esa-sceva/satcom-chunk-collection huggingface dataset:
## 4 Mathematical Model
### Battery Model  
The battery characteristics that play a significant role in designing a hybrid renewable energy system are battery capacity, battery voltage, battery state of charge, depth of discharge, days of autonomy, efficiency, and lifetime of battery.  
The nominal capacity of the battery bank is the maximum state of charge \(SOC_{\text{max}}\) of the battery. The minimum state of charge of the battery, \(SOC_{\text{min}}\), is the lower limit that does not discharge below the minimum state of charge. The \(DOD\) is used to describe how deeply the battery is discharged and is expressed in Equation (4) [24]:  
\[DOD=1-SOC_{\text{min}} \tag{4}\]  
Based on Equation (4), the \(DOD\) for the _\"Trojan L16P\"_ battery is 70%, which means that the battery has delivered 70% of its energy and has 30% of its energy reserved. \(DOD\) can always be treated as how much energy the battery delivered. A battery bank is used as a backup system and is sized to meet the load demand when the renewable energy resources failed to satisfy the load. The number of days a fully charged battery can feed the load without any contribution of auxiliary power sources is represented by days of autonomy. The battery bank autonomy is the ratio of the battery bank size to the electric load (LTE-macro BS). HOMER calculates the battery bank autonomy (\(A_{\text{hutt}}\)) by using the following equation [24]:  
\[A_{\text{hutt}}=\frac{N_{\text{hutt}}\times V_{nom}\times Q_{nom}\Big{(}1- \frac{SOC_{\text{min}}}{100}\Big{)}(24\text{ h/d})}{L_{\text{prim}-avg}(1000 \text{ Wh/kWh})} \tag{5}\]  
where \(N_{\text{hutt}}\) is the number of batteries in the battery bank, \(V_{nom}\) is the nominal voltage of a single battery (V), \(Q_{nom}\) is the nominal capacity of a single battery (Ah), and \(L_{\text{prim},\text{max}}\) is the average daily LTE-macro BS load (kWh). Battery life is an important factor that has a direct impact on replacement costs. Two independent factors may limit the lifetime of the battery bank: the lifetime throughput and the battery float life. HOMER calculates the battery bank life (\(R_{\text{hutt}}\)) based on these two factors as given in the following equation [24]:  
\[R_{\text{hutt}}=\text{min}\Bigg{(}\frac{N_{\text{hutt}}\times Q_{lifetime}}{Q_{ \text{h}trpt}},R_{\text{hutt},f}\Bigg{)} \tag{6}\]  
where \(Q_{lifetime}\) is the lifetime throughput of a single battery (kWh), \(Q_{\text{h}trpt}\) is the annual battery throughput (kWh/year), and \(R_{\text{h}trpt}\) is battery float life (year).
## 2 Materials and Methods
### Feature Wavebands Selection Algorithms
#### 2.6.1 Uninformative Variables Elimination  
The UVE algorithm is a feature wavelength selection algorithm based on statistical stability analysis. Its core is to first introduce a matrix of random variables of the same dimension into the original spectral matrix to construct an extension matrix, then use PLSR to calculate the regression coefficient matrix B of this extension matrix, and calculate the coefficient of variation (CV) of each variable with Equation (2), so as to select the characteristic wavelengths that have a stable contribution to the target variables.  
\[CV=\frac{mean(b_{i})}{Std(b_{i})} \tag{2}\]  
where \(b\) represents the regression coefficient, \(i\) represents the i-th column vector in the spectral matrix and CV is defined as the ratio of the mean value to the standard deviation of the regression coefficient. The CV value is used to evaluate the stability of the regression coefficient of the variable. The larger the CV, the more significant the contribution of the variable to the model. The maximum CV value (\(CV_{max}\)) of the random variable matrix is used as the screening threshold, and the variables whose CV values are lower than the threshold are eliminated, and the effective variables are retained for the construction of the final regression model [29].
## 2 Downlink Beamforming Design and Uplink Power Allocation
### Methodology: Deep Learning-Based Downlink Beamforming Design and Uplink Power Allocation
#### 2.2.2 Network Architecture  
The architecture of the constructed DNN is shown in Figure 2, of which goal is to efficiently compute (or predict) the solution to the problem (P1\({}^{\prime}\)) in the downlink or (P2\({}^{\prime}\)) in the uplink.  
