esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 The Model
### Dynamic Programming Formulation  
We consider a total of \(T\) periods. In period \(t\), the population size of potential customers is \(N-\sum_{i=1}^{m}S_{i,t}\). Each potential customer either subscribes to a data plan or does not join the network. Let \(Y_{i,t}\) be the number of new customers subscribing to data plan \(i\) in period \(t\). Therefore, we can build a multinomial distribution model for \(Y_{t}=(Y_{1,t},\cdots,Y_{m,t})\); that is, \(Y_{t}\sim\text{PN}(N-\sum_{i=1}^{m}S_{i,t}:\lambda p_{1,t},\cdots,\lambda p_{ m,t})\). For all \(0\leq\sum_{i=1}^{m}y_{i,t}\leq N-\sum_{i=1}^{m}S_{i,t}\), we have the probability mass function:  
\[\Pr(Y_{t}=y_{t}) = \Pr(Y_{1,t}=y_{1,t},\cdots,Y_{m,t}=y_{m,t})\] \[= \frac{(N-\sum\limits_{i=1}^{m}S_{i,t})!(1-\lambda)^{(N-\sum \limits_{i=1}^{m}S_{i,t}-\sum\limits_{i=1}^{m}y_{i,t})}(\lambda p_{1,t})^{y_{1, t}}\cdots(\lambda p_{m,t})^{y_{m,t}}}{(N-\sum\limits_{i=1}^{m}S_{i,t}-\sum\limits_{i=1}^ {m}y_{i,t})!(y_{1,t})!\cdots(y_{m,t})!}.\]  
Similar to the classification we employ for subscribed customers, we classify new customers into three categories and denote \(Y_{i,t}^{A}\), \(Y_{i,t}^{B}\), and \(Y_{i,t}^{C}\) as the number of new customers in the \(A\), \(B\), and \(C\) categories, respectively. In addition, we assume that \(Y_{i,t}^{C}/(Y_{i,t}^{B}+Y_{i,t}^{C})=w_{i}\). The willingness to purchase supplementary data packages is heterogeneous for customers with different data plans, but homogeneous for old customers and new customers.  
Let \(L_{i,t}\) be the number of customers quitting plan \(i\) at the end of period \(t\). A subscribed customer either does not quit the service or quits the service at the end of period. Therefore, we can build a binomial distribution model for \(L_{t}=(L_{1,t},\cdots,L_{m,t})\); that is, \(L_{i,t}\sim\text{B}(S_{i,t},q_{i,t})\). For all \(0\leq l_{i,t}\leq S_{i,t}\), we have the probability mass function:  
\[\Pr(L_{t}=l_{t}) = \Pr(L_{1,t}=l_{1,t})\cdots\cdots\Pr(L_{m,t}=l_{m,t})\] \[= \prod_{i=1}^{m}\frac{S_{i,t}!}{l_{i,t}!(S_{i,t}-l_{i,t})!}(q_{i,t })^{l_{t}}(1-q_{i,t})^{S_{i,t}-l_{i,t}}.\]  
Let \(V_{t}(S_{t})\) be the service provider's maximum revenue from period \(t\) to the end, starting at state \(S_{t}=(S_{1,t},\cdots,S_{m,t})\) at the beginning of period \(t\). The dynamic programming problem, which is to maximize \(V_{t}(S_{t})\) by choosing the right \(C_{i,t}\), can be written as follows:  
**(DP1)**: \[V_{t}(S_{t})\] \[= \sum_{i=1}^{m}\Bigl{(}\mathbb{E}[S_{i,t}^{A}]+\mathbb{E}[S_{i,t}^ {B}]\Bigr{)}\cdot b_{i}+\sum_{i=1}^{m}\sum_{k=1}^{k^{*}}\mathbb{E}[S_{i,t}^{C,k}]\cdot(b_{i}+k\cdot b_{i}^{s})+\mathbb{E}[Y_{t+1}(S_{t+1})]\Bigr{\}},\quad \forall\ t.\]  
The transition function is \(S_{t+1}=S_{t}+Y_{t}-L_{t}\), and the boundary conditions are \(V_{T+1}(S_{T+1})=0\) for all \(S_{T+1}\).
