esa-sceva/satcom-chunk-collection huggingface dataset:
# Implementation and Evaluation of Activity-Based Congestion Management Using P4 (P4-ABC)
## 3 Activity-Based Congestion Management (ABC)
### Discussion  
Ingress nodes are configured per controlled aggregate with traffic descriptors, the memory for rate measurement, and a reference rate, and they require measurement state for each aggregate. If the number of traffic aggregates on ingress nodes is moderate, this seems feasible. Forwarding nodes are configured per egress port with parameters for activity averaging and activity AQM, and they require averaging state for each egress port. As the number of egress ports is low, ABC scales well for core nodes.  
As packet dropping depends on activity values contained in packet headers, activity meters and forwarding nodes should be trusted devices. Otherwise, malicious users can avoid packet drops by inserting low activity values and obtain unfairly high throughput at the expense of other users.  
Reference rates \(R_{r}\) specific to aggregates may be used to differentiate their achievable throughput in case of congestion. Moreover, ABC has been extended to support different delay classes, i.e., aggregate-specific throughput and forwarding delay can be controlled independently of each other. Detailed simulation results backing these claims and recommendations for parameter settings are provided in [6].  
We conclude that ABC provides scalable, QoS-aware congestion management for closed networking domains.
# An Efficient Relayed Broadcasting Based on the Duplication Estimation Model for IoT Applications
## 3 Duplication Suppression and Re-Queuing  
The proposed mechanism consists of two components. The first one is a method of determining the probability of discarding a frame to suppress redundancy and another one is a method attempting the re-queuing of frames to compensate for excessive suppression and unsuccessful transmissions. We first introduce the duplication ratio, which plays a key role in both methods, and then propose two methods.
## 3 Numerical Modelling
### Motion Equations
Thus, the vibratory closing speedcan be defined as the vector sum of the closing velocity \(v_{0}\) and vibratory velocity \(y^{\prime}\). In fact, the emergency gate was in transient water and had a small vibration response before the gate started to close, which was called the vibration adaption. During the vibration adaptation, the emergency gate vibrated with a single degree of freedom at its initial position. After the vibration adaptation was completed, the gate-closing process officially started. Moreover, there are two main problems that can arise in the closing process. Firstly, when the emergency gate vibrates, the gate movement trend might change. The friction force direction alters and transitions between kinetic and static friction, influencing the holding force \(f(t)\) in Equation (2). Secondly, the gate motion pattern would change. If the steel rope relaxed, it meant that the gate was no longer bound by the steel rope, and it would gradually slow down according to [PERSON]'s second law of motion. The phenomenon of steel rope relaxation appeared in physical model test [15]. Thus, only the steel rope was in the tension state, the emergency gate vertical vibration in the closing process can be simplified to a single degree of freedom vibration. The hydrodynamic loads on the gate plates and flow discharge were taken as the focus in a numerical simulation. The relationship between the flow discharge and the hydrodynamic loads and gate vertical vibration was explored. The hydrodynamic loads and flow discharge were monitored, and the positions of the monitoring surface were displayed in Figure 3. As can be seen from Figure 3, the 'flow1' and 'flow2' represented the flow discharge monitoring surface. 'flow2' was the sum of 'flow1' and the supplementary flow from the gate shaft. The other surfaces denoted the monitoring surface of hydrodynamic loads.
