esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Materials and Methods
### Statement of the Variational Problem  
One of the most widely used methods for solving inverse problems of mathematical physics is reducing Equations (9)-(12) and (13) to an optimal control problem.  
The aim of the problem is to find the initial values of \(G^{0}(x)eW_{2}^{2}(0,2l)\) so that the corresponding solution to Equation (9) approaches the specified desired value of \(Q^{1}(x)\).  
More precisely, our problem is to minimize the objective functional, as follows:  
\[cJ\Big{(}G^{0}\Big{)}=\int\limits_{0}^{2l}\Big{[}Q\Big{(}T,x;G^{0}(x)\Big{)}- Q^{1}(x)\Big{]}^{2}dx\to min. \tag{14}\]  
on the admissible control set, \(G^{0}(x)\subset W_{2}^{2}(0,2l)\).  
Here, \(Q\big{(}T,x;G^{0}(x)\big{)}\) represents the solution's, \(Q(T,x)\), dependence on Equations (9)-(12) and (13) using the initial conditions.  
Minimize the functional using the gradient method as follows [20]:  
\[G_{n+1}=G_{n}-\alpha\cdot\int^{l}G_{n},\qquad\quad n=0,1,2,\ldots, \tag{15}\]  
where \(\alpha\) is a relaxation parameter.  
The choice of relaxation parameter determines the gradient method, which plays an important role. The relaxation parameter \(\alpha\) determines the length of the gradient descent step and has a direct impact on the convergence rate of the iteration process. A value of \(\alpha\) that is too large can lead to divergence of the method, while a value that is too small can lead to slow convergence.  
In practice, the choice of \(\alpha\) is made either empirically (based on preliminary tests) or using adaptive strategies such as the steepest descent method, where \(\alpha\) is selected at each iteration to minimize the functional along the current direction. In this study, \(\alpha\) was taken as constant and selected in such a way as to ensure a stable monotonic decrease in the values of the functional \(J(G_{n}^{0})\) with an acceptable number of iterations.  
The procedure for obtaining the variational and conjugate problems is as follows:  
1. Let us consider the variation of the functional, \(\delta J\big{(}G^{0}\big{)}\), under the perturbation, \(\delta G^{0}\).
2. We introduce the perturbed solution, \(\tilde{Q}(t,x)\), and define \(\delta Q(t,x)=\tilde{Q}(t,x)-Q(t,x)\).
3. We perform a convolution of the variation through the unknown function, \(Q^{*}(t,x)\), satisfying the following conjugate equation: \[A^{*}Q^{*}=\frac{\partial^{2}Q^{*}}{\partial t^{2}}-2a\frac{\partial Q^{*}}{ \partial t}-c^{2}\frac{\partial^{2}Q^{*}}{\partial x^{2}}=0,\] (16) with the following boundary conditions: \[Q^{*}(T,x)=0,\ \ \frac{\partial Q^{*}}{\partial t}(T,x)=2\Big{[}Q \Big{(}T,x;G^{0}\Big{)}-Q^{1}(x)\Big{]},\] (17) \[Q^{*}(t,0)=0,\ \ \ Q^{*}(t,2l)=0.\] (18)
4. Then, the Frechet derivative of the functional takes the following the form: \[J^{\prime}(G_{n}^{0})=-Q^{*}(0,x),\]  
All intermediate calculations, including integration by parts and proof of the identity, are given in Appendix A.
## 4 Experimental Results and Discussion
### Setting of Experiments
#### 4.1.2 Experimental Environment and Parameters of Training  
We used Numpy, Pandas, and Pytorch, which are famous Python packages to represent, normalize, and construct autoencoder and prediction models in practice. We performed the experimental program on a high-performance computer. The fundamental configuration of this computer is i7-4790 3.6 Ghz, 4 core, 16 GB memory, NVIDIA geforce GTX 1080 Ti. The five baseline models used for comparison were from scikit-learn 1.2.1, which are LogisticRegression, RandomForestClassifier, LinearSVC, KNeighborsClassifier and MultinomialNB. These models are most commonly used by researchers to predict students' performance [2]. The parameters of these models were the default values provided by scikit-learn.  
