esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 The Iterative Process for the Steady-State Allen-Cahn Equation  
At the start, we utilize \(p_{ij}=p_{ij}^{0}\) and (\(u\), \(u_{x}\), \(u_{y}\)) are calculated by  
\[u(x,y)=\sum_{i=1}^{m}\sum_{j-1}^{i}p_{ij}s_{ij}x^{i-j}y^{j-1}, \tag{20}\]  
\[u_{x}(x,y)=\sum_{i=1}^{m}\sum_{j-1}^{i}p_{ij}(i-j)s_{ij}x^{i-j-1}y^{j-1}, \tag{21}\]  
\[u_{y}(x,y)=\sum_{i=1}^{m}\sum_{j-1}^{i}p_{ij}(j-1)s_{ij}x^{i-j}y^{j-2}, \tag{22}\]  
After that, upon collocating \(n_{k}\) points to satisfy the boundary conditions (2) and (3) and the field equation \(\mathbf{Ap}=\mathbf{b}\), we can formulate a coefficient matrix \(\mathbf{A}\) from the left-hand side of the field equation with the aid of Equations (7)-(10), and then by employing the multiple-scale \(s_{ij}\), therefore \(\mathbf{P}\) via Equation (18). Meanwhile a tentative right-hand side \(\mathbf{b}_{0}\) is acquired from the right-hand side of Equation (1) by introducing Equations (20)-(22). Hence, we have a linear system with a different right-hand side:  
\[\mathbf{A}\mathbf{Q}\mathbf{p}=\mathbf{b}_{k}, \tag{23}\]  
whose normal form is handled by the CGM to generate a new coefficient \(p_{ij}^{1}\). Iteration is continued until convergence.  
The numerical processes this algorithm uses to resolve the steady-state AC equation are outlined in the following steps.  
(i) Given \(n_{1}\), \(n_{2}\) (\(n_{k}=n_{1}\times n_{2}\)), and \(m\) [\(n=m(m+1)/2\)].  
(ii) Given \(p_{ij}^{0}\).  
(iii) Given collocation points (\(x_{i}\), \(y_{i}\)), \(i=1\),..., \(n_{k}\).  
(iv) One-time only:  
Generate \(s_{ij}\), \(s_{ij}=\left\|\mathbf{p}_{1}\right\|/\left\|\mathbf{p}_{k}\right\|\),  
Generate \(\mathbf{Q}\) from \(M_{k}=s_{ij}\) and Equation (18),  
\[\mathbf{I}=\mathbf{A}\mathbf{Q}. \tag{24}\]  
(v) For \(k=0\), \(1\), \(2\),..., \(\cdot\) reiteration as follows:  
Compute \(u\), \(u_{x}\), \(u_{y}\) from Equations (20)-(22)  
Generate \(\mathbf{b}_{k}\) from the right-hand side of Equation (1)  
Resolve the normal form of \(\mathbf{I}\mathbf{p}=\mathbf{b}_{k}\) to acquire  
\[p_{ij}^{k+1} \tag{25}\]If \(p_{ij}^{k}\) converges in accordance with a given stopping criterion \(\sqrt{\sum_{i=1}^{m}\sum_{j=1}^{i}\left(p_{ij}^{k+1}-p_{ij}^{k}\right)^{2}}<\varepsilon _{2}\), which is a named relative distance coefficient, then stop; otherwise, go to step (iv).
## 4 Results and Discussion
### DoA Estimation Results
 \\ \hline \(\{V^{n_{up}}\}\) & \(\{1,\,2,\,3,\,4,\,5,6\}\) & 6 \\ \hline \(\{V^{n_{mid}}\}\) & \(\{13,14,15,16,17,18\}\) & 6 \\ \hline \(\{V^{n_{down}}\}\) & \(\{7,8,9,10,11,12\}\) & 6 \\ \hline \(\{V^{n_{up}},V^{n_{mid}}\}\) & \(\{1,\,2,\,3,\,4,\,5,6,\) & 12 \\ \hline \(\{V^{n_{up}},V^{n_{down}}\}\) & \(\{1,\,2,\,3,\,4,\,5 Figure 11: RMSE and precision values calculated using the proposed detailed DoA testing method, which involves all elevation angles during testing process, for the generalized PPCC-MCP algorithm relying on combinations of specific steering vector sets: (**a**) \(\{V^{n_{\pi}}\}\); (**b**) \(\{V^{n_{\pi}}\}\); (**c**) \(\{V^{n_{\pi}}\}\); (**d**) \(\{V^{n_{\pi}},V^{n_{\pi}}\}\); (**e**) \(\{V^{n_{\pi}},V^{n_{\pi}}\}\); (**f**) \(\{V^{n_{\pi}},V^{n_{\pi}}\}\). To verify the performance of generalized PPCC-MCP algorithm for different SNR levels, two additional DoA tests, with SNR = 5 dB and SNR = 0 dB, were performed. As it can easily be noticed in Figure 13, the most accurate results in both cases can be obtained for only 12 steering vectors when \(\{V^{m_{mid}},V^{m_{down}}\}\) steering vectors set is used. Therefore, two-row ESPAR antenna together with the proposed generalized PPCC-MCP algorithm can successfully be used for RSS-based DoA estimation in WSN nodes and gateways, even in noisy environments.
