esa-sceva/satcom-chunk-collection huggingface dataset:
## 1 Introduction
\begin{array}{ll} \left(\mu_{\mathcal{C}}(r)\wedge\mu_{\mathcal{C}}(s)\right)e^{i(\alpha_{ \mathcal{C}}(r)\wedge\alpha_{\mathcal{C}}(s))}&\text{if }\mu_{\mathcal{D}}(rs)e^{i\alpha_{ \mathcal{D}}(rs)}=0,\\ \left(\mu_{\mathcal{C}}(r)\wedge\mu_{\mathcal{C}}(s)\right)e^{i(\alpha_{ \mathcal{C}}(r)\wedge\alpha_{\mathcal{C}}(s))}-\mu_{\mathcal{D}}(rs)e^{i\alpha _{\mathcal{D}}(rs)}&\text{if }0<\mu_{\mathcal{D}}(rs)e^{i\alpha_{ \mathcal{D}}(rs)}\leq 1.\end{array} \right.\)__  
\[\overline{\
u_{\mathcal{D}}(rs)e^{i\beta_{\mathcal{D}}(rs)}}=\left\{ \begin{array}{ll} \left(\
u_{\mathcal{C}}(r)\vee\
u_{\mathcal{C}}(s)\right)e^{i(\beta_{ \mathcal{C}}(r)\vee\beta_{\mathcal{C}}(s))}&\text{if }\
u_{\mathcal{D}}(rs)e^{i\beta_{ \mathcal{D}}(rs)}=0,\\ \left(\
u_{\mathcal{C}}(r)\vee\
u_{\mathcal{C}}(s)\right)e^{i(\beta_{ \mathcal{C}}(r)\vee\beta_{\mathcal{C}}(s))}-\
u_{\mathcal{D}}(rs)e^{i\beta_{ \mathcal{D}}(rs)}&\text{if }0<\
u_{\mathcal{D}}(rs)e^{i\beta_{ \mathcal{D}}(rs)}\leq 1.\end{array} \right.\]  
**Example 4**. : _Consider a CPFG \(\mathcal{G}=(\mathcal{C},\mathcal{D})\) on \(C=\{s_{1},s_{2},s_{3},s_{4}\}\), as in Figure 3, defined by:_  
\[\mathcal{C} = \left\langle\left(\frac{s_{1}}{0.7e^{i2\pi(0.8)}},\frac{s_{2}}{0.8e^{i2\pi(0.7)}},\frac{s_{3}}{0.6e^{i2\pi(0.6)}},\frac{s_{4}}{0.9e^{i2\pi(0.7) }}\right),\left(\frac{s_{1}}{0.4e^{i2\pi(0.6)}},\frac{s_{2}}{0.3e^{i2\pi(0.5)}},\frac{s_{3}}{0.5e^{i2\pi(0.3)}},\frac{s_{4}}{0.2e^{i2\pi(0.4)}}\right)\right\rangle,\] \[\mathcal{D} = \left\langle\left(\frac{s_{1}s_{4}}{0.2e^{i2\pi(0.4)}},\frac{s_{2 }s_{4}}{0.8e^{i2\pi(0.7)}},\frac{s_{3}s_{4}}{0.3e^{i2\pi(0.2)}}\right),\left( \frac{s_{1}s_{4}}{0.3e^{i2\pi(0.5)}},\frac{s_{2}s_{4}}{0.3e^{i2\pi(0.5)}}, \frac{s_{3}s_{4}}{0.4e^{i2\pi(0.3)}}\right)\right\rangle.\] \[\left(0.7e^{i2\pi(0.8)},0.4e^{i2\pi(0.6)}\right)\]  
Figure 3: Complex Pythagorean fuzzy graph. **Theorem 1**: _The complement of a complement of CPFG is a CPFG itself, that is, \(\overline{\overline{\mathcal{G}}}=\mathcal{G}\)._  
Suppose that \(\mathcal{G}\) is a CPFG.
# FCN-Based 3D Reconstruction with Multi-Source Photometric Stereo
## 2 Materials and Methods
### Loss Function  
With the U-shaped network based on the code-decode structure, it was easy to lose some details in the training process, and the result of the final output 3D reconstruction was not accurate enough. We propose a loss function which is suitable for the task optimization based on our network structure--that is, we add two regularization constraints on the basis of the L2 loss function, and the training loss for each sample is set to  
\[L_{depth}=\|Z-\overline{Z}\|^{2}+\lambda\|I-\overline{I}\|^{2}, \tag{2}\]  
where \(Z\) and \(\overline{Z}\) denote the predicted depth and the ground truth, and respectively, \(I\) and \(\overline{I}\) are the predicted RGB images and the original RGB images. \(\lambda\) is a custom parameter. Here, we have set it to \(1\times 10^{4}\). As described in Section 2.2, our network structure reconstructed the original image of the corresponding light source while predicting the depth value. In the previous experiments, we found that training the network with L2 loss alone can make the network converge, but its reconstruction effect was not good enough. The defect area of the samples had different reflective characteristics under different angles of light, which was an unavoidable phenomenon in the use of the Photometric Stereo method to solve the three-dimensional reconstruction problem. Therefore, the reconstruction results obtained by simply optimizing the depth of each pixel were largely affected by the highlights in the RGB images, and it was not easy to obtain reasonable reconstruction results. Using two regularization constraints, that is, based on the original depth value as the goal of optimization, the original image is also the optimization goal of the network, which could play the role of additional constraints in the network training so as to weaken the influence of the highlight in the input images and make the reconstruction results closer to the real situation. By minimizing the sum of the deviations between the two prediction targets and the GT, our new loss function could improve the effectiveness of feature extraction. Compared with simply predicting the depth value of each pixel position and calculating their loss, this operation, similar to the image restoration, could help correct the prediction results of the network. In Section 4.2, we further evaluate the effectiveness of our new loss function.
