esa-sceva/satcom-chunk-collection huggingface dataset:
## 5 Imbalance-Inducing Postprocessing
### Dynamic Program to Optimize Cuts
```
0: Graph \(G\), number of partitions \(k\), fixed ordering \(\pi\) of vertices
0: A partition of \(V(G)\) into \(k\) parts
1: Let \(n=|V(G)|\) be number of vertices in \(G\)
2:for all\(1\leq i\leq j\leq n\)do
3: Compute \(w(\pi(i\to j))\), the total weight of interval \(\pi(\to j)\)
4:for all\(1\leq i\leq j\leq n\)do
5:if\(w(\pi(i\to j))\leq(1+\alpha)\frac{w(V)}{k}\)then
6:\(A_{i,j,1}\gets 0\)
7:else
8:\(A_{i,j,1}\leftarrow\infty\)
9:for all\(q=2\) to \(k\)do
10:if\(q=\lfloor k/2^{l}\rfloor\) or \(q=\lceil k/2^{l}\rceil\) for some \(l\geq 0\)then
11:for all\(1\leq i\leq j\leq n\)do
12:for all\(i-1\leq p<j\)do
13: Compute \(C(i,p,j)\), the total length of edges going from \(\pi(i\to j)\) to \(\pi(j+1\to k)\)
14:\(v\gets A_{i,p,\lfloor\frac{q}{2}\rfloor}+A_{p+1,j,\lceil\frac{q}{2} \rceil}+C(i,p,j)\)
15:if\(A_{i,j,q}>v\)then
16:\(A(i,j,q)\gets v\)
17:return\(A_{1,n,k}\)
```  
**Algorithm 4**\(\texttt{ImbalanceDP}(G,k,\pi)\)We start by rewriting the recurrence as  
\[A_{i,j,q}=\min_{i-1\leq k<j}\left[A_{i,k,\lfloor\frac{q}{2}\rfloor}+A_{k+1,j, \lceil\frac{q}{2}\rceil}+C(i,k,j)\right]. \tag{3}\]  
Then, computing the desired value \(A_{1,n,k}\) only requires the computation of \(A_{i,j,q}\) where \(q\) is either \(\lfloor\frac{k}{2^{l}}\rfloor\) or \(\lceil\frac{k}{2^{l}}\rceil\) for some \(l\geq 0\). This reduces the running time to \(O(n^{3}\log k)\) and a bottom-up DP computation needs no more than three different values for \(q\), hence the memory requirement is \(O(n^{2})\).
## 4 Computational Complexity of 3D Sound Field Reconstruction  
The three-dimensional surface of the target machinery is obtained by stereo vision technology, and the sound field is reconstructed on this surface. Therefore, it is possible to avoid the reconstruction of the sound field in the redundant area outside the organization area and reduce the computational complexity. At the same time, however, it also increases computation in some steps. The following is the analysis process of the amount of computation during positioning.  
The computations for beamforming when reconstructing the sound field mainly comes from two aspects: (1) the number of reconstruction points, (2) the amount of computations inside each reconstruction point. Through the binocular camera and extracting the operating mechanism area, the number of reconstruction points can be reduced. But the method in this paper also increases the amount of computations for 3D information extraction and internal coordinate conversion of each reconstructed point.  
In CBF, L is the number of data points of the acoustic signal, the reconstruction surface contains N reconstruction points, and the number of microphones is M. According to the beamforming principle in Section 2.1, the main computations for a single reconstruction point include:  
1. Calculating the distance vector from each microphone to the reconstructed point, which includes 3 M times of square/multiplication/division, M times of root, and 5 M times of addition/subtraction;
2. In formula (1) M times the multiplication/division and addition/subtraction are required to calculate the time delay;
3. Equation (2) performs compensation summation and normalized sound pressure complex output for each channel, which requires about 14 \(\times\) M \(\times\) L times of multiplication/division, and M times the natural number exponential operations, and M times of addition/subtraction calculations.
## 1 Introduction  
In gas turbine engines, NOx emissions can be reduced through the use of lean premixed combustion technologies (LPC) [1]. In contrast to traditional non-premixed combustion, lean premixed combustion processes are more susceptible to combustion instability [2, 3]. In the gas turbine industry, Helmholtz resonators and perforated combustor liner absorbers are two common approaches that have been adopted to attenuate large amplitude pressure oscillations in gas turbine combustors [4, 5, 6]. Helmholtz resonators are able to provide very high attenuation at their resonant frequency. Perforated combustor liners were originally conceived as a means to provide enhanced cooling of gas turbine liners [7]. However, with the appropriate design, they are not only lighter and more compact but they also offer the potential to attenuate pressure fluctuations over a much broader frequency range compared to single-neck Helmholtz resonators [8, 9].  
