esa-sceva/satcom-chunk-collection huggingface dataset:
# Compaction of Church Numerals
## 2 Preliminaries
### Church Numerals  
It is known that natural numbers are represented as _Church numerals_ on \(\lambda\)-terms. Also, some \(\lambda\)-terms enabling arithmetic operations on Church numerals are provided.  
**Definition 6** (Church numerals).: _For natural number \(n\), its Church numeral, denoted by \(\mathcal{C}(n)\), is_  
\[\mathcal{C}(n):=\lambda f\lambda x.\overbrace{f\left(f\cdots\left(f\right)\ x \right)}^{n}.\]  
**Corollary 2** (Arithmetic operations on Church numerals).: _Let \(n_{1}\) and \(n_{2}\) be natural numbers. Then we obtain three \(\lambda\)-terms \(\mathrm{Add}(n_{1},n_{2})\), \(\mathrm{Mul}(n_{1},n_{2})\), and \(\mathrm{Tet}(n_{1},n_{2})\), such that \(\mathrm{Add}(n_{1},n_{2})\longrightarrow_{\beta}^{*}\mathcal{C}(n_{1}+n_{2})\), \(\mathrm{Mul}(n_{1},n_{2})\longrightarrow_{\beta}^{*}\mathcal{C}(n_{1}\cdot n_{ 2})\), and \(\mathrm{Tet}(n_{1},n_{2})\longrightarrow_{\beta}^{*}\mathcal{C}(n_{2}n_{1})\), respectively, as follows:_  
\[\mathrm{Add}(n_{1},n_{2}) = \left(\lambda p.\lambda q.\lambda f.\lambda x.p\ f\left(q\ f\ x \right)\right)\mathcal{C}(n_{1})\ \mathcal{C}(n_{2}),\] \[\mathrm{Mul}(n_{1},n_{2}) = \left(\lambda p.\lambda q.\lambda f.\lambda x.p\left(q\ f\ x \right)\right)\mathcal{C}(n_{1})\ \mathcal{C}(n_{2}),\] \[\mathrm{Tet}(n_{1},n_{2}) = \left(\lambda p.\lambda f.\lambda x.\overbrace{p\ \overbrace{p\cdots\ \ }}^{n_{2}}\ f\ x\right)\mathcal{C}(n_{1}).\]  
As can be seen in Corollary 2, in each \(\lambda\)-term, one \(\lambda\)-abstraction occurs first, and one or two Church numerals follow it. We call the former \(\lambda\)-abstraction and the following Church numerals _function term_ and _argument terms_, respectively. For example, for \(\mathrm{Add}(n_{1},n_{2})\), \(\left(\lambda p.\lambda q.\lambda f.\lambda x.p\ f\left(q\ f\ x\right)\right)\) is the function term and the following \(\mathcal{C}(n_{1})\) and \(\mathcal{C}(n_{2})\) are the argument terms.
## 5 Proposed Reliable, Energy Optimized and Void Aware Routing Protocol  
This research study proposes the implementation of a clustering-based routing protocol to reinforce network performance by cutting down the incidence of void issues and efficient energy utilization by balancing the energy usage among nodes. In this aspect, the nodes are positioned strategically within the underwater region.
# Reinforcement Learning Based Relay Selection for Underwater Acoustic Cooperative Networks
## 3 RL Based Relay Selection Method for UWA Cooperative Networks  
With the description of system model, the system actions are discrete, which are corresponding to the selection of different relay nodes. For a given system model, the UWA relay selection process is comparable to the state transition process, where the agent selects best relay based on the current system state and then obtains the next system state. The system state in the next round is only related to current state and action, and is independent of the other previous states and actions. Therefore, the relay selection process can be modeled as Markov Decision Process.  
Reinforcement learning can derive optimal strategy for MDP system through the interactions with the environment by \"attempt and failure\" mechanism. The basic principle is that if the chosen action receives a larger reward from the environment, the probability that the agent adopting this action strategy in the future will increase. On the contrary, when the less reward is obtained, the probability that the agent choosing the action will be weakened.  
Theoretical relay selection strategies often assume that the channel state information is ideal. However, in the dynamically changed UWA channel, the channel state is time and frequency- varying and with outdated property. Reinforcement learning can train the best action strategy \(a\) according to the known channel state \(s\) and the corresponding reward \(r\), and finally obtain the best relay selection. RL relay selection can work without prior channel knowledge and system model. And even with delayed imperfect CSI, it can still train the action under specific available states, which reveals the relationship between channel and actions.
