esa-sceva/satcom-chunk-collection huggingface dataset:
## 4 Optimization Model
### Uniform Deployment Optimization  
For a uniform deployment scheme, the value of \(n_{i,j}\) is a constant. Full coverage of the target area is required before the deployment is initialized. If all sensors in some grid of the network are out of energy, the coverage requirement will not be satisfied. The problem of finding an optimal \(d\) that maximizes the WSN's lifetime where only one sensor is located at each grid, subject to the coverage, connectivity and success transmission rate constraints, can be formulated as  
\[\begin{array}{l}\max\quad\min_{i=1}^{L}\left(\min_{j=1}^{6i}\frac{E_{0}}{E_{ i,j}}\right)t\\ \mathrm{subject\ to}\qquad\qquad\qquad S>S^{*},\\ \qquad\qquad\qquad\qquad\qquad\qquad R_{s}<d\leq\sqrt{3}R_{s},\\ \qquad\qquad\qquad\frac{\sqrt{3}}{3}R_{t}<d\leq R_{t},\end{array} \tag{7}\]  
where \(S^{*}\) is the requirement of the success transmission rate. In Equation (2), \(S>S^{*}\) requires that the success transmission rate for the whole network is at least \(S^{*}\), \(d>R_{s}\) is the assumption for PEAS (see Equation (2)), \(d\leq\sqrt{3}R_{s}\) is the requirement of the full coverage for the target area (see Equation (2)), \(d>\frac{\sqrt{3}}{3}R_{t}\) is the assumption that data transmission is constrained between neighboring sensors (see Equation (11)), and \(d\leq R_{t}\) is the requirement of the connectivity between the locations of neighboring sensors (see Equation (12)).  
This model is a nonlinear programming problem, which can be solved by the generalized reduced gradient method. If the lifetime requirement of the WSN is specified as \(\tau^{*}\), the minimal number of sensors at location \((i,j)\) can be calculated as  
\[n_{i,j}=\lceil\frac{\tau^{*}}{\tau}\rceil, \tag{8}\]  
where \(\tau\) is the optimal lifetime. The minimal total number of sensors is  
\[N=3L(L+1)\lceil\frac{\tau^{*}}{\tau}\rceil, \tag{9}\]  
where \(L\) is the number of layers.
## 3 Controller Design  
### Anti-Saturation Controller Design Based on Finite-Time Stabilization  
Define the error of the system as follows:  
\[\mathbf{e}_{1}=\mathbf{x}_{1}-\mathbf{x}_{1d}-\mathbf{\lambda}_{1} \tag{10}\]\[\mathbf{e}_{2}=\mathbf{x}_{2}-\mathbf{x}_{2d}-\mathbf{\lambda}_{2} \tag{11}\]  
where \(\mathbf{e}_{1}= \begin{bmatrix}e_{1,\phi}&e_{1,\theta}&e_{1,\phi}\end{bmatrix} ^{T}\) corresponds to the angle error of the attitude, \(\mathbf{e}_{2}= \begin{bmatrix}e_{2,p}&e_{2,q}&e_{2,r}\end{bmatrix} ^{T}\) corresponds to the velocity error of the angle, and \(\mathbf{x}_{1d}\in R^{3}\) and \(\mathbf{x}_{2d}\in R^{3}\) denote the desired attitude angle and the desired angular velocity of the air-frame. \(\mathbf{\lambda}_{1}= \begin{bmatrix}\lambda_{1,\phi},\lambda_{1,\theta}, \lambda_{1,\phi}\end{bmatrix} ^{T}\) and \(\mathbf{\lambda}_{2}= \begin{bmatrix}\lambda_{2,p},\lambda_{2,q},\lambda_{2,r }\end{bmatrix} ^{T}\) are the states of the anti-saturation auxiliary system. The anti-saturation auxiliary system in this paper is designed as follows:  
\[\dot{\mathbf{\lambda}}_{1}=-\mathbf{K}_{1}\mathbf{\lambda}_{1}-\mathbf{K}_{2 }|\mathbf{\lambda}_{1}|^{m/n}sign(\mathbf{e}_{1})+\mathbf{b}_{1}\mathbf{ \lambda}_{2} \tag{12}\]  
\[\dot{\mathbf{\lambda}}_{2}=-\mathbf{K}_{3}\mathbf{\lambda}_{2}-\mathbf{K}_{4 }|\mathbf{\lambda}_{2}|^{m/n}sign(\mathbf{e}_{2})+\mathbf{G}\Delta\mathbf{u} \tag{13}\]  
where \(\Delta\mathbf{u}=\mathbf{u}_{1}-\mathbf{u}\), \(\mathbf{u}\) is the output of the controller. \(m\) and \(n\) are both positive odd numbers, \(\mathbf{b}_{1}\in R^{3\times 3}\), \(\mathbf{K}_{1}\in R^{3\times 3}\), \(\mathbf{K}_{2}\in R^{3\times 3}\), \(\mathbf{K}_{3}\in R^{3\times 3}\), and \(\mathbf{K}_{4}\in R^{3\times 3}\) are both diagonal matrices, and the entries in the matrices are all positive constants. From Equations (12) and (13), it can be seen that the two auxiliary states of the anti-saturation auxiliary system can converge asymptotically to zero when \(\Delta\mathbf{u}=0\). Therefore, the anti-saturation system remains inactive in the absence of saturation events; and the two states of the anti-saturation auxiliary system will no longer be zero when \(\Delta\mathbf{u}\