There are several critical parameters in the training autoencoder and prediction model. According to the configuration of the computer and the properties of the experimental dataset, we carried out many preexperiments, aiming to reduce the value of the loss function as much as possible and avoid overfitting. The selected training parameters are shown in Table 3.  
Figure 4: Proportion of students with different performance in the dataset.
## 5 Results
### Lidars' Performance in Presence of the Motion  
#### 5.2.1 Rotational Motion: Yaw (Rotation along Z Axis)  
The statistical analysis of lidar data during yaw motion (tests 19, 20, 21, 48, and 49) is shown in the second row of Figure 6. All of the above test cases have similar amplitudes (\(A_{0}=39^{\circ}\)), but different frequencies (\(f_{0}\)) see Table A1. The moving lidars have a lower average wind speed than the reference ones except in test 49 for both WindCube V1 and ZephIR 300. In test 48, ZephIR 300 moving has slightly higher mean wind speeds (Figure 6 Yaw: a, b). Additionally, the WindCube V1 pair's TI estimates are lower than those of ZephIR, except in test 49 (Figure 6 Yaw: c, d). Interestingly, the moving ZephIR 300 estimates less TI than the reference ZephIR 300 in the majority of cases. The APE is higher for WindCube V1, exceeding 14%, while ZephIR 300 has a maximum of 5% APE (Figure 7 Yaw: a, b). The highest APE is observed in test cases with high frequencies. Furthermore, the correlation between the moving and reference lidars varies greatly, ranging from 0.28 to 0.86. The lowest correlation occurs in test 49 with a 0.25 Hz frequency, while the highest correlation occurs in test 21 with \(f_{0}=0.05\) Hz (Figure 7 Yaw: c, d).
# Optical Design of a Miniaturized Airborne Push-Broom Spectrometer
## 6 Integrated System and Image Quality Evaluation  
### Integrated System  
The front objective lens and the Offner spectrometer are combined as shown in Figure 11. The overall optical system has a volume of \(120\times 50\times 90\) mm.
# MScope: A Reliable Battery for Functional Status Assessment in Multiple Sclerosis
## 4 Discussion
Additionally, this study included only 13% male participants, which, while reflective of the higher prevalence of MS in women, limits the generalizability of our findings to male patients. Future studies should aim to include a more balanced gender representation. Another limitation was the short interval of 72 h between the two assessment sessions. This time frame may not have been sufficient to mitigate the effects of fatigue, which is particularly prevalent in this population. Moreover, fatigue was not specifically controlled or measured, which could influence the results. Future studies should consider incorporating longer recovery periods and explicitly monitoring fatigue to minimize its impact on the reliability of the assessments. Another notable limitation is the lack of familiarization trials, which might impact not only the reproducibility but also the variability and heteroscedasticity of results. However, the decision to forego familiarization reflects real-world clinical contexts, where PwMS are typically not familiarized with assessment protocols prior to testing. While most functional tests included in this study do not require familiarization, future research could compare reliability outcomes between familiarized and non-familiarized groups to evaluate potential benefits, particularly in functional and isometric strength tests. Although the MScope test battery has demonstrated high reproducibility, further validation against gold-standard tests--such as isokinetic assessments for strength and gas analysis for cardiorespiratory capacity--would provide a more robust validation framework. Additionally, applying this battery to a broader sample of MS patients would facilitate the creation of a more extensive database, potentially supporting the classification of frailty levels based on structural, functional, and neuromuscular parameters. This, in turn, could guide the development of individualized treatment plans aimed at slowing neurodegeneration and enhancing quality of life in MS patients.