## 6 Conclusions  
This paper tried to study the energy and transmission efficiency problem of smart home supporting fronthaul transport network. The efficiency is improved by reconfigure the TWDM-PON. We also took the load balancing in the fronthaul links into consideration. Specifically, we considered employing an INLP model to formulate the joint optimization problem, which has exponential complexity. Afterwards we provided an adaptive GA based approach to reduce the complexity of the INLP method. The results showed that the active units of fronthaul including transceivers, ONUs, and RRUs could be dynamically switched on/off with the traffic variation by using the proposed GA, leading to a significant energy saving in TWDM-PON enabled fronthaul. Moreover, transmission efficiency has been improved with the joint optimization methods. The maximum transmission efficiency increased by about 87% with INLP method in off-peak periods. Moreover, with the proposed INLP method and adaptive GA, the fronthaul network was dynamically reconstructed based on the amount of traffic served by each fronthaul link. The load imbalance of TWDM-PON enabled reconfigurable fronthaul was further reduced independent of traffic variation during a day. Compared to the INLP method, almost the same performance could be achieved using an adaptive GA approach, with less complexity.  
In the future, machine learning algorithm could be adopted for real-time prediction and response for better performance, such as artificial neural network and deep reinforcement learning. However, the vulnerability of machine learning should be considered to avoid unexpected reliability and security issues during network automation.  
Conceptualization, R.G.; methodology, R.G. and G.W.; validation, G.W.; formal analysis, R.G. and G.W.; investigation, R.G., Z.L. and Y.J.; supervision, Y.J.; writing--original draft preparation, R.G. and G.W.; writing--review and editing, R.G., Z.L. and Y.J.; funding acquisition, R.G. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Science and Technology Major Project of China (No. 2018 ZX03001018).  
The authors declare no conflict of interest.  
Figure 6: Load balancing conditions with different methods.
## 3. Results and Discussion
### Volume-Fixed Near-Equal Optimal Bale Dimensions Design
#### 3.2.2 Example 2  
Film parameters and overlaps constraints from Example 1 are taken, again. Bale volume \(V_{b0}=1.357\) m\({}^{3}\) is assumed together with orders of near-equilibrium \(\varepsilon_{0}=0.05\) and \(\varepsilon_{0}=0.1\). Integer \(p_{b}\), bottom \(\bar{k}_{fb}(p_{b})\) and upper \(\bar{k}_{fb}\), \(\overline{\bar{k}}_{fb}\) bounds, parameters \(k_{fb,ne}\) and closed intervals \(\mathcal{K}_{2}\) of \(k_{fb}\) are given in Table 3. In all tested examples \(k_{fb,ne}<k_{fb}(p_{b})\). The upper bound of the closed interval of \(k_{fb}\) defined by Equation (29) is determined by \(\hat{k}_{fb}(p_{b})\), or \(\overline{\hat{k}}_{fb}(p_{b})\), or \(k_{fb,max}\)--there is no rule here. For any \(k_{fb}\in\mathcal{K}_{2}\) the formulas from Equation (34) for computing \(\delta\) are presented in the penultimate column. In the last column film usage \(FC(p_{b})\), Equation (35), is given. For most \(p_{b}\in\mathcal{P}_{2}\) the closed intervals \(\mathcal{K}_{2}(p_{b})\) are wide enough to select a practically convenient overlap ratio \(k_{fb}\). In some cases this interval is very narrow, e.g., for \(p_{l}=10\), \(p_{b}=6\), we have \(\mathcal{K}_{2}=[0.200,\ 0.204]\); however, \(k_{fb}=0.2\) is acceptable from the engineering point of view. For \(\varepsilon_{0}=0.05\) and \(p_{l}=4,6,8\) set \(\mathcal{P}_{2}\) is composed of only one number \(p_{b}\) of bottom film layers and this \(p_{b}\) solves Problem 2. For \(p_{l}=10,12,14,16\) there are at least two \(p_{b}\) for which the set \(\mathcal{K}_{2}(p_{b})\) is nonempty, the optimal film usage \(FC\big{(}p_{b}^{*}\big{)}\) defined in Equation (36) is marked by bold in Table 3. For \(\varepsilon_{0}=0.05\), according to Equations (5) and (6), the optimal bale dimensions \(D_{b}^{*}=1.22\) m, \(H_{b}^{*}=1.162\) m, for \(\varepsilon_{0}=0.1\) we have \(D_{b}^{*}=1.239\) m, \(H_{b}^{*}=1.126\) m. If \(\varepsilon_{0}=0.05\) is assumed, then for \(p_{l}=4,6,8\) the overlaps \(k_{fb}=0.3\) and \(\delta=0.2195\cong 0.22\) can be applied. For \(p_{l}=10\) Problem 2 is solved for the same overlaps for \(p_{b}=5\) yielding minimal film usage. Similarly, for \(p_{l}=16\) and \(p_{b}=8\). For \(p_{l}=12\) solution to Problem 2 is composed by \(p_{b}=7\) and, for example, \(k_{fb}=0.2\) and \(\delta=0.272\). For \(p_{l}=14\) we have: \(p_{b}=6\) and \(k_{fb}=0.4\) and \(\delta=0.184\). Similarly, based on the data from Table 3, the solutions to Problem 2 can be found for the greater order \(\varepsilon_{0}=0.1\).
