esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Materials and Methods
### Sample for F1 Hybrid Selection  
Samples were collected on days 21, 35, 44, and 50 of the flowering treatment (short-daylight treatment), and leaf and infloresence parts were sampled. Samples from the top, middle, and bottom were collected and freeze-dried (iSinBioBase Co., Dongduchoen, Korea). After drying, the sample was pulverized to a homogeneous particle size of 12 mesh using a chopper (YPT-1402; Young Polymer Tech Co., Incheon, Korea), and 0.1 g of the sample was added to 30 mL pure-grade MeOH (Daejung Chemicals and Metals Co., Ltd., Siheung, Korea). Ultrasonic extraction using JEIO TECH ultrasonicator (Daejeon, Korea) was performed at 23 \(\pm\) 2 \({}^{\circ}\)C for 30 min. The extracted supernatant was filtered through a 0.45 \(\upmu\)m syringe filter (Advantec, Tokyo, Japan) and transferred to HPLC vials. Components were analyzed by HPLC at a wavelength of 220 nm with an LC-20 AD (Shimadzu Co., Kyoto, Japan) instrument, using internal standards (CBDA (Cerilliant, Round Rock, TX, USA) \(\triangle\)9-THCA (Sigma-Aldrich Co., St. Louis, MO, USA), and \(\Delta\)9-THC (CAYMAN, Ann Arbor, MI, USA)). HPLC conditions are shown in Table 2. The gradient conditions were as follows: 70% B initially, 70% B for 2 min, 85% B for 6 min, 70% B for 1 min, and 70% B for 3 min.  
\begin{table}
\begin{tabular}{c c c} \hline
**Nutrient Name** & **A Solution (50 L)** & **B Solution (50 L)** \\ \hline Ca(NO\({}_{3}\))\(\cdot\)4H\({}_{2}\)O & 1.50 kg & \\ KNO\({}_{3}\) & 3.79 kg & 3.79 kg \\ (NH\({}_{4}\))H\({}_{2}\)PO\({}_{4}\) & & 1.60 kg \\ MgSO\({}_{4}\) & & 4.30 kg \\ Fe-EDTA\({}_{4}\) & 460.0 g & \\ MnSO\({}_{4}\) & & 30.8 g \\ H\({}_{3}\)BO\({}_{3}\) & & 57.2 g \\ ZnSO\({}_{4}\) & & 3.6 g \\ CuSO\({}_{4}\) & & 1.3 g \\ (NH\({}_{4}\))\({}_{6}\)Mo\({}_{7}\)O\({}_{24}\)\(\cdot\)4H\({}_{2}\)O & & 0.4 g \\ \hline \end{tabular} Solutions A and B were mixed to maintain an EC range between 1.2 to 1.7 (dSm\({}^{-2}\)), pH 6.0.  
\end{table}
Table 1: Nutrient solution composition.  
Figure 2: LED light spectrum.  
Plant height, leaf length, leaf width, branch number, stem diameter, inflorescence number, petiole color (red%), stem color (red%), and plant diameter were evaluated when samples were collected on day 50 of the flowering treatment. The redness was calculated as the ratio of the red part area to the green part area, and the CBD production per cubic meter was calculated using Equation (1).  
\[\text{Total CBD production per cubic meter }(\text{g})=\frac{\text{a}\times\text{b}}{\text{Width}^{2} \times\text{height}} \tag{1}\]  
a, Total CBD concentration (ppm; \(\mu\)g/g).  
b, dry weight of leaf or inflorescence (g).  
The width and height were used in centimeter
# Semi-Direct Point-Line Visual Inertial Odometry for MAVs
## 2 Mathematical Formulation
### IMU Pre-Integration  
The raw IMU measurements (angular velocity \(\boldsymbol{\hat{\omega}}\) and acceleration \(\mathbf{\hat{a}}\)) are affected by gravity \(\mathbf{g}^{w}\), bias \(\mathbf{b}\) and noise \(\mathbf{n}\)[10]:  
\[\begin{array}{l}\boldsymbol{\hat{\omega}}=\boldsymbol{\omega}+\mathbf{b}_{ \omega}+\mathbf{n}_{\omega},\\ \mathbf{\hat{a}}=\mathbf{a}+\mathbf{b}_{\mathrm{a}}+\mathbf{R}_{\omega}^{b} \mathbf{g}^{w}+\mathbf{n}_{\mathrm{a}}\end{array} \tag{1}\]  
where, \(\boldsymbol{\omega}\) and \(\mathbf{a}\) are the real IMU measurements.  