## 4 Passenger Flow Assignment Model
### Generalized Travel Cost  
There are many alternative travel paths between spatiotemporal O-D pairs, and the choice of passenger travel path is affected by multiple factors. Generally, the generalized travel cost is established to analyze the passenger's travel path choice behavior. The travel cost is composed of waiting time cost, in-vehicle time cost, transfer time cost, and congestion penalty. Meanwhile, the fare cost is considered in generalized travel cost due to the different trains with diversified fare policies. Basic notations related to generalized travel cost are listed in Table 2.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Symbol** & **Definition** \\ \hline \(\text{CW}_{(i,j)}^{k}\) & Waiting time cost of \(k\)th path of O–D pair \((i,j)\). \\ \hline \(\text{C}_{(i,j)}^{k}\) & In-vehicle time cost of \(k\)th path of O–D pair \((i,j)\). \\ \hline \(\text{CT}_{(i,j)}^{k}\) & Transfer time cost of \(k\)th path of O–D pair \((i,j)\). \\ \hline \(\text{CT}_{(i,j)}^{k}\) & Fare cost of \(k\)th path of O–D pair \((i,j)\). \\ \hline \(\text{C}_{(i,j)}^{k}\) & Generalized travel time cost of \(k\)th path of O–D pair \((i,j)\). \\ \hline \(\delta_{(i,j),k}^{a}\) & Binary variable, if arc \(a\) is on the \(k\)th path of O–D pair \((i,j)\) then \(\delta_{(i,j),k}^{a}=1\), otherwise \(\delta_{(i,j),k}^{a}=0\). \\ \hline \(c_{p}(a)\) & Time of running arc \(a\) consider congestion penalty. \\ \hline \(E_{\text{W}}\) & Set of waiting arcs. \\ \hline \(E_{R}\) & Set of running arcs. \\ \hline \(E_{S}\) & Set of station-stop arcs. \\ \hline \(E_{T}\) & Set of transfer arcs. \\ \hline \(Z\) & Number of seats. \\ \hline \(cp\) & Maximum train capacity. \\ \hline \(\delta_{1},\delta_{2}\) & Coefficients of congestion penalty function. \\ \hline \(q_{a}\) & Passenger flow on arc \(a\). \\ \hline \(\alpha_{1}\) & Sensitivity of passengers to transfer time. \\ \hline \(\alpha_{2}\) & Penalty of transfer times. \\ \hline \(n_{tf}\) & Transfer times on passenger travel path. \\ \hline \hline \end{tabular}
\end{table}
Table 2: Passenger generalized travel cost related notations.
# Dynamic Multi-Target Self-Organization Hunting Control of Multi-Agent Systems
## 3 Establishment of a Task Allocation Model
### Self-Organizing Distributed Collaborative Task Allocation Optimization Model
\(k_{0}>0\) is the weight of the velocity error between the agents, \(k_{1}>0\) is the weight of the position error between agent \(i\) and target \(g\), and \(k_{2}>0\) is the weight of the velocity error between agent \(i\) and target \(g\). \[\phi(\mathbf{x}_{j}-\mathbf{x}_{i})=\frac{1}{2}[(a+b)\sigma(\|\mathbf{x}_{j}-\mathbf{x}_{i}\| -d_{\min}+\frac{b-a}{\sqrt{4 ab}})+a-b]\cdot(\|\mathbf{x}_{j}-\mathbf{x}_{i}\|-d_{\min}) \tag{14}\]  
Here, \(\sigma(z)=z/\sqrt{1+z^{2}}\), and \(a\) and \(b\) are constant and \(0<a\leq b\). Equation (13) gives the control strategy for the multi-agent system. The first summation in Equation (13) is a control term that ensures the convergence of all the agents in the system, the second summation term maintains the velocity consensus of all the agent, the third makes certain that the agent is close to the target, and the fourth term guarantees that the agent can maintain the velocity consensus with the target. Thus, using Equation (13), we may suppose that the subgroup of multi-agent systems can finally hunt its target. Under the consideration of the control inputs \(\mathbf{u}_{i}\), the system can achieve stability. We can use the Lyapunov function method for proof. Firstly, we can define the position error of agent \(i\): \(e_{x_{i}}=\mathbf{x}_{i}-\mathbf{x}_{g}\), and the velocity error is: \(e_{\mathbf{v}_{i}}=\mathbf{v}_{i}-\mathbf{v}_{g}\). Then, the Lyapunov function is chosen as:  
