esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Methods
### Data Collection and Reduction  
Three-dimensional motion and GRF data were recorded using eight near-infrared cameras (200 Hz; Vicon, Santa Rosa, CA, USA) and a floor-embedded force platform (2000 Hz; AMTI, Watertown, MA, USA), respectively. Spatial trajectories from the reflective markers were digitized as well using the Plug in Gait module of the Vicon Nexus software (Vicon, Centennial, CO, USA). Afterward, these trajectories and vertical GRF data were filtered using a fourth-order Butterworth low-pass filter with zero lag at a cut off frequency of 12 Hz, determined by residual analysis [35]. Then, smoothed marker coordinates were used to define segment axes and joint centers through the Plug in Gait model. Data from the initial contact (vertical GRF: >10 N) to the peak knee flexion during the first landing phase were also analyzed [36]. Subsequently, for the time to peak knee flexion, the number of frames from initial contact to peak knee flexion was converted into milliseconds (ms). Joint angleswere then calculated using a Cardan sequence (flexion/extension, adduction/abduction, and internal/external rotation). Next, joint moments (internal) were calculated by an inverse dynamic approach using anthropometric, kinematic (joint angle), and force (GRF) data. Finally, MATLAB (version 2020a, Math Works, Natick, MA, USA) software was used to reduce and extract the necessary data in the outcomes from Vicon Nexus.  
PFJS was calculated using a previously described mathematical model [30]. Then, the effective lever arm for quadriceps muscles was estimated at each time point based on the given knee joint angles (Equation (1) in Table 1). Subsequently, quadriceps muscle forces were also estimated by dividing the knee joint moment by the effective lever arm for the quadriceps (Equation (2)). The patellofemoral joint reaction force was estimated by multiplying the quadriceps muscle force with constant k (Equation (3)) [37], which represents the relationship between quadriceps muscle force and patellofemoral joint's compression force (Equation (4)). The patellofemoral joint contact area was estimated using a previously described equation [38] (Equation (5)). Then, the PFJS was determined by dividing the patellofemoral joint reaction force by the patellofemoral joint contact area (Equation (6)).
# Feasibility of Low Latency, Single-Sample Delay Resampling: A New Kriging Based Method
## 3 Test Methods and New Approach
### Evaluation of Reconstruction Accuracy  
The reconstruction accuracy was evaluated for Kriging and compared with Lagrange, Margolis, and Akima as reference methods. The root mean square error (RMSE) between the reconstructed signal and reference signal with a time resolution of 0.1 s was calculated as indicator value. The SNR for an input signal with \(\sigma\) = 1 is given by:  
\[SNR=-20\ log_{10}(\text{RMSE})\ \text{dB}. \tag{12}\]  
When reconstructing time-limited signals close to the Nyquist frequency, an error is unavoidable, especially when there are gaps in the signal longer than 3/\(f_{L}\) due to missing samples. The largest deviations occur at the edges of the measured time window. The RMSE was calculated separately for the first and last 5 s at the margins, and for the remaining centre of the measured window in the group-delay scenario. The single-delay scenario showed high errors for the first sensor samples, when neither future nor sufficient past samples were available. The first 10 s were therefore ignored in the RMSE calculation.  
During a frequency swapping, the band limit \(f_{L}\) of the test signal was increased until the error became so high that the reconstruction was useless. The threshold for an acceptable error \(E_{Max}\) was set to RMSE = 0.01, which is equivalent to SNR = 40 dB. A higher SNR is possible but requires lower \(f_{L}\) or higher \(f_{S}\). To assess the suitability of various resampling methods at high \(f_{L}\), the maximum band limit \(f_{40}\) was determined, which ensured the error remained below the threshold \(E_{Max}\). Conversion to the OSR can be achieved using  
\[\text{OSR}=\frac{f_{s}}{2\cdot f_{40}}. \tag{13}\]  
The first round of simulations was carried out for the group-delay scenario. The bandlimited noise test signal produced lower errors compared to sine waves with the same \(f_{L}\). The signal energy is evenly distributed over lower frequencies for the bandlimited noise. Tests were focused on the sine wave inputs as they represent the worst-case input.