# Fast Fractional-Order Terminal Sliding Mode Control for Seven-Axis Robot Manipulator
## 3 Controller Design
### Stability Analysis  
The asymptotic stability of reaching the sliding surface is proved by using Lemma 1 as follows. For the \(j\)-th joint, substituting the equivalent control input (27) to the dynamics (14) and (26), then applying \(1=sgn(s_{j})sgn(s_{j})\) yields (see Appendix B)  
\[\begin{array}{l}s_{jc}D_{0,t}^{\beta_{j}}s_{j}=-s_{j}(k_{1}s_{j}+k_{2}sig(s_ {j})^{\mathbf{r}_{2j}})-s_{j}sgn(s_{j})D_{0,t}^{\beta_{j}+\alpha_{j}-2}(k_{3j} +\widetilde{\mathbf{\Psi}}_{j}sgn(s_{j}))\\ +D_{0,t}^{1-\beta_{j}-\alpha_{j}}[k_{1j}s_{j}+k_{2j}s_{j}sig(s_{j})^{\mathbf{r }_{2j}}]_{t=0}\frac{1-\beta_{j}-\alpha_{j}}{\Gamma(2-\beta_{j}-\alpha_{j})} \end{array} \tag{28}\]  
As \(k_{3j}\geq\Omega_{j}>\left|\widetilde{\mathbf{\Psi}}_{j}\right|\)  
\[D_{0,t}^{\beta_{j}+\alpha_{j}-2}(k_{3j}+\widetilde{\mathbf{\Psi}}_{j}sgn(s_{j }))>0 \tag{29}\]  
Additionally, for given parameters \(\beta_{j}\) and \(\alpha_{j}\), \(D_{0,t}^{1-\beta_{j}-\alpha_{j}}[k_{1j}s_{j}s_{j}+k_{2j}s_{j}sig(s_{j})^{ \mathbf{r}_{2j}}]_{t=0}\) is a positive constant. As \(\frac{1-\beta_{j}-\alpha_{j}}{\Gamma(2-\beta_{j}-\alpha_{j})}\) is a decreasing function of time \(t\), \(\frac{1-\beta_{j}-\alpha_{j}}{\Gamma(2-\beta_{j}-\alpha_{j})}\approx 0\) when \(t\) is large. Hence, after a period of time \(t\),  
\[\begin{array}{l}s_{jc}D_{0,t}^{\beta_{j}}s_{j}\approx-s_{j}(k_{1j}s_{j}+k_{2 j}sig(s_{j})^{\mathbf{r}_{2j}})-s_{j}sgn(s_{j})D_{0,t}^{\beta_{j}+\alpha_{j}-2}(k_{3j} +\widetilde{\mathbf{\Psi}}_{j}sgn(s_{j}))\\ \leq-s_{j}(k_{1j}s_{j}+k_{2}sig(s_{j})^{\mathbf{r}_{2j}})\leq 0,\ \forall s_{j}. \end{array} \tag{30}\]  
Depending on Lemma 1, the sliding manifold \(s_{j}\) is asymptotically stable and can reach \(s_{j}=0\) from any initial condition.  
After reaching the sliding surface (i.e., \(s_{j}=0\))  
\[e_{jc}D_{0,t}^{\alpha_{j}}e_{j}=-\lambda_{1j}e_{j}sig(e_{j})^{r_{1j}}\leq 0 \tag{31}\]  
\(e_{jc}D_{0,t}^{\alpha_{j}}e_{j}=0\) only if \(e_{j}=0\). It satisfies the asymptotically stable condition in Lemma 1.  
**Remark 2**.: _The asymptotic stability of the reaching mode and sliding mode is proved. However, the finite reaching time has not been obtained in this research. An explicit solution of a fractional differential equation with a nonlinear term cannot be solved, neither can an analysis solution. Despite this, in the tracking control of a robot manipulator, the fast convergence is more critical than the finite-time stability. It ensures an overall small tracking error. The fast convergence of FFOTSMC is discussed and obtained by analyzing the convergence characteristics of FOSMC and TSMC in Appendix A._
## 4 Results
### Statistical Analysis of Results  
We use the \(t\)-test to determine whether there is a significant statistical difference between quantitative metrics calculated for different methods. Lateral FWHM, CR, CNR, gCNR, and sSNR calculated in all simulated and experimental images are used to evaluate the significant improvements of proposed methods. A paired \(t\)-test was performed between NSVD-based methods and methods without the use of NSVD at a 5% significance level. The results indicate that NSVD does not effectively help the lateral FWHM. However, compared to CPWC and CWPC+SVD, the CR and CNR improvements obtained by CPWC+NSVD are significant. Furthermore, CF+NSVD, GCF+NSVD, and SLSC+NSVD show significant improvements of CR, CNR, gCNR, and sSNR compared with corresponding CF, GCF, and SLSC, respectively.  
Because of the complicated tissue in in vivo images, the overall improvement of NSVD is hard to judge using only the results in Figure 15. We chose several different background regions to calculate metrics and statistically assess significant improvement. Figure 16 shows the barplot of CR, CNR, and sSNR of in vivo images obtained by different imaging methods. The results of the paired \(t\)-test at a 5% significance level show the significant improvements in CR and CNR of CPWC+NSVD as compared to CPWC and CPWC+SVD, while CR, CNR, gCNR, and sSNR improvements are also significant between an adaptive weighting method with NSVD and without the use of NSVD.