A number of parameters impact the ability of perforated wall liners to attenuate pressure fluctuations. Geometric factors include the liner geometry [10, 11, 12], liner thickness [13, 14] and the shape of the cavity [15, 16, 17]. Flow parameters include the sound pressure level [18; 19; 20], bias flow and grazing flow velocity [21; 22; 23; 24] and temperature of the grazing flow [25; 26; 27]. Attenuation performance also depends on periphery acoustic boundary conditions including incident angles and the size of perforated liners [28].  
From a computational perspective, detailed resolution of the very large number of small-scale effusion cooling holes is computationally too expensive as a practical engineering tool [29; 30; 31]. Simple empirical models are unable to predict acoustic attenuation by a perforated liner over a broad range of applications, resulting in the continued reliance upon traditional experimental techniques.  
[PERSON] et al. [32] proposed that a perforated wall can be represented by a homogeneous physical velocity porous media model (PVPM model), rendering detailed resolution of the perforations unnecessary. The model was demonstrated to be able to account for flow pressure drops across the liner and, through extensive validation, was shown to be able to accurately capture acoustic damping effects in a range of normal incidence conditions. The model was validated both for linear and non-linear damping regimes and in bias flows where inertial effects are dominant.  
The model of [PERSON] et al. [32] was, however, only validated for the normal incidence of a sound wave, consequently restricting the range of practical application. In this paper, the model is further extended to the following:  
* Where the noise signal propagates in parallel with a perforated liner without a mean flow;
* Where the noise signal propagates in parallel with a perforated liner in the presence of a mean bias flow;
* Where the noise signal propagates in parallel with a perforated liner in the presence of a mean grazing flow;
* Where the noise signal propagates in parallel with a perforated liner in the presence of coexisting bias and grazing flows;
* Where the grazing flow is of higher temperatures.
## 4 Vibration Characteristics for Bearing Clearance Monitoring
### Dynamic Force Analysis  
Considering that the dynamic force exhibited an impulse wave with a certain width in a contact cycle, without loss of generality, maximum force of the first ball was extracted under different clearance and load conditions. Figure 11a,b depict the dynamic forces under the load of 1600 N and the clearance of 10 \(\upmu\)m, respectively. Under the same load, the width of the dynamic force decreased with the clearances, while the magnitude increased with the clearances. Separately, under the same clearance, only the magnitude increased with the loads, while the width remained unchanged.  
To explore the influence of dynamic force on bearing life, the maximum of the dynamic force under all conditions is shown in Figure 12a. The results showed an uptrend in both directions. Compared with 0 \(\upmu\)m under each load, the increased proportion of the magnitude also showed an uptrend with the increase in clearances, as shown in Figure 12b. However, the proportion displayed an opposite trend with the increase in loads. This means that under relatively light load, the influence of clearances on dynamic force is more significant. Taking the load of 1600 N as an example, when clearances ranged from 0 to 100 \(\upmu\)m, the maximum dynamic force increased by about 30%. Such an increase can cause a reduction in life factor by about 30% [16], as the amplitude and profile of dynamic force significantly influence the bearing fatigue life [16; 32]. In this way, it could provide sufficient lead time for WT maintenance [33].  