## 3 Bearing Fault Diagnosis Based on Deep Learning
### Experimental Process  
The experimental and algorithmic flow chart is shown in Figure 8. Firstly, the divided training, validation, and test datasets are pre-processed by FFT as the input of the neural network. The training set is disrupted and divided into several consecutive small batches of  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**NO**} & \multirow{2}{*}{**Layer Type**} & \multirow{2}{*}{**Kernel/Stride**} & \multicolumn{2}{c}{**Output Size**} & \multicolumn{2}{c}{**Kernel**} & \multirow{2}{*}{**Padding**} \\  & & & **Width \(\times\) Depth** & & **Channel Size** & \\ \hline \(1\) & Input & — & 1024 \(\times\) 1 & — & — \\  & Convolution & \(16\times 1/16\times 1\) & \(64\times 8\) & & 8 & Same \\  & Pooling & \(2\times 1/2\times 1\) & \(32\times 8\) & & — & Valid \\  & Convolution & \(32\times 1/16\times 1\) & \(64\times 8\) & & 8 & Same \\
2 & Pooling & \(2\times 1/2\times 1\) & \(32\times 8\) & & — & Valid \\  & Convolution & \(64\times 1/16\times 1\) & \(64\times 8\) & & 8 & Same \\  & Pooling & \(2\times 1/2\times 1\) & \(32\times 8\) & & — & Valid \\  & Convolution & \(96\times 1/16\times 1\) & \(64\times 8\) & & 8 & Same \\  & Pooling & \(2\times 1/2\times 1\) & \(32\times 8\) & & — & Valid \\
3 & Dropout & — & \(32\times 32\) & — & — & — \\
4 & Convolution & \(3\times 1/1\times 1\) & \(32\times 32\) & & 32 & Same \\
5 & Pooling & \(2\times 1/2\times 1\) & \(16\times 32\) & — & Valid \\
6 & Convolution & \(3\times 1/1\times 1\) & \(16\times 64\) & 64 & Same \\
7 & Pooling & \(2\times 1/2\times 1\) & \(8\times 64\) & — & Valid \\
8 & Convolution & \(3\times 1/1\times 1\) & \(8\times 64\) & 64 & Same \\
9 & Pooling & \(2\times 1/2\times 1\) & \(4\times 64\) & — & Valid \\
10 & Convolution & \(3\times 1/1\times 1\) & \(2\times 64\) & 64 & Valid \\
11 & Pooling & \(2\times 1/2\times 1\) & \(1\times 64\) & — & Valid \\
12 & GRU & — & \(1\times 60\) & 60 & — \\
13 & GRU & — & \(30\) & 30 & — \\
14 & Softmax & — & \(4\) & 4 & — \\ \hline \hline \end{tabular}
\end{table}
Table 4: Detailed parameters of the network model.  
data (Mini Batches), each containing 256 sample data. The FFT processed training samples are then input to the neural network model, and feature extraction is performed by the first layer of the multi-scale large convolutional kernel followed by multiple small convolutional layers and pooling layers. Finally, the feature sequence information after the convolutional layer is processed by the GRU recurrent neural network, and the corresponding fault classification labels are output by the four neurons of the fully connected layer.  
The model training uses a cross-entropy loss function and Adam optimizer for gradient update of output samples. The loss function of the validation set is used as the monitor, and if the loss function of the validation set does not decrease for 100 consecutive epochs, the model with the smallest loss function is used as the optimal model. After that, the test set data are input to the optimal model and the fault diagnosis classification accuracy is output.  
Figure 8: Experimental process.
## 2 Theory and Model
### The Separation Model Based on Low-Rank Constraints  
Robust principal component analysis (RPCA) [16; 17] is one of the low-rank restoration methods, which, early on, was applied in the field of image processing. It decomposes a matrix \(D\) into two matrices: \(D=L+E\), where \(L\) is a low-rank matrix, and \(E\) is a sparse matrix which represents noise.  
However, the noise from the vibration signal of mechanical equipment is not sparse. The noise in the vibration signal is mostly Gaussian colored noise and white noise. In order to explore the nature of the noise term in the vibration signal, the Lilliefors method [18] is used for the Gaussian detection of the vibration signal in Section 5. Assume the Gaussian distribution value is 0. If the confidence level is >0.05, the assumption is true. The test result shows that confidence level is 0.27 > 0.05. The detection result is that the noise of the mechanical vibration signal has a Gaussian distribution. Therefore, sparsity cannot be used to describe noise in mechanical vibration signals.  