\[ \begin{array}{rl}l&=\frac{1}{2}\sum\limits_{i=1}^{N_{\text{t}}}\left(\|\mathbf{ \varepsilon}_{\mathbf{x}_{i}}\|^{2}+\|\mathbf{\varepsilon}_{\mathbf{v}_{i}}\|^{2}+\phi(\|\bm {x}_{j}-\mathbf{x}_{i}\|)\right)\\ &=\frac{1}{2}\sum\limits_{i=1}^{N_{\text{t}}}\left((\mathbf{x}_{i}-\mathbf{x}_{g})^{T}( \mathbf{x}_{i}-\mathbf{x}_{g})+(\mathbf{v}_{i}-\mathbf{v}_{g})^{T}(\mathbf{v}_{i}-\mathbf{v}_{g})+\phi( \|\mathbf{x}_{j}-\mathbf{x}_{i}\|)\right)\end{array}  \tag{15}\]  
From [PERSON] et al. [30], we know that the positive semidefinite matrix \(L(t)\) and \(H(t)\) are in existence for the derivation of the Lyapunov function,  
\[\dot{l}=-(\mathbf{v}_{i}-\mathbf{v}_{g})^{T}[(L(t)+H(t))\otimes I_{n}](\mathbf{v}_{i}-\bm {v}_{g}) \tag{16}\]  
\(\dot{l}\leq 0\) because \(L(t)+H(t)\) is a positive semidefinite matrix. Then, we may obtain \(l(t)\leq l(0)\), \(t>0\). Thus, \(\|\mathbf{x}_{i}-\mathbf{x}_{g}\|\leq\sqrt{2l(t)}\leq\sqrt{2l(0)}\). This inequality tells us that agent \(i\) can catch up with the target. Meanwhile, according to the LaSalle invariance principle, for each hunting subgroup, \(\mathbf{v}_{1}=\mathbf{v}_{2}=\cdots=\mathbf{v}_{N_{\text{t}}}=\mathbf{v}_{g}\). The above hunting control model shows that the entire hunting process is achieved by obtaining the position error and velocity error of the target through the agent. That is to say, throughout the entire hunting process, the agent does not need to know the target's motion state to hunt.
## 3 Results and Analysis of the Filed Measurements
### Exhaust Fume System
#### 3.4.3 Oil Fume Emission Concentration  
(1) Indoor oil fume generation--observed value  
Field observation found that the amount of oil fume produced was different when cooking different dishes. In order to quantitatively analyze the influence of cooking methods on the amount of oil fume produced, the amount of oil fume produced during cooking of stove No.1 was divided into four categories: no oil fumes (none), a small number of oil fumes (little), more oil fumes (more), and a large number of oil fumes (much), as shown in Figure 14.  
We can see from Figure 14 that during breakfast and lunch stew, the amount of oil fume was less, and a large amount of oil fume was produced during lunch stir-frying. In addition, boiling and stewing were the main cooking methods in the non-oil smoke production stage. When frying food produced little or more oil fume, when frying food produced more or much oil fumes. In summary, the production of oil fume was closely related to cooking methods, and the order from high to low was stir-frying, frying, stewing, and boiling.  
Figure 13: The exhaust airflow rate and the makeup airflow rate of the test kitchen.  
2. Oil fume emission concentration at discharge outlet-test value Figure 15 shows the oil fume emission concentration at the discharge outlet. It can be seen from Figure 15 that the oil fume emission concentration at the discharge outlet met the national standard GB18483-2001 [32]. However, the results did not meet the Tianjin standard DB12/644-2016 [41], that was because the purification equipment used in this exhaust fume system was produced and installed in April 2015, while the Tianjin standard was issued in 2016.