eq 0\). The errors of the system are defined as Equations (10) and (11). In contrast to the common definitions of the errors, the errors of Equations (10) and (11) include the auxiliary system states. Therefore, when saturation occurs, the error will be adaptively adjusted to produce a slightly smaller error, based on which the controller produces a slightly smaller amount of control such that the control command exits the saturated region or is maintained in a shallow saturated region. This is the design idea and control method of the anti-saturation auxiliary system in this paper, and the overall stability of the system will be proved by Lyapunov stability.
# A Cross-Layer, Anomaly-Based IDS for WSN and MANET
## 1 Introduction
In stage two, the CCIs are sent to a fusion center (or supernode) that in turn applies an algorithm which calculates the AMoF for each sniffer's data related to the node under test (NUT). This is done by calculating the accumulated variation of CCIs using a sliding window approach. An iterative slope fitting is performed in conjunction with the AMoF calculation process to establish a detection threshold. In the CCI calculations, to be described in the sequel, the usage of higher variance for larger groups of random variables has been favored to using smaller groups in the same sample space. Figure 1: Simplified architecture of the proposed intrusion detection system (IDS). The C4.5 decision tree-based IDS is adopted due to its simplicity and reliability of performance [4; 5; 6; 7; 8; 9; 10]. An ensemble of decision trees, known as a random forest, is also adopted in this work due to its superior performance, especially when dealing with variability when compared to C4.5 decision trees. This point is very important, since we use the variation of the correctly classified instances (CCIs) as a major feature to differentiate between normal and malicious nodes. The random forest is considered to be one of the most effective data mining techniques [11]. A detailed comparison between different learning algorithms based on training time, computational complexity and resources consumption can be found in [12]. The data acquisition scheme used in the proposed IDS is based on promiscuous monitoring, and it relies on eavesdropping on the traffic activity of the neighboring nodes [13; 14]. Dedicated sniffers use the collected data which consists of packet traces from MAC and network layers to build a model for normal and abnormal behavior at the node level. This paper is divided into the following sections. Section 2 presents a brief introduction about the blackhole attack in MANET, while Section 3 presents mathematical modeling for the CCIs. It has been determined that, despite having a mathematical model for the CCIs, it is extremely difficult to find an analytical form for the AMoF. This motivates the utilization of a more tractable heuristic approach. The system architecture and a heuristic multilevel detection approach utilizing decision trees and linear regression is described in detail in Section 4. In Section 5, the experimental setup is explained in detail. Results and a discussion are provided in Section 6. A brief survey of related work is also presented in Section 7. Finally, Section 8 is devoted to conclusions and thoughts about future work.
## 3 Control Law  
We introduce how to control the pursuer's speed. We assumed that the pursuer at time index \(k\) can estimate the evader speed \(v_{k}^{e}\). \(v_{k}^{p}\) can change with respect to \(k\) as long as  
\[v_{k}^{p}>v_{k}^{e} \tag{11}\]  
is met at each time step \(k\).  
