esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Experimental Verification Using Benchmark Test Functions  
In this section, the improved reptile search algorithm (IRSA) was tested using 23 standard benchmark functions [46]. These functions were unimodal, multimodal, and fixed-dimension minimization problems. The specifications of the test functions are provided in Tables A1-A3. For further verification, the IRSA results were compared with the RSA algorithm and also with other classical and state-of-the-art metaheuristic techniques, like barnacle mating optimizer (BMO) [47], particle swarm optimization (PSO) [48], grey wolf optimizer (GWO) [49], arithmetic optimization algorithm (AOA) [50], and dynamic group-based cooperative optimization algorithm (DGCO) [51]. The numbers of iterations taken were 500 and 350, with a fixed population size of 50. For IRSA, \(\alpha\) and \(\beta\) were set to 0.1. Furthermore, statistical analysis was performed by considering 30 runs for various performance measures like best, worse, and average values and standard deviation (STD). Lastly, time complexity analysis was performed on CEC-2019 test functions. The simulations were performed using a desktop computer Core i5 with 12 GB RAM. The software used for the simulation was MATLAB (R2018a).
## 4 Blockchain-Based LWE-CP-ABE Data Sharing Scheme  
### Overview of Blockchain-Based LWE-CP-ABE  
To ensure efficient data sharing and access policy updating on the blockchain, all activities of the ciphertext access control scheme, such as generating the public parameters, secret keys, and oracle functions, are written into the distributed ledger on blockchain. Users can access the authorized data through their user attribute secret key controlled over the blockchain, which matches their attributes, and complete the secure and traceable data sharing. The blockchain-based data-sharing framework of the LWE-CP-ABE is shown in Figure 2. Here, the blockchain system is built with pre-quantum cryptography for master key management and immutable storage of transactions, and CP-ABE is constructed with post-quantum cryptography for access and sharing of ciphertext. The system characters play particular roles described as follows:  
(1) User (DO, DU). It includes the data owner (DO) and the data user (DU).  
When a DO wants to share this information with DU, they can create a policy with the LSSS matrix to grant access to DU. Thus DO generates the global parameters, encrypts the corresponding message, and uploads the transactions to the blockchain.  
At the same time, if different DUs want to access the data, they must request the secret keys from the nodes on the blockchain. The DUs use it to decrypt the ciphertext obtained from the third-party storage;  
(2) Third-party storage (TPS). It provides API storage services for encrypted data, such as distributed file-sharing network IPFS, and its hash addresses are stored on the blockchain;  
(3) Blockchain Network (BN). It comprises a participant node on the blockchain that stands ready to provide decentralized key management services and creates a symmetric key for the master secret key of CP-ABE for the data users. Additionally, the blockchainsystem provides traceability and auditability of transactions involved in the LWE-CP-ABE access control protocol;  
(4) Key Management Network (KMN). A group of blockchain nodes that provides an application of the Proxy Re-Encryption (PRE) scheme ensuring the security of the master-secret key distribution in the LWE-CPABE encryption algorithm.
## 3 Results
### Serum-Specific IgE Measurements  
Serum-specific IgE measured by ImmunoCAP(tm) (monoplex, Thermo Fisher Scientific, Uppsala, Sweden) for almond was positive in 10/27 cases. Specific IgE measured by ISAC (multiplex, Thermo Fisher Scientific, Uppsala, Sweden) was positive in all 42 sera. Specific IgE was positive in 18/20 for Mal d1 (apple), 40/42 for Cor a1 (hazelnut), 20/22 for Pru p1 (peach), 19/28 for Ara h8 (peanut), and 3/30 for Jug r 1 (walnut). The median and range of all IgE measurements are shown in Table 4.  