## 3 Catalytic Advanced Oxidation Processes (AOPs)
### Peracetic Acid (PAA) Activation  
Peracetic acid (PAA) has emerged as an alternative to H\({}_{2}\)O\({}_{2}\) and persulfate for the treatment of persistent contaminants in wastewater [47]. In a recent study, [PERSON] et al. [48] used SDB to activate PAA for the degradation of fluoroquinolone antibiotics (FQs) at neutral pH, where non-radical pathways were found to play a predominant role. \(\pi\)-conjugated structures and carbon-rich functional moieties on SDB's surface facilitated electron transfer processes, thereby promoting singlet oxygen (\({}^{1}\)O\({}_{2}\)) generation. Simultaneously, the iron species present in the biochar can catalyze PAA activation, contributing to the formation of organic radicals, e.g., CH\({}_{3}\)COO- and CH\({}_{3}\)COOO-. Except for the traditional ROS, recent observations verified that the high efficacy in PAA-based systems was attributed to PFRs on the SDB surface that facilitate PAA decomposition. For example, [PERSON] et al. [49] demonstrated that SDB efficiently activated PAA for the degradation of 4-chlorophenylenol, achieving a rate constant of 0.051/(M-min). The primary mechanism identified in the study indicates that the activation of PAA by SDB is largely governed by quinone/hydroquinone groups and residual metals on the SDB. These components play a crucial role in the formation of PFRs, which facilitate the activation process. Given the relatively recent exploration of PAA-based AOPs, the promising performance of SDB catalysts highlights their potential for advancing alternative disinfection and oxidation strategies in wastewater treatment.
# Effects of Heavy Rainfall on Shallow Foundations in Bukit Timah Granite in Singapore
## 3 Simulation Results  
### Effects of Rainfall Intensity and Duration on Matric Suction Changes  
Changes in the matric suction of the model were plotted against the rainfall intensities in various groundwater table locations in Figure 6. A general trend was observed between the two different groundwater table locations, where the initial matric suction decreased greatly at the 8 mm/h rainfall intensity but reached a constant after the 20 mm/h rainfall intensity. This could be attributed to the infiltration capacity of the soil, where it reached its maximum capacity at 20 mm/h of rainfall. Thus, the rate of the decreasing matric suction remained constant. A difference in initial matric suction of the two different groundwater table locations also affected the initial infiltration capacity of the soil, where it was lower as compared to fully saturated soil due to the increase in tensile forces between the soil particles and water, restricting the incoming rainfall infiltration's flow path, thus, decreasing the permeability [33].  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Soil Type** & **Footing Size** & **Groundwater Table Position** & **Rainfall Intensities** & **Duration** \\ \hline \multirow{3}{*}{Bukit Timah} & & 0 mm/h & 1 day \\  & & 5 m/10 m below & 8 mm/h & 2 day \\  & & ground level & 20 mm/h & 3 day \\  & & & 32 mm/h & 4 day \\ \hline \hline \end{tabular}
\end{table}
Table 2: Summary of controlling parameters used in the simulations.  
Figure 5: Sequential processes of finite element (FE) analysis.  
Another trend observed in the curves was the difference in matric suctions between the different durations of rainfall. Despite reaching a steady state of matric suction after \(20\,\mathrm{mm}/\mathrm{h}\) of rainfall intensity and the maximum infiltration capacity, increases in the duration of rainfall also decreased the matric suction by a particular amount. Due to the maximum capacity of infiltration reached, only with a longer time period can the water infiltrate through the soil and decrease the matric suction, along with increasing the groundwater table. This is usually the case for soils with lower permeability, where rainfall with higher durations and a lower intensity is applied to the soil to study the change in matric suction, while the reverse is true for soils with higher permeability [4, 12, 13, 14].
# A Feature-Based Cost Estimation Model for Wind Turbine Blade Spar Caps
## 3 Cost Model Methodology, Selection of Cost Modelling Approach
### Technical Cost Modelling: Tooling, Capital, Labor, Production Rate
#### 3.3.3 Levelized Cost of Electricity (LCOE)  
Data for wind turbine installed costs, lifetime electricity generation for 20 and 25 years, and lifetime O and M costs for 20 and 25 years were generated by the model using cost data from Table 7. Retrofit spar cap cost data for CFRP and GFRP was taken from calculated cost curves for 35 to 75 m. LCOE was then calculated and compared for each of the three scenarios. Costs were discounted in each year to arrive at a net present value for LCOE using a realistic discount rate.  