# Development of a Pre-Evaluation and Health Monitoring System for FAST Cable-Net Structure
## 3 Establishment of the FAST MST Model
### Verification of the Accuracy of the MST Model  
FAST consists of 6670 main cables, of which 150 main cables are connected to the ring beam and fixed on the lug plate. Sensors are installed on these edge main cables and can measure the cable force in them. Therefore, the errors between the surveying value of these main cable forces and the theoretically calculated value can be used to verify whether the model meets the accuracy requirements of the measurement after calibration.  
According to China's Cable Structure Technical Specification Code (JGJ 257-2012), after establishing tension in the FAST cable-net structure, the allowable error limit of tension is \(\pm 10\%\). Seeing that the magnetic flux sensor measurement error is approximately 3% in the  
Figure 5: Flow chart of the updating process.  
basic spherical state, if the error between the calculated and measured cable forces of 150 edge main cables is less than 13%, the MST model has been successfully updated [18].  
In October 2019, we first performed a thorough measurement of the data, as mentioned earlier, updated the MST model, and verified the accuracy of the new model. The force of 150 edge main cables was measured in the basic sphere state. Errors of main cable force between the measurement and analysis are indicated in Figure 6. The ambient temperature was about 22 \({}^{\circ}\)C during the measurement.  
The calculated values of stress in edge main cables are between 629.9 MPa and 732.6 MPa, while the values of stress that occurred in analysed cables range from 673.7 MPa to 707.2 MPa. As seen from the figure, the maximum error between the measurement and theoretical analysis is 11.3%, while all errors obey normal distribution. This conforms to the standard of the specification. Because the breaking stress of FAST main cables is 1860 MPa, the overall cable net is still at a low level of stress and has a high safety factor. This result proves the accuracy of the above-mentioned FAST model update method. The reliability of the new model is verified, which provides a guarantee for the subsequent construction and regular operation of the PHM system.
## 5 Experiment and Result Analysis
### Feature Data Selection
#### 5.1.2 Feature Screening  
Upon obtaining the image of the rare earth element solution, the original features of the image are categorized as color features, texture features, and key features. Using the  
Figure 4: EMRAB-CNN model structure diagram.  
original feature as input and the component content of Pr and Nd elements as output, the original features are standardized. The data is subsequently partitioned into a training set and a test set, with the test set comprising 19% of the overall data. The RF-RFECV algorithm is used to select the relevant features from the training set. The length of recursive feature elimination in each iteration is set to 1, and the number of cross-validations is set to 3, 5, 7, and 9. The optimal feature dimension is determined based on the average value of the feature dimensions corresponding to the multiple cross-validation results, as depicted in Figure 5:  
As illustrated in Figure 5, the RF score of the model increases with the increase in feature dimensions. When the feature dimension of the model increases from 1 to 9, the model score sees a significant rise. However, when the dimension of the model exceeds 9, the score results exhibit an oscillating phenomenon. Moreover, as the feature dimension continues to increase, the model's equal division decreases. It is speculated that as the feature dimension increases, the complexity of the model increases with it, potentially leading to an overfitting phenomenon that results in deteriorating performance.  