It appeared that other allergen components were only positive in a few cases; hazelnut Cor a8 and peach Pru p3 (both lipid transfer proteins [LTP]) were only positive in two and one patients, respectively, while major 2S album  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Serum Specific IgE Measurements**} \\ \hline  & & _n =_ & **Positive _n =_** & **Mean ISU** & **Range ISU** \\ \hline Almond * & & 27 & 10 & 0.60 * & 0.0–2.98 * \\ Apple & Mal d1 & 20 & 18 & 15.38 & 0–64.1 \\ Hazelnut & Cor a1 & 42 & 40 & 7.42 & 0–31.2 \\  & Cor a8 & 42 & 2 & 1.34 & 0–54.4 \\  & Cor a9 & 42 & 2 & 0.30 & 0–9.83 \\  & Cor a14 & 42 & 3 & 3.03 & 0–105.6 \\ Peach & Pru p1 & 22 & 20 & 7.50 & 0–60.9 \\  & Pru p3 & 22 & 1 & 0.23 & 0–4.67 \\ Peanut & Ara h2 & 28 & 5 & 1.56 & 0–20.3 \\  & Ara h6 & 28 & 5 & 1.15 & 0–14.4 \\  & Ara h8 & 28 & 19 & 2.88 & 0–14.0 \\  & Ara h9 & 28 & 3 & 3.39 & 0–8.29 \\ Walnut & Jug r1 & 30 & 3 & 2.41 & 0–65 \\  & Jug r3 & 30 & 0 & 0 & 0 \\ \hline \hline \end{tabular} \(n\) = number; * = measured by ImmunoCAP(tm) Thermo Fisher Scientific, Uppsala, Sweden  
\end{table}
Table 4: Serum specific IgE measurements.  
Figure 2: SPT-HEP results of ALK and HM extracts in relation to symptoms (proportion of agreement) and CI of 6 food allergens. ALK = Allergy Laboratories Kopenhagen, Denmark; HM = homemade.  
h2 and Ara h6 were only positive in three, five and five cases, respectively. Proportion of agreement calculations were not feasible for these allergen components due to low power.  
The proportion of agreement of specific IgE measurements in relation to symptoms and CI was calculated: for almond: 0.29 (CI 0.11-0.47); apple (Mal d1; PR10): 0.79 (CI 0.61-0.97); hazelnut (Cor a1; PR10): 0.80 (CI 0.68-0.93); peach (Pru p1; PR-10): 0.73 (CI 0.54-0.91); peanut (Ara h8; PR10): 0.71 (CI 0.53-0.89); and for walnut (Jug r1; 2S albumine): 0.21 (CI 0.05-0.37).
# Multi-Objective Gate Allocation Problem Based on Multi-Commodity Network Flow Model
## 6 Conclusions  
The flight-to-gate allocation has always been one of the core issues for the operation of airport surfaces. In order to generate an effective and efficient gate allocation scheme and improve the operating efficiency of the airport surface, a multi-objective optimization model for gate allocation was established based on the multi-commodity network flow, which considers the multiple interests of passengers, airlines, and airports. To solve this model, a linear weighting technique was applied, and its various weight combinations were discussed using clustering algorithms. The variance of idle time was also introduced to evaluate the pros and cons of different solutions. Experiments using actual operating data show that the model can reasonably allocate gate resources with a high utilization and robustness. The proposed model can be regarded as a powerful decision support tool for air traffic controllers. According to the published flight plan, it can quickly generate a reasonable gate allocation scheme to realize the airport resource scheduling and configuration in the pre-tactical stage.  
Future work will verify the generalizability of the proposed model in more diverse operational data. In addition, how to combine other resources of the airport, such as taxiways, runways, etc., to deeply examine the surface resource scheduling problem at the micro level is also an interesting topic.  
Conceptualization, J.D. and M.H.; methodology, J.D. and J.Y.; software, J.D. and W.Z.; validation, J.D., M.H., J.Y. and W.Z.; formal analysis, J.D.; investigation, J.Y.; resources, M.H.; data curation, J.Y.; writing--original draft preparation, J.D. and J.Y.; writing--review and editing, J.D. and M.H.; visualization, J.D. and W.Z.; supervision, M.H.; project administration, M.H.; funding acquisition, J.D., M.H., J.Y. and W.Z. All authors have read and agreed to the published version of the manuscript.  
This work is partially supported by the National Key R&D Program of China (2021 YFB1600500), National Natural Science Foundation of China (52002178, 71731001), Natural Science Foundation of Jiangsu Province (BK20190416), Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX22_0377, KYCX22_0373), Interdisciplinary Innovation Fund for Doctoral Students of Nanjing University of Aeronautics and Astronautics (KKCXJ)202202), and China Scholarship Council (202106830100, 202106830077).  
