esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Results  
### Characterization of Tricyclene by GC-MS  
The biosynthetic pathway of tricyclene is presented (Figure 1A). To produce tricyclene in _E. coli_, we used a two-plasmid system to modulate the MVA pathway and the biosynthesis of tricyclene. The plasmid pAC-6409 mva consisting of seven heterologous MVA pathway genes were shown to provide IPP and DMAPP. To convert IPP/DMAPP to tricyclene, a GPPS from _Abias grandis_ and a TS were assembled into a single operon driven by the IPTG-induced trc promoter in plasmid 3933-agGPPS. The predicted TSs from different plant species are shown in Table S3. To avoid low protein expression in _E. coli_, genes coding TSs were codon adapted. After the fermentation, the n-dodecane covering agent was collected and measured by GC-MS. As a result, only TS 1411 from _Nicotiana sylvestris_ presented a detectable peak at 3.38 min (Figure 1B), which was the same as the retention time of the tricyclene standard (Figure 1C). The compound was identified as tricyclene by comparing the mass spectrum of the main peak in the sample at 3.38 min with a tricyclene standard (Figure 1D,E). The relative ion abundances of molecular ions (136.1 \(m/z\)) and other abundant ions in the experimental samples were consistent with those of the tricyclene standard. These results demonstrate that the two-plasmid system enabled tricyclene production in E. coli, albeit at a low titer of 0.060 mg/L. In our previous experiments, we successfully synthesized \(\alpha\),\(\beta\)-Pinene and achieved a higher titer of 104.6 mg/L. The disparity in the synthesis pathway between pinene and tricyclene lies in the variation in terpene synthase, suggesting that the expression and culture conditions of TS might account for the comparatively lower titer of tricyclene [33].
# CSNOMA: Carrier Sense Non-Orthogonal Multiple Access
## 4 Carrier Sense Non-Orthogonal Multiple Access (CSNOMA)
### Optimal Carrier Sensing Range  
Figure 4 shows ASE as a function of the carrier sensing range \(r_{s}\). The value \(r_{s}\) varies from 0 to five times larger than the transmission distance. As shown in Figure 4, an optimal carrier sensing range exists that maximizes ASE. As the target SIR increases, the optimal carrier sensing range becomes larger in order to decrease the aggregate interference level. Equation (9) is a differentiable function of \(r_{s}\), and we can apply a simple gradient method to obtain the optimal \(r_{s}\) that maximizes ASE:  
\[r_{s}^{(k+1)}=r_{s}^{(k)}-\omega^{(k)}\
abla\eta(r_{s}^{(k)}), \tag{10}\]  
where \(\omega^{(k)}\) is a step size, where fixed small value (greater than zero and less than 1) or the value found by line search minimization of \(\eta(r_{s}-\omega\
abla\eta(r_{s}))\) over \(\omega\)[46].  
Figure 4: The area spectral efficiency of CSNOMA as a function of the carrier sensing range. The transmission distance \(r_{t}\) is 5 and the node density is 0.05. Different target SIR values are used (\(\beta\) = 0 dB and 3 dB).
## 7 Challenges and Limitations  
While RFEH presents a promising solution for powering low-energy devices and supporting sustainable wireless technologies, several technical and practical challenges remain that hinder its widespread adoption. These limitations span from energy conversion inefficiencies to regulatory concerns, requiring continued research and innovation.
# Characterization of Shallow Sedimentary Layers in the Oran Region Using Ambient Vibration Data
## 3 Methodology and Data Processing
### HVSR Technique  
The HVSR (Horizontal-to-Vertical Spectral Ratio) technique is used to estimate the resonance frequency of the soil and its corresponding amplitude, based on ambient vibration measurements. This method was initially proposed by [32] and further developed by [33]. An updated and detailed review of the HVSR methodology can be found in [34]. To generate the HVSR curve, horizontal and vertical components are required. The recording time has been reduced and split into several windows of a predetermined duration. An anti-triggering algorithm has been employed to select only the stationary windows for further processing. For each selected window, the spectra of the three components (NS, EW, Z) have been calculated and smoothed using the Konno-Ohmachi technique [35]. The horizontal spectrum (H) has been calculated by averaging the NS EW spectra using the quadratic mean. Subsequently, it has been divided by the spectrum of the vertical component (V), providing the corresponding HVSR curve. Combining the results obtained for each analyzed window, the mean HVSR curve, together with the corresponding standard deviation, has been estimated for each station. The described HVSR processing has been carried out using the Geopsy module from the Geopsy package (release 2.10.1) [36]. Finally, an average HVSR curve has also been obtained for each array using the Dinver module from the Geopsy package (release 2.10.1) [36]. The fundamental frequency, which is well correlated with the resonance frequency of the soil, corresponds to the frequency of the HVSR peak.  