###### Abstract  
Permafrost, as a soil type under unique environmental conditions, has bearing characteristics that are highly susceptible to thermo-hydraulic environments. Rapid evaluation of the bearing characteristics of in situ permafrost at various depths in perennially frozen regions is a critical scientific issue urgently needing resolution in the road design and construction sectors in China. To address this, this study investigates the correlation between CPT parameters and laboratory mechanical indices under the combined effects of multiple factors in frozen sandy soils. By conducting both CPT and CBR tests on frozen sandy soils, the study analyzes the trends in changes in cone tip resistance (\(q_{\rm c}\)) and CBR values under the influence of temperature (\(T\)), moisture content (\(\omega\)), and compaction degree (\(K\)) and establishes a functional relationship between them. Based on the standard requirements for indoor CBR, an evaluation criterion using \(q_{\rm c}\) for assessing the bearing capacity of frozen sandy soil is proposed. The results indicate that both CBR values and \(q_{\rm c}\) increase initially and then stabilize as \(K\) increases. With decreasing temperature, both indices stabilize after an initial increase, with turning points at \(-3.1\)\({}^{\circ}\)C for CBR values and \(-2.5\)\({}^{\circ}\)C for \(q_{\rm c}\). As \(\omega\) increases, both indices first increase and then stabilize, with a turning point at \(40\%\omega\). There is a robust linear relationship between the CBR values and \(q_{\rm c}\), with the ratio of predicted CBR values to actual values showing a histogram and log-normal distribution accounting for \(81\%\) and \(51.3\%\), respectively, within a \(20\%\) accuracy level, indicating good predictive performance. Referring to the highway subgrade specifications for indoor CBR, a standard for evaluating the bearing capacity of frozen sandy soils using CPT technology is proposed. This study provides new insights for geological surveys in perennially frozen regions and a theoretical basis for the application of CPT technology in evaluating the bearing capacity of permafrost.  
frozen sandy soil; cone penetration test (CPT); California bearing ratio (CBR); bearing capacity evaluation +
Footnote †: journal: applied sciences
# Two-Party Quantum Private Comparison Protocol Based on Rotational Encryption
## 5 Security Analysis
### Outsider Attacks
Therefore, the probability of determining the valid state for a decoy photon is given by the following:  
\[p=\frac{1}{2}\bigg{(}F+\frac{1}{2}\bigg{)} \tag{13}\]  
The overall probability of detecting [PERSON] for \(\delta\) decoy photons is expressed as follows:  
\[P_{\text{detected}}=1-p^{\delta} \tag{14}\]  
As \(\delta\) increases sufficiently, the probability approaches \(1\). Without the loss of generality, let us assume that [PERSON] performs this attack on the single-photon state \(SE_{A}^{i}=|0\rangle\) (for [PERSON]) and \(SE_{B}^{i}=|1\rangle\) (for [PERSON]). Under this scenario, it follows that she can obtain no information regarding \(S_{A}^{i}\) and \(S_{B}^{i}\). From Equations (9) and (10), we derive the following relationships:  
\[ \begin{array}{c}U^{*}\big{(}|SE_{A}^{i}\rangle|E_{i}\rangle\big{)}=U^{*} \big{(}\cos\frac{a_{i}}{2}|0\rangle+\sin\frac{a_{i}}{2}|1\rangle\big{)}|E_{i }\rangle\\ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad=|0\rangle \big{(}a_{0}\cos\frac{a_{i}}{2}|e_{00}\rangle+a_{1}\sin\frac{a_{i}}{2}|e_{10} \rangle\big{)}\\ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad+|1\rangle\big{(}b_{0} \cos\frac{a_{i}}{2}|e_{01}\rangle+b_{1}\sin\frac{a_{i}}{2}|e_{11}\rangle \big{)}\end{array}  \tag{15}\]  
\[\begin{array}{c}U^{*}\big{(}|SE_{B}^{i}\rangle|E_{i}\rangle\big{)}=U^{*} \Big{(}-\sin\frac{b_{i}}{2}|0\rangle+\cos\frac{b_{i}}{2}|1\rangle\Big{)}|E_{ i}\rangle\\ \  
of the decoy photons. [PERSON] can discard these decoy photons in \(SE\prime_{A}\) and \(SE\prime_{B}\) to obtain \(SE_{A}\) and \(SE_{B}\) and measure these particles using the measurement operator \(M=|1\rangle\langle 1|\) to obtain the measurement outcomes \(MA_{i}\) and \(MB_{i}\) for [PERSON]'s and [PERSON]'s encoded qubits, respectively. Suppose that \(SE^{i}_{A}=|0\rangle\) (for [PERSON]) and \(SE^{i}_{B}=|1\rangle\) (for [PERSON]), we have  