# Wind Turbine Power Curve Modelling with Logistic Functions Based on Quantile Regression
###### Abstract  
The wind turbine power curve (WPTC) is of great significance for wind power forecasting, condition monitoring, and energy assessment. This paper proposes a novel WTPC modelling method with logistic functions based on quantile regression (QRLF). Firstly, we combine the asymmetric absolute value function from the quantile regression (QR) cost function with logistic functions (LF), so that the proposed method can describe the uncertainty of wind power by the fitting curves of different quantiles without considering the prior distribution of wind power. Among them, three optimization algorithms are selected to make comparative studies. Secondly, an adaptive outlier filtering method is developed based on QRLF, which can eliminate the outliers by the symmetrical relationship of power distribution. Lastly, supervisory control and data acquisition (SCADA) data collected from wind turbines in three wind farms are used to evaluate the performance of the proposed method. Five evaluation metrics are applied for the comparative analysis. Compared with typical WTPC models, QRLF has better fitting performance in both deterministic and probabilistic power curve modeling.  
logistic function; quantile regression; outlier filtering; wind turbine power curve; wind power
# Towards Collaborative and Dynamic Spectrum Sharing via Interpretation of Spectrum Access Policies
## 5 Policies
### Higher-Level Policies  
Policies that are based on logical conditions cannot be represented as hypercubes. In our approach, we represent policies as SPARQL _Update_ expressions augmented with the SpectralSPARQL extension (c.f. Section 4.1). The Update mechanism of SPARQL allows making conditional changes in the knowledge base, which fits well with the condition-action structure of the policies.  
As an example, consider a policy expressed in natural language:  
Figure 8: An Example of Policies.  
```
``` Policy1:
``` Allow transmission for a transmitter \(T\) if one of the following conditions is met: \(\bullet\)\(T\) is located at least 2 km from _NodeX_; its Tx power is below \(P_{1}\); and its modulation and coding scheme is QPSK. \(\bullet\)\(T\) is located at least 3 km from _NodeX_; its Tx power is below \(P_{2}\); and its modulation and coding scheme is 16 QAM. ```
This policy can be expressed as a SpectralSPARQL Update expression, as shown in Listing 1. Note how the two subexpressions (surrounded by curly brackets) of the _WHERE_ clause directly correspond to the different conditions in the natural text.
``` INSERT{?request:hasDecision:allow } WHERE{ {?requesta:TransmissionRequest; :forNode:?Node1.?Node1a:Emitter; :hasMCSQPSK; :hasTxPower?TxPower; :distanceToNodeX?distance. FILTER(?distance>2000&&TxPower<P1) } UNION {?requesta:TransmissionRequest; :forNode:?Node1.?Node1 aEmitter; :hasMCS16 QAM; :hasTxPower?TxPower; :distanceToNodeX?distance. FILTER(?distance>3000&&TxPower<P2) } } ```  
**6. An Implementation of a Policy Based Spectrum Sharing System**  
In this section, we describe how the Cognitive Radio Engine architecture described in Section 3 was implemented in our experimental system.