\begin{table}
\begin{tabular}{r c c c c c c c c c} \hline \hline
**Bore Diameter** & \multicolumn{2}{c}{**C2**} & \multicolumn{2}{c}{**CN**} & \multicolumn{2}{c}{**C3**} & \multicolumn{2}{c}{**C4**} & \multicolumn{2}{c}{**C5**} \\
**d (mm)** & & **(\(\upmu\)m)** & & **(\(\upmu\)m)** & & **(\(\upmu\)m)** & & **(\(\upmu\)m)** & \\
**over Include** & **Min Max** & **Min Max** & **Min Max** & **Min Max** & **Min Max** & **Min Max** \\ \hline — & 2.5 & 0 & 6 & 4 & 11 & 10 & 20 & — & — & — \\
2.5 & 6 & 0 & 7 & 2 & 13 & 8 & 23 & — & — & — \\
6 & 10 & 0 & 7 & 2 & 13 & 8 & 23 & 14 & 29 & 20 & 37 \\
10 & 18 & 0 & 9 & 3 & 18 & 11 & 25 & 18
# Integrated Radar and Communications Waveform Design Based on Multi-Symbol OFDM
## 3 IRC Waveform Design Objective
### Pmepr  
The PMEPR is often used to measure the envelope fluctuations of waveforms. For a discrete-time IRC waveform \(s(q)\), the PMEPR is defined as the ratio of the maximum power to the average power [10], i.e.,  
\[\mathrm{PMEPR}_{s(q)}=\frac{\max\limits_{q\in\mathcal{T}}|s(q)|^{2}}{E[|s(q)| ^{2}]} \tag{9}\]  
where \(\mathcal{T}\) is the time interval over which the PMEPR is calculated, and \(E\big{[}|s(q)|^{2}\big{]}=P_{X}+\frac{1}{M}\sum\limits_{m=0}^{M-1}\sum\limits _{n\in\mathcal{R}}|C_{n,m}|^{2}\) is the average power of the waveform \(s(q)\), and \(P_{X}=\frac{1}{M}\sum\limits_{m=0}^{M-1}\sum\limits_{n\in\mathcal{R}^{c}}|X_{ n,m}|^{2}\).  
At the baseband, OFDM symbols sampled at the Nyquist rate have no equivalent PMEPR to consecutive symbols. Therefore, oversampling at least four times is usually required [10]. In this paper, the \(J\)-times oversampling operation is implemented by inserting zeros, i.e., inserting \((J-1)N\) zeros to the middle of \(X_{n,m}+C_{n,m}\), and the IDFT operation is applied to the extended vector \(X^{\prime}_{n,m}+C^{\prime}_{n,m}=[X_{-N/2,m}+C_{-N/2,m},\ldots,X_{-1,m}+C_{-1, m},\underbrace{0,\ldots,0}_{(J-1)Nzeros},X_{0,m}+C_{0,m},\ldots,X_{N/2-1,m}+C_{N/ 2-1,m}]\). For this case, the interval \(\mathcal{T}\) in (9) is \([0,MQ-1]\), where \(Q=JN\).  
A commonly used measure of the PMEPR is to consider the complementary cumulative distribution function (CCDF) defined as  
\[\mathrm{CCDF}=\mathrm{Pr}(\mathrm{PMEPR}>\zeta) \tag{10}\]  
where \(\zeta\) is the PMEPR threshold.  
The real and imaginary parts of the input communication symbol \(X_{n}\) are assumed to be independent and identically distributed with zero mean and variance \(\sigma^{2}\). Based on the central limit theorem, the real and imaginary parts of the initial waveform \(s_{X}(q)\) for large \(N\) (\(N\geq 64\)[37]) are independent and identically distributed Gaussian random processes with zero mean and variance \(\sigma^{2}\). Then its amplitude \(|s_{X}(q)|\) obeys the Rayleigh distribution, which means that the PMEPR of the initial waveform is large [11], as shown in Figure 3, where the CCDFs of the PMEPR for OFDM waveforms with different subcarrier numbers are shown. However, a PMEPR exceeding 11 dB is not practical and will negatively affect the performance of the IRC systems. Therefore, the PMEPR optimization of such a waveform is necessary and a topic of the paper.
## 5 Results and Discussion
### The Influence of the Constructive Parameters of the Shelf on the Profile of Gas Flow Velocities
The gas flow velocity in the outloading space reaches its maximum value at \(L_{cd}\)/\(L_{dev}\) = 0.15 for shelves with a perforation degree from 0% to 30%. If \(L_{cd}\)/\(L_{dev}\) < 0.15, the gas flow velocity in the outloading space decreases since the hydraulic resistance to the gas flow through the outloading space is increased so much that most of the flow passes through the holes of the shelf. If the shelf contact has a perforation degree of 0% (solid shelf), there is no redistribution, and the gas flow velocity in the outloading space continuously increases with reduction of \(L_{cd}\)/\(L_{dev}\) ratio (Figure 5, curve 1). A change in the constructive parameters of the shelf has a significant effect on the uneven profile of gas flow velocities. It is reasonable to represent its quantitative measure by the dimensionless coefficient of the gas flow uneven distribution \(n\), which is the ratio of the gas flow passing through the outloading space \(V_{o.s. }\) to its quantity in the holes of the shelf \(V\) (Figure 6). Figure 5: The dependence of the gas flow velocity in the outloading space on the constructive parameters of the shelf. Shelf perforation degree \(\psi\): 1–4—respectively, 0%, 5%, 15%, 30%. The tilt angle of the shelf—\(\gamma\) = 25\({}^{\circ}\). Gas flow velocity in the free cross-section—1.65 m/s. If the coefficient of the gas flow uneven distribution is more than 1, the gas flow passes mainly through the outloading space, and if less than 1--through the holes of the inclined shelf. If the coefficient of the gas flow uneven distribution is 1, the flow is distributed in equal amounts both through the outloading space and through the holes of the shelf.
