esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Results and Discussion
### Reliability of Tie-Line Data  
The obtained experimental tie-line data were tested for reliability using the [PERSON] [53] (Equation (4)) and [PERSON] [54] (Equation (5)) correlations. These correlations are commonly used for consistency of phase equilibrium data [55; 56; 57]. The equations are obtained by:  
\[\ln\left(\frac{w_{1}^{II}}{w_{2}^{II}}\right)=a+b\ln\left(\frac{w_{1}^{I}}{w_{3} ^{I}}\right), \tag{4}\]  
\[w_{1}^{I}=a^{\prime}+b^{\prime}\frac{w_{1}^{I}}{w_{2}^{II}}, \tag{5}\]  
where the subscripts of the mass fractions indicate the component (lactic acid = 1, water = 2, and AE = 3), the superscripts represent the phase (surfactant = \(I\) and aqueous = \(II\)), \(a\) and \(b\) are the parameters of the Hand correlation, and; \(a^{\prime}\) and \(b^{\prime}\) are the parameters of the Bachman correlation. The correlations plots including the parameters are presented in Figure 5. The linearity of the plots, as reflected in their correlation factors (\(r^{2}\)) close to unity, indicates a high degree of reliability of the measured tie-line data.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Extractant 1** & **Diluent** & \
\begin{tabular}{c} **Distribution** \\ **Coefficient, \(D_{1}\)** \\ \end{tabular} &
\begin{tabular}{c} **Extraction** \\ **Efficiency, \(E\)(\%)** \\ \end{tabular} & **Ref.** \\ \hline MIBK & - & 0.13 & 11.5 & [45] \\ TOA/methylene chloride & Chlorobenzene & 0.20 & 16.7 & [41] \\ TBA & MIBK & 0.21 & 17.4 & [41] \\ Alamine & Octanol & 0.62 & 38.3 & [1] \\ AE & - & 0.58–0.91 & 36.7–47.6 & [This study] \\ TBP & - & 0.95 & 48.8 & [41] \\ TOA/TPA & - & 1.20 & 54.5 & [46] \\ TOA & Chlorobutane & 1.40 & 58.3 & [47] \\ TOA & Methylene & 1.45 & 59.2 & [47] \\ TOA/methylene chloride & Heptane & 2.14 & 68.2 & [41] \\ TOPO & Xylene & 2.20 & 68.8 & [48] \\ TOA/methylene chloride & Hexane & 2.52 & 71.6 & [41] \\ Alamine 336 & Chloroform & 5.30 & 84.1 & [45] \\ Alamine 336 & MIBK & 8.30 & 89.2 & [45] \\ Trilauryl amine & Xylene & 8.30 & 89.2 & [45] \\ TOA & Chloroform & 9.44 & 90.4 & [41] \\ Alamine 336 & Oleyl alcohol & 13.00 & 92.9 & [49] \\ Alamine 336 & Decanol & 23.37 & 95.9 & [50] \\ Alamine 336 & Octanol & 25.95 & 96.3 & [51] \\ \hline \hline \end{tabular}  
* MIBK—Methylisobutylketone, TOA—Tri-\(n\)-octylamine, TBA—Tributyl amine, TBP—Tri-\(n\)-butyl phosphate, TPA—Tripropylamine, TOPO—Trioctylphosphine oxide.  
\end{table}
Table 4: Comparison of solvents for extraction of lactic acid from aqueous solution.
## 2 Overview of Retrieval-Augmented Generation  
The Retrieval-Augmented Generation (RAG) framework integrates retrieval-based and generative models by leveraging information extracted from external sources (typically databases) to improve the quality of generated outputs. The three core processes in the RAG framework--retrieval, augmentation, and generation--are illustrated in Figure 1.  
During the retrieval stage, a query is first constructed from the user's input prompt that targets an LLM. The query is based on the content of the prompt, which is then used to search for most similar or relevant documents from external knowledge sources. A retriever then calculates the similarity between the user query and the returned results from the knowledge source in order to select the most pertinent documents. To optimize this process,  
Figure 1: Main processes in an RAG framework.  
pre-retrieval enhancements can be applied to refine the query, ensuring that more efficient and effective document retrieval is conducted [8; 9]. Post-retrieval enhancements may also be used to increase the utility of the retrieved documents for the subsequent generation tasks [10].  