The constructed DNN uses the channel vector between the BS and the \(k\)-th UAV as the input and yields the optimal beamforming vector for the \(k\)-th UAV in the downlink scenario or optimal transmit power for the \(k\)-th UAV in the uplink scenario. Specifically, the input and output of the constructed DNN, respectively, are represented as  
\[\begin{split}\text{Input}&=\begin{cases}[\text{Re}( \textbf{h}_{d,k}[n]),\text{Im}(\textbf{h}_{d,k}[n])]^{\top},&\text{for the downlink}\\ [\text{Re}(\textbf{h}_{u,k}[n]),\text{Im}(\textbf{h}_{u,k}[n])]^{\top},& \text{for the uplink}\end{cases}\\ \text{Output}&=\begin{cases}\hat{\textbf{w}}_{k,\rho}[n],&\text{for the downlink}\\ \hat{p}_{k,\rho}[n],&\text{for the uplink}\end{cases}\end{split} \tag{15}\]  
where \(\hat{\textbf{w}}_{k,\rho}[n]\) and \(\hat{p}_{k,\rho}[n]\) are the estimate of the solutions to (P1\({}^{\prime}\)) and (P2\({}^{\prime}\)) for the \(k\)-th UAV, respectively.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \((M,K)\) & **Conventional Scheme (Downlink)** & **Proposed Scheme** \\ \hline \((4,6)\) & **22,574** & 56,832 \\ \((8,6)\) & 361,192 & **125,952** \\ \((16,8)\) & 8,897,462 & **401,408** \\ \((32,8)\) & 142,359,398 & **1,064,960** \\ \((64,10)\) & 3,183,252,921 & **3,973,120** \\ \((128,10)\) & 50,930,046,742 & **13,189,120** \\ \hline \hline \end{tabular}
\end{table}
Table 2: Computational complexities for the various \((M,K)\) pairs in the downlink.  
Figure 2: The network structure and loss function of the proposed scheme.  
The activation function decides whether or not a neuron will be activated or not and transferred to the next layer. It helps in the process of backpropagation because of their differentiable property. During the training process, the loss function is updated, and the activation function makes the gradient descent curves to achieve their local minima. We select the exponential linear unit (ELU) [28] as the activation function, which is a widely adopted activation function to alleviate various practical issues related to training (e.g., vanishing/exploding gradient [29] and dying ReLU problem [30]), which is given by  
\[\text{ELU}(x)=\begin{cases}x,&\text{if }x>0\\ \mu(\exp{(x)}-1),&\text{if }x\leq 0\end{cases} \tag{16}\]  
where \(x\) denotes an input feature, and \(\mu\) represents a hyperparameter that controls the saturation value.
## 1 Introduction  
Diabetic foot ulcers (DFUs) are the most recognized complication in people with diabetes mellitus (DM). The global prevalence of DFUs was 6.3% in 2016 [1]. DFUs are correlated with an increased risk of death. Five percent of people with newly developed DFUs died within 12 months, and 42.2% of people with newly developed DFUs died within five years [2]. Prevention of DFUs is imperative in people with DM.  
The American Diabetes Association (ADA) recommends that people with DM with or without peripheral neuropathy should perform moderate-intensity aerobic exercise at least 150 min/week or vigorous aerobic exercise at least 75 min/week [3]. Exercise has been demonstrated to improve glycemic control [4], maintain body weight [5] and reduce the risk of cardiovascular disease [6]. However,exercise may also increase the risk for DFUs in people with DM because of increased plantar pressure during most weight-bearing exercises [7; 8; 9; 10]. Increased plantar pressure during weight-bearing activities has been demonstrated to be a major risk factor of DFUs [11; 12; 13].  