## 3 Results
### Performance Evaluation of All Proposed Models  
Figure 4 illustrates the outcomes of the ROC curve analysis for the training and testing datasets for the purpose of differentiating _EGFR_. Tables 3 and 4 display the AUC values for all tested ML classifiers for the training and test sets, respectively. The AUCs for the SVM learning method were highest for the training dataset (0.977) and the test dataset (0.869). Therefore, in terms of group differentiation, the SVM classifier model offered the optimal performance. In terms of the ML classifiers, the following ranges were recorded for the _EGFR_ group in the training set: precision (0.63-0.98), recall (0.78-0.98), F1-score (0.70-0.98), and support (41). For the _EGFR_+ group, these ranges were precision (0.69-0.99), recall (0.70-0.98), F1-score (0.74-0.99), and support (95). The highest scores were recorded for the SVM learning technique (Table 5). Similarly, in the test set, the ranges for the _EGFR_ group were precision (0.38-0.80), recall (0.64-0.85), F1-score (0.44-0.82), and support (11). The ranges for the _EGFR_+ group were precision (0.74-0.88), recall (0.71-0.85), F1-score (0.55-0.87), and support (Table 6). The use of the SVM learning technique generated the highest scores (Table 7).  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Classifier** & **AUC** & **95\% CI** & **Sensitivity** & **Specificity** \\ \hline KNN & 0.658 & 0.47–0.84 & 0.50 & 0.67 \\ \hline SVM & 0.869 & 0.63–0.92 & 1.00 & 0.97 \\ \hline XGBoost & 0.758 & 0.61–0.84 & 0.00 & 0.93 \\ \hline RF & 0.725 & 0.62–0.82 & 0.00 & 1 \\ \hline LR & 0.708 & 0.66–0.86 & 0.25 & 0.9 \\ \hline DT & 0.583 & 0.45–0.72 & 0.00 & 0.97 \\ \hline \end{tabular}
\end{table}
Table 4: ROC results with six classifiers of the test set.  
Figure 4: The results for the ROC curve analysis for (a) the training and (b) test datasets to differentiate _EGFR_ mutation status are shown in the figure, including the AUC values for all tested ML classifiers for the training and testing sets. The AUCs of the SVM learning method were highest for both the training (0.977) and test datasets (0.869). Note that red and green indicate _EGFR_ wild-type and _EGFR_ mutant in the ROC curves, respectively.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Classifier** & **Training set** & **Test set** & **Classifier** & **Training set** & **Test set** \\ \hline \multirow{4}{*}{**EGFR-WT**} & \multirow{4}{*}{Precision} & \multirow{4}{*}{0.88} & \multirow{4}{*}{0.98} & \multirow{4}{*}{0.79} & \multirow{4}{*}{0.73} \\ \cline{2-2} \cline{5-6}  & & & & & \\ \cline{1-1} \cline{2-6}  & & & & & \\ \cline{1-1} \cline{2-6}  & & & & & \\ \cline{1-1} \cline{2-6}  & & & & & \\ \hline \multirow{4}{*}{**EGFR-WT**} & \multirow{4}{*}{0.86} & \multirow{4}{*}{0.98} & \multirow{4}{*}{0.76} & \multirow{4}{*}{0.80} & \multirow{4}{*}{0.98} \\ \cline{2-2} \cline{5-6}  & & & & & \\ \cline{1-1} \cline{2-6}  & & & & & \\ \cline{1-1} \cline{2-6}  & & & & & \\ \hline \end{tabular}
\end{table}
Table 5: The results of the four indicators—precision, recall, F1-score, and support—in the training set.
## 4 Discussion
### Barriers and Limitations  
There are some significant barriers and limitations to this review. These arise largely from large data gaps for certain livestock categories, a variety of non-standardized methodologies for accounting for energy use in livestock and agricultural systems, including the selection of functional units and system boundaries, and is compounded by the diversity and heterogeneity of livestock production systems. In this regard, for a more comprehensive and accurate understanding of energy use in livestock systems, there is a necessity to develop a standardized methodology and terminology for measuring, evaluating, and comparing with other studies on energy use on livestock farms. In our view, this is a prerequisite for further research on energy use research in livestock systems.  