The directional response of the sites has also been examined by rotating the HVSR curves at all azimuths ranging from 0\({}^{\circ}\) to 180\({}^{\circ}\), with a step of 10\({}^{\circ}\). This analysis has been carried out using the Geopsy H/V ROTATE module.
# On the Capacity of Optical Backbone Networks
## 4 Link and Network Capacity
### Link Capacity
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \
\begin{tabular}{c} **Symbol** \\ **(Gbaud)** \\ \end{tabular} & \(N_{ch}\) & \(B_{WDM}\) & \(\Delta\
u_{ch}(\mathbf{GHz})\) & \
\begin{tabular}{c} \(SE\) \\ **(bit/s/Hz)** \\ \end{tabular} &
\begin{tabular}{c} \(C_{ch}\) \\ **(Tbit/s)** \\ \end{tabular} & \(\boldsymbol{L}\) **(km)** & **Ref.** \\ \hline
32 & 117 & 4400 & 37.5 & 6.7 & 0.25 & 29.25 & 1600 & [36] \\
64 & 59 & 4400 & 75.0 & 6.7 & 0.50 & 29.50 & 650 & [36] \\
96 & 41 & 4100 & 100.0 & 10.0 & 1.00 & 41.00 & 100 & [37] \\
128 & 35 & 4800 & 137.5 & 10.9 & 1.49 & 52.15 & 80 & [38] \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Published experimental results for channel and links capacities. Figure 5: Link capacity versus the optical channel power for various symbol rates: (**a**) link length of 400 km; (**b**) link length of 800 km. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \
\begin{tabular}{c} **Symbol Rate** \\ **(Gbaud)** \\ \end{tabular} & \(N_{ch}\) &
\begin{tabular}{c} \(C_{ch}\) **(Tbit/s)** \\ \(L\) **= 400 km** \\ \end{tabular} & \(\boldsymbol{C_{ch}}\) **(Tbit/s)** & \(\boldsymbol{P_{ch}^{opt}}\)**(dBm)** & \(\boldsymbol{P_{tot}}\) **(dBm)** \\ \hline
32 & 150 & 0.44 & 0.37 & \(-\)2.15 & 19.61 \\
64 & 75 & 0.88 & 0.75 & 0.89 & 19.64 \\
96 & 50 & 1.31 & 1.12 & 2.65 & 19.64 \\
128 & 37 & 1.77 & 1.52 & 3.89 & 19.57 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Channel capacities and optical powers per channel.
## 2 TLS Measurement and Data Compression
### Voxelization and Octree Data Structure  
Voxelization conceptualizes geospatial spaces and express them as volume elements (voxels) using voxel data structures. A voxel is a rectangular parallelepiped block defined in terms of its length (l), width (w), and height (h) and voxel position is indexed by column (i), row (j) and layer (k). The laser scanning point (x, y, z) is transformed to the position of the voxel (i, j, k) [45].  
Octree is a data representation method that creates a bounding box for a given shape, and stores it as a visualization object if the shape is contained in the hexahedron equally divided in the x, y, and z coordinates [46]. The octree divides the bisected space in each direction of the x, y, and z axes into eight subspaces and expresses them in a finer area. The eight sub-spaces can be stored in a tree structure as an element called a node, and the depth level of the octree is determined by the number of divided bounding boxes [47]. In this study, the 3D object model (Voxel model) is first generated to easily remove empty nodes by checking empty cells in the sub and left nodes. Thus, it is efficient to implement segmentation and octree in the spatial properties of 3D objects rather than in irregularly distributed point clouds.  
Octree has the largest number of leaf nodes corresponding to \(N_{L}=8^{\text{D}}\), and this is equivalent to a 3D grid with a resolution of \(2^{\text{D}}\times 2^{\text{D}}\times 2^{\text{D}}\). Figure 2 shows the number of nodes according to the octree depth level. Here, octree is used to improve processing speed and to save space, and the depth first (DF)-representation proposed by [PERSON] [48] is the most popular way to encode octree. This method sequentially stores the information of the nodes encountered in a depth-first search of the octree, and each node is displayed by black, white, and gray, as shown in Figure 2. A black node indicates that the area is full. A white node means it is completely empty, and a gray node meansthe node is partially black. The gray nodes here indicate that further segmentation may be required. The hexes marked as black or white no longer split. An octree can be set to a level of depth to be divided or can be repeatedly divided by setting the size of the bounding box.
