esa-sceva/satcom-chunk-collection huggingface dataset:
# A Parallel Algorithm for Dividing Octonions
## 2 Short Background  
Consider the problem of dividing two octonions  
\[d=a/b, \tag{1}\]  
where  
\[a =(a_{0}+e_{1}a_{1}+e_{2}a_{2}+e_{3}a_{3}+e_{4}a_{4}+e_{5}a_{5}+e_{6}a_{6}+e_{7 }a_{7}),\] \[b =(b_{0}+e_{1}b_{1}+e_{2}b_{2}+e_{3}b_{3}+e_{4}b_{4}+e_{5}b_{5}+e_{6 }b_{6}+e_{7}b_{7}),\] \[d =(d_{0}+e_{1}d_{1}+e_{2}d_{2}+e_{3}d_{3}+e_{4}d_{4}+e_{5}d_{5}+e_{ 6}d_{6}+e_{7}d_{7}),\]  
and \(\{a_{i}\},\{b_{i}\},\{d_{i}\}\in R;\{e_{i}\},i=0,1,\ldots,7\) are imaginary units. The division operation (1) can be written as the multiplication of the octonion-dividend \(a\) by the conjugate octonion-divisor \(b^{*}\) divided by the square of the norm of the quaternion-divisor \(R\)  
\[d=ab^{*}/R, \tag{2}\]  
where  
\[b^{*}=(b_{0}-e_{1}b_{1}-e_{2}b_{2}-e_{3}b_{3}-e_{4}b_{4}-e_{5}b_{5}-e_{6}b_{6} -e_{7}b_{7})\]  
\[R=b_{0}^{2}+b_{1}^{2}+b_{2}^{2}+b_{3}^{2}+b_{4}^{2}+b_{5}^{2}+b_{6}^{2}+b_{7}^ {2},\]  
The rules for multiplying the octonion imaginary units are presented in Table 1[1].  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \(\times\) & 1 & \(e_{1}\) & \(e_{2}\) & \(e_{3}\) & \(e_{4}\) & \(e_{5}\) & \(e_{6}\) & \(e_{7}\) \\ \hline
1 & 1 & \(e_{1}\) & \(e_{2}\) & \(e_{3}\) & \(e_{  
The operation of division (2) can be rewritten in the matrices-vector form [32; 33; 34]  
\[\mathbf{Y}_{8\times 1}=\eta_{8}\mathbf{O}_{8}\mathbf{X}_{8\times 1}, \tag{3}\]  
where \(\eta_{8}\) is a scalar matrix  
\[\boldsymbol{\eta}_{8}=\eta\mathbf{I}_{8},\]  
\(\mathbf{I}_{N}\) is the identity matrix of order \(N\), \(\eta\) is a inverse of the square of the norm of the quaternion-divisor  
\[\eta=1/R,\]  
\(\mathbf{Y}_{8\times 1}\) and \(\mathbf{X}_{8\times 1}\) are the vector representation of the quotient \(d\) and octonion-dividend \(a\), respectively  
\[\mathbf{Y}_{8\times 1}=[y_{0},y_{1},y_{2},y_{3},y_{4},y_{5},y_{6},y_{7}]^{T },\quad y_{i}=d_{i},i=\overline{0,7},\]  
\[\mathbf{X}_{8\times 1}=[x_{0},x_{1},x_{2},x_{3},x_{4},x_{5},x_{6},x_{7}]^{T}, \quad x_{i}=a_{i},i=\overline{0,7},\]  
and \(\mathbf{O}_{8}\) is the left real matrix representation of the conjugate octonion-divisor  
\[\mathbf{O}_{8}=\left[\begin{array}{cccccccc}b_{0}&b_{1}&b_{2}&b_{3}&b_{4}&b_ {5}&b_{6}&b_{7}\\ -b_{1}&b_{0}&b_{3}&-b_{2}&b_{5}&-b_{4}&-b_{7}&b_{6}\\ -b_{2}&-b_{3}&b_{0}&b_{1}&b_{6}&b_{7}&-b_{4}&-b_{5}\\ -b_{3}&b_{2}&-b_{1}&b_{0}&b_{7}&-b_{6}&b_{5}&-b_{4}\\ -b_{4}&-b_{5}&-b_{6}&-b_{7}&b_{0}&b_{1}&b_{2}&b_{3}\\ -b_{5}&b_{4}&-b_{7}&b_{6}&-b_{1}&b_{0}&-b_{3}&b_{2}\\ -b_{6}&b_{7}&b_{4}&-b_{5}&-b_{2}&b_{3}&b_{0}&-b_{1}\\ -b_{7}&-b_{6}&b_{5}&b_{4}&-b_{3}&-b_{2}&b_{1}&b_{0}\end{array}\right]. \tag{4}\]  
The direct multiplication of the vector-matrix product in Equation (3) requires 72 multipliers, 63 adders, 8 squaers and one divider of real numbers. The authors proposed some tricks, which reduce the multiplicative complexity of this operation to 38 real multiplications at the price of 56 more real additions.