Our strategy in the terminal phase is to slow down the pursuer's speed as long as (11) is met. This implies that in the terminal phase, we update the pursuer's speed using  
\[v_{k+1}^{p}=max(v_{k}^{p}-a_{m}T,v_{k+1}^{e}+\epsilon). \tag{12}\]  
Here, \(\epsilon>0\) is a small constant. Note that \(v_{k+1}^{e}\) is available, since the pursuer at time index \(k\) can estimate the evader's velocities \(\mathbf{v}_{k}^{e}\) and \(\mathbf{v}_{k+1}^{e}\). (12) implies that (11) is met at each time step.  
We next introduce the heading control \(\mathbf{u}_{k}\) to achieve motion camouflage. \(\mathbf{u}_{k}\) is chosen so that the pursuer moves to \(\mathbf{h}_{k}\). At every time index \(k\), the heading controller is given as follows. _At every time index \(k\), the pursuer selects the new heading command \(\mathbf{u}_{k}\) as \(\frac{\mathbf{h}_{k}-\mathbf{r}_{k}^{p}}{\|\mathbf{h}_{k}-\mathbf{r}_{k}^{p}\|}\)._  
Consider the situation where the distance between \(\mathbf{r}_{k}^{p}\) and \(\mathbf{r}_{k+1}^{e}\) is less than \(v_{k}^{p}T\). In this situation, the pursuer moves towards \(\mathbf{r}_{k+1}^{e}\) directly, while not using \(\mathbf{u}_{k}=\frac{\mathbf{h}_{k}-\mathbf{r}_{k}^{p}}{\|\mathbf{h}_{k}-\mathbf{r}_{k}^{p}\|}\). In this way, the evader is captured at time index \(k+1\).  
In practice, the pursuer cannot turn with infinite acceleration. Suppose that the maximum turn rate of the pursuer is \(q\) radians per second. In the case where the angle formed by \(\mathbf{u}_{k-1}\) and the new heading command, \(\frac{\mathbf{h}_{k}-\mathbf{r}_{k}^{p}}{\|\mathbf{h}_{k}-\mathbf{r}_{k}^{p}\|}\), is bigger than \(qT\) radians, then the heading command \(\frac{\mathbf{h}_{k}-\mathbf{r}_{k}^{p}}{\|\mathbf{h}_{k}-\mathbf{r}_{k}^{p}\|}\) cannot be achieved within one sampling interval. This case, we select \(\mathbf{u}_{k}\) using the following method.  
Let \(\mathbf{u}_{k}^{1}=\mathbf{R}(qT)\mathbf{u}_{k-1}\), where \(\mathbf{R}(qT)=\left(\begin{array}{cc}cos(qT)&sin(qT)\\ -sin(qT)&cos(qT)\end{array}\right)\). In addition, let \(\mathbf{u}_{k}^{2}=\mathbf{R}(-qT)\mathbf{u}_{k-1}\). If \(\|\frac{\mathbf{h}_{k}-\mathbf{r}_{k}^{p}}{\|\mathbf{h}_{k}-\mathbf{r}_{k}^{ 2}\|}-\mathbf{u}_{k}^{1}\|<\|\frac{\mathbf{h}_{k}-\mathbf{r}_{k}^{p}}{\| \mathbf{h}_{k}-\mathbf{r}_{k}^{p}\|}-\mathbf{u}_{k}^{2}\|\), then we set \(\mathbf{u}_{k}=\mathbf{u}_{k}^{1}\). Otherwise, we set \(\mathbf{u}_{k}=\mathbf{u}_{k}^{2}\). In this manner, the heading command \(\mathbf{u}_{k}\) can be achieved within one sampling interval.  
In the following sections associated with analysis (Sections 3.1, 3.2, and 4), it is assumed that \(q=\inf\). This implies that we analyze the performance of our chasing controller, not considering the maximum turn rate of the pursuer. In the Simulation section, we set \(q=\pi/6\) radians per second.
## 3 Method Validation
### Error Analysis  
We select the existing viewing platforms in Fenghuang Town as the observation points and calculate the average value of the landscape visual evaluation scores for each observation point. We use the average value as the actual value in the root mean square error calculation. With the observation point as the center, as the radius increases by 500 m, we calculate the landscape visual evaluation scores for four target points corresponding to central angles of 90\({}^{\circ}\), 180\({}^{\circ}\), 270\({}^{\circ}\) and 360\({}^{\circ}\) and use them as the predicted values in the root mean square error calculation. Finally, the root mean square error (_RMSE_) of the landscape visual evaluation scores for different error radii is calculated as shown in Figure 14. The formula for the root mean square error is:  
\[RMSE=\sqrt{\frac{\sum\limits_{i=1}^{n=4}X_{i}-x}{n}} \tag{18}\]  
where \(n\) represents the number of target points, \(X_{i}\) represents the predicted values and \(x\) represents the actual values.  