Not applicable.  
Due to the nature of this research, participants of this study did not agree for their data to be shared publicly, so supporting data are not available.  
The authors declare no conflict of interest.
# Bias and Variance Analysis of Contemporary Symbolic Regression Methods
## 3 Experiments  
Our analysis builds upon the data sets and models of the SRBench benchmark [8]. SRBench provides an in-depth analysis of performance and model size of contemporary SR methods on many data sets. The methodology and the results of this benchmark fit perfectly for our purpose, and we can rely on a reviewed setting of algorithms and benchmark data.  
SRBench uses the data sets of the PMLB benchmark suite [9; 18], the Feynman Symbolic Regression Database [19] and the ODE-Strogatz repository [20]. In total, it contains both real world data and generated data, where the ground truth and noise distribution is known. In this work, we will use SRBench's results on the 116 datasets from the Feynman  
Figure 2: Polynomial regression performed on the data from Figure 1 with different polynomial degrees as hyperparameter. The left column shows in each plot 20 different polynomials that were trained on different training sets. The right column shows the distribution and histogram of the error of 1000 different polynomials at \(x=4\) and reveal bias and variance of the algorithm and its hyper-parameters.  
Symbolic Regression Database because the ground truth and data distribution is known, so we can arbitrarily generate new data. We refer to those problems as Feynman problems in the following. The Feynman problems are mostly low-dimensional, nonlinear expression that were taken from physics textbooks [21].  
In SRBench, four different noise levels \(\sigma\) are used for Feynman problems. Given a problem-specific ground truth \(f(x)\), training data \(y\) for one problem are generated with \(y=f(x)+\epsilon,\epsilon\sim\mathrm{N}(0,\sigma)\) and \(\sigma\in\{0,0.001,0.01,0.1\}\), with \(\mathrm{N}(0,0)\) meaning no noise. This results in 464 combinations of data sets and noise levels. For each of those 464 problems, ten models were trained in the SRBench benchmark per algorithm. A different training set is sampled for each of the ten models [8]. All ten models were trained with the same hyperparameters, which is suitable for our study, because bias and variance are only caused by the search procedure and not by differences in hyperparameters.  
We compare both the accuracy, the model size, bias, and variance. We use the root mean squared error (RMSE) to measure the accuracy, since it is on the same scale as the applied noise and therefore the bias and variance. The model size is the number of symbols in the model as defined in SRBench [13]. The model size describes the inverse of parsimony and is used as a notion of simplicity of a model.
## 2 Background
### Generalized Partial Response (GPR) Target and Equalizer
\[\mathbf{C}^{T}\mathbf{g}=\alpha, \tag{11}\]  
where \(\alpha\) is constant in, and  
\[\mathbf{C}^{T}= \begin{bmatrix}0&0&0&0&1&0&0&0&0\end{bmatrix} , \tag{12}\]  
With (10) and (12), we can present the optimized problem as below. \[ \begin{split}\underset{\begin{subarray}{c}t_{\mathbf{g}}\\ \text{s.t.}\end{subarray}}{\text{argmin}}(e[j,k])\\ \text{s.t.}&\mathbf{C}^{T}\mathbf{g}=\alpha\end{split}  \tag{13}\]  
To solve (13), the Lagrange function is used as below. \[L=e[j,k]-2\lambda\Big{(}\mathbf{C}^{T}\mathbf{g}-\alpha\Big{)}, \tag{14}\]  
where \(\lambda\) is a vector containing the Lagrange multipliers. The answers of (14) are presented as follows:  