The IMU state propagation from the consecutive frame \(b_{k}\) to \(b_{k+1}\) can be given by:  
\[\begin{array}{l}\mathbf{P}_{b_{k+1}}^{w}=\mathbf{p}_{b_{k}}^{w}+\mathbf{v}_ {b_{k}}^{w}\Delta t_{k}-\frac{1}{2}\mathbf{g}^{w}\Delta t_{k}{}^{2}+\mathbf{R} _{b_{k}}^{w}\boldsymbol{a}_{b_{k+1}}^{b_{k}}\\ \mathbf{v}_{b_{k+1}}^{w}=\mathbf{v}_{b_{k}}^{w}-\mathbf{g}^{w}\Delta t_{k}+ \mathbf{R}_{b_{k}}^{w}\boldsymbol{\ell}_{b_{k+1}}^{b_{k}}\\ \mathbf{q}_{b_{k+1}}^{w}=\mathbf{q}_{b_{k}}^{w}\otimes\gamma_{b_{k+1}}^{b_{k}} \end{array} \tag{2}\]  
where,  
\[\begin{array}{l}\boldsymbol{a}_{b_{k+1}}^{b_{k}}=\iint_{t\in[t_{k},t_{k+1}]} \mathbf{R}_{b}^{b_{k}}(\mathbf{\hat{a}}_{t}-\mathbf{b}_{\mathrm{a}_{t}})dt^{2 }\\ \boldsymbol{\beta}_{b_{k+1}}^{b_{k}}=\iint_{t\in[t_{k},t_{k+1}]}\mathbf{R}_{b}^ {b_{k}}(\mathbf{\hat{a}}_{t}-\mathbf{b}_{\mathrm{a}_{t}})dt\\ \boldsymbol{\gamma}_{b_{k+1}}^{b_{k}}=\iint_{t\in[t_{k},t_{k+1}]}\frac{1}{2} \mathbf{\Omega}(\boldsymbol{\hat{\omega}}_{t}-\mathbf{b}_{\mathrm{a}_{t}}) \boldsymbol{\gamma}_{t}^{b_{k}}dt\end{array} \tag{3}\]  
where \(\boldsymbol{a}_{b_{k+1}}^{b_{k}}\), \(\boldsymbol{\beta}_{b_{k+1}}^{b_{k}}\) and \(\boldsymbol{\gamma}_{b_{k+1}}^{b_{k}}\) are the pre-integrated measurements, and \(\mathbf{\Omega}(\boldsymbol{\omega})=\left[\begin{array}{cc}-\lfloor \boldsymbol{\omega}\rfloor_{\times}&\boldsymbol{\omega}\\ -\boldsymbol{\omega}^{T}&0\end{array}\right]\).
## 5 Conclusions and Future Works  
This research proposes a GRU-Attention deep neural network as a strategic reference for stock trading. With the theoretical assistance of technical indicators, the effectiveness of the deep network for forecasting financial commodity trends is not limited to the accuracy of the forecast, and the probability of the forecast category can be directly applied to the design of stock market trading strategies. The experimental target is Taiwan Semiconductor Manufacturing Co., Ltd. (TSMC, TPE:2330), which is currently the world's largest foundry semiconductor manufacturer. The model uses the stock price data of 4 January 2016-11 May 2021 for training and testing, and the price of 20 April 2020-11 May 2021 for trading strategy backtesting. The main contributions of this study are summarized as follows:  
1. [leftmargin=*]
2. Famous financial commodity analysis tools such as Relative Strength Index and Bias Ratio can effectively assist the prediction accuracy of time series neural networks. 3. Taking the TPE: 2330 as an example, the proposed GRU-Attention model can achieve an average prediction accuracy of more than 70%. 4. With the aid of RSI and BIAS TIs, the rising points predicted by the model can be positively paid in most cases. 5. Compared with other deep network and non-deep network models, the proposed approach has a significant performance improvement in prediction accuracy. The limitation of the conclusions of this study lies in the use of RSI and BIAS technical indicators, which are combined in the GRU + Attention model. If other technical indicators are used, the indicator normalization method must be redesigned and retrained. The future works of this research include the following:  
1. [leftmargin=*]
2. Extend the concepts proposed in this study to other non-sequential networks, such as CNN, Transformer, etc. 3. Apply the proposed model to other types of financial products, such as futures, options, day trading, etc. 4. Extend the deep learning trading strategies to the investment portfolio of different financial products. 5. Future research on the use of deep networks for trading strategies can be extended to investment portfolios. 6. Cryptocurrency is a popular commodity in the current investment market, and this research can be extended to the analysis of cryptocurrency trends.