As shown in Figure 14, we can see that the root mean square error of the landscape visual evaluation scores increases significantly when the error radius exceeds 1000 m, indicating that the landscape visual effect is basically consistent within a range of 1000 m. Therefore, the error range is defined as a circle with a radius of 1000 m centered on the original observation platform. Using error analysis (Figure 15), we see that observation points 5, 6 and 10 are all within the error range, indicating that their landscape visual effects are consistent with the actual situation, further verifying the effectiveness of the proposed viewshed analysis optimization algorithm and landscape visual evaluation method.  
Figure 14: Root mean square error of landscape visual evaluation scores with different error radii.
# Improving Passband Characteristics in Chebyshev Sharpened Comb Decimation Filters
## 3 Passband Compensation of Chebyshev Sharpened Combs from [8; 10; 11]
### Coleman Chebyshev Sharpened Comb [8]
#### 3.2.2 Wideband Compensation  
The passband frequency \(\omega_{p}=1/2M\), and \(M=16\).  
* Compensator \(C_{2}\)  
We first consider the compensator \(C_{2}\) from (6). The optimal compensator coefficients are \(C_{210}=0.7904\) and \(C_{220}=0.8596\), resulting in \(\delta_{\rm o}=0.0239\) dB. The corresponding SPT coefficients are shown in Table 2. It can be observed that, with fifteen adders, we have approximately optimum compensation.  
Figure 2 contrasts the passband magnitude responses of the Coleman non-compensated, optimum compensated and the SPT compensated with \(N_{2}=12\).  
Figure 1: Compensation of Coleman Chebyshev comb [8], \(M=16\), with the narrowband filter \(C_{1}\). Overall magnitude responses and passband zooms: (**a**) Overall magnitude responses of Coleman non-compensated and optimal compensated filters; (**b**) Passband zoom of Coleman non-compensated, optimal compensated and SPT compensated filters with \(N_{1}=5\).  
Figure 2: Compensation of Coleman sharpening filter [8], \(M=16\), with the wideband filter \(C_{2}\). Passband magnitude responses of non-compensated, optimal compensated and SPT compensated and SPT compensated with \(N_{2}=12\).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \(C_{21}\) & \(C_{22}\) & \(\delta_{2}\) [dB] & \(N_{2}\) \\ \hline \(2^{0}\)-\(2^{-2}\) & \(2^{0}\)-\(2^{-3}\) & 0.1232 & 11 \\ \(2^{0}\)-\(2^{-2}+2^{-5}\) & \(2^{0}\)-\(2^{-3}\) & 0.0307 & 12 \\ \(2^{0}\)-\(2^{-2}+2^{-5}\) & \(2^{0}\)-\(2^{-3}+2^{-7}\) & 0.0297 & 13 \\ \(2^{0}\)-\(2^{-2}+2^{-5}+2^{-8}\) & \(2^{0}\)-\(2^{-3}\)-\(2^{-10}\) & 0.0271 & 14 \\ \(2^{0}\)-\(2^{-2}+2^{-5}+2^{-7}\) & \(2^{0}\)-\(2^{-3}\)-\(2^{-6}+2^{-8}\) & **0.0247** & **15** \\ \hline \hline \end{tabular}
\end{table}
Table 2: SPT compensator \(C_{2}\) coefficients, passband deviations and the number of adders.  
* Compensator \(C_{3}\)  
The optimal compensator coefficients are \(C_{31\text{o}}=0.7250\) and \(C_{32\text{o}}=1.3138\), resulting in \(\delta_{0}=0.045\) dB. The corresponding SPT coefficients are shown in Table 3. We obtain approximately optimum compensation with thirteen and sixteen adders.  
Figure 3 compares the Coleman non-compensated filter passbands, compensated with the optimum filter and compensated with the SPT filter, \(N_{3}=12\).  
The corresponding MATLAB programs are given in the Supplementary Material.