\[\lambda=\bigg{(}\mathbf{C}^{T}\Big{(}E\Big{\{}\mathbf{aa}^{T}\Big{\}}-E\{ \mathbf{ya}\}^{T}E\{\mathbf{yy}\}^{-1}E\{\mathbf{ya}\}\Big{)}^{-1}\mathbf{C} \bigg{)}^{-1}\alpha, \tag{15}\]  
\[\mathbf{g}=\bigg{(}E\Big{\{}\mathbf{aa}^{T}\Big{\}}-E\Big{\{}\mathbf{ya}^{T} \Big{\}}^{T}E\Big{\{}\mathbf{yy}^{T}\Big{\}}E\Big{\{}\mathbf{ya}^{T}\Big{\}} \bigg{)}^{-1}\mathbf{C}\lambda,\text{ and} \tag{16}\]  
\[\mathbf{f}=E\Big{\{}\mathbf{yy}^{T}\Big{\}}^{-1}E\{\mathbf{ya}\}\mathbf{g}. \tag{17}\]  
After using (15)-(17) to obtain \(\mathbf{g}\) and \(\mathbf{f}\), we can analyze the GPR target as below. \[\mathbf{G}= \begin{bmatrix}g_{-1,-1}&g_{-1,0}&g_{-1,1}\\ g_{0,-1}&g_{0,0}&g_{0,1}\\ g_{1,-1}&g_{1,0}&g_{1,1}\end{bmatrix} = \begin{bmatrix}pr&pl_{2}&pr\\ l_{1}r&l_{1}l_{2}&l_{1}r\\ pr&pl_{2}&pr\end{bmatrix} = \begin{bmatrix}p\\ l_{1}\\ p\end{bmatrix}\begin{bmatrix}r&l_{2}&r\end{bmatrix} , \tag{18}\]  
where \(r\) and \(p\) are the horizontal and vertical interferences, respectively, and \(l_{1}\) and \(l_{2}\) are the general parameters to fit the form of the GPR target \(\mathbf{G}\). We set \(l_{1}=1\) and obtain the parameters as below. \[r=g_{0,1}, \tag{19}\]  
\[p=\frac{g_{1,0}}{g_{0,0}}, \tag{20}\]  
\[l_{2}=g_{0,0}. \tag{21}\]
# LEO-Augmented GNSS Based on Communication Navigation Integrated Signal
## 1 Introduction
### Methods for Signal Integration  
There are mainly three kinds of methods to realize integration of navigation signal and communication signal. They are described as follows [13; 14]:  
Method 1: Low-power navigation signal is added to the communication signal. Equation (1) is the expression for method 1 and Figure 1 shows the power spectral density (PSD) of the signal generated by method 1.  
\[s(t)=s_{c}(t)+s_{nw}(t) \tag{1}\]  
Method 2: The navigation signal is launched in multiple frames. The expression is shown in panel (  
The bandwidth of the signal can also be composed of multiple unit bands as Equation (3).  
In the concept of STL, the navigation signal is created by method 2. The length of STL signal is 20.32 ms and the bandwidth is one unit band. Limited bandwidth and time length means that the STL signal is of limited performance.  
\(CNSR\) is used in this paper to describe the communication navigation signal power rate in the following parts. It is expressed as  
\[CNSR=P_{c}/P_{nav} \tag{5}\]  
where \(P_{c}\) is the power of the communication signal and \(P_{nav}\) is the power of the navigation signal.
# A Review of the Control Plane Scalability Approaches in Software Defined Networking
## 2 Topology Based Scalability
### Centralized Controller Designs  
The centralized design creates networks that are easy to manage which can fulfil the requirements of small to medium-sized networks, see Figure 3. However, the design fails in managing more complex network environments like data centers and large-scale networks. This is due to the large amount of network traffic that would overload the controller. Thus, this design is less scalable compared to the distributed designs. Some approaches devoted to address its limitations, the most prominent solutions to this date are Ethane [10] and NOX [11].  
Figure 2: Classification of Control Plane Scalability Approaches.  
Ethane architecture [10] aims at enhancing the enterprise networks by allowing network administrators to define policies where each request that does not match a flow entry has to pass through the controller. Three concerns are addressed by the Ethane architecture. First, high-level names policies should govern the network. Second, in order to improve the network control and view, these policies handles packets follow paths. Third, the network enforces consistent binding between packets and their origin (i.e., user, machine, address, etc.).  
