esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Background
### FEM Formulation and Setup  
In the Helmholtz equation, \(p\) stands for the acoustic pressure, \(\Delta\) for the Laplacian operator and \(k\) for the wave number.  
\[\Delta p(\mathbf{x})+k^{2}p(\mathbf{x})=0 \tag{5}\]  
According to the following equation, the normal derivative of the acoustic pressure \(p\) is associated with the normal fluid particle velocity \(u_{f}\):\[u_{f}(\mathbf{x})=\frac{1}{i\omega\rho_{f}}\frac{\partial p(\mathbf{x})}{\partial n (\mathbf{x})} \tag{6}\]  
In this equation, \(n(\mathbf{x})\) is the outward normal vector at a field point \(\mathbf{x}\) and \(\rho_{f}\) is the average density of the fluid.  
As a next step, a weak formulation with weighting function \(\chi(\mathbf{x})\) was used, and the equation is formed as follows [45]:  
\[\begin{array}{c}\int\limits_{\Omega}\chi(\mathbf{x})\left(\Delta p(\mathbf{x })+k^{2}p(\mathbf{x})\right)\mathrm{d}\Omega(\mathbf{x})\\ =\int\limits_{\Gamma}\chi(\mathbf{x})i\omega\rho_{f}u_{f}(\mathbf{x})\mathrm{d }\Gamma(\mathbf{x})+\int\limits_{\Omega}\left(\
abla\chi(\mathbf{x})\
abla p( \mathbf{x})-k^{2}\chi(\mathbf{x})p(\mathbf{x})\right)\mathrm{d}\Omega( \mathbf{x})=0\end{array} \tag{7}\]  
In this notation,\(\Omega\) and \(\Gamma\) are the domain and boundary, respectively. Therefore, the acoustic pressure and particle velocity are shown as follows [45]:  
\[\begin{array}{c}p(\mathbf{x})=\sum\limits_{n=1}^{N}\Phi_{n}(\mathbf{x})p_{n }\\ u_{f}(\mathbf{x})=\sum\limits_{n=1}^{N}\Phi_{n}(\mathbf{x})u_{n}\end{array} \tag{8}\]  
Finally,\(\Phi_{n}(\mathbf{x})\) is a basis function and \(p_{n}\) and \(u_{n}\) are the discrete acoustic pressure and fluid particle velocity at point \(\mathbf{x}\). Adding Equation (9) to Equation (8) [45]:  
\[\left(\mathbf{K}-\mathrm{i}k\mathbf{C}-k^{2}\mathbf{M}\right)\mathbf{p}= \mathbf{f} \tag{9}\]  
**K, C** and \(\mathbf{M}\) are the stiffness, damping and mass matrices. Vector \(\mathbf{f}\) accounts for the source and vector and \(\mathbf{p}\) accounts for the sound pressure values at the nodal locations.
## 6 Discussion
### System Design Evaluation and Future Challenges during Development Process
This would subject the inner core structure to chemical stress [38]. At low temperatures, the fluids inside could freeze, expand and damage the liner structures and films accordingly. An impairment of the structural behaviour and mechanical properties of the rigid liner structures can also be accompanied by a reduction of the in-service life of the acoustic liner or a significant disturbance of adjacent systems. A suitable integration of drainage solutions into the broadband effective acoustic liners has to be analysed in further studies. The vibration loads in aircraft engines can vary depending on the position of the system in the aircraft engine [37]. Accordingly, the excitation of the film structures by vibrations of adjacent systems and subsystems must be considered during the design phase. In order to fully exploit the broadband noise damping characteristics provided by the flexible film structures (also in different flight phases), an appropriate adaptation of the film dimensioning and the film's mechanical properties is indispensable. Likewise, there must be taken care not to negatively influence the adjacent systems by the vibration excitation of the acoustic liner. In addition, there is the possibility that sound reflections from the liner surface overlap with the sound waves of adjacent systems [37]. The resulting sound characteristics could lie outside the effective damping design range of the acoustic liners. An increased background noise and a higher excitation of other adjacent systems would be the result. To counteract this, the sound emission of adjacent systems should be included in the design process of the acoustic liners with flexible structures.