# Dual Residual Denoising Autoencoder with Channel Attention Mechanism for Modulation of Signals
## 3 DRdA-CA Architecture Details
### Loss Function  
In the existing work, most denoising autoencoders use the two loss functions of Mean Absolute Error (MAE) and Mean Square Error (MSE), and carry out parameter estimation by minimizing the error. MAE is the average absolute value of the true value minus the predicted value. By contrast, MSE is the average square of the absolute value of the predicted value minus the true value. Both MSE and MAE range from 0 to infinity, and they can be calculated, respectively, using  
\[MAE=\frac{1}{N}\quad\sum_{i=1}^{N}|(s_{i}-s_{i}^{\prime\prime})| \tag{6}\]  
\[MSE=\frac{1}{N}\quad\sum_{i=1}^{N}|(s_{i}-s_{i}^{\prime\prime})|^{2} \tag{7}\]  
where \(N\) is the length of the input signal, \(s_{i}\) is the noise-free signal value, and \(s_{i}^{\prime\prime}\) is the signal-reconstructed value (predicted value) output from our autoencoder, the same as below. The problem existing in the MAE training process is that the update gradient is always the same. Even for a small loss value, the gradient is relatively large, which is not  
Figure 4: Decoding block.  
conducive to a training model. Unlike MAE, MSE will assign more weight to outliers, and, at the expense of the error of other samples, the model will be updated towards reducing the error of the outliers, which will result in the performance degradation of the model. In order to overcome the above defects and make the output of the denoising autoencoder more accurate, the SLL is adopted in the proposed DRdA-CA in this paper. The SLL is calculated as follows:  
\[SLL(s,s^{\prime\prime})=\frac{1}{N}\sum_{i=1}^{N}z_{i} \tag{8}\]  
where the variable \(z_{i}\) is defined as follows:  
\[z_{i}=\left\{\begin{array}{l}0.5\times|s_{i}-s_{i}^{\prime\prime}|^{2},\text {if}|s_{i}-s_{i}^{\prime\prime}|<1\\ |s_{i}-s_{i}^{\prime\prime}|-0.5,\text{otherwise}\end{array}\right. \tag{9}\]  
It is clear that SLL is an integration of MSE and MAE. When taking the derivative of SLL, we have:  
\[\frac{\text{d}SSL}{\text{d}s_{i}}\quad=\left\{\begin{array}{l}s_{i},\text{if }|s_{i}|<1\\ \pm 1,\text{otherwise}\end{array}\right. \tag{10}\]  
In Equation (10), it can be seen that, when \(s_{i}\) is small, the derivative of SSL with respect to \(s_{i}\) also becomes small. Otherwise, the absolute value of the derivative reaches the upper bound of 1, and the network stability will not be impacted by the large derivative. As we know, MSE has derivatives at the origin and is easy to converge, and, in the boundary area, MAE enables our denoising autoencoder to correct back when the error tends to be large. Regarding the two error metrics, therefore, the SLL is more robust with respect to outliers.
