esa-sceva/satcom-chunk-collection huggingface dataset:
## 4 Discussion
Other studies of ours imply that static guidance with trephine bur apicoectomy does provide a comparable accuracy to the accuracy of static guide-assisted implant placement documented in the literature [23; 32]. It is not unrealistic to assume that in practice, trephine apicoectomy with static guidance can achieve the accuracy needed for the high efficiency we observed; however, further investigation is clearly necessary. To have comparable results, our sample needed to reflect the incidence of SNCs described in the literature. According to [PERSON] [6], the incidence of SNCs in maxillary central incisors was 24%, 26% in lateral incisors, and 30% in amines. [PERSON] and colleagues detected comparable ratios of SNCs in their study: 46% of central incisors, 29% of lateral incisors, and 38% of amines [38]. [PERSON] and co-workers showed that SNCs were detectable in over 60% of the examined teeth [39]. In the present study, we found SNCs in 24.6% of the central incisors, 9.6% of the lateral incisors, and 20.6% of the amines. Interestingly, in our study, the incidence of SNCs was lower in the case of lateral incisors compared to the data reported in the literature [40; 41; 42]. This is a relative limitation of the study, resulting from the smaller number of lateral incisors in the original group of specimens. Thus, conclusions should not be generalized to this tooth type based on our results. The authors consider it an interesting finding that within the limitations of our study, the mean number of SNCs in canines (2.75 \(\pm\) 2.30) was higher than in central incisors (1.86 \(\pm\) 0.77) or lateral incisors (1.86 \(\pm\) 1.06). Furthermore, only in canines did we observe  
Figure 6: Residual SNCs as a result of operator error: the trephine was misaligned to the right, and this resulted in an asymmetric section. figures >4 SNCs (up to 8). Whether this finding indicates a unique characteristic of canines is too early to tell, as the (scarce) literature focusing on canine root canal anatomy concentrates almost exclusively on morphology, not the occurrence of SNCs in the apical area [43; 44]. Finally, readers are encouraged to interpret the outcomes of this study in light of its inherent strengths and limitations. To the best of our knowledge, this marks the first endeavor to assess the efficacy of trephine apicoectomy in terms of supernumerary canal (SNC) elimination. The significance of this inquiry is underscored by the procedure's increasing prevalence, despite a dearth of preclinical data substantiating its non-inferiority to the conventional approach. Another notable strength lies in this study's utilization of micro-CT, enabling the precise quantification of SNCs, including the smallest ones. However, it is essential to acknowledge that this study is fundamentally exploratory, characterized by a relatively modest sample size, which is a definite limitation. Additionally, this study's in vitro design curtails the direct transferability of results to clinical contexts.
## 3 Data and Methods
### Method  
#### 3.2.1 Region Selection  
A landslide is a downslope movement of rock or soil occurring on the surface of a rupture in which much of the material often moves as a coherent or semi-coherent mass with little internal deformation [39, 40]. Landslides triggered by the earthquake often showed the following characteristics on remote sensing images: vegetation was disturbed, the deposits could be clearly identified at the foot of the slope along roads or rivers, and the interrupted region showed a bright white or dark brown contrast compared with the surrounding slopes. Debris flow is a common type of fast-moving mass movement in which loose soil, rock, and sometimes organic matter combine with water to form a slurry that flows downslope [41]. Debris flows usually start on steep hills as liquefied shallow landslides, and continue flowing down and through channels, accumulating water, sand, mud, trees, and other material. When the flows reach canyon mouths or flatter ground, the debris spreads over a broad area [42]. On remote sensing images, debris flows are usually characterized as an obvious flow channel and forms a large alluvial fan at the foot of the slope (Figure 2b).  
After the earthquake, aftershocks and heavy rain led to thousands of secondary geologic hazards, including landslides, debris flows, and barrier lakes. To illustrate the changes representing environmental restoration and human settlement reconstruction, representative study areas were selected. In this study, we first used a visual interpretation method to select large-scale landslides by comparing a Landsat TM image from 2007 and airborne optical images from 2008 and finally selected 15 geologic hazard sites distributed throughout the severely damaged areas (red points in Figure 1) with high quality of minimal or no cloud contamination in most of the flight year above the site. Each hazard site contained several landslides, with the locations and attributes shown in Table 2. Then, the corresponding images covering every hazard site were selected from 2008, 2009, and 2011 airborne optical images. Because of the poor data quality of the images from 2009 of the No. 14 site and from 2008 of the No. 15 site,  
Figure 2: Airborne remote sensing images of Wenjiagou, Qingping Town, Mianzhu City (site No. 1) taken on 23 May 2008 (**a**) and 7 July 2011 (**b**).  
the analyses of these two sites' secondary geologic hazard development were based on images from 2008, 2010, and 2011 and from 2009, 2010, and 2011, respectively.