###### Abstract
Second, all CNs join and are dubbed Coarse Boundary Cycles (CBCs). Each CBC is then assigned a unique ID to define each hole. Third, all boundaries circling the hole are connected. Fourth, the boundary availability is checked by sending a message to all 1-hop neighbors waiting for a reply. [PERSON] [7] proposed a Self-Detection Boundary Recognition (SDBR) which examines every node as if it has a closed cycle or a broken path. For the closed cycle, each node constructs a 2-hop neighbor, selecting any node and then moving in one direction to reach the starting point. If this node is a closed path, then it will mark the internal node. Otherwise, it is marked as a boundary node. [PERSON] [8] proposed a Border Coverage Protocol (BCP) consisting of three steps. First, the nodes close to the network boundary are detected. Each node broadcasts its location, ID, and sensing range to the base station nodes on the border. Second, all nodes selected in the previous step send the message to their one-hop neighbors. Any node receiving this message mark becomes a transfer node. Third, the boundary nodes selected in the first step are replaced by transfer nodes, which are then considered the new boundary nodes. In this paper, we have proposed a method to select boundary nodes. Selected boundary nodes have the responsibility of catching the JRSS. We applied an extended Kalman filter to estimate the position of the jammer at each time step. We utilized the signal-to-noise ratio to define boundary nodes while the jammer is moving.
# Practical V2I Secure Communication Schemes for Heterogeneous VANETs
## 4 Four Heterogeneous Signcryption Schemes for V2I Communication Scenarios  
In this section, four heterogeneous signcryption schemes are presented to support secure heterogeneous V2I communication. For brevity, we make PKI\(\rightarrow\)IBC to indicate a sender in a PKI system transmits a message to a recipient in an IBC. In turn, IBC\(\rightarrow\)PKI indicates a sender registered in an IBC transmits a message to a receiver in a PKI system. Many-to-one or one-to-many means the sender is multiple or single, and the receiver is single or multiple, which correspond to the two most common scenarios extracted from real V2I communication. The first scheme is called MOHSC-I (many-to-one heterogeneous signcryption), which is suitable for an RSU in an IBC to receive \(n\) ciphertexts of \(\{m_{i}\}_{i=1}^{n}\) from \(n\) vehicles who are in a PKI system. In turn, the second construction is named OMHSC-I (one-to-many heterogeneous signcryption), which is suitable for the condition that an RSU in a PKI system to broadcast the cipher of \(m\) to \(n\) vehicles who are in IBC. The direction of the latter two schemes is opposite to the former schemes i.e., from IBC to PKI. The third scheme is named MOHSC-II (many-to-one heterogeneous signcryption) and the fourth construction is called OMHSC-II (one-to-many heterogeneous signcryption).
# Large-Language-Model-Enabled Text Semantic Communication Systems
## 1 Introduction
The main contributions of this paper are as follows:  
* A novel LLM-SC framework for text in wireless communication featuring a dual-component structure: (a) a semantic encoder utilizing LLM's tokenizer for joint source-channel coding, and (b) a semantic knowledge base built by LLM's unsupervised pre-training. This knowledge base provides prior probability distributions of language sequences, enabling optimal decoding at the receiver. This is the first application of LLM to the physical-layer encoding and decoding in semantic communication. By using LLMs to probabilistically model transmitted language sequences, we achieve a communication paradigm that balances semantic-level and technical-level performance. We investigate the relationship between the training process of LLMs and the optimization goals of semantic communication, proposing the training of a semantic encoder using LLMs' tokenizer training and the construction of a semantic knowledge base using LLM unsupervised pre-training. * The optimal detection for LLM-SC is derived, and beam search algorithm from the domain of NLP is introduced to reduce complexity. This algorithm strikes a balance in complexity between Viterbi decoding algorithm and greedy decoding algorithm, thereby ensuring both high decoding efficiency and maintaining decoding reliability. Comparative simulations demonstrate that exploring the optimal paths with a beam size in the order of tens yields quite excellent decoding performance compared to traversing a vocabulary of tens of thousands. Moreover, when the beam size exceeds 20, the performance improvements by further increasing the beam size become negligible. * The semantic-level and technical-level performance of LLM-SC under AWGN and Rayleigh fading channels are evaluated, without requiring any additional re-training and fine-tuning on the existing LLM. Results show that LLM-SC outperforms the classical DeepSC in semantic-level metrics at an SNR above 3 dB and can achieve error-free semantic transmission at high SNRs, a contribution unattainable by DeepSC; moreover, in terms of technical-level metrics, LLM-SC exhibits superior coding efficiency compared to classical text compression algorithms and achieves optimal BER performance across the entire SNR curve at the same equivalent joint source-channel coding rate.