## 2 Reliability Analysis and Reliability-Based Design Optimization
### Reliability-Based Design Optimization  
One of the goals in structural optimization is to find the optimal solutions in a given design domain subjected to tractions and displacement boundary conditions while satisfying given design constraints. When the reliability analysis of a structure under uncertainty is incorporated into structural optimization, it is referred to as RBDO. RBDO aims to achieve the optimal design under given probabilistic constraints, arising from uncertainties in material properties or loads. The component RBDO (CRBDO) approach seeks to satisfy the probabilistic constraint regarding each failure event. A CRBDO problem can be formulated as  
\[\begin{array}{ll}\underset{\mathbf{d},\mathbf{u}_{\mathbf{x}}}{\text{min}}&f _{obj}(\mathbf{d},\mathbf{\mu}_{\mathbf{x}})\\ \text{s.t.}&P_{fi}=P[g_{i}(\mathbf{d},\mathbf{x})\leq 0]\leq P_{fi}{}^{t},i=1, \ldots,n_{c}\\ &\mathbf{d}^{\text{t}}\leq\mathbf{d}<\mathbf{d}^{\text{u}}\end{array} \tag{7}\]  
Figure 1: Illustration of the first-order reliability method (FORM) for a component reliability problem.  
where \(f_{\text{d}ij}\) is the objective function; \(\mathbf{d}\) is a vector of deterministic design variables; \(\mu_{\mathbf{x}}\) is the vector of the means of random variable \(\mathbf{x}\); \(P[g_{i}(\mathbf{d},\mathbf{x})\leq 0]\) is the failure probability of the \(i\)-th limit-state function \(g_{i}(\cdot)\); \(P_{ff}{}^{\text{t}}\) represents the target failure probability of the \(i\)-th limit-state; \(n_{c}\) is the number of probabilistic constraints; and \(\mathbf{d}^{\text{l}}\) and \(\mathbf{d}^{\text{u}}\) are the lower bounds of design variables and upper bounds of design variables, respectively. This problem is solved by generating and solving a sequence of explicit subproblems that are approximations of Equation (7). Optimization algorithms, such as sequential linear programming (SLP), sequential quadratic programming (SQP; [41]), convex linearization (COLIN; [42]), optimality criteria (OC; [43]), and method of moving asymptotes (MMA; [44]), incorporate information about the sensitivity of objective and probabilistic constraint functions to solve subproblems.
# Intelligent Transmit Antenna Selection Schemes for High-Rate Fully Generalized Spatial Modulation
## 2 System Model of FGSM Transceiver
\begin{array}{c}y_{1}\\ y_{2}\\ y_{3}\\ y_{4}\end{array} \right]=\left[ \begin{array}{c}h_{11}\\ h_{21}\\ h_{31}\\ h_{41}\end{array} \right]s_{1}+\left[ \begin{array}{c}h_{12}\\ h_{22}\\ h_{32}\\ h_{42}\end{array} \right]s_{1}+\left[ \begin{array}{c}\eta_{1}\\ \eta_{2}\\ \eta_{3}\\ \eta_{4}\end{array} \right]. \tag{8}\]  
For the double antenna operational case, the generalized form of the received signal is given by  
\[\boldsymbol{y}=\left(\boldsymbol{h}_{j_{1}}+\boldsymbol{h}_{j_{2}}\right)s_{m }+\boldsymbol{\eta},j_{1}\
eq j_{2},j_{1},j_{2}\in\{1,2,..N_{tx}\},m\in\{1,2,...M\}. \tag{9}\]  
For the \(N_{A}\) number of functional antennas, the generalized form of the received signal is represented as follows:  
\[\boldsymbol{y}=\left(\sum_{a=1}^{N_{A}}\boldsymbol{h}_{j_{a}}\right)s_{m}+ \boldsymbol{\eta},j_{a}\in\{1,2,...N_{tx}\},m\in\{1,2,...M\}. \tag{10}\]  
When a receiver possesses perfect CQI, the maximum likelihood detection for the FGSM system with \(N_{A}\) functional antennas is given by  
\[\left[\hat{j}_{a,a=1,2..N_{A}},\hat{s}_{m}\right]=\underset{j_{a,a-1,2..N_{A} },\boldsymbol{s}=}{\arg\min}\left\|\boldsymbol{y}-\left(\sum_{a=1}^{N_{A}} \boldsymbol{h}_{j_{a}}\right)s_{m}\right\|^{2}. \tag{11}\]
## 5 Results
### Major and Trace Element Characteristics
#### 5.2.1 Late Triassic Basalts  
Late Triassic basalts have SiO\({}_{2}\) contents ranging from 41.48 to 44.39%, TiO\({}_{2}\) from 0.71 to 1.66%, Al\({}_{2}\)O\({}_{3}\) from 2.46 to 5.31%, K\({}_{2}\)O + Na\({}_{2}\)O from 0.21% to 0.42%, CaO from 8.64 to 13.03%, TFe\({}_{2}\)O\({}_{3}\) from 14.97 to 20.39%, MgO from 20.85 to 25.00%, and low concentrations MnO and P\({}_{2}\)O\({}_{5}\). On the Total alkali vs. silica (TAS) diagram (Figure 4a), the samples are plotted in the piciro-basalt field. On the K\({}_{2}\)O vs. SiO\({}_{2}\) diagram (Figure 4b), they are plotted in low-potassium calc-alkaline field. On the MgO vs. SiO\({}_{2}\) diagram (Figure 4c), they are plotted in the komatitic field (five samples) and mellitite field (one sample). Therefore, the assemblages of late Triassic basalts are komatites-meliilitite.  