NOX operating system [11] was proposed due to the need for a centralized and uniform program interface that would make networks easier to manage. It handles the packets with basis on a flow's first packet traversing through the controller. This approach enables comprehensive control and observation of the network traffic. Researchers have investigated whether NOX and other generalized solutions are able to handle characteristic requirements of specialized networks such as data centers.  
Both approaches NOX and Ethane are proposed to deal with the limitations of the centralized design. NOX enabled more manageable network on a single controller, however, the network size that it can handle is relatively small compared to the distributed designs. On the other hand, Ethane enables easy use of centralized controllers in enterprise networks, however, it fails in handling large enterprise networks. Despite the efforts of the researchers that constructed these proposals, it seems that centralized controller designs cannot keep up with the distributed designs in terms of scalability and throughput. Moreover, both approaches do not take into consideration the single point of failure risk. Apparently, depending on a single central controller is a huge risk as the whole network goes offline in case of controller failure.
## 2 Nonlinear Wiener Process with Covariates  
### Nonlinear Wiener Process  
Due to a typical feature that a product's degradation path can increase or decrease, Wiener process models have been extensively applied to most degradation failure products.  
For a specific product, assuming \(X(t)\) to be the performance value of the product at time \(t\), a nonlinear Wiener process model is usually expressed in Equation (1).  
\[X(t)=X(0)+\lambda\Lambda(t)+\sigma_{\text{B}}B(\Lambda(t)) \tag{1}\]  
where the initial value is assumed to \(X(0)=0\), the drift parameter describing degradation rate is \(\lambda\), the diffusion parameter depicting degradation variation is \(\sigma_{\text{B}}\), \(\Lambda(t)\) is the continuous non-decreasing function of time, and \(B(\Lambda(t))\) is the nonlinear Brownian motion which is applied to reflect the uncertainty of the degradation on the time axis.  
Assuming that the performance parameter of a product serves the Wiener process, \(T\) is the failure threshold of the performance parameter, the product's life can be defined as the first hitting time (FHT). In this case, the FHT of the product is usually represented as Equation (2).  
\[T=\inf\{t|X(t)\geq D\} \tag{2}\]  
where \(D\) is the failure threshold.  
Based on the nature of the Wiener process, it has the following characteristics:  
(1) The degradation increments are independent and identically distributed, following \(\Delta X(t)=X(t+\Delta t)-X(t)\sim N\big{(}\lambda\Delta\Lambda(t),\sigma_{ \text{B}}^{2}\Delta\Lambda(t)\big{)}\), and the probability density function (PDF) of \(\Delta X(t)\) is shown in Equation (3).  
\[f_{\Delta X}(\Delta x|\lambda,\sigma_{\text{B}})=\frac{1}{\sqrt{2\pi\sigma_{ \text{B}}^{2}\Lambda(t)}}\exp\left[-\frac{(\Delta x-\lambda\Lambda(t))^{2}}{2 \sigma_{\text{B}}^{2}\Lambda(t)}\right] \tag{3}\]  
(2) The FHT of the product obeys an inverse Gaussian distribution (IG), and the probability density function (PDF) and cumulative distribution function (CDF) of FHT are shown in Equations (4) and (5).  
\[f(t)=\frac{D}{\sqrt{2\pi\sigma_{\text{B}}^{2}\Lambda^{3}(t)}}\exp\left(-\frac {(D-\lambda\Lambda(t))^{2}}{2\sigma_{\text{B}}^{2}\Lambda(t)}\right)\frac{d \Lambda(t)}{dt} \tag{4}\]  
\[F(t)=\Phi\left(\frac{\lambda\Lambda(t)-D}{\sigma_{\text{B}}\sqrt{\Lambda(t)}} \right)+\exp\left(\frac{2\lambda D}{\sigma_{\text{B}}^{2}}\right)\Phi\left(- \frac{\lambda\Lambda(t)+D}{\sigma_{\text{B}}\sqrt{\Lambda(t)}}\right) \tag{5}\]  
where \(\Phi(\cdot)\) is the CDF of the standard normal distribution.