By combining the results of multiple cross-validations and comparing the scores of the feature dimensions, it is evident that the average score of RF-RFECV is the highest when the feature dimension is 11. This allows for the screening out of less important features in order to reduce feature redundancy. Therefore, the number of feature dimensions is selected to be 11, which is used to represent the overall information of the sample. Simultaneously, the feature importance of each feature is obtained, as shown in Figure 6, and the top 11 features in the figure are selected. The features are ranked in terms of their importance in descending order, as follows: extraction order, h, U, the mean value of the gray level co-occurrence matrix, Y, autocorrelation, v, V, contrast, s, and finally homogeneity. After screening by RF-RFECV, these 11 features are selected as mixed features.  
Figure 5: RF-RFECV feature dimension selection diagram.
## 4 Results
### Benchmarking Strategies  
Aiming to evaluate the performance of the policy obtained with our proposed DQN-based method against different strategies, two reference approaches were considered:  
**Optimum strategy:** for a given UE, based on the set of candidate cells \(A_{u}=\{C_{m,n}\}\) and \(N_{max}\) values, this strategy performs an exhaustive search process among all possible MC configurations at each time step and obtains the MC configuration that provides the highest reward. It is worth mentioning that it would not be a practical strategy for its implementation in real scenarios, mainly due to the large execution time for assessing all the possible MC configurations, so it is just considered as an upper bound of the DQN algorithm performance.  
**SINR-based strategy**: in this strategy, at every time step all the traffic of the UE is served by the cell with the highest SINR value. This strategy reflects the classical approach of cellular systems in which the UE is served only by one cell, which is the one that provides the best quality (i.e., the highest SINR value). This criterion is considered for example in the specification [34] for the cell selection procedure, as well as in the measurement report triggering criteria of [35] to determine when one cell becomes better than another one, so that this can be used when deciding a handover. In addition, different works have also considered an SINR-based criterion for determining the cell a UE is connected to in a cellular system, such as [36; 37]. It is worth mentioning that the SINR-based strategy can be implemented making use of handover procedures for changing the cell that the UE is connected to.
## 1 Introduction
### Research Significance and Research Status  
DTH hammer percussion drilling has high rock-breaking efficiency and strong advantages in hard rock drilling, which can reduce the cost of geothermal drilling [9; 10; 11; 12; 13; 14]. The DTH hammer drill bit mainly relies on the impact action to break rock; the bit buttons have strong impact resistance, but the shear resistance is relatively weak. When the hole diameter is large, the bit rotation speed is high, the impact frequency is low, the button diameter of edge button is small, and the compressive strength of rock is high, the space (in Figure 2) between the adjacent rock dents (the broken pit) left by the two adjacent bit buttons of the hammer impact will be large and result in the residual rock ridge. This residual rock ridge produces a tangential reaction force on the bit buttons, which causes the edge buttons to fracture and break. The broken edge buttons aggravate the vibration of the downhole drilling tool and the wear of other buttons and the bit body further. Consequently, the lifespan of the bit is shortened, while the rate of penetration and drilling efficiency are decreased and the drilling cost is increased [15; 16].  
Therefore, knowing how to improve the drilling efficiency and prolong the service life of the drill bit through the drill bit design is the key problem to be solved urgently in the field of geothermal drilling technology.  
Convex PDC (polycrystalline diamond compact) insert bit buttons with good thermal stability [17; 18] were adopted. [PERSON] and [PERSON] et al. studied the influence of button profile design on the rock crushing effect of PDC bit buttons [19; 20]. Based on spherical button interference assembly and air pressure, [PERSON], [PERSON], and [PERSON] et al. analyzed the static mechanism of cone bit insert button loss [21; 22; 23]. The application team, [PERSON], carried out the experiment of PDC bit crushing granite at 300 \({}^{\circ}\)C [24]. [PERSON] et al. established a PDC bit button crushing dry hot rock model through numerical simulation [25]. Research and application by PetroChina Great Wall Drilling Engineering Co., Ltd. and Sandia National Laboratories in the United States have demonstrated the success of PDC geothermal drilling [26; 27].  
In this paper, the failure modes of bit buttons in the process of large-diameter and hard formation geothermal drilling are studied and analyzed. A new type of anti-shear DTH hammer bit is designed by deeply analyzing the mechanism of rock breaking and the working principle of the bit. This type of the DTH hammer bit are mass-produced and widely applied in the field, achieving higher drilling efficiency, longer lifespan, and lower drilling costs.  
Figure 2: Drilling mechanisms of down-the-hole drilling [8].