Livestock, along with other sectors, will eventually move towards RES and high-efficiency technologies. While engineering this unavoidable transition, we also have to consider the way that the energy use is measured, calculated, and/or approximated and to whom the results are addressed. While LCA studies should be considered an indispensable tool in order to draw European and national policies in the livestock sector as whole, on-farm surveys, energy audits, and measurements should acquire a central role in EU countries. This will offer researchers, engineers, and farmers more tangible insight into on-farm energy use, enabling us to achieve the much-needed targeted interventions.  
In the context of a changing livestock system, the energy use profiles of livestock systems are expected to change considerably in the coming decades. From an animal welfare perspective, the BLE report on drivers of change and development in the EU livestock sector highlights that high intensity and stocking densities are neither sustainable nor desirable [35]. On a policy level, increasingly stringent emission and sustainability targets, along with the recent decisions at COP26 to decrease livestock-related emissions, support movements to more sustainable agricultural practices that reduce our reliance on fossil energy sources. Considering this, and in the context of the Green Deal, the Farm to Fork strategy [5], and the new common agricultural policy [81], considerable funds and support are expected to be made available to livestock farmers to transition away from fossil dependencies in the coming years [35].
# Time Series Forecasting Method Based on Multi-Scale Feature Fusion and Autoformer
## 3 Results
### Statistical Significance Analysis  
To verify the statistical significance of the model improvements, this study selected experimental results with the longest prediction horizon from each dataset: Apparel Sales  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{4}{c}{**Time Cost (s) on Different Datasets**} \\ \cline{2-5}  & **Apparel Sales** & **ILI** & **Exchange** & **Weather** \\ \hline MD–Autoformer & 1.134 & 0.512 & 22.671 & 192.809 \\ Autoformer & 1.082 & 0.493 & 19.342 & 182.560 \\ Informer & 0.568 & 0.291 & 8.197 & 67.081 \\ Reformer & 0.639 & 0.348 & 23.648 & 200.964 \\ DLinear & 0.046 & 0.026 & 0.247 & 2.882 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Comparison of average epoch time cost for Maximum Step Prediction Tasks on different datasets.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Dataset** & **Apparel Sales** & **ILI** & \multicolumn{2}{c}{**Exchange**} & \multicolumn{2}{c}{**Weather**} \\ \hline
**Metric** & **RMSE** & **MAE** & **RMSE** & **MAE** & **RMSE** & **MAE** & **RMSE** & **MAE** \\ \hline \(n=4\) & 2.403 & 0.922 & 1.330 & 0.784 & 0.583 & 0.411 & 0.530 & 0.325 \\ \(n=8\) & 2.396 & 0.920 & 1.354 & 0.791 & 0.601 & 0.436 & 0.541 & 0.330 \\ \(n=16\) & 2.389 & 0.914 & 1.318 & 0.777 & 0.591 & 0.420 & 0.549 & 0.336 \\ \(n=32\) & 2.424 & 0.938 & 1.343 & 0.786 & 0.612 & 0.434 & 0.568 & 0.345 \\ \hline \hline \end{tabular}
\end{table}
Table 9: MD–Autoformer performance under different choices of hyper-parameter \(n\) in the MSFFN. We adopt the forecasting setting as input-36-predict-48 for the ILI and Apparel Sales datasets, and input-96-predict-336 for the other datasets.  
(60 steps), ILI (60 steps), Exchange (720 steps), and Weather (720 steps). Paired \(t\)-tests were performed between MD-Autoformer and Autoformer to demonstrate the statistical significance of our improvements. The experimental data consisted of the MAE metric from 30 independent runs in each scenario.  
As shown in Table 10, MD-Autoformer achieves significantly lower MAE than Autoformer across all datasets. For the Apparel Sales and ILI datasets, the t-statistics are 57.63 and 47.91, respectively, with \(p\)-values less than the critical value \(\alpha\) = 0.01, indicating extremely significant differences. Similarly, for the Exchange and Weather datasets, the t-statistics are 20.70 and 20.95, respectively, also with \(p\)-values less than \(\alpha\) = 0.01. These results demonstrate that the improvements of MD-Autoformer over Autoformer are not only statistically significant but also highly reliable. The mean differences in MAE further confirm that MD-Autoformer provides more accurate forecasts than Autoformer.