Once the most relevant results are identified and returned, the process of augmentation takes place. This step typically involves concatenating the retrieved documents from the knowledge source with the original user input prompt to form the final prompt that is passed to the generative language model [8; 9]. This augmented prompt ensures that the LLM is provided with additional information that steers it towards generating a response that incorporates the relevant information from the external source. Augmentation can also be iterative or adaptive, where the generated response is used to extract more precise and contextually relevant content, thereby progressively refining the output [11; 12].  
Following the retrieval and incorporation of the documents into the LLM's input, the generation process combines the model's learned knowledge with the specific content retrieved from external sources. The LLM's attention layers focus on both the original input and the retrieved context, allowing the model to produce an output that integrates specific information from external documents [8; 9]. This approach reduces the model's reliance on its internal parameters and memorized knowledge, thereby decreasing the likelihood of generating factually incorrect or hallucinated information.  
The following sections provide detailed implementation insights into these three key processes.
# Computation of Implicit Representation of Volumetric Shells with Predefined Thickness
## 5 Examples
### Triply Periodic Minimal Surfaces (TPMSs)
#### 5.2.2 Gyroid  
A Gyroid is a TPMS that is described by the implicit equation  
\[\mathfrak{F}_{G}(\vec{x}) = \sin\left(\frac{2\pi x}{L}\right)\cos\left(\frac{2\pi y}{L} \right)+\sin\left(\frac{2\pi y}{L}\right)\cos\left(\frac{2\pi z}{L}\right) \tag{29}\] \[+\sin\left(\frac{2\pi z}{L}\right)\cos\left(\frac{2\pi x}{L} \right)=0,\]  
where \(L\) is the edge length of a cube circumscribing a unit cell of the Gyroid shown in Figure 1 together with the other surfaces investigated in this paper. With the emergence of 3D printing, Gyroids are of great interest since Gyroid-based patterns can be used to fill space while providing sufficient strength and low weight to the 3D-printed parts. Figure 2 shows the bodies generated with the third-order offset function of the Gyroid for various thicknesses.  
We employ the error measurement from Section 5.2.1 to validate the proposed method. Figure 3 shows the convergence of the different offset functions for varying thickness. It is observed that the predicted order of convergence is recovered. The first-order offset function appears to be converging with second-order for large enough thicknesses but approaches the predicted asymptote for thin shells.
# Review of Channel Estimation for Candidate Waveforms of Next Generation Networks
## 4 System Model Description of FBMC OFDM-OQAM and GFDM-OQAM
### Gfdm-OQAM Transceiver
#### 4.2.1.3 Receiver Description  
After the transmitted symbols have propagated through the wireless channel, the received signal can be expressed as:  
\[\vec{\hat{x}}_{R}[n]=\vec{\hat{\mathbf{H}}}\vec{\hat{x}}_{T}[n]+w[n], \tag{52}\]  
where \(\vec{\hat{x}}_{T}[n]\) is the transmitted signal with CP. If the CP is removed, the received signal is denoted as \(\vec{x}_{R}[n]\). The symbol \(w[n]\) in Equation (52) is the complex AWGN vector with zero mean and variance \(\sigma_{w}^{2}\). The notation \(\vec{\hat{\mathbf{H}}}\) (\(\vec{\hat{\mathbf{H}}}=circ(h(\hat{n}))\)) is the circulant channel matrix (CCM) having a band diagonal structure based on the channel impulse responses obtained from Equation (51) and it is obtained as described in Algorithm 1.  
Figure 20: Structure of GPDM-OQAM based transmitter.  