## 4 Results
### Carbon and Oxygen Isotope Characteristics
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline
**Wells** & \begin{tabular}{c} **Lithologic** \\ **Characters** \\ \end{tabular} & **La** & **Ce** & **Pr** & **Nd** & **Sm** & **Eu** & **Gd** & **Tb** & **Dy** & **Ho** & **Er** & **Tm** & **Yb** & **Lu** & \$Ce** & \$Eu** \\ \hline S334 & \begin{tabular}{c} crystal powder \\ dolomite \\ \end{tabular} & 3.46 & 7.26 & 0.88 & 3.9 & 1.07 & 0.25 & 1.14 & 0.24 & 1.13 & 0.2 & 0.5 & 0.06 & 0.38 & 0.06 & 0.98 & 0.69 \\ \hline T74 & limestone & 3.79 & 7.84 & 1.44 & 2.08 & 0.31 & 0.067 & 0.36 & 0.14 & 0.29 & 0.032 & 0.096 & 0.009 & 0.081 & 0.015 & 0.89 & 0.54 \\ \hline T8 & \begin{tabular}{c} crystal powder \\ dolomite \\ \end{tabular} & 2.86 & 5.83 & 0.74 & 3.34 & 0.71 & 0.13 & 0.65 & 0.12 & 0.61 & 0.12 & 0.33 & 0.04 & 0.27 & 0.04 & 0.94 & 0.58 \\ \hline S208 & \begin{tabular}{c} crystal powder \\ dolomite \\ \end{tabular} & 5.2 & 11.2 & 1.43 & 6.16 & 1.19 & 0.21 & 1.07 & 0.17 & 0.88 & 0.17 & 0.45 & 0.05 & 0.35 & 0.05 & 0.97 & 0.56 \\ \hline S126 & \begin{tabular}{c} crystal powder \\ dolomite \\ \end{tabular} & 10.1 & 21.8 & 2.84 & 13.2 & 3.65 & 0.64 & 3.23 & 0.6 & 3.04 & 0.58 & 1.67 & 0.22 & 1.45 & 0.21 & 0.97 & 0.56 \\ \hline S18 & \begin{tabular}{c} crystal powder \\ dolomite \\ \end{tabular} & 7.64 & 14.5 & 1.78 & 7.15 & 1.26 & 0.21 & 1.04 & 0.18 & 0.98 & 0.2 & 0.59 & 0.08 & 0.49 & 0.07 & 0.91 & 0.55 \\ \hline T74 & \begin{tabular}{c} fine crystalline \\ dolomite \\ \end{tabular} & 13.1 & 24.4 & 3.38 & 9.89 & 1.72 & 0.27 & 1.40 & 0.27 & 0.92 & 0.17 & 0.58 & 0.067 & 0.60 & 0.067 & 0.86 & 0.52 \\ \hline T74 & \begin{tabular}{c} fine crystalline \\ dolomite \\ \end{tabular} & 6.51 & 13.2 & 1.95 & 4.47 & 0.78 & 0.21 & 0.53 & 0.17 & 0.42 & 0.074 & 0.25 & 0.020 & 0.18 & 0.029 & 0.88 & 0.95 \\ \hline T74 & \begin{tabular}{c} fine crystalline \\ dolomite \\ \end{tabular} & 12.7 & 24.3 & 3.15 & 9.52 & 1.57 & 0.34 & 1.48 & 0.24 & 1.02 & 0.15 & 0.51 & 0.067 & 0.48 & 0.067 & 0.90 & 0.67 \\ \hline T74 & \begin{tabular}{c} fine crystalline \\ dolomite \\ \end{tabular} & 7.63 & 13.6 & 2.02 & 4.04 & 0.72 & 0.21 & 0.64 & 0.18 & 0.57 & 0.091 & 0.28 & 0.040 & 0.27 & 0.034 & 0.82 & 0.93 \\ \hline S18 & \
\begin{tabular}{c} crystal powder \\ dolomite \\ \end{tabular} & 2.01 & 4.05 & 0.56 & 2.96 & 1.14 & 0.26 & 1.47 & 0.33 & 1.55 & 0.26 & 0.7 & 0.09 & 0.58 & 0.09 & 0.91 & 0.61 \\ \hline S272 &
\begin{tabular}{c} crystal powder \\ dolomite \\ \end{tabular} & 1.31 & 2.34 & 0.28 & 1.2 & 0.24 & 0.04 & 0.21 & 0.04 & 0.17 & 0.03 & 0.09 & 0.01 & 0.06 & 0.01 & 0.89 & 0.53 \\ \hline  & NASC & 0.31 & 0.808 & 0.122 & 0.6 & 0.195 & 0.074 & 0.259 & 0.05 & 0.32 & 0.072 & 0.21 & 0.0324 & 0.209 & 0.033 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Rare earth element content of dolomite in the fifth member of the Majiagou Formation, the Ordos Basin (rare earth element content/\(10^{-6}\)).