## 3 Modeling of the VLC System and Its Components in the Indoor Environment
### Reflection Factor  
The reflection factor \(R(\theta_{ij},\theta_{r})\) describes how light is reflected on the mirror surface based on the angle of incidence \(\theta_{ij}\) and the angle of reflection \(\theta_{r}\). This factor depends on the refractive index of the mirror material and can be modeled using [PERSON]'s equations.  
[PERSON]'s equations provide the reflection of incident light on a surface when light passes between two media with different refractive indices. Considering a surface with a refractive index \(n_{1}\) and a reflective surface with a refractive index \(n_{2}\), the reflection factor can differ for the perpendicular and parallel polarization components of the incident light.  
For the perpendicular component (s-polarization), we have the following expression [4]:  
\[R_{s}(\theta_{ij})=\left|\frac{n_{1}\cos(\theta_{ij})-n_{2}\cos(\theta_{t})}{n _{1}\cos(\theta_{ij})+n_{2}\cos(\theta_{t})}\right|^{2}. \tag{7}\]  
The parallel component (p-polarization) can be modeled as [4]  
\[R_{p}(\theta_{ij})=\left|\frac{n_{2}\cos(\theta_{ij})-n_{1}\cos(\theta_{t})}{n _{2}\cos(\theta_{ij})+n_{1}\cos(\theta_{t})}\right|^{2}, \tag{8}\]  
where \(\theta_{t}\) is the transmission angle, obtained using [PERSON]'s law:  
\[n_{1}\sin(\theta_{ij})=n_{2}\sin(\theta_{t}). \tag{9}\]  
Finally, the total reflection factor for unpolarized light is then the average of both components, as follows:  
\[R(\theta_{ij})=\frac{1}{2}\big{[}R_{s}(\theta_{ij})+R_{p}(\theta_{ij})\big{]}. \tag{10}\]
## 5 The Proposed Solution
### Signal Features
#### 5.2.2 Mean, Variance and Cardinality of Over-Threshold Samples  
The second feature belongs to the amplitude domain and is defined as the mean value of the RSSI samples over the selected threshold \(\theta\). We define the vector containing all of the RSSI samples collected during the continuous observation window as \(\mathbf{S}=\{s_{0},\ s_{1},\ s_{2},\...,\ S_{N_{S}}\}\). Then, indicating with \(\mathbf{S^{(OT)}}\) the subset of \(\mathbf{S}\), such that \(\mathbf{S^{(OT)}}=\{s_{n}\in\mathbf{S}\ |\ s_{n}>\theta\}\):  
\[F_{M}=\frac{1}{N_{OT}}\sum_{i=1}^{N_{OT}}s_{i}^{(OT)} \tag{6}\]  
with \(N_{OT}\) representing the cardinality of \(\mathbf{S^{(OT)}}\), hence the number of above-threshold samples in the set. The third feature \(F_{V}\) follows directly from the definition of sample variance, hence using the same notation employed for \(F_{M}\):  
\[F_{V}=\frac{1}{N_{OT}}\sum_{i=1}^{N_{OT}}(s_{i}^{(OT)}-F_{M})^{2} \tag{7}\]  
The last feature \(F_{C}\) counts the occurrences of RSSI samples above the threshold and hence is simply the cardinality of the set \(\mathbf{S^{(OT)}}\). This feature nicely complements the previous two, adding information about the activity level of the interference source. It must be noted that while the signal features \(F_{M}\), \(F_{V}\) and \(F_{C}\) are scalars, the feature \(F_{B}\) is an \(M\)-element vector; hence the SVM feature-space will be \(M+3\)-dimensional, even using only four features.