Therefore, the received signal after equalisation is given as:  
\[x_{R}[n]=\vec{x}_{R}[n]H_{chan}^{-1}[n], \tag{53}\]  
where \(H\) is the Hermitian transpose operator and \(H_{chan}[n]\) are the fading coefficients obtained from the CE. Thus, the demodulated signal is given as:  
\[c_{R}[n]=\textbf{B}x_{R}[n], \tag{54}\]  
where **B** is the matched filter receiver matrix given as **B** = \(\textbf{A}^{H}\), and **A** is the \(N\times N\) transmitter modulation matrix.
## 4 Experimental Setup and Results
### Classification between Street Art and Illegal Graffiti
#### 4.1.2 Image Classification Limitations  
Due to the subjectivity concerning the differences between illegal graffiti and street art, this distinction sometimes becomes a bit blurred and contradictory. Sometimes, the distinction between these two groups of graffiti is already difficult to classify by a human. Usually, it depends on the person and their idea of art, which can vary considerably.  
Some images belonging to the set of street art (for example, the ones in Figure 14), taken from the website of the urban art gallery, may raise some doubt due to their resemblance to some images defined as illegal graffiti, as in the examples displayed in Figure 15.  
\begin{table}
\begin{tabular}{l l l l l} \hline \hline  & & \multicolumn{2}{c}{**Predicted Class**} & \\ \cline{3-5}  & & Illegal Graffiti & Street Art & W/o Graffiti \\ \hline \multirow{3}{*}{**Actual Class**} & Illegal Graffiti & 183 & 37 & 4 \\ \cline{2-5}  & Street Art & 13 & 202 & 9 \\ \cline{2-5}  & W/o Graffiti & 4 & 33 & 48 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Confusion matrix obtained with images from the test set.  
\begin{table}
\begin{tabular}{l l l} \hline \hline  & **Metric** & **Value** \\ \hline Accuracy & & 0.81 \\ \hline Balanced Accuracy & & 0.76 \\ \hline \multirow{3}{*}{Precision} & Street art & 0.92 \\  & Illegal graffiti & 0.74 \\  & Without graffiti & 0.79 \\ \hline \multirow{3}{*}{Recall} & Street art & 0.82 \\  & Illegal graffiti & 0.90 \\  & Without graffiti & 0.56 \\ \hline \multirow{3}{*}{F1-score} & Street art & 0.86 \\  & Illegal graffiti & 0.81 \\ \cline{1-1}  & Without graffiti & 0.66 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Classification metrics for the test set.  
Since the model is trained based on the classes of these images, it is expected that there will be some misclassifications in some cases, as in Figure 16 (left image). Other images, such as those in Figure 16 (central and right image), contain street art elements and illegal graffiti. However, since they were images taken from the Lisbon urban art gallery, they were classified as street art.  
There are also other cases where the image has a significant amplitude and the graffiti is at a considerable distance, and therefore may go unnoticed, as the pictures in Figure 17.  
Furthermore, the relevant difference between the number of images containing graffiti (street art and illegal) and without graffiti is quite significant, as displayed in Table 3, which may justify the differences between the performances obtained for these classes.  
Figure 16: Misclassified graffiti due to similarities between the two classes (**left**) and due to images also containing illegal graffiti ((**central**) and (**right**) images).  
Figure 14: Images labeled as street art.  
Figure 17: Examples of pictures where the graffiti is at a large distance.  
Figure 15: Images labeled as illegal graffiti.
## 2 Materials and Methods
### Sampling  
In all experimental series, digestate samples were sampled at approximately weekly intervals from both PB and CB containing SS and CS. A total of 68 SS samples and 96 CS samples were collected. The ID numbers assigned to the samples in each experimental series are presented in Table 3.  