Moreover, on the Zr/Ti vs. Nb/Y diagram (Figure 4d), they are plotted in the sub-alkaline basalts field. The spider diagrams of trace elements for Late Triassic basalts (Figure 5a) show the enrichment of elements such as U and Eu and depletion in elements like Ba, Nb, and Zr, with high field strength elements (HFSEs) such as Nb and Zr exhibiting negative anomalies. They have a rare earth element (REE) content ranging from 11.95 to 22.90 ppm, with the enrichment of light rare earths and depletion of heavy rare earths (Figure 5b).  
Figure 4: (**a**) Total alkali vs. silica (TAS) diagram (after [34]); the dashed line represents the alkaline and sub-alkaline boundary according to [PERSON], [PERSON] et al., 1971. (**b**) K\({}_{2}\)O vs. SiO\({}_{2}\) diagram (after [35]). (**c**) MgO vs. SiO\({}_{2}\) diagram (parameters and boundaries for komatitic, meimechite, picrite, and boninite are according to [36]), HMA/MA, LT-HMA, MT-HMA, T-HMA, and MA/basalt-melt boundaries are according to [37]; (**d**) Zr/Ti vs. Nb/Y diagram (according to [38]), Late Triassic basalt data are from [28], and Middle Jurassic basalt data are from [21; 29; 28].
# Comparing Approaches for Explaining DNN-Based Facial Expression Classifications
## 4 Experimental Setting  
### Dataset  
The dataset used for all models is the Karolinska Directed Emotional Faces (KDEF) dataset [36]. It consists of 4900 images of human faces displaying seven different emotional expressions. The expressions consist of the six basic emotions-anger, disgust, fear, happiness, sadness, surprise-as defined by [PERSON] [37], extended with neutral.  
In total, there were 70 participants (35 male, 35 female) who were each photographed twice for each of the expressions from five different angles (full left profile, half left profile, straight, half right profile, full right profile). Participants' faces were centered on a grid such that their eyes and mouths are positioned in fixed coordinates.  
We omitted all pictures with the full left profile and full right profile orientation, since those poses are much more difficult to classify and the goal of this research is not to develop the most all-round facial emotion classifier. Ultimately, we ended up with 1509 training set images (subject IDs 12-29), 504 validation set images (IDs 30-35) and 923 test set images (IDs 01-11). This split is used for all models. The class distribution was balanced.
## 4 RADC: Resource Allocation Based Data Classification
### Placement and Replacement of Data  
Unlike strategies that share the same space for all content, our strategy allocates the desired space for each content class. It is known that content placement and replacement in NDN is also an important feature that can improve the overall network performance. As shown in Figure 3, when the routers in the network receive the content, they classify it using the classification model. Then, the received content is placed in the corresponding space that was allocated to the same class. If the corresponding space is full, a replacement strategy will be applied to insert the received content by evicting another from the same class. We note that the design of our strategy allows us to adapt any replacement strategy to replace data of the same class, but for simplicity we use the Least Recently Used (LRU) method to replace the received data. In this strategy, the received data will replace the least recently used data [19].  
Figure 3: Data placement and replacement process.