# Comparative Study of Energy Savings for Various Control Strategies in the Tunnel Lighting System
## 4 Results
### Traffic Volume Impact on Energy Consumption  
The analysis in Section 2 demonstrated that the traffic volume does not affect the electrical costs of the tunnel lighting system for the LCL, TSCS, and DACS strategies but it does for the ICS strategy.  
Figure 9 shows the electrical costs of a tunnel lighting system as a function of traffic volume and tunnel length for the ICS strategy. The relationship for daily electricity cost versus tunnel length (\(L\)) and traffic volume (\(N\)) for the ICS strategy has a better fitting equation using a logarithmic function, which is shown in Equation (5).  
\[E_{\text{EC\_ICS}}=-2182-365.8169\ln L+885.3517\ln N+41.24\ln^{2}L-15.32\ln L \cdot\ln N-49.19\ln^{2}N, \tag{5}\]  
The coefficient of determination \(R^{2}\) is 0.9833, which means the reliability of the fitting equation is acceptable. The results show that daily energy consumption increases significantly with traffic volume for light traffic, while this increase is relatively small for a heavy traffic volume.
# Trends and Perspectives of mHealth in Obesity Control
## 4 Discussion
### Implications in the Healthcare  
This study presents ways to apply mHealth technologies to enhance obesity management and promote healthier lifestyles. Healthcare providers and technology developers can design innovative mHealth interventions that incorporate personalized features, be havioral change techniques, and user-centered design. By utilizing mobile apps, wearable devices, and telemedicine platforms, healthcare can provide tailored health education, self-monitoring tools, goal-setting, and real-time feedback, empowering patients to take an active role in managing their health.  
Remote monitoring and telemedicine services play a crucial role in obesity management. They enable timely interventions, proactive management of obesity-related complications, and improved access to specialized care, especially in underserved areas. Public health agencies and policymakers can leverage mHealth technologies to collect population data, identify high-risk groups, and implement targeted interventions for obesity prevention and healthy behavior promotion.  
mHealth tools can also help healthcare providers streamline workflows, facilitate patient communication, and enhance care coordination in obesity management. Integration with Electronic Health Records (EHRs) enables better data sharing and decision support, leading to more effective, patient-centered care. Furthermore, policymakers need to create policies and regulatory frameworks that support the responsible use of mHealth technologies, focusing on data privacy, reimbursement for telehealth services, and ethical AI practices.  
Obesity is a significant global health issue, and the effectiveness of mHealth interventions varies by country, healthcare system, and policy. This study explores the role of mobile health technologies in obesity control, focusing on regions with high obesity rates and advanced mHealth infrastructure, and highlights how personalized interventions and remote monitoring can improve obesity management.  
This study also emphasizes the challenge of equity and access in mHealth technologies. Socioeconomic barriers such as affordability, digital literacy, and infrastructure limitations can hinder the widespread adoption of these tools and worsen health disparities. To address these, this study recommends accessible design features, increased policy support, and targeted interventions.  
Moreover, this study underscores the importance of data privacy in mHealth technologies. Addressing issues such as informed consent, data anonymization, and user control is critical for building trust in these tools. Ethical considerations are essential for the successful adoption and long-term sustainability of mHealth technologies.  
Future research should focus on developing ethical frameworks that are culturally sensitive and comply with international standards. These frameworks are vital for fostering trust, ensuring equitable access, and safeguarding privacy and security in the use of mHealth solutions.
### Contribution  
The following summarizes the main contributions of this paper:  
* A comprehensive analysis of the SFC placement problem in dynamic IoT-MEC networks is presented. The SFC placement problem is formulated as an integer linear programming (ILP) problem to optimize the aggregate cost of resource usage and delay with appropriate weights related to an IoT-SR.
* In order to account for real-time network fluctuations, two MDP models are employed to formulate two subproblems, each with a corresponding DDQN network. These two networks are named the VNF placing network and the SFC path finding network (SPFN), and they are responsible for VNF selecting and SFC path allocation, respectively. Additionally, a unique reward function is constructed to enhance the acceptance rate of IoT-SRs.
* We propose a meta reinforcement learning-based SFC placement (MRL-SFCP) policy that integrates meta reinforcement learning and fuzzy logic to address the dynamic SFC placement problem while also considering network load balancing and the quality of service (QoS) requirement of the IoT-MEC network.
* Extensive simulations are conducted to demonstrate the performance of the MRL-SFCP. Comparative analysis with benchmark methods reveals that the MRL-SFCP achieves superior performance with regard to success acceptance rate, accepted traffic throughput, and average reward of IoT-SRs.