# P-Wave Detection Using a Fully Convolutional Neural Network in Electrocardiogram Images
## 3 Experimental Results
### Evaluation Metrics  
The performance of the P-wave detection algorithms were evaluated using three statistical measures: sensitivity (SE), positive predictivity (+P), and accuracy given by Equations (2)-(4), where TP represents the number of true positives (P-waves as detected similarly to the manually annotated P-waves), FN represents the number of false negatives (the annotated P-wave has not been detected by the proposed method), and FP represents the number of false positives (P-waves detected by the system but not similar to the manually annotated data).  
\[SE=\frac{TP}{TP+FN} \tag{2}\]  
\[+P=\frac{TP}{TP+FP} \tag{3}\]  
\[Accuracy=\frac{\#Correctly predicted data}{\#Total\ beats} \tag{4}\]  
Figure 4: Model accuracy chart, where the blue line represents the training accuracy, while the orange one represents the validation (testing) accuracy.
# Successful Tests on Detecting Pre-Earthquake Magnetic Field Signals from Space
This system also includes several high plateaus such as Iran, Turkey, Pamir, and Tibet, as well as three inland seas with an oceanic crust, namely the Mediterranean Sea, the Black Sea, and the Caspian Sea. The seismicity in this region (see Figures 1 and S1 for the earthquakes analyzed in this study) is attributed mostly to ongoing continental collisions, with a significant amount of seismic energy released annually (around 100 significant earthquakes/year). Analyzing earthquakes in this belt, specifically those with a magnitude greater than or equal to 5.0, and correlating them with satellite precursory anomalies can provide insights into the relationship between earthquake magnitude and magnetic field anomaly features. Focusing on a specific tectonic belt mitigates the possibility of confusing pre-earthquake related anomalies with anomalies related to other phenomena, although we must admit that some portions of the anomalies cannot be clearly attributed to the preparation of earthquakes. Confutation analysis is performed to assess the validity of the relationships discovered, establishing the base for an Operational Earthquake Prediction System (OEPS). A few words are here necessary to distinguish between prediction and forecasting. Prediction involves determining the specific time and location where a natural hazard of a given magnitude will occur. Although time, location, and magnitude are given with some uncertainty, the intention would be that they have enough accuracy that meaningful actions, such as evacuations, can be planned and implemented. Forecasting is a broader and less exact approach, offering a probabilistic estimate of a hazard happening. For example, a seismic hazard map in a certain region might state that there is a 25% chance of a magnitude 7.0 earthquake occurring within the next 20 years. According to the above definitions, the method we propose is closer to a prediction than a forecast. This is the reason we call it OEPS. Regarding the depth of the seismic events, we performed a simple comparison among the earthquakes with different hypocentral depths and occurring earthquakes: we split the earthquakes according to five classes of depth (30, 60, 90, and 120 km, and deeper hypocenters) and found that the percentages of earthquakes with anomalies were all very similar, ranging from 79 and 85%, with the highest percentage for the deepest class. Therefore, we finally decided to include all earthquakes in our analysis, independently of their depth.
# Experimental Analysis of Plantar Fascia Mechanical Properties in Subjects with Foot Pathologies
## 2 Materials and Methods
### Dissection and Treatment of Samples  
None of the feet of the involved subjects had signs of infection or had previously been treated surgically. Excised feet were dissected through a longitudinal cutaneous incision along the midline from the heel to the third toe. First, the skin was cut and raised medially and laterally, then the subcutaneous tissue was carefully removed to expose the PF. The fascia was isolated proximally to its calcaneal origin and distally up to the insertion in the metatarsophalangeal joints, removing muscle insertions and connections with contiguous structures. PF was treated with caution to prevent any tissue damage during dissection. In case of Ledderhose disease, nodular formation and immediately adjacent PF tissue were removed.  