## 2 The Models and Analyses
### Finding a Solution  
The system (1) can be rewritten as  
\[\frac{dp_{1}}{dt}=(c_{1}h(t)-m_{1}+f)p_{1}-c_{1}p_{1}^{2},\]  
\[\frac{dp_{2}}{dt}=(c_{2}h(t)-(c_{1}+c_{2})p_{1}-m_{2}+f)p_{2}-c_{2}p_{2}^{2},\]  
\[\frac{dp_{3}}{dt}=(c_{3}h(t)-(c_{1}+c_{3})p_{1}-(c_{2}+c_{3})p_{2}-m_{3}+f)p_{ 3}-c_{3}p_{3}^{2},\ldots,\]  
\[\frac{dp_{n}}{dt}=\left(c_{n}h(t)-\sum\limits_{i=1}^{n-1}{(c_{i}+c_{n})p_{i}}- m_{n}+f\right)p_{n}-c_{n}p_{n}^{2}\]  
Since \(A_{n}(t)=c_{n}h(t)-\sum\limits_{i=1}^{n-1}{(c_{i}+c_{n})p_{i}}-m_{n}+f\) is a function of \(t\), it can be viewed as a special case of the Bernoulli equation in the following form:  
\[\frac{dp_{n}}{dt}=A_{n}(t)p_{n}-c_{n}p_{n}^{2},\forall n\]  
where \(A_{1}(t)=c_{1}h(t)-m_{1}+f\) and \(A_{n}(t)=c_{n}h(t)-\sum\limits_{i=1}^{n-1}{(c_{i}+c_{n})p_{i}}-m_{n}+f,\forall n =2,\ldots\), whose solution can be solved analytically and recursively as  
\[\frac{1}{P_{n}(t)}=\frac{1}{P_{n}(0)}\exp\left(-\int\limits_{0}^{t}{A_{n}(\tau )d\tau}\right)+c_{n}\int\limits_{0}^{t}\exp\left(\int\limits_{t}^{t}{A_{n}( \tau)d\tau}\right)d\hat{\tau},\forall n \tag{5}\]  
**3. Varieties of Habitat Destruction and Their Simulation Results**  
Three special cases of \(h(t)\) are considered in this study.
## 6 Conclusions  
In this paper, we study the detection and energy efficiency of massive MIMO systems with low-precision ADCs. The MMSE and LR-SIC detectors are studied. Their transmission power required for support a transmission rate at a given reliability is compared. The circuit power consumption including the ADCs power consumption and the signal processing complexity are analyzed. Finally, the energy efficiency with different detection algorithms under different system settings are compared. The results show that nonlinear receivers achieve better error rates but also require higher complexity. However, the EE-optimal choice of the signal detection algorithms depends highly on the concrete scenarios. In general, fewer receiver antennas, higher reliability requirement, larger cell size may require nonlinear detectors to be used to achieve the highest EE. While the linear detector may be more advantageous when the transmission power required is low, such as when the number of BS antennas is large, cell size is small, etc.  
It should be noted that the framework presented in this paper can be adapted to analyze systems based on different modulation schemes (e.g., multiple-PSK (M-PSK), multiple- Quadrature Amplitude Modulation (M-QAM)), signal detectors, channel models, transceiver architectures, and power allocation schemes, by characterizing the error rate performance and computational complexity of the detector concerned. Other future work may include the extension to multiple-cell scenarios and wireless sensor networks.  
Conceptualization, Z.X., L.G.; methodology, Z.X., J.Z., T.L.; software, J.Z., L.G.; validation, J.T., T.L.; formal analysis, J.Z., J.T.; investigation, J.Z.; resources, Z.X., L.G.; data curation, J.Z.; writing-original draft preparation, J.Z., J.T.; writing-review and editing, Z.X., T.L., F.Z., J.T.; visualization, J.Z., J.T.; supervision, Z.X., L.G., F.Z.; project administration, Z.X., L.G., F.Z.; funding acquisition, Z.X., F.Z., J.T. All authors have read and agreed to the published version of the manuscript.  
This research was funded by NSFC under Grant 61601325.  
The authors declare no conflict of interest.
## 4 Results and Evaluation
### Proposed Representations  
The first comparison we performed was between the three different representations proposed in this paper. As seen in Figures 2 and 3, the worst performing representation is Meaningcloud in both metrics. This representation allows obtaining an average F1 score of 0.5076, having the best performance with the database of Kaggle with an average performance of 0.8459. The worst performance of this metric was with the LOSADA2018 database with an average performance of 0.1390. For the AUC, the worst performance is given by the Meaningcloud representation, having its best average performance of 0.8562 with Kaggle and its worst average performance of 0.5 with LOSADA2018; the predictions were not better than random predictions.  
On the other hand, the best F1 performance was achieved by the combined representation with an average performance of 0.6457 taking into consideration all the databases. The best performance is with the database Kaggle with an average performance of 0.9586. The representation that gives the best AUC performance is again the combined representation, with its best average performance of 0.9621 with Kaggle and its worst average performance of 0.7170 with LOSADA2018.  