# Hybrid Representation of Sensor Data for the Classification of Driving Behaviour
## 2 Background
### RNNs
#### 2.2.2 GRUs  
GRUs are more efficient than LSTMs, since they have less parameters and no output gate. Each recurrent unit adaptively captures dependencies in different time scales. As is the case with LSTMs, GRUs have gating units that modulate the flow of information inside the unit, yet without separate memory cells. The activation of the GRU at time \(\mathbf{h_{t}^{j}}\) is a linear interpolation between the previous activation \(\mathbf{h_{t-1}^{j}}\) and the candidate activation \(\mathbf{\overset{-j}{h_{t}}}\):  
\[\mathbf{\overset{-j}{h_{t}}}+\left(1-z_{t}^{j}\right)\mathbf{h_{t-1}^{j}}+z_{t}^ {j}\mathbf{\overset{-j}{h_{t}}} \tag{10}\]  
where an update gate \(\mathbf{z_{t}^{j}}\) determined the extent of activation or content update. The update gate is computed by:  
\[\mathbf{z_{t}^{j}}=\sigma(\mathbf{W_{z}x_{t}}+\mathbf{U_{z}h_{t-1}})^{j} \tag{11}\]  
This process of deriving a linear sum between the existing state and the new state is similar to the process of LSTMs. However, GRUs do not have any control mechanism determining the extent of state exposure and expose the entire state each time.  
The candidate activation \(\mathbf{\overset{-j}{h_{t}}}\) is computed similarly to that of the traditional recurrent unit (Equation (3)) and [23]:  
\[\mathbf{\overset{-j}{h_{t}}}=\tanh(\mathbf{Wx_{t}}+\mathbf{U}(\mathbf{r_{t} }^{\circ}\mathbf{h_{t-1}}))^{j} \tag{12}\]  
where \(\mathbf{r_{t}}\) is a set of reset gates and \({}^{\circ}\) is element-wise multiplication. When off (\(\mathbf{r}\) close to 0), the reset gate effectively makes the unit act as if it is reading the first symbol of an input sequence, allowing it to forget the previously computed state. The reset gate \(\mathbf{r}\) is computed similarly to the update gate:  
\[\mathbf{r_{t}^{j}}=\sigma(\mathbf{W_{r}x_{t}}+\mathbf{U_{r}h_{t-1}})^{j} \tag{13}\]
# Precise Mission Process Control Based on a Novel Dual-Code Group Network Plan Diagram
## 5 Mission Process Control Strategy
### Control Strategy Solution
#### 5.2.4 Solving of Control Strategy
```
1:\(\text{Sale}(t_{c},m_{i}^{*},\hat{K}^{*}(t_{c}),N_{m_{i}^{*}}(t_{c}),\bar{\mathbf{u}}_{m _{i}^{*}}(t_{c}))\)
2:current control time \(t_{c}\)
3:mission \(m_{i}^{*}\)
4:critical path \(\mathbf{\hat{K}}^{*}(t_{c})\)
5:the demand \(N_{m_{i}^{*}}(t_{c})\) of mission \(m_{i}^{*}\)
6:control quantity \(\bar{\mathbf{u}}_{m_{i}^{*}}(t_{c})\)
7:the control quantity \(\mathbf{u}_{m_{i}^{*}}(t_{c})\) of satisfying the demand of mission \(m_{i}^{*}\)
8:Step1:judge recursion end conditions
9:if\(\mathbf{u}_{m_{i}^{*}}(t_{c})\) is None then
10:\(\bar{\mathbf{u}}_{m_{i}^{*}}(t_{c})\leftarrow\emptyset\)
11:if\(e_{m_{i}^{*}}(t_{c})\leq 0\)then
12:return\(\bar{\mathbf{u}}_{m_{i}^{*}}(t_{c})\)
13:create an empty set \(\mathbf{u}_{m_{i}^{*}}(t_{c})\) that stores all control quantities
14:endif
15:endif
16:Step2:forward sale
17:\(u_{m_{i}}(t_{c})\gets 0\)\(\triangleright\)\(u_{m_{i}}(t_{c})\) is the control quantity of mission \(m_{i}\)
18:for\(m_{j}\)in\(\mathcal{FM}_{m_{i}^{*}}\)do
19:\(N\gets N_{m_{i}^{*}}(t_{c})\)\(\triangleright\) record sale demand
20:if\(s_{m_{j}}(t_{c})=0\)then