After dissection, the PF were kept at \(-20\)\({}^{\circ}\)C and unfrozen approximately one hour before mechanical testing by immersing them in physiological solution (PBS, phosphate buffered solution) at room temperature.  
PF was cut along the proximal-distal direction to obtain three rectangular samples for each subject, with a total sample length of 25 mm and nominal width of 5 mm. This number of samples was selected to obtain well balanced data for all the subjects, based on the area of the smallest available PF among different subjects.  
A portion of PF dissected from a patient and the typical cut of samples for mechanical testing are shown in Figure 1a. The effective width and thickness of each sample were measured on images taken from top and side views of the sample positioned on a flat surface. The images were analyzed with the software ImageJ (NIH) [29].  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline  & \multicolumn{10}{c}{**Pathologic**} & \multicolumn{10}{c}{**Healthy**} \\ \hline  & \multicolumn{3}{c}{**Ledderhose Disease**} & \multicolumn{3}{c}{**Diabetes**} & \multicolumn{3}{c}{**Healthy**} \\ \hline subject ID code & L1 & L2 & L3 & L4 & L5 & D1 & D2 & D3 & D4 & H1 & H2 & H3 & H4 & H5 \\ sex & M & F & F & M & F & M & F & M & M & F & M & M & M & F \\ mass (kg) & 80 & 88 & 55 & 60 & 72 & 70 & 55 & 78 & 92 & 50 & 82 & 136 & 75 & 68 \\ height (cm) & 175 & 156 & 160 & 175 & 170 & 165 & 160 & 180 & 170 & 155 & 178 & 183 & 165 & 185 \\ BMI (kg/m\({}^{2}\)) & 26.1 & 36.2 & 21.5 & 19.6 & 24.9 & 25.7 & 21.5 & 24.1 & 31.8 & 20.8 & 25.9 & 40.6 & 27.5 & 19.9 \\ age (y) & 50 & 50 & 42 & 32 & 60 & 76 & 65 & 72 & 65 & 82 & 78 & 67 & 67 & 81 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Characteristics of the subjects involved in the study.  
Figure 1: Portion of dissected Plantar Fascia (PF) from midfoot region and disposition of samples cut along the fiber direction (**a**); lateral view of gripped PF sample under mechanical testing (**b**).
## 2 System Model
### The First Scenario
In this case, the phases can be modified as \(\theta_{1n}^{(D_{1})}=\phi_{1n}+\delta_{1n}^{(D_{1})}\) for \(1n=1,\ldots,N_{1}\) and \(\theta_{2n}^{(D_{1})}=\phi_{2n}+\delta_{2n}^{(D_{1})}\) for \(2n=1,\ldots,N_{2}\)[35], while the maximal \(\gamma_{D_{1}}^{(1)}\) can be written as  
\[\gamma_{D_{1}}^{(1)}=\frac{\gamma\chi_{1}\Big{|}A_{1}^{(1)}+A_{2}^{(1)}\Big{|}^ {2}}{\gamma\chi_{2}\Big{|}A_{1}^{(1)}+A_{2}^{(1)}\Big{|}^{2}+\Big{(}\Upsilon_{ S}^{2}+\Upsilon_{D_{1}}^{2}\Big{)}\gamma\Big{|}A_{1}^{(1)}+A_{2}^{(1)} \Big{|}^{2}+1}. \tag{5}\]  
The achievable rate for the \(D_{1}\) is given as  
\[R_{D_{1}}^{(1)}=\log_{2}\Big{(}1+\gamma_{D_{1}}^{(1)}\Big{)}. \tag{6}\]  
The overall received signal at the user \(D_{2}\) is given as [36]  
\[y_{D_{2}}^{(1)}=\Bigg{(}\sum\limits_{n=1}^{N_{1}}h_{S_{1},n}h_{I_{1}D_{2},n} \eta_{1n}e^{\theta_{1n}^{(D_{2})}}+\sum\limits_{n=1}^{N_{2}}h_{S_{1},n}h_{I_{ 2}D_{2},n}\eta_{2n}e^{i\theta_{2n}^{(D_{2})}}\Bigg{)}(\sqrt{P\chi_{1}}x_{1}+ \sqrt{P\chi_{2}}x_{2}+\tau_{S})+\tau_{D_{22}}+n_{D_{2}}, \tag{7}\]  
where \(\theta_{1n}^{(D_{2})}\) stands for the adjustable phase applied by the \(n\)th reflecting element of the \(S-I_{1}-D_{2}\), and \(\theta_{2n}^{(D_{2})}\) is the adjustable phase applied by the \(n\)th reflecting element of the \(S-I_{2}-D_{2}\). In addition, \(h_{I_{1}D_{2},n}\)and \(h_{I_{2}D_{2},n}\) are the channel gains with \(h_{I_{1}D_{2},n}=d_{I_{1}D_{2}}^{-a/2}h_{I_{1}D_{2},n}e^{-j\delta_{1n}^{(D_{2})}}\) and \(h_{I_{2}D_{2},n}=d_{I_{2}D_{2}}^{-a/2}h_{I_{2}D_{2},n}e^{-j\delta_{2n}^{(D_{2}) }}\)[35], where \(d_{I_{1}D_{2}}\) and \(d_{I_{2}D_{2}}\) are the distances for the \(I_{1}-D_{2}\) link and \(I_{2}-D_{2}\) link, respectively, and \(\delta_{1n}^{(D_{2})}\) and \(\delta_{2n}^{(D_{2})}\) are the phases of the channel gains. \(\overline{h}_{I_{1}D_{2},n}\) and \(\overline{h}_{I_{2}D_{2},n}\) following a Rayleigh distribution are the amplitudes of the channel gains. Moreover, we assume that the IRS has the full knowledge of the channel phases of \(h_{I_{1}D_{2},n}\) and \(h_{I_{2}D_{2},n}\). The hardware impairments at the \(D_{2}\) is denoted as [35]  