## 1 Introduction  
### Geodynamic and Volcanological Framework  
The Central American Volcanic Arc (CAVA) results from the subduction of Cocos and Nazca plates beneath the Caribbean (Figure 1), and extends nearly continuously from Guatem to Panama for more than 1500 km [1]. In contrast to the MORB-like oceanic crust (produced at the East Pacific Rise) that subducts underneath Guatem to north-western Costa Rica, the oceanic crust formed at the Cocos-Nazca spreading centre, overprinted by Galapagos Hotspot tracks dated 13-14.5 Ma offshore of Costa Rica, is thought to subduct beneath central Costa Rica and Panama [2; 3; 4].  
The age of the subducting Cocos lithosphere is about 26 Ma along most parts of the subduction zone, except along central Costa Rica, where it is 25 to 17 Ma. The Cocos Ridge, located off the coast of southern Costa Rica (Figure 1), divides the subducting lithosphere into two segments (Cocos and Nazca plates, N-S striking Panama Fracture Zone): the northern is old and cool, while the southern is young and warm [5]. The Cocos materials in the north-western part subduct at a rate of \(\sim\)80-90 mm/yr [6] and at a moderately steep angle (62.2\({}^{\circ}\)) beneath Nicaragua, at 56.9\({}^{\circ}\) beneath El Salvador and Guatem, and at 58.9\({}^{\circ}\) beneath Costa Rica [7; 8; 9]. In southern and Central Costa Rica, the volcanic arc becomes largely inactive at the Cordillera de Talamanca for \(\sim\)150 km [10]. Seismic data indicate that a slab window is present beneath southern Costa Rica and Panama, where adakites are erupted [4; 7]. This window would be compatible with the numerous hotspot tracks and fracture zones on the subducting Cocos and Nazca plates that clogged the subduction zone, triggered detachment of a major portion of the slab and made it relatively easy to tear.  
In Panama, the arc segment does not register volcanic activity, except for three volcanic centres that showed signs of eruptions in recent times: Baru, La Yeguada, and El Valle [11; 12; 13; 14; 15]. This arc segment results from the oblique angle subduction of the Nazca plate, which subducts beneath the Panama block at a rate of \(\sim\)40 mm/yr [6].  
According to [16; 17; 18; 19], crustal thickness decreases from Guatem (50-40 km) to Nicaragua (30 km), increases across Costa Rica (up to 45 km), and finally thins again in western and central Panama (\(\sim\)30 km).
# Prediction of Air Pollution Concentration Based on mRMR and Echo State Network
## 4 Results and Discussion
### Data Description  
This paper selects 8759 samples of hourly air pollution data from January to December 2016 in Haidian District, Beijing. The dataset is from the US Embassy (Harvard University Geographic Analysis Center Dataverse), including the average concentration of PM\({}_{2.5}\), PM\({}_{10}\), NO\({}_{2}\), CO, O\({}_{3}\), and SO\({}_{2}\) per hour, and hourly temperature (T), pressure (P), humidity (H), wind speed (WS) and wind direction (WD).  
Because PM\({}_{2.5}\) is a particulate matter that can enter the lungs, it has a great impact on human health and the quality of atmospheric environment. Therefore, predicting PM\({}_{2.5}\) concentration can not only make an estimate of environmental quality, but also have a greater impact on better environmental governance and human health. This paper uses five predictive indicators to evaluate the prediction results of PM\({}_{2.5}\) time series, namely root mean square error (RMSE), normalized root mean square error (NRMSE), mean absolute error (MAE), symmetric mean absolute percentage error (SMAPE) and Pearson correlation coefficient (R).  