\begin{table}
\begin{tabular}{c c c c c c} \hline  & & \multicolumn{2}{c}{**SS**} & \multicolumn{2}{c}{**CS**} \\ \hline \multirow{3}{*}{**Series**} & \multirow{3}{*}{**Samples**} & **PB \({}^{\mathbf{a}}\)** & **CB \({}^{\mathbf{b}}\)** & **PB** & **CB** \\ \cline{3-6}  & & & & \multicolumn{3}{c}{**Sample ID**} \\ \hline \multirow{6}{*}{**1**} & 1 & SS D1.1 & SS C1.1 & CS D1.1 & CS C1.1 \\  & 2 & SS D1.2 & SS C1.2 & CS D1.2 & CS C1.2 \\  & 3 & SS D1.3 & SS C1.3 & CS D1.3 & CS C1.3 \\  & 4 & SS D1.4 & SS C1.4 & CS D1.4 & CS C1.4 \\  & 5 & & & & CS D1.5 & CS C1.5 \\  & 6 & & x & & CS D1.6 & CS C1.6 \\ \hline \multirow{6}{*}{**2**} & 1 & SS D2.1 & SS C2.1 & CS D2.1 & CS C2.1 \\  & 2 & SS D2.2 & SS C2.2 & CS D2.2 & CS C2.2 \\  & 3 & SS D2.3 & SS C2.3 & CS D2.3 & CS C2.3 \\  & 4 & SS D2.4 & SS C2.4 & CS D2.4 & CS C2.4 \\  & 5 & SS D2.5 & SS C2.5 & CS D2.5 & CS C2.5 \\  & 6 & & x & & CS D2.6 & CS C2.6 \\ \hline \multirow{6}{*}{**3**} & 1 & SS D3.1 & SS C3.1 & CS D3.1 & CS C3.1 \\  & 2 & SS D3.2 & SS C3.2 & CS D3.2 & CS C3.2 \\  & 3 & SS D3.3 & SS C3.3 & CS D3.3 & CS C3.3 \\  & 4 & SS D3.4 & SS C3.4 & CS D3.4 & CS C3.4 \\  & 5 & & x & & CS D3.5 & CS C3.5 \\  & 6 & & x & & CS D3.6 & CS C3.6 \\ \hline \multirow{6}{*}{**4**} & 1 & SS D4.1 & SS C4.1 & CS D4.1 & CS C4.1 \\  & 2 & SS D4.2 & SS C4.2 & CS D4.2 & CS C4.2 \\  & 3 & SS D4.3 & SS C4.3 & CS D4.3 & CS C4.3 \\  & 4 & SS D4.4 & SS C4.4 & CS D4.4 & CS C4.4 \\  & 5 & SS D4.5 & SS C4.5 & CS D4.5 & CS C4.5 \\  & 6 & & x & & CS D4.6 & CS C4.6 \\ \hline \multirow{6}{*}{**5**} & 1 & SS D5.1 & SS C5.1 & CS D5.1 & CS C5.1 \\  & 2 & SS D5.2 & SS C5.2 & CS D5.2 & CS C5.2 \\  & 3 & SS D5.3 & SS C5.3 & CS D5.3 & CS C5.3 \\  & 4 & SS D5.4 & SS C5.4 & CS D5.4 & CS C5.4 \\  & 5 & SS D5.5 & SS C5.5 & CS D5.5 & CS C5.5 \\  & 6 & & x & & CS D5.6 & CS C5.6 \\ \hline \end{tabular}
\end{table}
Table 3: Identification numbers (Samples No. 1–No. 9) assigned to SS and CS samples collected from process (PB) and control (CB) bioreactors during the AD process in each experimental series (Series 1–7).
# Instantaneous Networking Service Availability for Disaster Recovery
## 8 Conclusions  
In this paper, we examined the network restoration by utilizing instant networking service availability (I-NSA). Compared with conventional methods for measuring the networking availability, I-NSA is an integrated factor that involves both network connectivity and user distribution among various areas. I-NSA has its unique features that facilitate the design of novel networking services such as Local-and-Instant Clouds for disaster resilience. First, the I-NSA measures the networking  
\begin{table}
\begin{tabular}{p{142.3 pt} p{142.3 pt}} \hline \hline
**State Transitions of an LI-Cloud Server** & **Conditions of Transitions** \\ \hline Transition 1 & the LI-Cloud server is powered on, and launches its local services \\ \hline Transition 2 & the LI-Cloud is connected to the Internet \\ \hline Transition 3 & the LI-Cloud is connected to other LI-Clouds before the connection to the Internet \\ \hline Transition 4 & the LI-Cloud is connected to the Internet after the connection with other LI-Clouds \\ \hline Transition 5 & 6 & 7 \\ \hline \hline \end{tabular}
\end{table}
Table 4: State transition conditions of an LI-Cloud server.  