## 5 Discussion
Owing to the pushing of the Australian plate, the movement rate of the Obi Island microplate in the south was increased (\(U_{1}\) is approximately 6 cm/a) (Figure 8c), while that of Halmahera Island microplate in the north was relatively low (\(U_{2}\) is approximately 4 cm/a) as it was hardly affected by the pushing of the Australian plate (Figure 8b). As depicted in Figure 8c, the Obi Island microplate in the south moved at a higher rate and formed a high-temperature area favorable for arc magmatic activity faster above the slope of the subduction zone, thereby leading to the earlier formation of the Obi Island arc volcanic activity in the late Miocene (10 Ma). In contrast, Halmahera Island microplate in the north moved at a relatively lower rate,and it took a longer time to form a high-temperature zone conducive to magmatic activity beneath the arc, resulting in the later formation of the Halmahera arc volcanic activity in the late Pliocene (5 Ma) (Figure 8b). It is significant to note that the arc magmatism induced by subduction is primarily governed by temperature, pressure, and fluid. Our thermal simulation primarily examines how plate movement rate affects mantle wedge temperature as the subducting plate reaches dehydration depth. However, it does not consider the pressure factor. Pressure is indeed important in affecting rock melting, as the melting point of rocks decreases with increasing pressure. During upward migration, the partial melt beneath the volcanic arc experiences pressure reduction, which can further induce melting, thereby enhancing the supply of molten magma and accelerating its ascent [37]. Nevertheless, this process is highly complex and is typically affected by many factors, such as the upward migration distance and the thickness of the overriding lithosphere, which fall outside the scope of our research. Consequently, our results represent only one potential dynamic explanation for the volcanic age disparity observed in the Halmahera arc. The underlying causes for these differences are likely to be more intricate and varied, necessitating additional data and more comprehensive models for further investigation. Figure 7: Plate tectonic reconstruction in the Halmahera arc and its vicinity (modified after [6,8]). (**a**) The plate tectonics in the Halmahera arc and its vicinity at 2 Ma, where the yellow arrow represents the pushing of the Australian plate against the Halmahera arc. (**b**) The evolution of plate tectonics in Halmahera and its vicinity since 20 Ma. The black arrow represents the pushing of the Australian plate against the Halmahera arc. (**b1–b6**) are the plate tectonic characteristics of each stage.
## 5 Multi-Replication in Data Centric Storage
### GHT with multiple replicas  
[PERSON] _et al._, the original DCS authors, were already aware of this problem and proposed a grid-structured multi-replication system [30; 31]. They assume a square sensornet field that is divided into \(4^{d}\) grids, being \(d\) the so-called network depth. The original home node is established as defined in GHT, that is applying a hash function over the event type. After that, \(4^{d}-1\) mirror replicas are allocated in the same relative position inside each cell of the grid. Figure 2(a) shows a multi-replication scenario with \(d\) = 1 and Figure 2(b) with \(d\) = 2. Of course the coordinates shown in the figures refer just to space locations, thus the closest node to each location is the home replica node in that grid. This mechanism is recursive, because replicas of level \(d\) are also replicas of level \(d+1\).  
With this system, a producer generating an event stores it in the closest replication node. Then, in order to retrieve all the data related to a particular event, a consumer queries the top home node (\(d=0\)). This one in turn forwards the query to the remaining first level replicas (\(d=1\)), that in turn do the same with their second level replicas (\(d=2\)), and so on, in a recursive manner. The replies to the query travel the same path back to the original home node, which finally sends the information back to the consumer. Therefore, the information retrieval is based on a hierarchical routing that also relies on GPSR. Figure 3 depicts an scenario example including both production and consumption communications.  
There are no further discussion of multi-replication in [30; 31], but just a final remark: the proposed muti-replication environment reduces the storage cost in front of using a single home node, but increases the query cost, since now consumer packets travel longer to get the information.  
This work is the first one introducing the possibility of using several home nodes instead of only one. However, the authors do not provide any way to determine a suitable \(d\) in order to minimize the query cost.