\[MA_{i}=\Big{|}SE^{i}_{A}\Big{\rangle}|1\rangle\langle 1|\Big{|}SE^{i}_{A}\Big{\rangle} =\sin^{2}\frac{a_{i}}{2} \tag{20}\]  
\[MB_{i}=\Big{|}SE^{i}_{B}\Big{\rangle}|1\rangle\langle 1|\Big{|}SE^{i}_{B} \Big{\rangle}=\cos^{2}\frac{b_{i}}{2} \tag{21}\]  
where the measurement outcomes \(MA_{i}(MB_{i})\) are related with the encrypt key \(a_{i}\) (\(b_{i}\)). Therefore, [PERSON] cannot obtain [PERSON]'s (or [PERSON]'s) encoded qubits without knowledge of \(a_{i}\) (\(b_{i}\)). Case 4. The Trojan horse attacks  
The Trojan horse attacks primarily encompass two types: the invisible photon eavesdropping attack and the delay-photon attack [45; 46], and they are effective only in bidirectional channel communication. However, the quantum sequence is transmitted in a unidirectional quantum channel, which renders Trojan horse attacks ineffective. As a result, these attacks are automatically prevented by the design of the protocol, thereby enhancing its security against such threats. Based on the analysis presented above, we can concludethat the proposed protocol demonstrates strong resilience against external eavesdropping.
# A Review of Abnormal Crowd Behavior Recognition Technology Based on Computer Vision
## 4 Research Status of Abnormal Crowd Behavior Recognition
### Traditional Methods
#### 4.1.4 Methods Based on Clustering Discrimination  
Abnormal behavior recognition technology based on clustering is an unsupervised learning method. The core idea is to group behavior data into several clusters, most of which represent normal behavior patterns, and behaviors deviating from these clusters are regarded as abnormal.  
DBSCAN (Density-Based Spatial Clustering of Applications with Noise) is a density-based clustering algorithm that can identify clusters of any shape and can effectively mark noise points. For high-density crowd scenes, appropriate \(\varepsilon\) (neighborhood radius) and MinPts (minimum number of neighborhood points) parameters are selected, where \(\varepsilon\) determines the definition of density and MinPts determines the minimum number of points required to form a dense area. Then, DBSCAN clustering analysis is used to identify dense crowd areas under normal behavior patterns and detect abnormal points that cannot be assigned to any cluster. [PERSON] et al. [41] proposed a method combining DBSCAN and neural networks for the dynamic detection of abnormal crowd behaviors in video analysis. This method uses the density-based feature of the DBSCAN algorithm to identify the dense areas of the crowd in video surveillance and further analyzes the behavior patterns of these areas through neural networks to identify abnormal behaviors that are different from normal behavior patterns.  
In summary, Table 3 summarizes the design idea, advantages, and disadvantages of the above various abnormal behavior recognition technologies based on traditional methods. Although these traditional methods can effectively identify abnormal behaviors to a certain extent, a common limitation is that they still rely on manually designed features and artificially set thresholds, with limited adaptability to complex and changeable scenarios, and can be vulnerable to interference from environmental factors. In addition, traditional methods cannot usually automatically learn deep-seated behavior patterns, resulting in limited generalization ability prone to false positives and false negatives. Therefore, there is an urgent need to seek new methods, which should have a strong automatic feature learning ability, adapt well to complex patterns, and capture subtle differences in crowd behaviors more accurately.
## 4 Experimental Validation  
In this section, we evaluate SHAT by answering the following evaluation questions:  
* EQ1. Does the model trained by SHAT achieve the accuracy higher than those of the state-of-the-art methods?
* RQ2. How robust is SHAT to various heterogeneous environments in terms of the model convergence?
* RQ3. How effective are parameter sharding techniques on SHAT in terms of training performance?