It is important to denote that the difference between the results of the combined and Paralleldots representations has no significant difference in the F1 score, according to a Wilcoxon signed-ranks test [62], which gives a p-value of 0.1416. Nevertheless, it does present a significant difference in the AUC metric with a p-value of 0.02444.  
We chose combined as the best representation, given the results, and used it as the point of comparison with other representations and classifiers.  
After determining the best representation using PBC4 cip, we used that representation to compare it with the results of other proposals. Since we only have results for three of the five databases using the LOSADA2016 and LOSADA2018 representation and classification technique, the results are divided into two sets. Figures 4 and 5 present the comparison between our representation and the representations of LOSADA2016 and LOSADA2018 for the available databases, which are CSSRS, DDVHSM, and Kaggle. Figures 6 and 7 present the comparison between our representation and the representations of Parser tree, VAD, and BOW tf-idf for all databases.
## 2 Experimental Details
### Specimen Configuration  
#### 2.2.1 Geometrical Size and Mechanical Properties  
The connecting components were composed of GFRP plates, which were 300 mm \(\times\) 40 mm \(\times\) 6 mm, the bolt-hole diameter \(D\) was 8 mm, and the hole center was 60 mm from the end of the plate. The bolt hole diameter and bolt hole spacing selection were based on American Society of Civil Engineers design guide for FRP composite connections [1]. The GFRP plates were made via a pultrusion process. The fiber volume fraction was 40%. The fiber was oriented at angles of 45\({}^{\circ}\)/90\({}^{\circ}\)/0\({}^{\circ}\). All the information was provided by the manufacturers. The austenitic stainless-steel 304 plates measured 205 mm \(\times\) 40 mm \(\times\) 5 mm, the bolt-hole diameter \(D\) was 8 mm, and the center of the hole was 40 mm from the end of the plate. The mechanical properties of the plates are presented in Table 1. The mechanical properties of the stainless-steel plates and those of the GFRP plates were based on the technical data provided by the manufacturers. The washer had an outer diameter \(D_{0}\) of 14 mm and an inner diameter \(d_{0}\) of 6 mm. The material of the high-strength bolt was stainless-steel, grade A4-80, with a nominal diameter of 6 mm. The size of the test specimen is shown in Figure 1.
## 4 Methodology
### Feature Importance
#### 4.2.2 Information-Theory Feature Importance  
In this approach, we created a pool of feature subsets by assigning each feature a binary (on/off) selection value. The pool members were generated randomly using a uniform distribution, aiming to cover a specified percentage of the entire feature combination space \(2^{n}\), where \(n\) was the total number of features. A neural network (as described in the previous subsection) was trained and tested for each subset in the pool to obtain the \(R^{2}\) performance metric. This random sampling strategy was more computationally feasible than exhaustively testing every possible subset while capturing a broad representation of feature combinations. To determine the overall contribution of each feature, we measured the change in model performance when the feature was present versus when it was absent. Let \(S_{i}\) be the randomly generated subsets that include \(X_{i}\) and \(E_{i}\) the subsets that exclude features. We then computed the difference in the performance metric (e.g., \(\Delta R^{2}\)) and averaged these differences across all subsets. Equation (5) denotes the features' information gain, representing the performance metric \(R^{2}\). Here \(M_{i}\) is the set of common feature subsets, ignoring the feature \(X_{i}\). A larger value \(IG(X_{i})\) indicates that the feature \(X_{i}\) provides greater unique information, contributing more significantly to the prediction task.  
\[\begin{split} IG(X_{i})=\frac{1}{|M_{i}|}\sum\limits_{mcM_{i}} \left[P(m\cup\{X_{i}\})-P(m)\right]\\ M_{i}=S_{i}\ \cap\ E_{i}\end{split} \tag{5}\]
# SALMA: A Novel Middlebox Infrastructure System Based on Integrated Subnets
## 1 Introduction
We found that a large number of the investigated middleboxes are highly underutilized. * We solved the challenges raised, i.e., the policy chaining of middleboxes, topology dependence, and consolidation challenge, by proposing SALMA. This is the main contribution of this paper. * We invented a novel encoding mechanism by exploiting a correlation between the service policy chaining and the address space in packet headers in order to allow the forwarded packets to traverse a pre-definded sequence of middleboxes.