## 4 Discussion
vomitoria_ oviposition, our findings are in line with the evidence reported by [PERSON] et al. [20]. In their oviposition deterrence tests (conducted under laboratory conditions for 24 h with the same blowfly _C. vomitoria_ as the target pest), they found that the treatment of beef with their _P. nigrum_ EO-enriched CH solution (at 0.23 \(\mu\)L EO cm\({}^{-2}\) of treated surface) was the most effective. Treatment with an ethanolic solution of the same _P. nigrum_ EO was also promising, but as already mentioned, EOs are volatile, and their bioactivity is better preserved when added to a stabilising matrix such as CH. Our EO-CH formulations (at a similar amount of 0.25 \(\mu\)L EO cm\({}^{-2}\)) were able to significantly protect beef from blowfly oviposition for up to 96 h, confirming the stabilising effect of CH on the EOs' composition. Compounds such as \(\delta\)-2-carene, 1,8-cineole, m-cymene, linalool, p-menthene, \(\beta\)-phellandrene, and \(\gamma\)-terpinene were likely responsible for this deterrent activity, as they were the most abundant plant secondary metabolites among the VOCs released by the EO-containing beef samples. Concerning the use of other EOs as deterrents against _C. vomitoria_ blowflies, several studies have been conducted involving EOs extracted from aromatic plants used as culinary herbs and spices, but always unformulated (simply diluted in ethanol). For instance, a tarragon EO at 0.05 \(\upmu\)L EO cm\({}^{-2}\) completely (100%) protected beef for 24 h [59]. At 0.32 \(\upmu\)L EO cm\({}^{-2}\), [PERSON] et al. [60] achieved 90% protection of pork for 24 h using a thymol/\(\gamma\)-terpinene chemotype oregano EO. [PERSON] et al. [61] also reported complete protection of pork for 24 h with a garlic EO starting from 1.25 \(\upmu\)L EO cm\({}^{-2}\) and nearly 70% protection for 72 h, but with a higher amount of 5.0 \(\upmu\)L EO cm\({}^{-2}\). These studies suggest that, even if such EOs are effective deterrents against _C. vomitoria_, high concentrations are necessary to obtain substantial protection of meat products over a beneficial period. Building upon this, there have been promising attempts to formulate EOs or their chemical components in liquid, film, or nanoparticle CH to enhance and prolong their efficacy against insect pests [19]. Among the deterrent solutions proposed, we can list liquid CH enriched with a mandarin EO to protect kumquat fruits from the oviposition of _Ceratitis capitata_ (Diptera: Tephritidae) for up to 96 h [23] or with bay and black pepper EOs to shield ham and cheese from _Piophila casei_ (Diptera: Piophilidae) over the same period of time [62]. Furthermore, a CH coating with a field ferulago EO applied to common beans hindered the oviposition by _Acanthoscelides obtetus_ (Coleoptera: Chrysomelidae) for 14 days [63]. As a repellent, a bitter orange EO-CH film had a long-lasting effect on _Stiophilus oryzae_ (Coleoptera: Dryophtoridae) for up to 28 days [64].
## 3 Result and Discussion
### Relationship between Protein Degradation or Oxidation and the Flavors of Bacon  
To explore the relationship between DAPs and volatile compounds in bacon during LTS, DAPs were screened based on an FC of \(\geq\)3 or \(\leq\)0.1 and a \(p\)-value of \(<\)0.01. The correlation analysis (Figure 5A,B) revealed 57 positively correlated proteins and 27 negatively correlated proteins correlated with volatile compounds. Protein degradation was the main pathway for the formation of volatile compounds. Endopeptidases (cathepsin and calpain) degrade myofibrillar structures by breaking peptide bonds inside proteins, producing macromolecular polypeptides, whereas exopeptidases (aminophenedases and tri- and dipeptidyl peptidases) further hydrolyze macromolecular polypeptides into smaller taste peptides and large amounts of free amino acids, which typically produce the flavor of the final product [44]. Additionally, 27 characteristic proteins were identified to be related to volatile compounds formed from protein degradation in the flavor compound formation pathway; the specific protein-related information is shown in Table 4. The main Kyoto Encyclopedia of Genes and Genomes (KEGG) pathways involved were metabolic pathways, carbon metabolism, propanoate metabolism, the TCA cycle, and amino acid catabolism. According to KEGG pathway enrichment analysis, amino acid metabolism pathways, including glutathione, cysteine, methionine, arginine, proline, alanine, aspartate, and glutamate metabolism pathways, were affected at every stage of LTS. The results of the KEGG analysis aligned with those of previous studies [6], showing that interactions with the TCA cycle can significantly affect purine and amino acid metabolisms, which ultimately impact flavor regulation. Figure 5C shows the correlation analysis between the levels of characteristic volatile compounds and the degradation or oxidation of proteins, further demonstrating the relationship between protein and flavor compounds. The results indicated that volatile compounds were positively correlated with TCA and free amino acids and negatively correlated with the concentration of myofibrillar and sarcoplasmic proteins. This suggests that protein degradation plays a key role in flavor formation. It has been demonstrated that free amino acids are the primary compounds produced by protein hydrolysis and that the interactions between these compounds are the most critical factors leading to changes in volatile compounds [10]. This is consistent with the results of proteomics. This study found a positive correlation between volatile compounds and carbonyl content and a negative correlation between volatile compounds and total sulfhydryl content, aligning with the findings of previous analyses [45]. Carbonyl compounds, such as aldehydes and  
ketones, significantly influence the flavor of meat products, and these substances are mostly generated by protein oxidation [46].