\[\text{RMSE}=\sqrt{\frac{1}{N}\underset{t=1}{\overset{N}{\sum}}[\hat{y}(t)-y(t) ]^{2}} \tag{12}\]  
\[\text{NRMSE}=\frac{1}{\overset{N}{\underset{g\text{max}}{-}}\overset{N}{\underset {g\text{min}}{\sqrt{\frac{1}{N}\underset{t=1}{\overset{N}{\sum}}[\hat{y}(t)-y( t)]^{2}}}}} \tag{13}\]  
\[\text{MAE}=\frac{1}{N}\underset{t=1}{\overset{N}{\underset{t=1}{\overset{N}{ \sum}}}[\hat{y}(t)-y(t)]} \tag{14}\]  
\[\text{SMAPE}=\frac{1}{N}\underset{t=1}{\overset{N}{\underset{t=1}{\overset{N} {\sum}}}\frac{\left|y(t)-\hat{y}(t)\right|}{\left(\left|\hat{y}(t)\right|+ \left|y(t)\right|\right)/2}} \tag{15}\]  
\[\text{R}=\frac{\underset{t=1}{\overset{N}{\underset{t=1}{\overset{N}{\sum}} }}\left(y(t)-\overline{y}(t)\right)\left(\hat{y}(t)-\overline{\hat{y}}(t) \right)}{\sqrt{\underset{t=1}{\overset{N}{\underset{t=1}{\overset{N}{\sum}} }}\left(y(t)-\overline{y}(t)\right)^{2}\underset{t=1}{\overset{N}{\underset{ t=1}{\overset{N}{\sum}}}}\left(\hat{y}(t)-\overline{\hat{y}}(t)\right)^{2}}} \tag{16}\]  
where \(N\) is the number of samples, \(\hat{y}(t)\) is the predicted output, and \(y(t)\) is the target value.  
In the above evaluation indicators, the smaller the values of the estimated indicators of RMSE, NRMSE, MAE, and SMAPE are, the better the prediction results of the model are. R = 1 indicates that \(\hat{y}(t)\) and \(y(t)\) are linear correlation, and R = 0 indicates there is no correlation. When R \(\in(0,1)\), it indicates that there is a correlation, and the larger value is, the stronger the linear correlation is.
# A Semantic Segmentation Algorithm Using FCN with Combination of BSLIC
## 5 Conclusions  
In this paper, an improved image semantic segmentation algorithm is proposed. The BSLIC superpixel edge information is combined with the original FCN model, where superpixel semantic annotation is applied to the combination process. The superpixel semantic annotation is abiding by four criteria, so that the detailed structures of an object can be kept to some extent. The four criteria cover every situation of superpixel semantic annotation process and give each one a solution to acquire a clearer edge of the target. The algorithm not only inherits the high-level feature extraction ability of the FCN model, but it also takes full advantages of the low-level features that are extracted by BSLIC. Compared with the FCN semantic segmentation model, the pixel accuracy of the proposed algorithm on PASCAL VOC 2012 dataset is 77.14%, which is 3.86%, 1.41%, and 1.28% higher than that of FCN-32s, FCN-16s, and FCN-8s, respectively. The experiment results prove that our method is available and effective. The proposed method combines FCN with BSLIC by using the four criteria, and the introduction of other modules might provide optimized solution to extent the application.  
[PERSON] and [PERSON] conceived and designed the experiments; [PERSON] performed the experiments; [PERSON] and [PERSON] analyzed the data; [PERSON] contributed analysis tools; and [PERSON] and [PERSON] wrote the paper.  
**Conflicts of Interest:** The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Compare 1** & **Compare 2** & **Compare 3** \\ \hline
**Method** & **Ours** & **FCN-32s** & **Ours** & **FCN-16s** & **Ours** & **FCN-8s** \\ \hline
**Advantage Category** & 20 & 1 & 15 & 6 & 16 & 5 \\
**Increased Ratio** & 95.24\% (20/21) & & 71.43\% (15/21) & & 76.19\% (16/21) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Pair-wise comparison of IoU score.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Metric** & **mIoU** & **PA** \\ \hline
**FCN-32s** & 59.4 & 73.27 \\
**FCN-16s** & 62.3 & 75.73 \\
**FCN-8s** & 62.6 & 75.85 \\
**Ours** & 62.8 * & 77.14 * \\
**SegNet** & 59.9 & - \\
**UNIST\_GDN\_FCN** & 62.2 & - \\ \hline \hline \end{tabular}  
* Means the best score in a metric.  