## 3 Results
### Mean and Median Values of Each Deviation and Comparison with Previous Reviews  
The median and IQR values of implant angular deviation, apical lateral deviation, coronal lateral deviation and vertical (depth) deviation were 3.07\({}^{\circ}\) (2.52-3.54\({}^{\circ}\)), 0.96 mm (0.75-1.42 mm), 0.76 mm (0.57-1.37 mm) and 0.71 mm (0.61-0.88 mm), respectively. (A Shapiro-Wilk test revealed that the deviation data did not show any normal distributions except for vertical deviations, and the present data were described as median and IQR.) To compare the present results with previous studies, the results reported in previous systematic reviews and meta-analyses are shown in Table 2[24, 25, 26, 27]. Most of the previous studies reported the data as means and 95% confidential intervals; the present data were also described in this way, for easy comparison. These deviations were similar to the results of previous studies, although this observation was not analyzed statistically.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \begin{tabular}{c} Incisors and Canines \\ \end{tabular} & \
\begin{tabular}{c} 8(0) \({}^{\star}\) \\ \end{tabular} &
\begin{tabular}{c} 2 (1) \({}^{\star}\) \\ \end{tabular} \\ \hline Premolars and Molars & 30 (6) \({}^{\star}\) & 26 (13) \({}^{\star}\) \\ \hline \hline \end{tabular} \({}^{\star}\) Total number of implants (the number of implants placed in open-flap surgery).  
\end{table}
Table 1: Distribution of implants.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \begin{tabular}{c} **Angular** \\ **Deviations (\({}^{\circ}\))** \\ \end{tabular} & \begin{tabular}{c} **Apical** \\ **Deviation** \\ **(mm)** \\ \end{tabular} & \begin{tabular}{c} **Coronal** \\ **Deviation** \\ **(mm)** \\ \end{tabular} & \begin{tabular}{c} **Vertical** \\ **Deviation** \\ **(mm)** \\ \end{tabular} \\ \hline \begin{tabular}{c} [PERSON] et al. [24] \\ (mean \(\pm\) SD) \\ \end{tabular} & 3.98 \(\pm\) 0.33 & 1.40 \(\pm\) 0.12 & 1.10 \(\pm\) 0.99 & 0.74 \(\pm\) 0.10 \\ \hline \begin{tabular}{c} [PERSON] et al. [25] (mean, \\ 95\% CI) \\ \end{tabular} & 4.22 (2.74, 5.68) & 1.45 (1.19, 1.72) & 1.11 (0.96, 1.26) & Not analyzed \\ \hline \begin{tabular}{c} [PERSON] et al. [26] \\ (mean, 95\% CI) \\ \end{tabular} & 4.10 (3.12, 5.10) & 1.33(0.98, 1.68). & 1.00 (0.83, 1.16) & Not analyzed \\ \hline \begin{tabular}{c} [PERSON] et al. [27] \\ (mean, 95\% CI) \\ \end{tabular} & 3.68 (3.61, 3.74) & 0.90 (0.83, 0.97) & 0.69 (0.67, 0.72) & 0.73 (0.70, 0.76) \\ \hline \
\begin{tabular}{c} Present study (mean, \\ 95\% CI) \\ \end{tabular} & 2.93 (2.75, 3.10) & 1.15 (1.01, 1.29) & 0.96 (0.84, 1.08) & 0.71 (0.66, 0.77) \\ \hline
\begin{tabular}{c} Present study (median, IQR) \\ \end{tabular} & 3.07 (2.52–3.54) & 0.96 (0.75–1.42) & 0.76 (0.57–1.37) & 0.71 (0.61–0.88) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Results of deviations in previous studies and the present study.
# Electronic Voting System Using an Enterprise Blockchain
## 2 Blockchain
### Hyperledger Fabric (HF)  
Hyperledger Fabric 2.2 [14] is the blockchain platform chosen to develop this Proof of Concept (PoC) of an electronic voting system. Hyperledger Fabric is an open-source enterprise-grade permissioned distributed ledger technology (DLT) platform established under the Linux Foundation [17,18]. It focuses on the use of authorized blockchain networks for distributed commercial applications with the following elements: consensus  
Figure 1: Blocks committed in a ledger.  