People with a history of DFUs have been shown to have stiffer plantar tissue [14; 15; 16]. An increase in plantar stiffness is due to the effect of high blood glucose on increasing intermolecular cross-linking of structural proteins [17]. The stiffer plantar tissue may reduce the attenuating capacity of plantar tissues in response to mechanical stresses during weight-bearing activities, such as brisk walking and jogging, thus increasing risk for DFUs. In the literature, there are only a few studies investigating the effect of exercise intensities on the mechanical property of the plantar foot. [PERSON] et al. demonstrated that the stiffer plantar pad may increase forefoot stress by 38% and 50% at the first and second metatarsal heads, respectively [18]. [PERSON] et al. showed that people with DM had significantly greater effective Young's modulus and initial modulus of quasi-linear viscoelasticity compared to people without DM. They also demonstrated that the plantar pressure gradient and mechanical properties were significantly correlated [16]. [PERSON] et al. used magnetic resonance imaging (MRI) to study plantar tissue mechanical property and demonstrated that plantar stiffness in people with DM was 2.00-3.43 times compared to people without DM [19]. However, there is no study investigating the effect of various intensities of exercise (e.g., walking at different speeds and durations (i.e., the most common form of exercise in daily living)) on the changes of mechanical property of the plantar foot in people without and with DM.  
To the best of our knowledge, this is the first study investigating the effect of different walking intensities on the mechanical property of the plantar foot. The results from this study can provide a foundation to understand the effect of different weight-bearing exercises on the changes of mechanical property of plantar tissue in people at risk for foot ulcers.
# Miniature Coil for Wireless Power and Data Transfer through Aluminum +
## 2 Miniature Coil
### Load Effect  
The miniature coil was designed to have an input resistance of a few ohms that will allow efficient rectification and matching while providing high harvested power [22]. Figure 4 shows the circuit diagram used for measuring harvested power. Parallel capacitors, \(C_{tx}=C_{rx}=24\) uF, are used to resonate the system at 2 kHz to maximize power transfer [23]. Load \(R_{L}\) was varied in the range 1 \(\Omega\)-1 k\(\Omega\) to find an optimal value. Figure 5 shows measured results of harvested power and received voltage for different loads. The optimal load is 4 \(\Omega\) and harvests 180 mW with 8.5 W of input power. As load \(R_{L}\) rises, the received voltage increases while the harvested power decreases. At a 4 \(\Omega\) load, the harvested power peaks at 180 mW, while the received voltage is 850 mV\({}_{\text{rms}}\), which should be high enough to achieve rectifier efficiencies between 45-62% [24]. The 4 \(\Omega\) load provides an optimal impedance match at the output of the receiving coil.
## 4 A Multi-View Detecting Framework
### View 2: Measuring Attribute Value Similarity
```
Input: Event log \(L\), threshold \(\theta_{a}\) Output: \(S_{n}\): Set of Attribute Value Similarities for all Pairs of Activities
1 foreach\(a\in A\)do
2 ifHasNumericalValueAttribute(a)then
3\(DataSet_{a}\leftarrow\) ExtractAttribute(\(a\));
4\(Q_{1a},Q_{3a}\leftarrow\) CalculatePercentles(\(a\));
5 Clusters \(\leftarrow\) AgglomerativeHierarchicalClustering(\(Q_{1a},Q_{3a},\theta_{a}\));
6 foreach\(C\in Clusters\)do
7 ifsize(\(C\)\(\leq\) 1 then
8 continue;
9 else
10 foreach\(a,b\in C\)do
11\(H_{a},H_{b}\leftarrow\) MakeHistograms(\(DataSet_{a},DataSet_{b}\));
12\(H_{abW}\leftarrow\) CalculateWeight(\(H_{a}\));
13\(H_{bW}\leftarrow\) CalculateWeight(\(H_{b}\));
14 Attribute Value Similarity = EMD(\(H_{a},H_{ab},H_{b},H_{bW},D_{d}\));
15\(S_{n}\leftarrow\) Attribute Value Similarity;
16
17 return\(S_{n}\)
```  
**Algorithm 2**Attribute Value Similarity  
The ground distance function \(D_{d}\) for EMD between any two attribute clusters \(p_{i},q_{j}\) from histograms is defined as  
\[D_{d}=|p_{j}-q_{j}|. \tag{5}\]  
_Principle._ Because both \(p_{i},q_{j}\) are numerical values, it takes less effort to transfer \(p_{i}\) to \(q_{j}\) if they are close to each other. We adopt the difference between \(p_{i}\) and \(q_{j}\) as the ground distance function.