The achievable rate for the \(D_{2}\) is given as  
\[R_{2}^{(1)}=\log_{2}\Bigl{(}1+\min\Bigl{\{}\gamma_{x_{1},D_{2}}^{(1)}\gamma_{x_{2},D_{2}}^{(1)}\Bigr{\}}\Bigr{)}. \tag{12}\]
# Node-Based QoS-Aware Security Framework for Sinkhole Attacks in Mobile Ad-Hoc Networks
## 4 QoS-Aware Security Framework: Proposed Scheme
### QoS-Aware Adaptive Routing  
The routing protocol, OLSR, facilitates all routing in the network. OLSR works by using a link-state algorithm that constantly works with the routing table. The routing table is flexible to adaptive routing as the topology is dynamic and needs constant updating. The packets will use an optimal path as directed by the MPRs to the destination. Nodes can exchange updates and route table information. Adaptive routing allows the routing path to change over time as the topology in which the nodes operate is ever-changing. Another role-player component in our framework is packet switching. Packet switching is regarded as a higher-level decision-making entity responsible for driving packets from source to destination. The routing protocol, OLSR's flowchart in the proposed framework is shown in Figure 2 where we proposed a few changes towards some of the traditional operations of the protocol to accommodate QoS and increase efficiency in terms of performance. Figure 3 illustrates the flowchart of our modified OLSR protocol. This also includes a proposal of how performance is optimized when there is a malicious node in the network. MPRs still play a critical role in terms of propagating TC messages through to the routing table. An unauthenticated node will be regarded as a malicious node and will be isolated from the network. At first, the node will be sent a fake HELLO message, then selected as an MPR, and then blacklisted at the routing table. After routing, packets are sent to the data link layer where there is packet queue management, MAC differentiator, and available bandwidth estimator. Under packet queue management, there is packet scheduling, priority scheduling, and packet forwarding [22].
## 4 Results
### Energy Harvesting Calculation  
The methodology presented by [19] was used for power input calculation in each satellite considering orbital parameters from the CubeSat FloripaSat-I [4], as shown in Table 3. Finally, the spacecraft's attitude adopted here is the NADIR where one specific face of the satellite is always directed towards the Earth's surface.  
This is a nearly-circular orbit with 623 km of altitude, which results in a period of 96 min, whose fraction is spent under the Earth's shadow where there is no power input. Each CubeSat of the constellation is in this same orbit, but equally spaced from each other, e.g., for the constellation with two spacecrafts the angular displacement (true anomaly) is 180\({}^{\circ}\), while for the constellation with three satellites the displacement is 120\({}^{\circ}\).  
With these parameters the power input vector was obtained and multiplied by an Electrical Power System efficiency of 0.85, resulting in the power available for the tasks in each satellite--input for the MILP formulation.