## 5 Conclusions  
In this paper, we proposed a monitoring system that uses a MIMO-OOK scheme that is based on an OCC system. The proposed scheme uses a Rol method, which can detect dozens of users with high accuracy, making it compatible with almost all types of commercially available cameras, including the rolling-shutter camera and global-shutter camera. Furthermore, our advances in SNR measurements with different exposure times confirm that the performance of the system depends on the work distance and exposure time. Finally, we implemented the bit error rate of the proposed scheme using different distances to highlight the system's effectiveness in comparison with similar systems.  
Supplementary Materials: Supplementary Materials can be seen at [[http://www.mdpi.com/2076-3417/9/23/5103/s1](http://www.mdpi.com/2076-3417/9/23/5103/s1)]([http://www.mdpi.com/2076-3417/9/23/5103/s1](http://www.mdpi.com/2076-3417/9/23/5103/s1)). The supplementary material video shows the implementation of the proposal with temperature and humidity sensors at the distance of 20 m.  
**Author Contributions:** All authors contributed to this paper: [PERSON] and [PERSON] proposed the idea and the simulation methodology: [PERSON] optimized the software, proposed and designed the scheme, performed all experiments, and wrote the paper: [PERSON] verified the experiment process and results and reviewed and edited the paper: and [PERSON] supervised the work and provided funding support.  
**Funding:** This research was supported by the MSIT (Ministry of Science and ICT), Korea, under the ITRC (Information Technology Research Center) support program (IITP-2018-0-01396) supervised by the IITP (Institute for Information and communications Technology Promotion).  
**Conflicts of Interest:** The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{|l|c|c|} \hline \multicolumn{3}{|c|}{Transmitter Side} \\ \hline The number of LEDs & 1 & 2 & 3 \\ \hline Clock rate & \multicolumn{3}{c|}{20 Hz} \\ \hline LED type & \multicolumn{3}{c|}{5V DC-0.2 W} \\ \hline \multicolumn{3}{|c|}{Receiver Side} \\ \hline Camera type & \multicolumn{3}{c|}{PointGrey rolling shutter camera} \\ \hline Camera frame rate & \multicolumn{3}{c|}{60 fps} \\ \hline \multicolumn{3}{|c|}{Throughput} \\ \hline Bit rate & 20 bps & 40 bps & 60 bps \\ \hline \end{tabular}
\end{table}
Table 2: Characteristic parameters for MIMO-C-OOK scheme for implementation.  
Figure 14: Bit Error Rate of MIMO-OOK system with different exposure times.
# Revolution or Evolution? Technical Requirements and Considerations towards 6G Mobile Communications
## 6 Enablers for 6G and Relevant Technical Preparation and Implementation
### Edge Intelligence  
Fifth generation promises to make changes in three different domains: higher speed, design system SDN, and support for edge computing. The latter can have a transformative impact, because, effectively, what edge computing offers is to the end-users of the 5G network. It provides the capability of having systems running locally or at very close edges without going globally. Therefore, it is desirable for end-users to have an environment that could provide a private, secure, and effective connectivity to an edge server. Such a system could facilitate running AI workloads, data analysis, and mining anonymization encryption at a local site [95; 96].  