# Signal to Noise Ratio of a Coded Slit Hyperspectral Sensor
## 2 Materials and Methods: The Signal to Noise (SNR) Model
### The SNR Model for Assessing the Utility of CA Multiplexed Sensing
The signal for each case (in terms of number of photoelectrons) can be related to a common rate in both cases: \(\mathbf{f}=\hat{\mathbf{f}}\Delta t^{c}\) and \(\mathbf{f}^{m}=\hat{\mathbf{f}}\Delta t^{m}\) where the superscript \(c\) denotes for the case of the conventional sensor, and the superscript \(m\) denotes the same for the multiplexed sensor, \(\Delta t\) represents the integration time. Since the coded aperture sensing effectively has \(\frac{(N+1)}{2}\) times as many slits (openings) as that of the conventional sensor, we may assume that the optical input (i.e., light levels) at the detector of the multiplexed sensing will be greater by this factor as the first approximation. Thus when the illumination is intense it may assume that \(\Delta t^{c}=\frac{N+1}{2}\Delta t^{m}\). However, in situations where constraints on integration time which limits the frame rate are required, the integration times of both sensing methods can be the same as the detectors in both cases will not be saturated. Under this situation the noise source may be dominated by the signal-independent term. Assume \(\sum_{i=1}^{N}\langle f_{i}^{m}\rangle=N\langle f_{n}^{m}\rangle\) and \(\langle d\rangle=0\) it is seen that:  
\(\frac{\text{SNR}^{m}}{\text{SNR}^{c}}=\frac{1}{\sqrt{N}}\) when \(\Delta t^{c}=\frac{N+1}{2}\Delta t^{m}\), _However \(\frac{\text{SNR}^{m}}{\text{SNR}^{c}}=\frac{N+1}{2\sqrt{N}}\) when \(\Delta t^{c}=\Delta t^{m}\) and \(\sigma^{2}\gg f_{m}\)_  
It can be seen that the SNR of the conventional sensor may be better than that of the multiplexed version by at least a factor of \(\sqrt{N}\), when the illumination is strong. However, it is also observed that the SNR of the multiplexed sensor may be better by the same factor when the illumination is weak. This observation is consistent with the expectation that the multiplexed sensing has the advantage when the noise level is independent of the signal source, but it is not when under abundant signals scenarios where shot noise are dominant [6]. The integration time of the CA sensing can be made by using the approximation \(\sum_{i=1}^{N}\langle f_{i}\rangle=Nf_{n}\) which is reasonably not accurate enough for many, if not all wavebands, i.e., for all values of \(n\). To help the data analysis further, we can make use of the following observations: (1). The total number of non-zero elements in any row of the CA sensing matrix is about \(\frac{(N+1)}{2}\). (2). Thus the maximum of any element in \(\mathbf{y}\) is approximately the sum of all elements of \(\mathbf{f}\) that are greater than the median of \(\mathbf{f}\). Furthermore, it is also noted that the SNR can be further improved by averaging the results of multiple exposures of the scene, even when the illumination of the scene is strong and light is abundant.