\end{table}
Table 5: The mean intersection over union (mIoU) and pixel accuracy (PA) scores of all the methods.
## 3 Results
### Crop Level, Thinning Performance and Grape Juice Composition
#### 3.6.2 Grape Juice Composition
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Treatment**} & \multicolumn{4}{c}{\(p\)**-Values**} \\ \hline
**Parameter** & **VSP** & **SMPH** & **SMPH GA** & **SMPH BT** & **SMPH ST** & **Vintage** & **Treatment** & **Vintage** \\ \hline
**Yield [\(\mathbf{h}\) ha\({}^{-1}\)]** & 13.82 \(\mathbf{c}\)\(\mathbf{c}\)\(\mathbf{+}\) 4.25 & 22.27 \(\mathbf{a}\)\(\mathbf{+}\) 4.60 & 18.19 \(\mathbf{b}\)\(\mathbf{+}\) 6.24 & 13.96 \(\mathbf{c}\)\(\mathbf{+}\) 2.80 & 14.89 \(\mathbf{c}\)\(\mathbf{+}\) 5.22 & \(p\)\(<\) 0.001 & \(p\)\(<\) 0.001 & \(p\)\(<\) 0.001 \\ \hline
**Yield per vine** [kg] & 3.32 \(\mathbf{c}\)\(\mathbf{+}\) 1.02 & 5.34 \(\mathbf{a}\)\(\mathbf{+}\) 1.10 & 4.37 \(\mathbf{b}\)\(\mathbf{+}\) 1.50 & 3.35 \(\mathbf{c}\)\(\mathbf{+}\) 0.67 & 3.57 \(\mathbf{c}\)\(\mathbf{+}\) 1.25 & \(p\)\(<\) 0.001 & \(p\)\(<\) 0.001 & \(p\)\(<\) 0.001 \\ \hline
**Total soluble solids [\(\mathbf{b}\) Bra]** & 21.56 \(\mathbf{+}\) 1.33 & 20.48 \(\mathbf{+}\) 0.81 & 21.02 \(\mathbf{+}\) 0.55 & 21.57 \(\mathbf{+}\) 1.05 & 21.16 \(\mathbf{+}\) 1.32 & \(p\)\(=\) 0.001 & \(p\)\(=\) 0.295 & \(p\)\(=\) 0.011 \\ \hline
**Reducing sugars [\(\mathbf{g}\) L\({}^{-1}\)]** & 210.31 \(\mathbf{+}\) 15.72 & 198.02 \(\mathbf{+}\) 8.57 & 204.44 \(\mathbf{+}\) 5.99 & 210.86 \(\mathbf{+}\) 11.61 & 206.06 \(\mathbf{+}\) 14.97 & \(p\)\(=\) 0.002 & \(p\)\(=\) 0.263 & \(p\)\(=\) 0.008 \\ \hline
**Extract [\(\mathbf{g}\) L\({}^{-1}\)]** & 234.23 \(\mathbf{+}\) 15.38 & 221.76 \(\mathbf{+}\) 9.43 & 227.98 \(\mathbf{+}\) 6.30 & 234.37 \(\mathbf{+}\) 12.11 & 229.59 \(\mathbf{+}\) 15.25 & \(p\)\(=\) 0.001 & \(p\)\(=\) 0.295 & \(p\)\(=\) 0.011 \\ \hline
**Total acidity [\(\mathbf{g}\) L\({}^{-1}\)]** & 12.43 \(\mathbf{+}\) 3.55 & 10.53 \(\mathbf{+}\) 2.53 & 10.64 \(\mathbf{+}\) 2.99 & 9.68 \(\mathbf{+}\) 2.75 & 10.27 \(\mathbf{+}\) 2.92 & \(p\)\(<\) 0.001 & \(p\)\(=\) 0.491 & \(p\)\(=\) 0.999 \\ \hline
**Taratic acid** [\(\mathbf{g}\) L\({}^{-1}\)]** & 6.49 \(\mathbf{a}\)\(\mathbf{+}\) 1.94 & 6.11 \(\mathbf{b}\)\(\mathbf{+}\) 1.13 & 5.85 \(\mathbf{c}\)\(\mathbf{+}\) 1.28 & 5.78 \(\mathbf{c}\)\(\mathbf{+}\) 1.04 & 5.98 \(\mathbf{b}\)\(\mathbf{+}\) 1.18 & \(p\)\(<\) 0.001 & \(p\)\(<\) 0.001 & \(p\)\(<\) 0.001 \\ \hline
**Malic acid [\(\mathbf{g}\) L\({}^{-1}\)]** & 6.38 \(\mathbf{+}\) 2.30 & 5.02 \(\mathbf{+}\) 2.08 & 5.33 \(\mathbf{+}\) 2.19 & 4.61 \(\mathbf{+}\) 2.03 & 4.99 \(\mathbf{+}\) 2.22 & \(p\)\(<\) 0.001 & \(p\)\(=\) 0.298 & \(p\)\(=\) 0.9996 \\ \hline
**Taratic acid [\(\mathbf{g}\) L\({}^{-1}\)]** & 1.09 \(\mathbf{+}\) 0.29 & 1.42 \(\mathbf{+}\) 0.68 & 1.24 \(\mathbf{+}\) 0.48 & 1.47 \(\mathbf{+}\) 0.64 & 1.41 \(\mathbf{+}\) 0.66 & \(p\)\(<\) 0.001 & \(p\)\(<\) 0.533 & \(p\)\(<\) 0.576 \\ \hline
**TSS to TA ratio** & 1.90 \(\mathbf{d}\)\(\mathbf{+}\) 0.66 & 2.03 \(\
## 3 Results
### Microbial Community Structure
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Tassis**} & \multicolumn{2}{c}{**Nitrifters**} & \multicolumn{2}{c}{**Methantotrophs**} & \multicolumn{2}{c}{**Methanogens**} & \multicolumn{2}{c}{**Dentifirters**} & \multicolumn{2}{c}{**Costifidaeaceae**} \\ \cline{2-11}  & **Material** & **Archael** & **Archael** & & & & & & **Cluster 1 and II** & **Cluster IV** \\  & _amoA_ & _amoA_ & _pmoA_ & _mccA_ & _nirK_ & _nirS_ & _nosZ_ & _165 \(\sigma\)DNA_ & 165 \(\sigma\)DNA_ & 165 \(\sigma\)DNA_ \\ \hline Control & 1.0 (0.15) ab & 1.1 (0.44) & 1.0 (0.03) a & 1.0 (0.10) b & 1.0 (0.14) b & 1.0 (0.08) & 1.0 (0.11) ab & 0.9 (0.05) bc & 1.0 (0.16) d \\ Dig1 & 0.8 (0.09) b & 2.0 (0.28) & 0.9 (0.15) ab & 541. (6.55) a & 1.4 (0.07) ab & 1.1 (0.00) ab & 1.1 (0.00) ab & 4.1 (0.00) a & 2.1 (1.35) ab \\ Dig2 & 0.8 (0.25) b & 2.0 (0.70) & 0.8 (0.06) abc & 42.0 (13.3) a & 1.2 (0.14) ab & 1.2 (0.08) & 1.0 (0.03) ab & 2.5 (1.58) ab & 152.1 (1.57) bc \\ Bio2 & 0.8 (0.15) b & 2.5 (0.47) b & 0.6 (0.02) c & 1.8 (0.09) b & 1.2 (0.31) a & 1.1 (0.11) & 1.0 (0.10) ab & 0.2 (0.18) c & 3.0 (2.25) d \\ Bio10v & 1.2 (0.22) ab & 1.2 (0.64) b & 1.0 (0.03) a & 1.8 (0.30) b & 5.8 (0.02) b & 0.9 (0.02) b & 1.1 (0.005) ab & 0.1 (0.005) c & 2.4 (0.36) d \\ Dig1+b02v & 0.7 (0.08) b & 2.3 (0.29) & 0.8 (0.13) bc & 62.6 (0.70) a & 1.7 (0.74) ab & 1.1 (0.29) & 0.9 (0.08) b & 0.6 (0.50) bc & 18.1 (1.0) abc \\ Dig2+b02v & 1.5 (0.32) a & 1.5 (0.32) & 0.7 (0.00) bc & 642. (5.87) a & 2.2 (0.49) a & 1.2 (0.18) & 1.1 (0.06) ab & 0.1 (0.01) c & 2.2 (0.83) a \\ Dig1+b101v & 0.8 (0.12) b & 2.6 (1.40) b & 0.7 (0.07) bc & 50.2 (0.24) a & 1.1 (0.15) b & 0.9 (0.09) b & 1.0 (0.09) ab & 0.0 (0.00) c & 148.3 (.79) c \\ Dig2+b010v & 1.0 (0.19) b & 1.3 (0.15) b & 0.8 (0.00) abc & 51.8 (11.6) a & 1.4 (0.29) ab & 1.1 (0.13) & 1.2 (0.22) a & 0.3 (0.13) c & 14.4 (1.61) bc \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Relative abundance of the target microbial groups versus bacterial 165 rDNA (standard errors in parenthesis). Different letters indicate significant differences (Fisher’s least Significant Difference, LSD). Bio, biochar; Dig1, digestate from reactor 1; Dig2, digestate from reactor 2.