Assumptions  
* Power generated from an off-shore wind speed of 15 m/s (Equation (3)).
* Capacity Factor 0.2 for 20 years [1] and 0.3 for a 5 year extension following refit [1].
* Air density: 1.23 g/cm\({}^{3}\).
* Turbine installed costs, O and M costs [1].
* Discount rate: 7% [35], power generation and O and M costs for 20 and 25 years.
* Cost data are based on three turbine blades.  
Summary  
A resource-based cost model was constructed from Equation (18) that accounts for materials, tooling, capital, labor, and utilities resources required for spar cap manufacture in the 35 to 75 m blade range. Available resource costs were material mass data for the 35 to 75 m range, tooling, capital, labor, and utilities for a 35 m spar cap (Calibration Standard) and a 10 m spar cap analogue (Reference Standard), and production rate for the 35 m spar cap. Technical cost modelling (TCM), was used to derive a Cost Scaling Feature Factor and Cost Factor Indices from known cost data in order to predict production rate and tooling, capital, and direct labor costs for the 40 to 75 m spar cap range.  
To estimate Levelized Cost of Energy for the three scenarios, cost data for turbine investment costs and operational and maintenance costs were calculated by the model based on literature values for investment cost per kW, O and M cost/kW/year, and rated power for each blade length, 35 to 75 m.
# Optimizing Nigella Oil Extraction Temperature for Sustainable Production
## 3 Results and Discussion
### Fatty Acid Composition
Some studies have aimed to elucidate the fatty acid contribution in different oils [68,69]. For example, [PERSON] et al. analyzed fatty acids in coconut oil, palm oil, vegetable oil, and palm kernel oil in Ghana, observing approximately 15%, 45%, 46%, and 19% fatty acids, respectively, relative to the total weight of these oils [68]. Similarly, [PERSON] et al. investigated the fatty acid composition in sunflower oil, korie oil, and red palm oil in Tanzania, reporting approximately 37%, 87%, and 70%, respectively, of fatty acids relative to the total oil weight, which exceeds the values observed in the present study [69]. The Nigella oil is known to contain not only fatty acids but also substantial concentrations of other non-volatile components, such as sterols, tocopherols, saponins, and alkaloids [70,71]. Moreover, a considerable portion of the volatile compounds, with thymoquinone being one of the most prominent in the oil, have also been well documented [72, 73, 74, 75]. Given the complex chemical composition of Nigella oil, it is likely that the remaining 82% is made up of both volatile and other nonvolatile components. Furthermore, the ratios of MUFAs/SFAs, PUFAs/SFAs, and (MUFAS + PUFAS)/SFAs indicate the nutritional quality of the oil for human consumption. A higher ratio of MUFAs/SFAs, PUFAs/SFAs, and (MUFAs + PUFAs)/SFAs signifies lower SFAs and higher concentrations of UFAs in the seeds. In our study, no significant differences were observed in these ratios, which were approximately 0.7, 2.8-3, and 3.6-3.7, respectively. The fatty acid ratios observed in the present study are comparable with the values reported in the literature, including [PERSON] et al., who have reported MUFAs/SFAs, PUFAs/SFAs, and (MUFAs + PUFAs)/SFAs in the range between 0.4 and 1.3, 4 and 6.4, and 4.6 and 7.3, respectively, when studying different genotypes of Nigella oil in India [49]. The fatty acid ratios observed in the present study are comparable with other alternative sources of Nigella oil as well, such as oregano oil [76] and sea buckthorn oil [77]. Furthermore, both the higher and the lower values of PUFAs/SFAs than the values observed in the present study have been reported by [PERSON] et al. while investigating different edible oils [78]. Their report showed PUFAs/SFAs ranging from 0.005 to 10.55, with coconut oil at the low end (0.005) and safflower oil at the high end (10.5). The coconut oil, corn oil, cottonseed oil, palm kernel oil, olive oil, and peanut oil displayed lower PUFAs/SFAs values compared to the results obtained in this study. On the other hand, linseed oil, soybean oil, sunflower seed oil, safflower oil, and canola oil exhibited comparatively higher values [78].