## 3 Proposed Sensing Waveform
### Signal Detection and Estimation
Subsequently, we obtain the detection threshold \(T_{\text{CFAR}}\) by multiplying \(P_{\text{CN}}\) by a factor \(\zeta\). If the power of \(z_{m,k}\) is greater than \(T_{\text{CFAR}}\), it means that the target exists, otherwise, it means that the target does not exist. Finally, we propose using the FTPR algorithm [41] to estimate the distance and velocity of the target. Specifically, we assume that the target is detected at the \(m_{t}\)th distance cell and the \(k_{t}\)th Doppler cell. We then obtain the \(\phi_{m_{t}}^{\prime}\) by taking the Doppler spectrum \(\phi_{m_{t}}\) of the \(m_{t}\)th range cell and setting the values of Doppler cells outside \([k_{t}-1,k_{t}+1]\) to zero, as given by  
\[\phi_{m_{t}}^{\prime}=\left\{ \begin{matrix}\phi_{m_{t}},k\in[k_{t}-1,k_{t}+1] \\ 0\,k\
otin[k_{t}-1,k_{t}+1]\end{matrix} \right. \tag{20}\]  
An inverse fast Fourier transform (IFFT) is performed on \(\phi_{m_{t}}^{\prime}\) and the Doppler frequency \(f_{d_{t}}\) is obtained by finding the phase slope, given by  
\[f_{d_{t}}=\frac{\text{Slope}(\angle\text{IFFT}[\phi_{m_{t}}^{\prime}])}{2\pi}\,, \tag{21}\]where IFFT\([x]\) denotes the IFFT of \(x\), \(\angle x\) stands for the phase of \(x\), and Slope\((x)\) represents the slope of \(x\). The speed of the target \(\hat{v_{t}}\) is estimated by  
\[\hat{v_{t}}=\frac{f_{d_{t}}\lambda}{2}, \tag{22}\]  
where \(\lambda\) is the wavelength. Similarly, the distance of the target \(\hat{r_{t}}\) is as follows:  
\[\hat{r_{t}}=\frac{f_{r_{t}}c}{2\Delta fB}, \tag{23}\]  
where \(c\) is the propagation velocity, \(B\) is the bandwidth. Regarding complexity, this paper focuses on analyzing the computational complexity of the NUDFT, DFT, IAA, and OMP. Since the number of iterations is difficult to predict, we consider the complexity per iteration, and study the convergence of the algorithms in terms of iterations, numerically, in our results. In all the computations, we only consider the highest-order terms and omit the low-order ones. For the NUDFT, there exists a fast algorithm NUFFT, which reduces the complexity of the method from \(\mathcal{O}(LK)\) to \(\mathcal{O}(L\log{(K)})\). Similarly, DFT also has a fast Fourier transform (FFT) with a computational complexity of \(\mathcal{O}(L\log{(L)})\). For IAA, its complexity is \(\mathcal{O}(L^{3}K^{3})\). Reference [38] suggests that after more than 10 iterations of IAA, its performance does not significantly improve. For OMP, its complexity is \(\mathcal{O}(L^{2}K)\). The number of iterations of OMP is affected by the sparsity of the target, and in the simulation experiments of this paper, the number of iterations is generally no more than 10 times.
## 3 Results and Discussion
### Evaluation of SPMESH Sheet-DART-MS vs. SPME-GC-MS  
#### 3.3.1 Ibmp  
Representative chronograms for IBMP and its deuterated standard in homogenate under optimized conditions are shown in Figure 4. For evaluation of IBMP measurements, 86 samples of Cabernet Sauvignon and Merlot grapes were used. IBMP concentrations ranged from undetectable (<2 ng/L) to 28 ng/L by SPME-GC-MS and <4 ng/L to 38 ng/L by SPMESH sheet -DART-MS-MS. These values fall within the typical range of IBMP found in grapes during ripening: 100 ng/L to less than 10 ng/L [25; 27]. Variation among detectable samples was 28% CV.  
A good correlation (\(R^{2}\) = 0.71) was found between IBMP measured by SPMESH sheet-DART-MS and SPME-GC-MS (Figure 3). The correlation between SPMESH sheet and SPME methods was weaker than in our previous work (\(R^{2}\) = 0.97) comparing \"one-shot\" SPMESH cards with SPME-GC-MS [19]. However, the current work measured IBMP at native concentrations (<40 ng/L), as opposed to earlier work, which used IBMP spikes in the range of 200-1000 ng/L. Based on the regression equation, SPMESH sheet-DART-MS measured higher concentrations than SPME-GC-MS for high IBMP samples (slope = 0.76), but lower concentrations for low IBMP samples (\(Y\)-intercept = 4.1). The observation that  
Figure 3: Initial (130 rpm, 50 \({}^{\circ}\)C, 30 min equilibration—gray open circles) and optimized (230 rpm, 70 \({}^{\circ}\)C, 1 h equilibration—green filled circles) correlation data for IBMP in Cabernet Sauvignon and Merlot grapes measured by SPMESH sheet-DART-MS, compared to SPME-GC-MS. Shaded areas represent 95% confidence intervals of the linear regression. Undetectable values were set to the square root of the limit of detection (IBMP = 2 ng/L for DART).  
SPME vs. SPMESH data has a slope \(<\)1 could arise from isobaric interferences on the SPMESH data set, but the reason for the non-zero intercept was unclear.