One of the earliest adopters of edge computing for the 5G mobile network systems is SK Telecom. They have devised a plan to implement the mobile edge architecture to decentralize the server architecture across South Korea, resulting in reduction of communication delays by up to 60% [97]. This is also part of the efforts to meet one of the \"5G triangle\", i.e., URLLC, which is expected to offer close to 1 ms latency.  
However, 5G faces some architectural limitations, such as network scalability. One thing that should be taken into account is that the network slices have to be implemented into an individual network router, which possibly leads to certain scalability issues. It is envisioned that in 6G, a new architecture with different approaches for supporting network slices should be available [96].  
Another limiting factor that 5G faces is the utilization of mmWave. Although mmWave can provide higher-speed communication, it is limited to short-range communication. In 6G, the trend is toward providing higher speeds via THz communications, further limiting the communication range. Therefore, to provide connectivity for things in an environment, all devices have to receive services under an access point (AP) in their vicinity. Such a type of connectivity is vulnerable to speed mismatch, for example, existence of a very high end on one side of the AP and a lower band and lower speed end on the other side. This leads to the need to enhance edge computing functionality [96].  
It is anticipated that 6G, with the smart exploitation of AI methodologies, would drive toward the robust edge capabilities to handle communication mismatch as well as new fundamental architecture to have more intelligent edge computing [98]. Thus, it is expected that existing edge computing technology will evolve into edge intelligence technology by 2030.
# Orthogonal Subblock Division Multiple Access for OFDM-IM-Based Multi-User VLC Systems
## 3 Results and Discussions
### Simulation Results  
In our simulations, we evaluate and compare the PAPR and BER performance of the considered four schemes. It can be clearly seen from Figure 3 that DFT-S-OFDM-SM-IM slightly outperforms OFDM-SM-IM and a PAPR reduction of 0.4 dB is obtained at a probability of \(10^{-3}\), which might be due to the existence of a large number of unmodulated subcarriers during OFDM modulation. In contrast, a substantial PAPR reduction of 1.9 dB at a probability of \(10^{-3}\) can be achieved by DFT-S-OFDM-DM-IM in comparison to OFDM-DM-IM. As a result, DFT spreading can be considered as an efficient way to reduce the PAPR of OFDM-IM, especially for OFDM-DM-IM. It should be noted that performing interleaved subcarrier multiplexing does not affect the PAPR performance of the above-mentioned schemes.  
Figure 4a shows the simulation BER versus signal-to-noise ratio (SNR) for OFDM-SM-IM and DFT-S-OFDM-SM-IM without and with interleaving over a low-pass VLC channel, where the noise is modeled as the additive white Gaussian noise (AWGN) and the adopted low-pass frequency response is measured from the experimental VLC system which can be found in Section 3.2. As we can see, OFDM-SM-IM with interleaving slightly outperforms OFDM-SM-IM without interleaving by an SNR gain of 0.5 dB at the 7% forward error correction (FEC) coding limit of BER = \(3.8\times 10^{-3}\). Moreover, an SNR gain of 1.2 dB can be obtained by DFT-S-OFDM-SM-IM without interleaving in comparison to OFDM-SM  
Figure 3: PAPR comparison of OFDM-SM-IM, DFT-S-OFDM-SM-IM, OFDM-DM-IM, and DFT-S-OFDM-DM-IM.  
IM without interleaving. It is clearly to see that the combination of DFT spreading and interleaving can lead to a significant 3-dB SNR gain for OFDM-SM-IM. Figure 4b depicts the simulation BER versus SNR for OFDM-DM-IM and DFT-S-OFDM-DM-IM without and with interleaving over the low-pass VLC channel. It can also be observed that DFT-S-OFDM-DM-IM with interleaving outperforms DFT-S-OFDM-DM-IM without interleaving, OFDM-DM-IM with interleaving and OFDM-DM-IM without interleaving by SNRs gain of 1.8, 2.4 and 3.5 dB, respectively.
