\frac{1.25}{\delta} \right)}\cdot\frac{\Delta_{2}}{\sigma}}+t\sqrt{2 ln\left(\frac{1.25}{\delta} \right)}\cdot\frac{\Delta_{2}}{\sigma}\left(e^{\sqrt{2 ln(1.25/\delta)}\cdot \frac{\Delta_{2}}{\sigma}}-1\right) \tag{15}\]  
Comparing with Equation (15), the advantages of the Equation (13) will continue to appear with the increase of iterations.