Therefore, according to the composition of the mechanical vibration signal, a low-rank constrained vibration source signal separation model is proposed:  
\[\begin{split}&\underset{L,A}{argmin}\quad rank(L)+\beta\times kur(A)\\ & s.t.\quad D=L+A\end{split} \tag{1}\]  
where \(\beta\) is a compromise factor, which can be understood as the weight between the vibration source signal and the noise, and \(kur(\) ) is the kurtosis function. The kurtosis is used to describe the approximate Gaussian degree of the data; the closer the kurtosis of the data is to 0, the higher the Gaussian degree. Because the rank function is non-convex, it is a non-deterministic polynomial problem (NPP). The nuclear norm is a convex approximation of the rank function [19]. Therefore, through convex relaxation, the model can be transformed into:  
\[\begin{split}&\underset{L,A}{argmin}\quad\left\|L\right\|_{*}+\beta \times kur(A)\\ & s.t.\quad D=L+A\end{split} \tag{2}\]  
where \(\left\|L\right\|_{*}\) is the nuclear norm of the \(L\).
# Long-Term and Decadal Sea-Level Trends of the Baltic Sea Using Along-Track Satellite Altimetry
## 5 Results
### Inter-Comparisons of SA-Based ASL Trends  
#### 5.4.1 SA Data Optimality Regarding the Distance to TG  
The utilization of along-track SA data provides an opportunity to investigate how sea-level trend estimates change regarding the distance from the coastline. Figure 10 and Table 6 present the SA-derived sea-level trend results, which range from 5 to 50 km away from the coast. In Figure 10, the data within each distance range are averaged, such as averaging the SA data from 5 to 20 km away from the TG station to determine the SA sea-level trend within that distance. Additionally, the TG-derived trend is depicted for comparison, providing insight into the expected sea level at the coast. This comparison aims to illustrate the variability in sea-level trends away from the TG station and potentially explore scenarios where the TG might not consistently offer the optimal location for determining precise sea-level trend estimates, depending on the specific purpose.  
Figure 10 illustrates the variability in sea level among stations and distances, highlighting that the dynamics observed at a TG station may not consistently represent the broader coastal area. For instance, at stations like Dirhami (#1) and Pori (#13), the TG trends are higher compared to the SA measurements, whereas at stations like Kolobrzeg (#5), they are lower. These variations may be attributed to persistent marine dynamics influencing coastal areas, such as surface waves causing wave set-up and set-down [81]. However, further investigation is required to fully understand and address these discrepancies in future studies. Meanwhile, Table 6 presents station-specific statistics, revealing only slight variations in RMSE across different distances (ranging from 1.47 to 1.63). Consequently, almost any distance within 50 km appears to be suitable. Notably, the largest RMSEs of 1.63 and 1.53 mm/yr are observed within the 10-15 km ranges from the coast. This discrepancy could be attributed to the specific coastal processes occurring within this distance range.
# Intra-Plot Variable N Fertilization in Winter Wheat through Machine Learning and Farmer Knowledge
###### Abstract  
The variable fertilization rate (VFR) technique has demonstrated its ability to reduce nutrient losses by adapting the fertilizer dose to crop needs. However, transferring this technology to farms is not easy. This study aimed to make a variable fertilization map in a commercial plot where there is no data from a yield monitor, combining machine learning techniques and farmer's knowledge. In addition to the normalized difference vegetation index (NDVI) obtained from Sentinel-2 and a digital elevation model (DEM), information captured by a yield monitor in 2019 was used to train and validate models. Among the 15 algorithms trained, the best result was obtained by the random forest (RF), with an RMSE of 496 and R\({}^{2}\) of 0.90. Using the \"leave one out\" technique, the capacity to predict an entire plot was tested. Finally, the RF algorithm was tested on a 12-hectare wheat plot where no yield data were available. The novelty of this work lies in the collaborative work developed between farmers and researchers to implement the VRF technique in plots where precise yield data do not exist and in the \"leave one out\" validation. The collaboration between scientists and farmers resulted in a very positive exchange of information that allowed the farmer to change the fertilization strategy of the whole farm and the scientists to better understand how soil properties and plot history affect yield.  
precision agriculture; nitrogen fertilization; NDVI; on-farm experimentation; yield prediction Article
## 4 Experimental Results
### Evaluation of E2 ED  
This is the ratio of the number of packets a receiver receives to the time needed to convey each packet. Figure 6 shows an end-to-end delay (E2 ED) analysis for the proposed and existing methods. The suggested method outperformed the previous systems, with a lower E2 ED (8.2 ms). When the number of nodes increases, the E2 ED will rise. According to Table 4, the E2 ED of the existing approaches, LEACH, EECRP, FEEC-IIR, and CL-IoT was 13, 12, 10, and 9 ms, respectively.