\begin{table}
\begin{tabular}{p{142.3 pt} p{142.3 pt}} \hline \hline
**State Transitions of a User** & **Conditions of Transitions** \\ \hline Transition 1 & the user obtains local networking services \\ \hline Transition 2 & the global networking service is available \\ \hline Transition 3 & the user is able to communicate with users associated with other LI-Clouds \\ \hline Transition 4 & the global networking is available when the LI-Cloud is connected to the Internet after the connection with other LI-Clouds \\ \hline Transition 5 & 6 & 7 \\ \hline \hline \end{tabular}
\end{table}
Table 3: State transition conditions of a user.  
service availability from the temporary and partial recovery of the network. Second, I-NSA allows us to assess the functionality and effectiveness of the network restoration process before the network is fully recovered. We especially examined the I-NSA of using LI-Clouds in a disaster situation. The evaluation results showed the significant improvement of networking service availability with utilization of LI-Clouds in various deployment scenarios of LI-Clouds.  
Conceptualization, R.T., T.S., and Y.S.; investigation, R.T. and T.S.; validation, R.T., T.S., and Y.S.; writing--review and editing, R.T., T.S., and Y.S. All authors have read and agreed to the published version of the manuscript.  
This research is in part supported by an SIP Program on national resilience (disaster prevention and mitigation).  
This work is in part supported by an SIP Program on national resilience (disaster prevention and mitigation).  
The authors declare no conflict of interest.
# GPP of a Chinese Savanna Ecosystem during Different
## 2 Materials and Methods
### Phenocam Data and Canopy Phenology Analysis
#### 2.4.3 Identifying Phenophase Transition Dates from GCC Values  
The R package phenopix was employed for image analysis and phenophase extraction, as documented in [48]. The annual GCC values derived from the digital photographs were processed using phenopix functions to assess phenology patterns. The seasonal GCC trajectories were fitted with a double logistic curve. The estimated dates of important phenophases of canopy development were calculated via the PhenoExtract function. The range of dates associated with notable green-up of the canopy in the ROI was defined as the start of the season (SOS). The peak of the season position (POP) is associated with the maximum canopy green vigor, which corresponds to the peak production. The end of the season (EOS) was defined as autumn, when the canopy becomes less vigorous and green, leaves begin to senesce, and the chlorophyll content decreases. To obtain estimates of important dates in canopy development (aka phenophases), we fit a double logistic curve to the seasonal GCC trajectories, with the equation proposed by [49]. Phenophases are computed via the method proposed by [50]. Specifically, we define the SOS and EOS as the days of the year when the first local maximum and the last local minimum in the rate of change in curvature (k1) occur, respectively. K1 is calculated on the basis of first and second derivatives of the double logistic equation, further defined in [50; 51] and graphically illustrated in [48]. The POP is defined as the day of the year when the seasonal maximum of the GCC is reached. Analysis of the GCC trajectories enabled the identification of two phenological stages (start and end of the active growth phase, i.e., the green-up and green-down phases, respectively). Notably, the SOS, POP, and EOS data were retrieved as the day of year (DOY) during the growing season.  
Specifically, considering the characteristic color index patterns of savannas, where there was no plateau phase following a color index increase (instead, the savannas directly transitioned from peak values to the decline phase), we segmented the phenological fitted line into two stages: the green-up (spring and summer growing periods, i.e., dates from the SOS to the POP) and green-down (autumn and winter senescence periods, i.e., dates from the POP to the EOS) phases. This simple phenophase division not only facilitates comparisons with the VPM results but also ensures consistency with the seasonal division of savannas commonly observed in other studies [2; 25]; namely, dry and wet seasons are generally distinguished.  
To address the different spatial resolutions of HLS (10-60 m) and MODIS (500 m) data, we validated the phenocam-derived phenophases against multiple representative points within the satellite imagery by visually comparing the phenology curves for consistency. This approach confirmed the applicability of phenocam data across the study area, ensuring spatial representativeness.