## 1 Introduction
### Coastal Monitoring
When utilizing diverse parameters from these modules or employing data acquired through different principles in scientific investigations, the reliability of the findings may be impacted by the inherent characteristics of these modules. The efficiency, safety, and precision of data acquisition in coastal mapping endeavors are significantly influenced by various UAVs and sensors, particularly when ground control points are lacking. When examining tidal flats, not using ground control points is crucial because there is a need to deploy measurements rapidly during the lowest tide. At the same time, due to the unique characteristics of the intertidal zone, placing image control points and finding ground features with distinct markers pose certain challenges.
## 5 Proposed Method
### Reward Function Design  
To encourage UAVs to search and track more targets, UAVs need to balance between tracking the already perceived targets and exploring the mission region. Besides, they should avoid overlapping the sensing range to maximize the total detection area. Rewards are used to shape expectations in reinforcement learning. Therefore, it is critical to devise reasonable rewards for the multi-UAV system. The reward function proposed in our paper consists of three rewards:  
\[r_{i,t}=r_{i,t}^{1}+r_{i,t}^{2}+r_{i,t}^{3}, \tag{34}\]  
where \(r_{i,t}\) is the reward for UAV \(U_{i}\) at timestep \(t\).  
**Tracking reward:** We use \(r_{i,t}^{1}\) to encourage UAVs to track the discovered targets. It is commonly believed that the closer the UAV is to a target, the better the UAV can track the target. Thus, the reward for UAV \(U_{i}\) to track target \(V_{k}\) at timestep \(t\) is as follows:  
\[r_{i,t}^{1}(V_{k})=\left\{\begin{array}{ll}1+(R_{s}-\|\mu_{i,t}-\
u_{k,t}\|) /R_{s},&\|\mu_{i,t}-\
u_{k,t}\|\leqslant R_{s}\\ 0,&\text{else}.\end{array}\right. \tag{35}\]  
And the reward of UAV \(U_{i}\) at timestep \(t\) for tracking multiple targets can be calculated as \(r_{i,t}^{1}=\omega_{1}\sum_{k=1}^{N_{V}}r_{i,t}^{1}(V_{k})\), where \(\omega_{1}\) is a positive coefficient.  
**Exploring reward:** The reward \(r_{i,t}^{2}\) encourages UAVs to explore the mission region and can be represented as follows:  
\[r_{i,t}^{2}=\omega_{2}(\beta_{i,t}-\beta_{i,t-1}), \tag{36}\]  
Figure 2: Network architecture of recurrent-MAPPO. (**a**) Policy network. (**b**) Value network.  
where \(\omega_{2}\) is a positive coefficient. In Equation (36), \(\beta_{i,t}\) denotes the local exploration rate of the mission area of UAV \(U_{i}\) at timestep \(t\) and \(\beta_{i,t}\) can be denoted as follows:  
\[\beta_{i,t}=\frac{1}{t}\frac{1}{L_{x}L_{y}}\sum_{x=1}^{L_{x}}\sum_{y=1}^{L_{y}} \mathcal{E}_{i,t}^{x,y}, \tag{37}\]  
which can be calculated using its local environment search status map \(\mathcal{E}_{i,t}\).  
**Overlapping punishment:** The reward \(r_{i,t}^{3}\) is designed as a punishment of UAV \(U_{i}\) for approaching UAV \(U_{j}\) too close, which can be represented as follows:  
\[r_{i,t}^{3}\big{(}U_{j}\big{)}=\left\{\begin{array}{ll}-\exp\Big{(}\big{(}2R _{s}-\big{\|}\mathbf{\mu}_{i,t}-\mathbf{\mu}_{j,t}\big{\|}\big{)}/\Big{(}2R_{s}\Big{)} \Big{)},&\big{\|}\mathbf{\mu}_{i,t}-\mathbf{\mu}_{j,t}\big{\|}\leqslant 2R_{s}\text{ and }i\
eq j\\ 0,&\text{else}.\end{array}\right. \tag{38}\]  
Therefore, the punishment of UAV \(U_{i}\) at timestep \(t\) for approaching multiple UAVs too close can be represented as \(r_{i,t}^{3}=\omega_{3}\sum_{j=1}^{N_{\text{U}_{i}}}r_{i,t}^{3}(U_{j})\), where \(\omega_{3}\) is a positive coefficient.