## 3 Background
### Gaussian Processes  
A Gaussian process (GP) is a powerful statistical tool that defines a distribution over functions, allowing for flexible modeling of unknown, complex functions with continuous domains (see, e.g., [PERSON] and [PERSON], 2006 [7]). Let \(\mathcal{T}\) be an arbitrary index set with a continuous domain, such as space or time, and let \(f=(f(t),t\in\mathcal{T})\) be a stochastic process defined over \(\mathcal{T}\). Then, \(f\) is called a second-order GP if the marginal distribution of any finite-dimensional subset of \(f\) is a multivariate Gaussian distribution. That is, for every \(n\) and \(t_{1},\ldots,t_{n}\in\mathcal{T}\),  
\[f\equiv(f(t_{1}),\ldots,f(t_{n}))^{\top}\sim\mathcal{N}_{n}(\mu,K),\]  
where \(\mu=(\mu(t_{1}),\ldots,\mu(t_{n}))^{\top}\) with \(\mu(t_{i})=E[f(t_{i})]\) is the mean vector, and \(K=(K_{ij})_{i,j=1}^{n}\) with \(K_{ij}\equiv K(t_{i},t_{j})=E[(f(t_{i})-\mu(t_{i}))(f(t_{j})-\mu(t_{j}))]\) is the covariance matrix. A GP is usually denoted as  
\[f\sim\mathcal{GP}(\mu,K).\]  
In Bayesian modeling, GPs serve as a prior distribution over function spaces, which is especially useful for non-parametric functions when the form of the function is unknown or too complex to model parametrically (see, e.g., [PERSON] et al., 2014 [12]; [PERSON], 2022 [13]). To illustrate this, suppose that we obtain a dataset \(\mathcal{D}=\{(y_{i},x_{i}),\ i=1,\ldots,n\}\), where \(y_{i}\) is a response variable and \(x_{i}=(x_{i1},\ldots,x_{ip})^{\top}\) is a \(p\)-dimensional vector of predictors that non-parametrically explains \(y_{i}\). Then, by assuming additive Gaussian noise, we model the relationship between the response and predictors as follows:  
\[y_{i} = f(x_{i})+\epsilon_{i},\ \epsilon_{i}\sim\mathcal{N}(0,\sigma^{2}),\] \[f\equiv(f_{1},\ldots,f_{n}) \sim \mathcal{GP}(\mu,K),\ f_{i}=f(x_{i}), \tag{1}\]where the mean vector (or mean function) \(\mu\) is typically taken to be zero, and the covariance matrix (or covariance function) is defined by commonly used the squared exponential kernel,  
\[K_{ij}=\tau_{f}^{2}\exp\left[-\frac{1}{2}\|x_{i}-x_{j}\|^{2}/l^{2}\right].\]  
Here, the parameter \(l\) is called a length-scale hyperparameter and \(\tau_{f}^{2}\) denotes the marginal variance, and these parameters control the shape of the Gaussian process ([PERSON], 2023 [14]).  
One of the key advantages of GPs is their ability to provide a full posterior predictive distribution when making predictions. This means that for any new predictors, GPs can provide both the expected value (mean) of the prediction and a measure of the uncertainty associated with that prediction. For example, let \(x_{*}=(x_{*1},\ldots,x_{*p})^{\top}\) be a new set of predictors that were not utilized in the model specified by (1). The predictions can be computed in the following closed form:  
\[f_{*}\mid x_{*},y,x\sim\mathcal{N}(\mu_{*},\Sigma_{*}),\]  
where the mean function and covariance function are given by  
\[\mu_{*} = K_{x_{*},x}[K+\sigma^{2}I]^{-1}y,\] \[\Sigma_{*} = K_{x_{*},x_{*}}-K_{x_{*},x}[K+\sigma^{2}I]^{-1}K_{x,x_{*}}.\]