## 3 Wind System Control at Variable Wind Speeds from 3 [m/s] up to \(V_{MAX}\) [m/s]
### Linearized System Analysis and Control
Option (2) The feedback controller is a double integrator with transfer function \(C(s)=(p_{1}s+p_{0})/s^{2}\). The closed-loop characteristic polynomial will be \(Ts^{3}+s^{2}+K_{f}p_{1}s+K_{f}p_{0}\) which may still offer stability for proper choice of \(p_{1},p_{0}\), but stability margin is significantly smaller. In this case, since the coefficient of \(s^{2}\) is 1, then for \(T<0\) (Cases 1 and 2b from Remark 5), it will be impossible to make a stable closed loop by any selection of \(p_{1},p_{0}\). We conclude that a double integrator is not feasible to be designed at the MPP; however, it may be designed at a suboptimal operating point such as in Case 2a in Remark 5. We consider a reasonable ramp-like variation for the wind speed as in \(V(t)=2.0071\times 10^{-3}t+3\), starting from \(V(0)=3\left[\frac{m}{s}\right]\) and up to the value \(V_{MAX}\). After extensive testing with selected pair values \((p_{1},p_{0})\) that make the closed loop stable around the linearization point, when testing in dynamic regime for the ramp-like \(V(t)\), only marginally stable control is achieved. This motivates the selection of the plain PI control algorithm revealed under Option 1, which will drive the control to be stable, fast and with acceptable steady state tracking error. For the operating point characterized by \(\mathcal{P}(V_{0}=4\left[m/s\right],n_{0}=15.30\ [\mathrm{rps}],f_{0}=0.953\ [ \mathrm{Hz}])\), we select \(p_{1}=-10,\ p_{0}=-30\) as the PI controller gain parameters leading to \(C_{PI}(s)=-(10s+30)/s\).
## 2 System Model
### OTFS Modulation
The element of \(\mathbf{Y}\) is given by  
\[Y_{l,k}=\sum_{l^{\prime}=0}^{M-1}\sum_{K^{\prime}=0}^{N-1}X_{l^{\prime},k^{ \prime}}H_{[l-l^{\prime}]_{M},[k-k^{\prime}]_{N}}e^{\phi(\alpha,\beta)}+V_{l,k} \tag{8}\]  
where \(H_{l,k}\) represents the channel matrix in the DD domain, and \(V_{l,k}\) denote the channel and additive white Gaussian noise in the DD domain. \([(\cdot)]_{M}\) represents \((\cdot)\) mod \(M\), and \([(\cdot)]_{N}\) represents \((\cdot)\) mod \(N\). As a compensated phase, \(\phi(\alpha,\beta)\) can be written as follows:  
\[\phi(\alpha,\beta)=\left\{ \begin{array}{cc}\frac{-j2\pi\beta((M-1)+\alpha)} {(M+N_{CP})N},&\beta\leq\frac{N}{2}\\ \frac{-j2\pi((\beta-N)(M-1)+\alpha)}{(M+N_{CP})N},&\beta>\frac{N}{2}\end{array} \right. \tag{9}\]  
where \(\alpha=[l-l^{\prime}]_{M}\), \(\beta=[k-k^{\prime}]_{N}\). Channels \(H_{l,k}\) in the DD domain can be obtained by using channels \(h_{q,l}\) in the time domain, leading to  
\[H_{l,k}=\sum_{i=1}^{N}h_{(i-1)(M+N_{CP})+1,[l]_{M}}e^{-j2\pi(i-1)\frac{1}{N}} \tag{10}\]  
Denoting the maximum delay as \(\tau_{max}\) and the maximum Doppler as \(\
u_{max}\), the maximum delay and Doppler of the grid in the DD domain can be written as \(L=\tau_{max}M\Delta f\) and \(K=\
u_{max}NT\), respectively. Therefore, the counts of the nonzero elements in \(\mathbf{H}\in\mathbb{C}^{M\times N}\) can be calculated as \(L\times(2K+1)\).