## 3 Methods
### ViT-Based Module with MSCA and FFN  
The conventional Transformer module utilizes the multi-head attention and multilayer perceptron (MLP) modules. Different from traditional methods, the approach introduced in this paper adopts the multi-scale convolutional attention (MSCA) module [6] and the feed-forward network (FFN) module. The MSCA module uses multi-branch depth-wise convolutions to extract information at different scales and employs depth-wise convolutions and 1 \(\times\) 1 convolutions to fuse information across different channels. The FFN module consists of deep-wise convolution and 1 \(\times\) 1 convolution layers. The remaining part, i.e., BN, refers to batch normalization, which helps stabilize training and accelerate the network's convergence rate. Based on such a structure, the ViT-based module with MSCA and FFN can be formulated as:  
Figure 3: Comparison of inference structures of three types of networks. (**a**–**c**) refer to the inference processes used in the traditional semantic segmentation network, mask classification network, and MCDCNet, respectively.  
\[\begin{split}\tilde{Z}&=\text{MSCA}\Big{(}\text{BN}\Big{(}Z^{l- 1}\Big{)}\Big{)}+Z^{l-1},\\ Z^{l}&=\text{FFN}\big{(}\text{BN}\big{(}\tilde{Z} \big{)}+\tilde{Z}\end{split} \tag{1}\]  
where \(\tilde{Z}\) and \(Z^{l}\) represent the outputs of the MSCA module and the FFN module. \(Z^{l-1}\) represents the input feature of the whole module shown in Figure 4. The detailed explanation of these formulas will be presented in the Appendix A on page 4.
# Performance Evaluation Method for Intelligent Computing Components for Space Applications
## 4 Benchmark Execution and Evaluation
### CoreMark-Pro Benchmark Experiment Results  
The CoreMark-Pro benchmark test measures the computational performance of a system by performing a series of basic arithmetic and logical operations. This benchmark can highlight the strengths and weaknesses of the processor. In this experiment, the configurations on the three platforms all use four multi-core CPUs for calculations, and the final CoreMark-PRO score is generated by processing them through Perl scripts. The ratio of single-core and multi-core experimental results is then calculated. The test results are shown in Table 2, where the scores represent the number of algorithm executions performed by the system in a fixed time.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Jetson AGX Xavier** & **ASUS FL8000** & **Loongson Platform** \\ \hline \multirow{2}{*}{CPU} & Nvidia Carmel & i7-8550U & 3A4000 \\  & 8-core 2.3 GHz & 4-core 1.8 GHz & 4-core 1.8 GHz \\ \hline \multirow{2}{*}{Three-level cache} & 4 MB & 8 MB & 8 MB \\ \hline \multirow{2}{*}{GPU} & Volta GV10B & Maxwell 940 MX & Veiglo BI-V100 \\  & 1.4 GHz & 1.2 GHz & 1.5 GHz \\ \hline \multirow{2}{*}{CUDA cores} & 512 CUDA cores & 384 CUDA cores & 3072 CUDA cores \\ \hline \multirow{2}{*}{Tensor cores} & Support & Not Support & Not Support \\ \hline \multirow{2}{*}{GPU memory} & 32 GB DDR4 & 2 GB G DDR5 & 32 GB HBM2 \\  & Sharing & Independent & Independent \\ \hline Power & 30 W/15 W/10 W & 15-200 W & 220 W \\ \hline \multirow{2}{*}{CUDA version} & CUDA11.4 & CUDA11.4 & CUDA10.2 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Basic performance parameters of experimental platforms.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Calculate Platform** & **Multi-Core** & **Single-Core** & **Scaling** \\ \hline Jetson AGX Xavier & 14,360.88 & 3734.97 & 3.84 \\ ASUS FL8000 & 22,599.79 & 6525.45 & 3.46 \\ Loongson platform & 7040.61 & 1927 & 3.65 \\ \hline \hline \end{tabular}
\end{table}
Table 2: CoreMark-Pro experiment results (unit: iter/s).  