# Generalization Investigation for Artificial Intelligence-Based Positioning in IIoT
## 5 Performance Evaluation and Discussion
### Scenario 0: Identical Configuration between Training Data Set and Test Data Set  
In this scenario, the training data set and test set are generated in the same configuration, including the same clutter parameter setting, ideal network synchronization and no receiving timing error. Results in this scenario can be regarded as the upper bound.  
Figures 8 and 9 show the positioning error for direct AI-based positioning and AI-based ToA prediction, respectively. For comparison, the positioning error of the classic positioning method TDOA is also depicted for reference.  
According to the simulation results, In the TDOA-based method, the positioning error at 90% CDF for the clutter parameter of {60%, 6 m, 2 m} is up to 14 m, and even in the scenario of clutter parameter of {40%, 2 m, 2 m}, the positioning error at 90% CDF is still up to 12 m. While for the AI-based solutions, the performance is improved greatly. Depending on the direct AI-based solution or indirect AI-based solution used, the performance is slightly different. Anyway, no matter which AI-based solution is used, the positioning error @90% is less than 1 m. In the clutter parameter of {60%, 6 m, 2 m}, the positioning error could achieve around 0.45-0.65 m if using the AI model trained by the data set with clutter parameter of {60%, 6 m, 2 m}. In the clutter parameter of {40%, 2 m, 2 m}, the positioning error could achieve around 0.75-0.85 m if using the AI model trained by the data set of inF-DH{40%, 2 m, 2 m}.
## 3 Results and Discussion  
### Interpretation of Analysis  
The X-ray diffractograms of the BS-HVL and BC-HVL are shown in Figures 2 and 3. Both materials show characteristic peaks at 20 = 15\({}^{\circ}\), 17\({}^{\circ}\), 18\({}^{\circ}\), 20\({}^{\circ}\) and 23\({}^{\circ}\) by diffraction of the (100), (020), (021), (110) and (200) planes of the hexagonal crystal lattice P31c(163) of sodium magnesium thiocyanate (Na\({}_{4}\)Mg(SCN)\({}_{6}\)) and crystals of magnesium iodide methanol (C\({}_{6}\)H\({}_{24}\)O\({}_{6}\)MgI\({}_{2}\)) and magnesium dodecanate (C\({}_{24}\)H\({}_{46}\)MgO\({}_{4}\)) and characteristic peaks at 20 = 13\({}^{\circ}\), 15\({}^{\circ}\), 25\({}^{\circ}\) and 28.5\({}^{\circ}\) by diffraction of the (0-12), (100), (024) and (0-15) planes of the triclinic crystal lattice P-1(2) and other crystal structure of calcium pyrazolone trihydrate (C\({}_{17}\)H\({}_{13}\)CaClN\({}_{4}\)O\({}_{7}\)S\({}_{2}\); 3H\({}_{2}\)O) and 1,3-Distearoyl-2-Palmitoylglycerol (C\({}_{55}\)H\({}_{106}\)O\({}_{6}\)) from the Triclinic P-1(2) crystal lattice. Most of the structure of BS-HVL and BC-HVL is amorphous, and the SEM might give a clear idea of the morphology of the investigated materials (Figure 5). This favors the adsorption of X-PR and MGC on both materials. The EDXA spectrum of BS-HVL (Figure 7a) also confirms the presence of a high percentage of carbon and oxygen in both materials, in addition to the presence of other elements such as K, P, Ca, Na and Si in BS-HVL. The EDXA spectrum of BC-HVL is shown in Figure 7b. After the adsorption of the X-PR and MGC dyes, the EDXA spectrum shows quite high percentages of carbon and oxygen, hence the fixation of both dyes inside the pores and on the surface of BS-HVL and BC-HVL. The SEM image also shows that the morphology of our material is modified after adsorption and the presence of the dye in the materials (Figure 6).  