21:if\(m_{j}\in\mathcal{K}^{*}(t_{c})\)then
22:if\(e_{m_{i}^{*}}(t_{c})>0\)then
23:\(u_{m_{k}}(t_{c})\leftarrow-e_{m_{i}^{*}}(t_{c})\)
24:add \(u_{m_{k}}(t_{c})\) to \(\bar{\mathbf{u}}_{m_{i}^{*}}(t_{c})\) and \(\mathbf{u}_{m_{i}^{*}}(t_{c})\), respectively
25:else
26:pass
27:endif
28:else
29:\(N_{m_{i}^{*}}(t_{c})\gets N_{m_{i}^{*}}(t_{c})-T_{PS}^{m_{j}}(t_{c})+T_{ PF}^{m_{i}^{*}}(t_{c})\)\(\triangleright\) the first reduction of demand \(N_{m_{i}^{*}}(t_{c})\)
30:if\(N_{m_{i}^{*}}(t_{c})>0\)then
31:if\(c_{m_{j}}=1\)then
32:\(u_{m_{k}}(t_{c})\leftarrow-\min(N_{m_{i}^{*}}(t_{c}),x_{m_{j}}(t_{c})-x_{m_{j }}^{\min})\)
33:add \(u_{m_{k}}(t_{c})\) to \(\bar{\mathbf{u}}_{m_{i}^{*}}(t_{c})\) and \(\mathbf{u}_{m_{i}^{*}}(t_{c})\), respectively
34:\(N_{m_{i}^{*}}(t_{c})\gets N_{m_{i}^{*}}(t_{c})-x_{m_{j}}(t_{c})+x_{m_{j}}^ {\min}\)\(\triangleright\) the second reduction of demand \(N_{m_{i}^{*}}(t_{c})\)\(\triangleright\)\(N_{m_{i}^{*}}(t_{c})\)
35:if\(N_{m_{i}^{*}}(t_{c})>0\)then
36:\(\mathbf{u}_{m_{j}}(t_{c})=\)Sale\((t_{c},m_{j},\hat{K}^{*}(t_{c}),N_{m_{i}^{*}}(t_{c}),\bar{\mathbf{u}}_{m_{i}^{*}}(t_{c}))\)\(\triangleright\) recursive call Algorithm 6
37:add \(\mathbf{u}_{m_{j}}(t_{c})\) to \(\mathbf{u}_{m_{i}^{*}}(t_{c})\)
38:endif
39:endif
40:endif
41:endif
42:endif
43:endfor
44:return\(\mathbf{u}_{m_{i}^{*}}(t_{c})\)
```  
**Algorithm 6** Sale Algorithm to calculate the control quantity
# Simulation Study of Dynamic Rotation and Deformation for Plasmonic Electric Field-Skyrmions
## Appendix A  
Skyrmion number \(S\) represents the topological properties of skyrmions. The calculation of skyrmions can be carried out by integrating the vectors that construct skyrmions. Here, we use the simplified expression in Equation (A1) of integration to characterize the topological properties of the initialized skyrmions obtained in our simulation experiments, as follows:  
\[\begin{split}& S=\frac{1}{4\pi\int}\int\frac{d\beta_{sp}(r_{s})}{d \tau_{s}}\frac{d\alpha_{sp}(\theta_{s})}{d\theta_{s}}\sin\beta_{sp}(r_{s})d\tau_ {s}d\theta_{s}\\ &=\frac{1}{4\pi}\int\limits_{0}^{\tau_{s}}dr_{s}d\theta_{s}\int \limits_{0}^{\pi}\frac{d\beta_{sp}(r_{s})}{d\tau_{s}}\frac{d\alpha_{sp}(\theta _{s})}{d\theta_{s}}\sin\beta_{sp}(r_{s})\\ &=\frac{1}{4\pi}\big{[}\cos\beta_{sp}(r_{s})\big{]}_{r_{s}=0}^{r_ {s}=r_{o}}\big{[}\alpha_{sp}(\theta_{s})\big{]}_{\theta_{s}=0}^{\theta_{s}=2 \pi}\\ &\quad-\frac{2\big{[}\cos\beta_{sp}(r_{s})\big{]}_{r_{s}=r_{o}}^{ \tau_{s}=r_{o}}=P}{\cdot}\\ &\quad-\frac{1}{2\pi}\big{[}\alpha_{sp}(\theta_{s})\big{]}_{ \theta_{s}=0}^{\theta_{s}=2\pi}=M\\ &=P\cdot M\end{split} \tag{10}\]  
The three-dimensional electric-field-vector diagram is shown in the top view in Figure 10. \(\theta_{s}\) and \(r_{s}\) are the angular coordinates and the radial coordinates of the electric-field-vector projection, respectively. The \(r_{o}\) is the radius of the skyrmion. The skyrmion is mapped to the unit spherical coordinate system [29], with polar coordinates of \(\alpha_{sp}(\theta_{s})=\theta_{s}\) and azimuthal coordinates of \(\beta_{sp}(r_{s})\). Therefore, Equation (10) indicates that the skyrmion number \(S\) can be regarded as the product of polarity \(P\) and vorticity \(M\)[31].  