Figure 2: Distributed network between peers.  
protocol between nodes; Certification Authority (CA); peer-to-peer protocol; common and distributed database whose integrity is maintained by all the nodes in the network; support for smart contracts authored in general-purpose programming languages such as Go, JavaScript/Typescript, Java; mechanism to establish different levels of privacy and visibility of information among members (companies, institutions, partnership, corporation, among others).
## 4 Machine Learning Based Mimetic Whistle Receiver  
The conventional machine learning detector may not obtain a great enough BER performance for the communications. Thus, a novel biomimetic demodulation method is proposed that detects the received bits from the distorted whistles by the UWA channel, using the additional link information. Please note that the proposed method does not estimate the UWA channels.  
Figure 3: (**a**) Link between adjacent whistle subgroups; (**b**) sequential link by H with input 0001.  
The transmitted biomimetic \(N\) whistles (\(\mathbf{W}=\{W_{1},W_{2},\cdots,W_{n},\cdots,W_{N}\}\)) go through the UWA channel (\(\mathbf{H}\)) and reach to the receiver sensor, and the noise (\(\mathbf{N}=\{N_{1},N_{2},\cdots,N_{n},\cdots,N_{N}\}\)) is added. The received whistle (\(\mathbf{Y}=\{Y_{1},Y_{2},\cdots,Y_{n},\cdots,Y_{N}\}\)) is modeled as,  
\[\mathbf{Y}=\mathbf{H}*\mathbf{W}+\mathbf{N} \tag{4}\]  
where \(*\) denotes a convolutional operation and all parameters are composed of vectors. As in Section 3, the \(n\)-th element (\(W_{n}\)) of the transmitted whistle vector (\(\mathbf{W}\)) represents randomly selected whistles chosen from the \(n\) -th subgroup (\(X_{n}\)) in the vector \(\mathbf{X}\).  
The purpose of the proposed method is to estimate the transmitted group index \(\hat{\mathbf{X}}\) from the received whistle \(\mathbf{Y}\) using the additional link information among sequential whistles. This estimation can be performed by finding a maximum probability of \(\hat{\mathbf{X}}\) for \(\mathbf{Y}\), and expressed as,  
\[\hat{\mathbf{X}}=\max_{\hat{X}_{1},\cdots,\hat{X}_{N}}p\Big{(}Y_{1}\in\hat{X} _{1},\cdots,Y_{n}\in\hat{X}_{n},\cdots,Y_{N}\in\hat{X}_{N}\Big{)} \tag{5}\]  
In Equation (5), in general, maximum likelihood sequence detection (MLSD) can be performed for the link information to increase the estimation performance of \(\hat{\mathbf{X}}\). However, when the transmitted whistles pass through the UWA channel, the received whistles are severely distorted by the UWA channel, and the maximum likelihood (ML) detector itself does not have a great enough detection performance. Thus, the MLSD does not provide a useful detection performance, despite the additional link information [23; 24].  
In order to achieve the large BER performance, the detection performance of the whistle itself needs to be improved, and then, the link information among whistles is jointly utilized. In Figures 1 and 2, the whistles have a nonlinear time-frequency change property, and are heavily distorted by the UWA channel. Thus, this paper develops a sophisticated machine learning detection method for attaining the large detection performance and the LSTM for utilizing the link information among whistles.
## 4 Discussion  
### Impact of Temperature on the Preservation of Fish Sperm  
The temperature conditions for preserving fish sperm included room temperature, low-temperature (0-4 \({}^{\circ}\)C), and ultra-low-temperature storage techniques [3]. Among these, reports on low-temperature (0-4 \({}^{\circ}\)C) storage schemes were more abundant and practical. For example, the sperm of yellow catfish showed better preservation at 4 \({}^{\circ}\)C compared to room temperature [4]. Similarly, the sperm of Amur sturgeon was effectively preserved at 4 \({}^{\circ}\)C [5], and the sperm of transgenic common carp exhibited better results at 4 \({}^{\circ}\)C than at room temperature (23 \({}^{\circ}\)C) [6]. In general, the preservation effectiveness at low temperatures was significantly better than at room temperature, consistent with our  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Groups** & **Hatching Rate (\%)** & **Celestial Eye Rate (\%)** \\ \hline
1 st Group & 92.33 \(\pm\) 0.72 \({}^{\mathrm{a}}\) & 47.76 \(\pm\) 9.04 \({}^{\mathrm{a}}\) \\
2 nd Group & 93.33 \(\pm\) 0.98 \({}^{\mathrm{a}}\) & All fly died on the second day \\
3 rd Group & 92.67 \(\pm\) 1.19 \({}^{\mathrm{a}}\) & 62.73 \(\pm\) 13.17 \({}^{\mathrm{a}}\) \\ \hline \hline \end{tabular} Note: Superscript letters indicate no significant differences (\(p>\) 0.05) within the same column.  