# Service Reliability Based on Fault Prediction and Container Migration in Edge Computing
## 5 Performance Evaluation
### Experimental Setup  
The network size was simulated as 500 m \(\times\) 500 m. Edge devices were evenly deployed in the geographic area, and only one container was deployed on each edge device. The edge devices currently considered are all homogeneous; that is, the resources (CPU, memory, and storage size) of each device are identical. Simultaneously, the edge devices can communicate with each other, and container migration can be performed between any pair of edge devices. Different containers require different amounts of resources.  
For preprocessing data for failure prediction, we used the public dataset BigML, which contains 8784 machine data with a recording interval of one hour, where each piece of data contains 28 attributes. Simultaneously, to accurately predict failure and provide sufficient time for subsequent container migration, the average interpolation method was used to interpolate the data at one hour intervals. That is, the average value of two consecutive records was calculated, and this calculated value was inserted between the two consecutive records. Finally, the interval between every two records was set to 15 min. Thus, we used data from the first 45 min to predict the state of the subsequent 15 min. The BigML dataset is a label-imbalanced dataset, with 8703 data points labeled as non-failure and 81 data points labeled as failure. We adopted the SMOTE algorithm [32] to solve this data imbalance problem, thereby ensuring the effectiveness of fault prediction.
# Optimal Configuration and Path Planning for UAV Swarms Using a Novel Localization Approach
## 3 Optimal Configuration Analysis  
In this section, a theoretical analysis of optimal sensor-emitter geometry in TDOA localization is given without considering any constraints. Analytic solutions are derived in both the static and movable emitter scenarios.
# SnoreLab Application in the Assessment of Obstructive Sleep Apnea Syndrome: A Pilot Study
## 4 Discussion
### Limitations  
Certainly, the small sample size (\(n=19\)) limits the generalizability of these findings. In this pilot study, the primary focus remains the potential use of SnoreLab in detecting obstructive events. Despite the limited number of cases, it may be intriguing to conduct a gender analysis in subsequent research with a larger cohort. Furthermore, future investigations could explore using SnoreLab as a sleep diary, as suggested by [PERSON] et al. [7], to validate or refute their findings. Also, the proportion of snoring determined by PSG was not compared with other measures like p-flow, warranting further analysis. Correlating snoring patterns with varying degrees of OSA severity in a larger, more diverse sample would provide valuable insights for comparing severity groups effectively.  