A higher score means that the processor can perform more computing tasks in a given time, reflecting its stronger performance. From the table above, it can be seen that for multi-core experimental results, the ASUS FL8000 platform has the highest CPU score, followed by the Jetson AGX Navier platform. The multi-core experimental scores of the Loongson platform are about half and one-third of that of the Jetson AGX Xavier platform and the ASUS FL8000 platform.
## 4 Evaluation
### Evaluation Metrics
\begin{bmatrix}s(P_{1},Q_{1})&s(P_{1},Q_{2})&\dots&s(P _{1},Q_{m_{Q}})\\ s(P_{2},Q_{1})&s(P_{2},Q_{2})&\dots&s(P_{2},Q_{m_{Q}})\\ \vdots&\vdots&\ddots&\vdots\\ s(P_{m_{P}},Q_{1})&s(P_{m_{P}},Q_{2})&\dots&s(P_{m_{P}},Q_{m_{Q}})\\ \end{bmatrix}  \tag{15}\]  
Based on the score matrix, the establishment matrix is calculated from the set of annotated patterns \(\Pi\) and the set of algorithm's output patterns \(\Xi\):  
\[S(\Pi,\Xi)= \begin{bmatrix}S(\mathcal{P}_{1},Q_{1})&S(\mathcal{P}_{1},Q_{2})& \dots&S(\mathcal{P}_{1},Q_{m_{Q}})\\ S(\mathcal{P}_{2},Q_{1})&S(\mathcal{P}_{2},Q_{2})&\dots&S(\mathcal{P}_{2},Q_ {m_{Q}})\\ \vdots&\vdots&\ddots&\vdots\\ S(\mathcal{P}_{np},\mathcal{Q}_{1})&S(\mathcal{P}_{np},\mathcal{Q}_{2})&\dots&S( \mathcal{P}_{np},\mathcal{Q}_{n_{Q}})\\ \end{bmatrix}  \tag{16}\]  
The establishment precision is thus defined as:  
\[P_{est}=\frac{1}{n_{\mathcal{Q}}}\sum_{j=1}^{n_{\mathcal{Q}}}\max\{S(\mathcal{ P}_{i},Q_{j})|i=1\dots n_{\mathcal{P}}\} \tag{17}\]  
The establishment recall is defined as:  
\[R_{est}=\frac{1}{n_{\mathcal{P}}}\sum_{j=1}^{n_{\mathcal{P}}}\max\{S(\mathcal{ P}_{i},Q_{j})|i=1\dots n_{\mathcal{Q}}\} \tag{18}\]  
Additionally, the establishment \(F_{1}\) score is calculated as:  
\[F1_{est}=2\times P_{est}\times R_{est}/(P_{est}+R_{est}) \tag{19}\]  
The establishment metrics reward a single match between the annotated and algorithm's patterns. To counterbalance this bias, the occurrence metrics are used. The occurrence metrics reward the algorithm's ability to find all occurrences of a single pattern. To loosen the exactness, the found patterns may be inexact. This inexactness is implemented using a threshold \(c\) (default values used in the 0.5 and 0.75), The indices \(\mathcal{I}\) of the establishment matrix with values greater than or equal this threshold \(c\) are considered discovered. The occurrence matrix \(O(\Pi,\Xi)\) is calculated using the following approach, starting with an empty \(n_{\mathcal{P}}\times n_{\mathcal{Q}}\) matrix and the establishment indices \(\mathcal{I}\):  
\[\forall(i,j)\in\mathcal{I}:O(\Pi,\Xi)[i,j]=s(\mathcal{P}_{i},\mathcal{Q}_{j}). \tag{20}\]  
The occurrence precision score is consequently calculated using the occurrence matrix as follows:  
\[P_{occ}=\frac{1}{n_{col}}\sum_{j=1}^{n_{\mathcal{Q}}}O(i,j)|i=1\dots n_{ \mathcal{P}}, \tag{21}\]  
where \(n_{col}\) represents the number of non-zero columns in occurrence matrix \(O\). The occurrence recall score is analogously calculated as:  
\[R_{occ}=\frac{1}{n_{row}}\sum_{j=1}^{n_{\mathcal{P}}}S(i,j)|i=1\dots n_{ \mathcal{Q}}, \tag{22}\]  
where \(n_{row}\) represents the number of non-zero rows in the occurrence matrix \(O\).