The images provided by the AFM analysis of the surface of the two materials give a clear idea that the surface of the seeds are rich with pillars (Figure 8a-c); on the other hand, biochar has a leash surface (Figure 8d). This difference between the natures of the surface can improve the adsorption capacity of the two colorants. Finally, the FTIR spectra of BS-HVL and BC-HVL were measured within the range of 500-4000 cm\({}^{-1}\) and are displayed in Figure 6, which shows OH\({}^{-}\) functions associating phenol and alcohol from 3200 to 3400 cm\({}^{-1}\), C-H cyclohexane bonds from 2850 to 2925 cm\({}^{-1}\), phosphine from 2280 to 2410 cm\({}^{-1}\), N-H primary amines from 1550 to 1650 cm\({}^{-1}\), C=O carboxylic acid from 1400 to 1450 cm\({}^{-1}\), C-O primary alcohols from 1050 to 1080 cm\({}^{-1}\), C-O ethers from 1000 to 1090 cm\({}^{-1}\), Ar-C from 850 to 890 cm\({}^{-1}\) and, finally, monosubstituted aromatics from 700 to 800 cm\({}^{-1}\). After adsorption, the FTIR spectrum (Figure 10) shows the appearance of the new functions in the BC-HVL. This shows that the two biomaterials used to removal the X-PR and MGC are cost effective.
## 3 Y-Branch Coupler
### 3 dB Alignment Tolerance of the Y-Branch Coupler  
Figure 6a shows the alignment of the SMF and Y-branch coupler. To achieve maximum coupling efficiency, it is necessary to carefully adjust the SMF along the \(x\), \(y\), and \(z\) directions, so that SMF center and coupler center can be on the same line and overlapped. In this section, 3 dB alignment tolerance of the Y-branch coupler is analyzed to quantitatively evaluate the difficulty of the alignment.  
Adjustments in the \(z\) direction are completed if there is no gap between the SMF and Y-branch coupler. These adjustments are relatively simple, so alignment tolerance in the \(z\) direction is not analyzed in this paper. Influence of the deviation between the SMF center and coupler center in the \(x-y\) plane on the coupling efficiency \(\eta_{\mathrm{y}}\) is shown in Figure 6b. In this figure, \(dx\) denotes the deviation between the SMF center and coupler center in the \(x\) direction, \(dy\) denotes the deviation in the \(y\) direction, color bar denotes the normalized coupling efficiency. It is clear to know that the greater the deviation between the SMF center and coupler center is, the lower the coupling efficiency will be. When deviation is outside the red circle, coupling efficiency drops to half of the maximum. Therefore, 3 dB alignment tolerance of the Y-branch coupler is \(\sqrt{dx^{2}+dy^{2}}\leq\) 1.10 \(\upmu\)m.
# Cooperative Jamming-Based Physical-Layer Group Secret and Private Key Generation
## 3 Group Secret and Private Key Generation Scheme
### Key Agreement
#### 3.2.2 The Second Step of Public Discussion
Consequently, they are unable to completely eliminate the influences of channels \(G_{2}\) and \(G_{3}\) when estimating \(G_{1}\). As a result, the security of the reference channel-based group key generation can be significantly enhanced._  
**Remark 3**. : _Note that the group SK and PK generation scheme can be directly extended to scenarios involving \(N(N>3)\) legitimate nodes, where legitimate members \(U_{1},U_{2},\ldots,U_{N}\) and the relay collectively form a star network, and the channel gain between \(U_{i}(i=1,2,\ldots,N)\) and the relay is denoted as \(G_{i}\). In this case, the coherence time \(T\) is divided into \(N\) time slots, i.e., \(T_{1},T_{2},\ldots,T_{N}\). In the channel measurement stage, the legitimate members \(U_{1},U_{2},\ldots,U_{N}\) obtain their respective observations of the relay channel \(G_{1},G_{2},\ldots,G_{N}\), while the relay acquires superimposed channel observations regarding \(G_{1}\) and \(G_{j}(j=2,3,\ldots,N)\). In the key agreement stage, \(U_{2},U_{3},\ldots,U_{N}\) obtain estimates of channel \(G_{1}\) through the first key agreement. Then, they agree on the same SK and PK as \(U_{1}\) through the second key agreement._
## 2 Design and Methods
### Design Selection  
In the process of material selection for a design, a Pugh decision matrix is employed. This systematic approach involves the utilization of a decision matrix to evaluate and compare alternatives, aiding in the identification of the most optimal design for the intended application. The decision matrix serves as a comprehensive tool, incorporating multiple criteria essential for the selection process. Each design was evaluated under 11 different design criteria to provide information regarding safety, functionality, and stability. This method facilitates an informed decision-making process, guiding the selection of the design that best aligns with the project requirements and objectives.  