\end{table}
Table 4: Effect of Cold Stimulation on the Celestial Goldfish Embryo’s Celestial Eye Rate.  
Figure 2: DNA content distribution curve of celestial goldfish standard and cold-treated groups. Note: The upper part of the figure represents the control group, while the lower part represents the experimental samples.  
experimental findings that the sperm of celestial goldfish was better preserved at 4 \({}^{\circ}\)C than at room temperature. Additionally, attempts were made in this experiment to freeze the sperm at \(-20\)\({}^{\circ}\)C, but it was observed that the sperm completely lost its viability, possibly due to damage caused by freezing. Ultra-low-temperature sperm preservation was complex in operation and challenging to promote in production. In contrast, refrigeration of sperm at 0-4 \({}^{\circ}\)C enhanced preservation effectiveness without cryoprotectants, eliminating the risk of sperm freezing [7]. Therefore, for short-term preservation of celestial goldfish sperm in practical production and related breeding experiments, it was recommended to use the refrigeration technique at 0-4 \({}^{\circ}\)C. This technique was simple to operate, facilitated short-distance transportation, and contributed to expanding the range of fish breeding combinations, thereby advancing the process of variety improvement.
## 3 Results and Discussions
### DIC, Ca and Mg in L/S = 5 Batches  
DIC, Ca, and Mg were analyzed in batches with L/S = 5. Figure 9 shows DIC, Ca and Mg concentrations at the end of the monitoring period. Biochar showed the highest value of DIC, with statistical differences in comparison to the control for both CS and SS soils. The elevated DIC concentration in Biochar batches was closely connected to the dissolution of carbonates and also explained the high initial pH values of these batches. Biochar also showed the largest values of Ca for both soils. The concentration of Ca in the Biochar CS batch (207.0 mg/L) was larger than the one in the Biochar SS batch (74.8 mg/L). This large difference could explain the gap of DOC concentrations between these two treatments [46]. This behavior was maintained even in Compost batches. Indeed, the Compost SS batches showed Ca concentrations higher than the Compost CS batches and, accordingly, Compost SS batches showed DOC concentrations higher than the Compost CS batches. With respect to Mg, the Compost SS batches showed an increase with significative statistical differences respect to the Control.
## 2 Research on UAV Path-Planning Problem
### Restrictive Condition  
UAVs are subject to multiple constraints in actual flight, and two types of constraints are considered in this paper when performing path planning. On the one hand, there is the impact of environmental factors on flight trajectories, including mountainous terrain, urban buildings and flight exclusion zones, which UAVs need to avoid when flying. On the other hand, the limitations of the UAV's own performance must be considered, including maximum flight speed, maximum yaw angle, and pitch angle.
## 6 Calculation of Parameters for Mudslide Mitigation
### Mudslide Superelevation at Bends  
Superelevation, also known as bend overweight, refers to the phenomenon where a mudslide thickens at a bend due to the higher velocity on the outside of the curve (concave bank) and the lower velocity on the inside of the curve (convex bank). This difference in velocity results in a redistribution of the flow, causing it to be thicker on the outside and thinner on the inside. The superelevation at a bend can be estimated using Equation (17):  
\[\Delta h=2.3\frac{Vc^{2}}{g}\log_{10}\frac{R_{2}}{R_{1}} \tag{17}\]  
where \(\Delta h\) represents the superelevation or bend overweight; \(R_{2}\) denotes the radius of curvature of the concave bank; \(R_{1}\) indicates the radius of curvature of the convex bank; \(Vc\) is the average mudslide velocity. The calculated superelevation values for each band are presented in Table 7.