We found that the initialized skyrmion has completed a polarity flip from \(0.5\pi\) to \(-0.5\pi\), the topological domain walls have not been broken, and the skyrmion number is 1. Certainly, as we undergo deformation, the topological number has been affected, and the topological properties of skyrmions were affected to some extent.
# Temperature Effects on Vibration-Based Damage Detection of a Reinforced Concrete Slab
## 5 Conclusions  
In this paper, a method that can distinguish natural frequencies changes due to normal temperature variations from abnormal damage is presented. Based on the vibration testing of a RC slab for one year, the relationship between temperature and test data was analyzed. The linear regressive and ARX models were established, and it was concluded that if the experimental natural frequency lies outside the confidence intervals, it was likely that the slab was damaged. Moreover, two simulated cases are constructed and PSO is adopted to identify the location and severity of the specified damage successfully.  
(1) The vibration testing of a laboratory simply supported RC slab has been performed for one year. During the period, temperatures and accelerations at different locations were monitored, and the variations of temperatures and natural frequencies were acquired. It was found that natural frequencies and damping ratios decrease with the increase of temperatures for the first four modes and there was no actual relation with MAC and temperature.  
(2) The mathematical derivation of a simply supported beam was performed and it was found that the influence of temperature dependence on the elastic modulus of concrete was the main reason for the change of natural frequencies. The relationship between the elastic modulus and the temperature was obtained by deducing the equation, and the specific parameters of the relationship between the temperature and the elastic modulus were obtained by analyzing the measured data.  
(3) The simple linear regressive model and the ARX model were constructed based on the vibration testing results, by analyzing the RMSE values of the model and measured data, it was found that the precision of the ARX model was better than that of the linear regressive model.  
(4) An objective statistical method based on ARX model was presented to detect and identify the location and severity of the simulated damage. A confidence interval was constructed to estimate the disturbance of natural frequencies due to temperature and two simulated damage cases were set up.  
Figure 17: Results of damage identification. (**a**) 5% uniform damage (20 \({}^{\circ}\)C). (**b**) 10% uniform damage (20 \({}^{\circ}\)C).  
PSO was adopted to identify the damage and validate the proposed model, and it was found that the method in this paper can distinguish the variations of natural frequencies due to normal temperature variations from those variations due to abnormal reasons such as structural damage.  
Conceptualization, software, validation, resources, data curation, writing-original draft preparation, must be acknowledged to [PERSON]. Methodology, formal analysis, project administration, funding acquisition, must be acknowledged to [PERSON]. Supervision must be acknowledged to [PERSON]. All authors have read and agreed to the published version of the manuscript.  
The authors declare that there are no conflicts of interest regarding the publication.
## 3 Materials and Methods
### Dual-Model Fine-Tuning Using Exponential Moving Average  
To further enhance segmentation quality, we introduce the twin model approach, as illustrated in Figure 3. Unlike a simple duplication of the pre-trained UNet++ model, the twin model utilizes a novel strategy where the model's weights are progressively refined using an exponential moving average (EMA) method [40]. Initially, the parameters of the pre-trained UNet++ model are copied to the twin model. During training, the twin model's parameters are updated using EMA, which improves the stability and accuracy of the final segmentation results.  