## 5 Discussion  
In order to understand the physical mechanisms causing the different behaviors in the scintillation profiles recorded by receivers, hereafter we split the discussion about scintillation events recorded at SANAE IV base from those recorded at Concordia station. Moreover, as the receiver located at SANAE IV base recorded phase without amplitude scintillation events, we discuss actual scintillation events separately, in which both the phase and the amplitude indices increase, from those showing only phase fluctuations.
# Vision-Based Distance Measurement in Advanced Driving Assistance Systems
## 3 Depth Map Estimation  
### Relationship between Disparity and Depth  
The depth estimation principle based on the left and right views is shown in Figure 1, where one image pair contains two images \(\mathbf{I}^{l}\) and \(\mathbf{I}^{r}\) captured simultaneously by the left and right cameras; \(f\) and \(b\) are the focal length and baseline distance, respectively, \(\mathbf{P}_{l}\) and \(\mathbf{P}_{r}\) are the projection points of the object point \(\mathbf{P}\) on the imaging planes of the left and right cameras, respectively, and \((x_{l},y_{l},f)\) and \((x_{r},y_{r},f)\) are the locations of \(\mathbf{P}_{l}\) and \(\mathbf{P}_{r}\) in the coordinate systems of the left and right camera body, respectively. To simplify the following description, we set \(y_{l}=0\) and \(y_{r}=0\). As shown in Figure 1, according to the property of similar triangles,  
\[\frac{x_{p}^{l}}{x_{l}}=\frac{z_{p}^{l}}{f},\ \frac{x_{p}^{r}}{x_{r}}=\frac{z_{p}^{ r}}{f} \tag{1}\]  
where \((x_{p}^{l},z_{p}^{l})\) and \((x_{p}^{r},z_{p}^{r})\) are the locations of Pin the coordinate systems of the left and right camera bodies, respectively. As \(x_{p}^{l}-x_{p}^{r}=b\) and \(z_{p}^{r}=z_{p}^{l}\), as shown in Figure 1, Equation (1) can be rewritten as follows:  
\[\frac{x_{p}^{l}}{x_{l}}=\frac{z_{p}^{l}}{f},\ \frac{x_{p}^{l}-b}{x_{r}}=\frac{z_{p }^{l}}{f}, \tag{2}\]  
further,  
\[z_{p}^{l}=\frac{fb}{d} \tag{3}\]  
where \(d=x_{l}-x_{r}\) is the left-right disparity and represents the difference in the location of point \(\mathbf{P}\) in the left and right images. From Equation (3), we find that \(z_{p}^{l}\), denoting the depth of point \(\mathbf{P}\) in the coordinate system of the left camera body, can be obtained if the baseline distance \(b\), the camera focal length \(f\), and the disparity \(d\) are all known. Therefore, depth estimation can be transformed into a problem of solving disparity map computation. Consequently, the main task of a deep learning network is to compute the disparity map from the input image pair.
## 5 Conclusions  
This study systematically evaluates the noise robustness and imaging performance of four computational holography encoding algorithms (detour-phase, modified off-axis reference, kinoform, and interference holography) through a dual-metric framework combining PSNR and SSIM. Key findings include:  
1. Noise-SNR Correlation: PSNR exhibits monotonic decay with increasing noise coefficients, showing accelerated reduction in low-noise regimes (\(\leq\)0.3, e.g., 36.3% drop for Lohmann III) and saturation attenuation in high-noise regimes (\(\geq\)0.5, e.g., 10.9% reduction for kinoforms), confirming PSNR's sensitivity to low noise but limited capacity in noise-dominant scenarios.
2. SSIM Robustness: SSIM demonstrates superior stability across all encoding methods, maintaining 0.9042 for modified Burckhardt encoding at noise coefficient 1.0 and sustaining SSIM >0.92 throughout Lee's grayscale encoding, validating its effectiveness in preserving edge/texture features to suppress visual distortions.
3. Encoding Optimization: Noise resistance improves significantly through method refinement. [PERSON]'s grayscale encoding achieves 19.09 dB PSNR at noise coefficient 1.0 (21% improvement over binary encoding), while Lohmann III enhances PSNR/SSIM by 94.2%/46% via aperture expansion (4\(\rightarrow\)12), with most pronounced gains at low apertures (4\(\rightarrow\)8).
4. Interference Holography: Continuous CGHs outperform binarized versions in reconstruction clarity (Figure 27e vs. Figure 27f), as amplitude information preservation in interference fringes mitigates grayscale dynamic range compression-induced distortion.