## 3 Results
### Mid Intertidal Zone  
In general, marked horizontal and vertical variations in the investigated trace elements were not observed. However, the subsoil layer (10-20 cm) tended to have a higher concentration of Zn and As, as compared to the surface soil layer (0-10 cm) and the bottom soil layer (20-30 cm) at most of the sampling locations. An unusually high concentration of Cd was recorded at Location S8 and an unusually high concentration of Hg was detected at Location S11. The mean values of various trace elements were comparable to those in the upper intertidal zone with a similar decreasing order being observed: Zn > Cr > Pb > Cu > As > Ni > Cd > Hg (Table 4). \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Sample** & **Depth** & **Cr** & **Ni** & **Cu** & **Zn** & **As** & **Cd** & **Hg** & **Pb** \\ \hline \multirow{4}{*}{S6} & \multirow{2}{*}{0–10 cm} & 95.45 \(\pm\) & 31.66 \(\pm\) & 41.39 \(\pm\) & 90.20 \(\pm\) & 26.06 \(\pm\) & 0.62 \(\pm\) & 0.19 \(\pm\) & 39.62 \(\pm\) \\  & & 2.52 & 0.32 & 7.39 & 1.60 & 0.52 \(\pm\) & 0.16 & 0.04 & 5.41 \\ \cline{2-10}  & \multirow{2}{*}{10–20 cm} & 10.84 \(\pm\) & 29.00 \(\pm\) & 37.78 \(\pm\) & 106.08 \(\pm\) & 32.15 \(\pm\) & 0.60 \(\pm\) & 0.18 \(\pm\) & 40.38 \(\pm\) \\  & & 1.57 & 0.88 & 1.93 & 4.56 & 9.64 & 0.04 & 0.02 & 1.83 \\ \cline{2-10}  & \multirow{2}{*}{20–30 cm} & 20–30 & 92.82 \(\pm\) & 29.02 \(\pm\) & 34.91 \(\pm\) & 82.33 \(\pm\) & 21.85 \(\pm\) & 2.32 \(\pm\) & 0.14 \(\pm\) & 41.27 \(\pm\) \\  & & 2.31 & 1.49 & 0.91 & 3.44 & 0.58 & 1.89 & 0.01 & 10.87 \\ \hline \multirow{4}{*}{S7} & \multirow{2}{*}{0–10 cm} & 93.31 \(\pm\) & 27.53 \(\pm\) & 33.48 \(\pm\) & 103.08 \(\pm\) & 20.40 \(\pm\) & 0.49 \(\pm\) & 0.15 \(\pm\) & 37.84 \(\pm\) \\  & & 1.79 & 0.05 & 0.99 & 2.81 & 0.96 & 0.01 & 0.01 & 0.38 \\ \cline{2-10}  & \multirow{2}{*}{10–20 cm} & 101.17 \(\pm\) & 30.61 \(\pm\) & 46.08 \(\pm\) & 181.25 \(\pm\) & 106.00 \(\pm\) & 2.26 \(\pm\) & 0.16 \(\pm\) & 81.20 \(\pm\) \\  & & 4.47 & 0.43 & 6.83 & 72.36 & 83.20 & 1.63 & 0.04 & 41.36 \\ \cline{2-10}  & \multirow{2}{*}{20–30 cm} & 20–30 & 100.95 \(\pm\) & 28.31 \(\pm\) & 43.14 \(\pm\) & 92.49 \(\pm\) & 22.68 \(\pm\) & 0.48 \(\pm\) & 0.13 \(\pm\) & 35.67 \(\pm\) \\  & & 1.15 & 0.53 & 6.83 & 4.69 & 0.85 & 0.02 & 0.03 & 0.62 \\ \hline \multirow{4}{*}{S8} & \multirow{2}{*}{0–10 cm} & 90.07 \(\pm\) & 29.98 \(\pm\) & 44.21 \(\pm\) & 109.70 \(\pm\) & 30.36 \(\pm\) & 4.03 \(\pm\) & 0.39 \(\pm\) & 64.78 \(\pm\) \\  & & 2.68 & 1.50 & 7.37 & 9.83 & 8.56 & 3.46 & 0.06 & 24.19 \\ \cline{2-10}  & \multirow{2}{*}{10–20 cm} & 10–20 & 94.22 \(\pm\) & 27.89 \(\pm\) & 43.36 \(\pm\) & 128.33 \(\pm\) & 51.37 \(\pm\) & 4.68 \(\pm\) & 0.33 \(\pm\) & 74.49 \(\pm\) \\  & & 4.34 & 1.68 & 5.46 & 7.07 & 27.64 & 3.38 & 0.03 & 29.23 \\ \cline{2-10}  & \multirow{2}{*}{20–30 cm} & 20–30 & 95.21 \(\pm\) & 27.33 \(\pm\) & 37.14 \(\pm\) & 107.32 \(\pm\) & 24.66 \(\pm\) & 2.26 \(\pm\) & 0.25 \(\pm\) & 47.33 \(\pm\) \\  & & 1.74 & 0.35 & 1.69 & 8.56 & 3.04 & 1.61 & 0.06 & 12.18 \\ \hline \end{tabular}
\end{table} 
Table 4: Mangrove soil-borne trace elements (mg/kg) in the mid intertidal zone.