The EMA method refines the model by computing a moving average of the model weights, effectively smoothing the updates across iterations. This approach contrasts with directly using the most recent model weights, leading to more robust performance. The EMA update rule for model weight \(\theta\) at time step \(t\) is given by  
\[\
u_{t}=\alpha\
u_{t-1}+(1-\alpha)\theta_{t}\]  
where \(\
u_{t}\) is the EMA weight at time \(t\), \(\theta_{t}\) is the current model weight, and \(\alpha\) is the smoothing coefficient, i.e., a hyperparameter controlling the rate of averaging, set to 0.999 as default.  
For the final fine-tuning, we minimize the Mean Squared Error (MSE between the predictions of the original model \(f(x,\theta)\) and the twin model \(f(x,\
u)\), as formulated by  
\[G(\theta)=\mathbb{E}_{x}\left[\|f(x,\theta)-f(x,\
u)\|^{2}\right]\]  
This loss function encourages the twin model to learn from the averaged weights, ensuring that it converges towards more accurate segmentation over time. This method provides a  
Figure 3: Flow chart of learning using twin model.  
powerful mechanism for refining the segmentation outputs, enabling the twin model to outperform conventional single-model approaches in terms of both accuracy and stability.
## 3 Samples and Experimental Methods
### Trace Elements  
Trace elements (Co, Li, Ni, Ba, V, Th, Zr, Cr, U) in shale samples were analyzed using an Agilent 7900 Inductively Coupled Plasma Mass Spectrometer (ICP-MS) (Agilent Technologies, Santa Clara, CA, USA). The samples were initially dissolved with hydrofluoric and nitric acids in a closed dissolver. Hydrofluoric acid was evaporated using an electric hot plate, and the residue was then re-dissolved in nitric acid under sealed conditions. After dilution, the samples were analyzed directly using the ICP-MS with an external standard method. Based on repeated measurements of the same sample, the standard deviation of the experimental results is 1%, and the error is 0.5%.
# Software Defined Networks in Wireless Sensor Architectures
## 3 Wireless Sensor Networks
### Wireless Sensor Networks Applicability
To start with, the preservation of machine health is an important task for which a WSN can help to gather data about the status of such machinery. It offers an important cost savings, and it enables new functionalities due to its ability to be set up in difficult or inaccessible places that a wired network could not offer. Moreover, WSNs are used for collecting environmental information such as the temperature of a fridge and the level of water in overflow tanks in nuclear power plants, among others. Next, monitoring the quality and level of water includes some tasks such as checking the quality of underground or surface water in order to protect the wastage of water. Finally, a WSN can be used to monitor the conditions of civil infrastructure and related geophysical processes in real time. Multimedia transmissions in WSNs include huge requirements of bandwidth, power consumption, QoS, treatment of gathered data, and routing protocols [53], among others. When a user is required to send a video, it needs an elevated bandwidth to be handled during the transmission. Consequently, this raised requirement is transformed into an increasing energy consumption. Some factors as delay and channel capacity, among others, directly affects the QoS of the network, and, therefore, the video delivery has to achieve a minimum level to ensure good reception of the video.
## 8 Targeting c-di-AMP PDEs  
Among the second messenger nucleotides, cyclic di-AMP (c-di-AMP) plays a crucial role in cell growth, survival, and virulence regulation, primarily in Gram-positive bacteria [79; 80; 81]. Its cellular levels are tightly controlled by two enzyme families: diadenylate cyclase (DACs), which synthesize c-di-AMP, and phosphodiesterases (PDEs), which degrade it.  
The first c-di-AMP hydrolyzing enzyme (PDE) was identified in Bacillus subtilis [82] and later found in Staphylococcus aureus [83], Listeria monocytogenes [84], and other Streptococcus species [85; 86]. PDE enzymes degrade c-di-AMP into phosphoadenyl adenosine (pApA), which is further broken down into AMP. There are four major classes of c-di-AMP PDEs which are GdpP, DhhP, PgpH and CdnP.
## 3 Results and Discussion
### Linear Discriminant Analysis  
Table 3 shows the confusion matrix in cross validation (Venetian blind, 5 segments) and the percentage of correct predictions for data set obtained by LDA are shown. The overall percentage of correct predictions in cross validation is 72%.  