5. Noise Thresholds: Visual lossless quality (SSIM > 0.95) is achievable at noise coefficients \(\leq\)0.3, while imaging usability at \(\geq\)0.7 requires combined strategies like noise-resistant encoding (e.g., Li's grayscale) or aperture optimization.  
These conclusions provide theoretical foundations for optimizing encoding strategies and parameters in computational holography systems operating under high-noise conditions.  
Y.L.: writing\(-\)original draft preparation; Y.Z.: methodology; D.J.: formal analysis; S.G.: data curation; M.Z.: writing\(-\)review and editing. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
**Institutional Review Board Statement:** Not applicable.  
Figure 27: The synthesis and reconstruction of computer-generated interferometric hologram in Fresnel domain.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Dataset available on request from the authors. The raw data supporting the conclusions of this article will be made available by the authors on request.  
**Conflicts of Interest:** The authors declare no conflict of interest.
# Capacity of Heterogeneous Mobile Wireless Networks with \(D\)-Delay Transmission Strategy
## 2 Definitions and Notations
### Per-Node Throughput Capacity  
If there exists a constant \(c_{4}<+\infty\) which satisfies the following inequality, we say that the per-node throughput is \(O(g(n))\):  
\[\lim_{n\rightarrow+\infty}\inf P\left(\lambda\left(n\right)=c_{4}g\left(n \right)\text{ is feasible}\right)<1\]  
and if there exist two constants \(0<c_{5}<c_{6}<+\infty\) which satisfy the following inequalities, we say that the per-node throughput capacity is \(\Theta(g(n))\):  
\[\lim_{n\rightarrow+\infty}\inf P\left(\lambda\left(n\right)=c_{5}g\left(n \right)\text{ is feasible}\right)=1\]  
\[\lim_{n\rightarrow+\infty}\inf P\left(\lambda\left(n\right)=c_{6}g\left(n \right)\text{ is feasible}\right)<1\]  
The following notations are listed throughout this paper. Given two functions \(f(n)\) and \(g(n)\):  
1. \(f(n)=O(g(n))\) means that there exist positive \(c\) and \(m\) so that \(f(n)\leq cg(n)\) holds for all \(n\geq m\);
2. \(f(n)=\Omega(g(n))\) means that there exist positive \(c\) and \(m\) so that \(f(n)\geq cg(n)\) holds for all \(n\geq m\), which also means \(g(n)=O(f(n))\);
3. \(f(n)=\Theta(g(n))\) means both \(f(n)=O(g(n))\) and \(f(n)=\Omega(g(n))\) hold;\(f(n)=O(g(n))\);
4. \(f(n)=o(g(n))\) means \(\lim f(n)/g(n)=0\).  
The remaining notations are listed in Table 1.  
\begin{table}
\begin{tabular}{c l} \hline \hline
**Notation** & **Definition** \\ \hline \(W\) & The total bandwidth of the networks, which means the highest transmission rate of each node. \\ \(W_{1}\) & The bandwidth of _ad hoc_ transmission mode. \\ \(W_{2}\) & The bandwidth of uplink sub-channel in helping transmission mode. \\ \(W_{3}\) & The bandwidth of downlink sub-channel in helping transmission mode. \\ \(n\) & The number of _ad hoc_ nodes in the networks. \\ \(m\) & The number of helping nodes in the networks. \\ \(D\) & The delay constraints. \\ \(\Delta\) & The guard zone size. \\ \(L_{1}\) & The transmission radius of source nodes in virtual channel model. \\ \(L_{2}\) & The transmission radius of relay nodes in virtual channel model. \\ \(\Lambda[T]\) & The total number of bits successfully delivered to destination nodes in \(T\) time slots. \\ \(e_{B}\) & The node storing bit \(B\). \\ \(L_{B}\) & The minimum distance between \(d_{B}\) and \(e_{B}\). \\ \(\lambda_{A}(n)\) & The per-node throughput contributed by _ad hoc_ transmission mode. \\ \(\lambda_{H}(n)\) & The per-node throughput contributed by helping transmission mode. \\ \(\lambda(n)\) & The per-node throughput capacity of the network. \\ \(H(B)\) & The number of hops of bit \(B\) in slow mobility model. \\ \(a_{B}^{n}\) & The transmission radius of bit \(B\) in its _ith_ hop in slow mobility model. \\ \hline \hline \end{tabular}
\end{table}
Table 1: Notations.