## 4 Results of Experiment and Simulation
### Description of De-Coupling Effect
#### 4.2.1 Simulation Results  
The simulation results are shown in Figure 9.  
Figure 8: The sinusoidal motion of the azimuth gimbal.  
Figure 6: The sinusoidal motion of the elevation gimbal.  
Figure 7: The coupling effect of the azimuth gimbal: (**a**) simulated coupling effect result; (**b**) experimental coupling effect result.  
From the simulation results, the following conclusions can be obtained: the conventional PID method has the worst performance, the peak to peak (\(p\)-\(p\)) value of tracking error is \(0.131^{\circ}\), the tracking error at time \(48.8\) s is \(0.058^{\circ}\); while the tracking error \(\Delta\theta_{a}\) of the conventional TSM method is \(1.75\times 10^{-3}(^{\circ})\) and the tracking error at time \(48.8\) s is \(-26.1\times 10^{-3}(^{\circ})\); the tracking error \(\Delta\theta_{a}\) of the NTSM method in reference is \(6.9\times 10^{-4}(^{\circ})\), the tracking error is \(-20.0\times 10^{-3}(^{\circ})\); the tracking error \(\Delta\theta_{a}\) of NFTSM is \(6.7\times 10^{-5}(^{\circ})\), and the tracking error at time \(48.8\) s is \(18.0\times 10^{-3}(^{\circ})\); the NFTSM the tracking error \(\Delta\theta_{a}\) is \(7.3\times 10^{-5}(^{\circ})\) and the tracking error at time \(48.8\) s is \(23.0\times 10^{-3}(^{\circ})\); the best performance corresponds to the BSNN-based NFTSM with a tracking error of \(1.1\times 10^{-5}(^{\circ})\) and the tracking error at time \(48.8\) s of \(7.8\times 10^{-3}(^{\circ})\). At time \(48.8\) s, the azimuth gimbal begins to perform the assigned sinusoidal motion from a still state. The simulation results show that the proposed BSNN has a better adaptive capability and the proposed controller shows better decoupling effect than other controllers.  
The forms of the B-spline curves are shown in Figure 10. It can be seen from the figure that both the positions and the shapes of the B-spline curves are changed.  
Figure 9: Comparative azimuth gimbal absolute angle simulation results with four different methods: **(a)** PID method; **(b)** TSM method in reference [19]; **(c)** NTSM method in reference [15]; **(d)** the proposed NFTSM method; **(e)** NFTSM-RBFNN method; **(f)** the proposed NFTSM-BSNN method.
## 3 MZFI Performance
The MZFI achieves a total wavelength shift of approximately 12 nm, as depicted by the black line in Figure 5. This behavior is highly advantageous for the generation of tunable and switchable multi-wavelength fiber emissions. Fringe visibility, on the other hand, is a measure of the contrast between the interference quality patterns for interferometric systems. The visibility was determined using the established expression \(V=\frac{I_{max}-I_{min}}{I_{max}+I_{min}}\), where \(I_{max}\) and \(I_{min}\) are the maximum and minimum intensities of the comb-like transmission output spectra [27]. The red line in Figure 5 shows that fringe visibility increases with curvature, reaching a maximum value of 0.56. This trend reflects the nonlinear relationship between curvature and fringe visibility. Specifically, the visibility rises as curvature increases, indicating an enhanced mode coupling efficiency. However, this effect is not linear, as fringe visibility can both increase and decrease with varying curvature values. This behavior stems from the complex interplay  
Figure 4: (**a**) The progressive modification of ASE spectrum with increasing curvature applied to the MZFI, (**b**) an inset in the range of 1541 to 1560 nm demonstrates an FSR of 5 nm. between curvature-induced stress and its impact on the effective refractive index, which affects the mode coupling efficiency. Fringe visibility plays a crucial role in the performance of fiber lasers. An increase in fringe visibility leads to a more defined interference pattern, enhancing the laser cavity's feedback mechanism. This improvement directly influences key parameters like the OSNR and the side mode suppression ratio (SMSR), as a stronger interference pattern helps amplify the desired signal wavelengths while suppressing noise and unwanted side modes. Consequently, this enhanced control over the laser's feedback facilitates the generation of multi-wavelength, switchable, or tunable lasers with greater stability and precision.