By LDA it has been possible to point out the discreet separation between urban-industrial and port prevalent wind directions macroareas, that by PCA was just hinted. It is possible to observe that the model assigned samples to the category represented by Urban-Industrial with good percentage of correct predictions (61%), but it assigned samples  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **PC1** & **PC2** & **PC3** & **PC4** & **PC5** & **PC6** & **PC7** \\ \hline Fe & **0.47** & 0.03 & \(-\)0.11 & 0.08 & 0.01 & \(-\)0.01 & 0.06 \\ V & **0.43** & 0.02 & 0.21 & 0.01 & \(-\)0.15 & \(-\)0.09 & \(-\)0.02 \\ Ni & **0.38** & \(-\)0.09 & 0.04 & 0.06 & 0.10 & 0.00 & \(-\)0.32 \\ Cu & 0.10 & \(-\)0.10 & \(-\)0.03 & **0.62** & 0.08 & 0.02 & \(-\)0.15 \\ Pb & \(-\)0.06 & \(-\)0.08 & \(-\)0.01 & \(-\)0.20 & 0.06 & 0.03 & **0.71** \\ Cd & 0.11 & 0.02 & 0.12 & 0.17 & 0.03 & \(-\)0.02 & **0.44** \\ Mn & **0.44** & 0.04 & \(-\)0.01 & \(-\)0.08 & 0.06 & 0.06 & 0.06 \\ OC & 0.17 & \(-\)0.06 & \(-\)0.07 & 0.04 & **0.41** & 0.10 & 0.09 \\ EC & 0.21 & \(-\)0.07 & \(-\)0.16 & **0.38** & 0.02 & \(-\)0.03 & **0.33** \\ Cl\(-\) & \(-\)0.14 & **0.51** & \(-\)0.10 & 0.19 & 0.02 & \(-\)0.04 & 0.03 \\ NO3\(-\) & \(-\)0.24 & 0.20 & 0.14 & **0.55** & \(-\)0.13 & 0.02 & 0.11 \\ SO4\(-\) & 0.04 & 0.02 & **0.64** & \(-\)0.06 & 0.06 & 0.00 & 0.02 \\ Na+ & 0.07 & **0.65** & 0.00 & \(-\)0.09 & 0.04 & \(-\)0.10 & \(-\)0.04 \\ NH4+ & \(-\)0.04 & \(-\)0.06 & **0.66** & 0.07 & \(-\)0.03 & 0.01 & 0.03 \\ K+ & 0.03 & 0.16 & 0.04 & \(-\)0.12 & **0.54** & \(-\)0.07 & 0.09 \\ Mg2+ & 0.16 & **0.46** & 0.07 & \(-\)0.09 & \(-\)0.04 & 0.25 & \(-\)0.04 \\ Ca2+ & 0.03 & 0.04 & \(-\)0.01 & 0.01 & 0.09 & **0.62** & 0.04 \\ WSOC & \(-\)0.20 & \(-\)0.07 & 0.07 & 0.11 & **0.68** & \(-\)0.01 & \(-\)0.16 \\ WSIC & \(-\)0.06 & \(-\)0.05 & 0.00 & 0.01 & \(-\)0.08 & **0.71** & \(-\)0.04 \\ Explained Variance (\%) & **28.7** & **16.5** & **10.3** & **8.3** & **6.9** & **5.3** & **4.9** \\ \hline \hline \end{tabular}
\end{table}
Table 2: Principal Component Analysis (PCA) Loading values. Values larger than 0.23 are highlighted in bold.  
to the category represented by Port with a high percentage of correct predictions, that is 83%: in fact, in this case, only 10 samples have been mispredicted on 58.
## 3 System Model and Problem Formulation  
### System Model  
As shown in Figure 1, a UAV swarm ad hoc network formed of a large number of drones is considered, where \(S\) unmanned aerial vehicles (UAVs) are randomly distributed in the task area. Let \(\mathcal{N}=\{1,2,\ldots,N\}\) represent the index set of the UAVs in the flying ad hoc network scenario as a drone formation. In the UAV ad hoc network, there is no center node and no cluster node, and every node has equal status. Each UAV is equipped with one omnidirectional antenna. All nodes work on the same frequency point, and TDMA mechanisms are adapted in the mac protocol of all UAVs for sharing the frequency point. Each node works in the time division duplex (TDD) mode, which transmits or receives packets at one slot only. There is one channel and there are \(N\) slots available for the multi-UAV network. The set of available time slots is denoted by \(\mathcal{T}=\{1,2,\ldots,N\}\).