## 4 Self-Healing Approaches
### Self-Healing Models and Frameworks
#### 4.1.3 Auto-Regressive Moving Average with Exogenous Input Model  
The auto-regressive moving average with exogenous input (ARMAX) model is a statistical model that combines both auto-regressive (AR) and moving average (MA) components with exogenous input. Ref. [2] explored combining artificial neural network (ANN) and auto-regressive moving average with an exogenous input model (ARMAX) to show how primitives correspond to the quality of service adaptively (QoS) based on the related primitive matrix. Ref. [2] through experiment demonstrate the implementation of a middleware that incorporates a self-adaptive approach based on the feedback control mechanism. The experiment's outcome, when tested using the RuBis benchmark and FIFA 1998 dataset, proves that the models (ANN and ARMAX) produce a more accurate result when compared to the state-of-the-art models. The resulting model from combining the two models in an experiment is S-ANN and S-ARMAX. The former handles the dynamic QoS sensitivity better and produces higher accuracy in events where QoS fluctuations occur, whereas the latter makes fewer errors when QoS fluctuations decrease. The ARMAX model is commonly used in time-series analysis to predict future values tina time series based on past values and exogenous inputs. The model can be estimated using various methods, such as maximum likelihood estimation or least square estimation, and evaluated using measures such as the Akaike information criterion (AIC) or Bayesian information criterion (BIC).
# Kinematic and Workspace Analysis of RRU-3 RSS: A Novel 2T2R Parallel Manipulator
## 3 Kinematic Analysis
### Inverse Position Problem  
By solving the inverse position problem, we obtain the input variables \((\beta_{1},\beta_{2},\beta_{3},\beta_{4})\) as a function of the known output variables \((x,z,\varphi,\theta)\). This problem is explicit, as the set of equations is decoupled in input variables, and each trigonometric equation of Equation (8a-d) can be solved individually using \(c\beta_{i}=\big{(}1-{t_{i}}^{2}\big{)}/\big{(}1+{t_{i}}^{2}\big{)}\) and \(s\beta_{i}=(2\!\cdot\!t_{i})/\big{(}1+{t_{i}}^{2}\big{)}\) trigonometric identities.  
However, for the case of the RRU-3 RSS PM, a geometrical approach can also be applied to solve the problem. In this approach, \(\mathbf{B}_{i}\) coordinates are the unknowns, whereas \(\mathbf{A}_{i}\) and \(\mathbf{C}_{i}\) are known data. The possible \(\mathbf{B}_{i}\) coordinates can be obtained as follows:  
* For the RRU KC: by solving the intersection between two circumferences contained in the \(XZ\) plane, one of center \(\mathbf{C}_{1}\) and radius \(R\) and, the other one of center \(\mathbf{A}_{1}\) and radius \(L\).
* For the RSS KCs: by obtaining the intersection between a circumference of center \(\mathbf{C}_{j}\) (\(j=2,3,4\)) and radius \(R\), and a sphere of center \(\mathbf{A}_{j}\) and radius \(L\).  
Nonetheless, the circumference-sphere intersection can be solved as an intersection of two circumferences, as shown in Figure 2. Hence, the approach applied to all KCs consists of solving the intersection points (\(\mathbf{B}_{i}\)) between two circumferences (contained in \(XZ\) planes) of center \(\mathbf{C}_{i}\) and \(\mathbf{A}^{\prime}{}_{i}\), and radius \(R\) and \(L{t_{i}}\), respectively. \(\mathbf{A}^{\prime}{}_{i}\) is the projection of \(\mathbf{A}_{i}\) in the \(XZ\) plane that contains the lower link of the \(i\)-th KC.  
The coordinates of \(\mathbf{B}_{i}\) are calculated using Equation (9), and then the values of the input variables (\(\beta_{i}\)) are obtained with Equation (3).  
\[\mathbf{B
## 4 Classification of Energy Efficient MAC Protocols for UWSNs
### Depth-Based Layering MAC (DL MAC)
#### 4.2.4. Hybrid-MAC (H-MAC)  
Both frequency domain and random-access MAC techniques are used in the hybrid-MAC (H-MAC) protocol [46]. To deliver data in a collision-free way, this protocol divides the time frame into two time slots, with each communicating node using one of the time slots to perform the task at hand. The random access-based second portion of this hybrid protocol is utilized to adjust the changing traffic conditions for communication between nodes in UWSNs [97]. This adaptation of hybrid H-MAC makes it a very suitable candidate where use of energy in the UWSNs is a big constraint [17]. The key differences between the ERCA-MAC, UAMC-MAC, P-MAC and H-MAC methods are shown in Table 5.