In addition to the variables already considered, including factors such as the presence of sinus disease, allergies, the use of allergy medications or nasal sprays, and neck circumference would have provided a more comprehensive comparison between the PSG and the application. These additional variables could potentially influence the outcomes, and their absence may limit the scope of our findings. Future studies should consider incorporating these factors to enhance the robustness of the analysis.  
Additionally, the use of concomitant environmental noise trackers would be beneficial to further validate this technology. Incorporating such trackers could provide more comprehensive data on external noise influences, thereby enhancing the robustness and accuracy of our findings.
## 2 The Proposed Method
### Time-Frequency Compression Fusion  
#### 2.1.1 Time-Reassigned Multisynchrosqueezing Transform  
TMSST redistributes the coefficients of time-frequency points to the time position indicated by the group delay estimation value to complete asynchronous compression  
Figure 1: Overall model architecture.  
transformation and obtains a new time-frequency plane, on which time redistribution operation is repeated. The group delay estimation of the signal can be expressed as:  
\[\hat{t}(\tau,v)=j\frac{\partial_{v}TSTFT_{\delta}(\tau,v)}{TSTFT_{\delta}(\tau,v)} \tag{1}\]  
where \(\tau\) stands for time shift factor and \(v\) for frequency shift factor, when the signal does not satisfy the ideal pulse signal, there is some error between the group delay estimation and the real-time calculated by Equation (1). Fortunately, it has been shown in the literature [12] that this error can be reduced by finding a new group delay on the assumption of the original \(\hat{t}(\tau,v)\) into \(\tau\).  
\[\left|\hat{t}(\hat{t}(\tau,v),v)-t\right|<\left|\hat{t}(\tau,v)-t\right| \tag{2}\]  
where \(t\) indicates the actual processing time of the signal, as \(\hat{t}(\hat{t}(\tau,v),v)\) is an iteration, this operation can be performed several times. As the number of iterations increases, the estimated group delay is closer to the actual processing time.  
\[\left|\hat{t}^{[N+1]}(\tau,v)-t\right|<\left|\hat{t}^{[N]}(\tau,v)-t\right| \tag{3}\]  
where \(N\) is a positive integer, indicating the number of iterations. \(\hat{t}^{[N]}(t,v)\) Indicates the group delay estimate obtained after N iterations of the time-frequency point. Specificly, \(\hat{t}^{[1]}(t,v)=\hat{t}(\tau,\hat{t}(\tau,v))\), \(\hat{t}^{[2]}(t,v)=\hat{t}(\tau,\hat{t}(\tau,\hat{t}(\tau,v)))\), \(\hat{t}^{[3]}(t,v)=\hat{t}(\tau,\hat{t}(\tau,\hat{t}(\tau,\hat{t}(\tau,v)))\), and so on, we get \(\hat{t}^{[N]}(t,v)\).  
After the new group delay estimation is obtained, the time-frequency coefficients of the traditional STFT can be redistributed, and the process can be expressed as:  
\[TMSST^{[N]}(\tau,v)=\int_{-\infty}^{+\infty}TSTFT(t,v)\delta(\tau-\hat{t}^{[N ]}(t,v))dt \tag{4}\]  
where \(TSTFT(t,v)\) is the traditional short-time Fourier transform of the model signal. \(TMSST^{[N]}(\tau,v)\) is the time-frequency representation of the final time redistribution N resynchronization compression transformation. The larger N is, the more compression times and the better energy concentration of the time-frequency image.
# Underlay Loosely Coupled Model for Public Safety Networks Based on Device-to-Device Communication
## 4 The D2D Loosely Coupled Model  
In the context of wireless communication based on handheld devices with limited autonomy, it is important to minimize the number of connections that should be handled by each pair. The computing power and energy consumption could then be optimized. Furthermore, when several paths are possible between group members, participant devices can receive many copies of the same packet. This requires an additional effort for packet cancellation, while D2D links can also be overloaded. Therefore, among the models proposed previously, the loosely coupled seems to be the most suitable by creating the minimum number of direct connections between participants.