In the context of the robotic walking training device (RWTD), efficiency pertains to streamlined rehabilitation task accomplishment, optimizing resource usage, and minimizing delays. Comfort relates to the overall well-being of patients, encompassing both physical and psychological ease. Stability involves the RWTD's ability to maintain balance and resist external forces for a secure environment. The decision matrix quantitatively compares designs, emphasizing safety, efficiency, smooth motion, and structural stability in the gait rehabilitation process.
## 2 Nutrition Profile of Hazelnuts, Almonds and Pistachios
### Pistachios  
The pistachio (_Pistacia vera_ L.) is an ancient nut, native to the Middle East, and is one of the oldest flowering nut trees, eaten since the prehistoric era [22].  
Pistachios, like all nuts, are high in fat content (45-49%) and primarily composed of mono- and polyunsaturated fatty acids, accounting for 23.3-69% and 14.4-15.4%, respectively. Saturated fatty acids constitute a smaller portion, at 5.9% to 11% [23]. Among fatty acids, oleic acid is the primary monounsaturated fatty acid, followed by linoleic acid, together constituting more than 60% of the total fatty acids. Oleic acid constituted approximately 66.2% of the total fatty acids, while linoleic acid also comprised 15.1% [14; 24].  
Pistachios are also a valuable source of vegetable protein (21%) [24], with approximately 2% arginine [25]. The total carbohydrate content is low (7.3), while the dietary fiber content is high, primarily insoluble fiber (10%) compared to soluble fiber (1%). Pistachios are also rich in minerals such as magnesium, calcium, potassium (1 g/100 g), and phosphorus [14; 24].  
Numerous studies have reported that pistachios are the only nut with a significant xanthophyll carotenoid content, such as lutein, which is present at 329 \(\upmu\)g/100 g [22]. They are also rich in vitamins, including ascorbic acid (5.60 mg/100 g) andtocopherol (2.17 g/100 g) [24]. Moreover, pistachios are a rich source of phenolic compounds, including anthocyanins, flavonoids, proanthocyanidins, flavonols, isoflav, flavones, stilbenes, phenolic acids, and hydrolysate tannins. These phytochemical compounds are more  
\begin{table}
\begin{tabular}{l c c} \hline \hline
**Nutritional Value** & **g/100 g** & **References** \\ \hline Protein & 14–35.1 & [14] \\ \hline Carbohydrates & 3.7–5.5 & [14; 21] \\ \hline Total fatty acids & 44–61 & [14] \\ \hline - Monounsaturated fatty acids & 62–80 & [14] \\ \hline Oleic acid & 58.1–71.3 & [18] \\ \hline - Polyunsaturated fatty acids & 19.8 & [14] \\ \hline Linoleic acid & 15.7–29.9 & [18] \\ \hline - Saturated fatty acids & 8.4 & [14] \\ \hline Palmitic acid & 5–9.7 & [14; 18] \\ \hline \hline \end{tabular}
\end{table}
Table 2: Nutritional value of almonds.  
concentrated in the skins than in the seeds. For example, the skin contains 5.865 mg/g of cyanidin-3-O-galactoside, 1.453 mg/g of gallic acid, and 0.377 mg/g of catechin. In contrast, pistachio kernels contain 0.0981 mg/g of quercetin-3-O-rutinoside, 0.0691 mg/g of genistein, and 0.047 mg/g of genistein-7-O-glucose. The green color of pistachio nuts is attributed to lutein and zeaxanthin, the two major xanthophyll carotenoids [25].  
Table 3 summarizes the main nutritional values of hazelnuts.