## 3 Methodology
### MSWT-DN Structure  
#### 3.2.1 Introduction to Network Components  
The MSWT-SSIDA architecture proposed in this paper combines several specially designed components, each of which has a unique contribution to the rain removal process. Despite the complexity of the architecture, each component works independently and collaborates in a complementary manner to improve the overall performance. The modular design ensures that each component can be optimized independently, allowing for greater flexibility and maintainability in the system. As shown in Figure 2, the entire network consists of four main modules:  
RSENet: this component is responsible for extracting the rain traces, helping the network to focus on the most relevant features for processing by subsequent modules. By separating the high-frequency rain trace portion through wavelet transform, RSENet accurately generates an approximate rain trace map, which provides key inputs for the deraining process.  
IMARM: feature fusion and reconstruction through multi-scale attention mechanism enhances the network's ability to extract features at different scales and improves the robustness of the network, especially when dealing with complex backgrounds. The IMARM enhances the ability to recognize rain trace regions by capturing details at different scales.  
U-Former: based on the Swin Transformer structure, it improves the feature extraction ability, especially when dealing with long-distance dependencies in the image, and further improves the accuracy of rain removal. The introduction of U-Former enables the network to effectively capture the global context information in the image, and improves the network's ability to deal with a wide range of rain marks.  
DRANet: removes rain traces while restoring the details of the image's background through spatial and channel attention mechanisms, avoiding the loss of background information. DRANet ensures the restoration of the background details while suppressing the interference in the rain trace region through residual learning and attention mechanisms.  
In summary, each module divides and collaborates with different functions to finally form an efficient rain removal network. Although the MSWT-SSIDA architecture contains multiple modules, its modular design makes it possible to optimize each module independently, thus improving the efficiency and maintainability of the whole system.  
Figure 2: Structure of MSWT-DN.
## Appendix: Ito Formula, Linear Solutions of SDEs and a Remark on Nonlinear Versions  
The above-mentioned algorithm is based on the fundamental theorem of stochastic calculus, also known as Ito Lemma or Ito Formula. Its proof can be found in e.g. [2, 8] and many other basic texts, and it traces back to its original [7].  
**Theorem 1**.: _Assume that \(F\in C^{1,2}([0,T]\times\mathbb{R}^{d})\) and \(X\) satisfies the Ito SDE (1). Then \(Y=F(t,X(t))\) satisfies (a.s.) the Ito SDE_  
\[dY = \mathcal{L}^{0}F(t,X(t))dt+\sum_{j=1}^{m}\mathcal{L}^{j}F(t,X(t) )dW_{j}(t) \tag{14}\]  
_on \(0\leq t\leq T\), where the differential operators \(\mathcal{L}^{0}\) and \(\mathcal{L}^{j}\) are defined as in (2) and (3), respectively._  
As seen in previous sections, the presented algorithm is based on transformations to linear systems of SDEs. The solutions of linear equations of SDEs  
\[dX(t) = (a_{0}+a_{1}X(t))dt+\sum_{j=1}^{m}(b_{0}^{j}+b_{1}^{j}X(t))dW_{j}(t) \tag{15}\]  
are well-known (see [2]).  
**Theorem 2**.: _The unique strong solution \(X\in\mathbb{R}^{d}\) satisfying the linear Ito SDE (15) with real constants \(a_{0}\), \(a_{1}\), \(b_{0}^{j}\) and \(b_{1}^{j}\in\mathbb{R}^{1}\) is given by_  
\[X(t) = \varphi(t)\left(X(0)+(a_{0}-\sum_{j=1}^{m}b_{0}^{j  
**Remark 1**.: _An extension of the algorithm to a nonlinear-PDE-based version is conceivable and subject to future research. For example, Equation (4) in step [1] and (5) in step [2] can be substituted by nonlinear systems of PDEs_  
\[\mathcal{L}^{0}F=G_{0}(t,x,F),\quad\mathcal{L}^{j}F=G_{j}(t,x,F) \tag{17}\]  
_with appropriate nonlinear functions \(G_{0}\) and \(G_{j}\), respectively. However, to find explicit expressions for common solutions \(F\) of \(m+1\)-dimensional systems of nonlinear PDEs such as (17) (i.e. \(G_{0}\) or \(G_{j}\) nonlinear in \(F\), \(j=1,2,...,m\)) seems to be an extremely difficult field of research._  
(c) 2010 by the author; licensee MDPI, Basel, Switzerland. This article is an Open Access article distributed under the terms and conditions of the Creative Commons Attribution license: [[http://creativecommons.org/licenses/by/3.0/](http://creativecommons.org/licenses/by/3.0/)]([http://creativecommons.org/licenses/by/3.0/](http://creativecommons.org/licenses/by/3.0/)).
## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c} \hline \multicolumn{5}{c}{**Function at Group Centroids**} \\ \hline \multirow{2}{*}{**Botanical Origin**} & \multicolumn{4}{c}{**Function**} \\ \cline{2-5}  & **1** & **2** & **3** & **4** \\ \hline Fir & \(-10.623\) & \(-5.151\) & \(-11.559\) & \(2.967\) \\ \hline Pine & \(-2.250\) & \(4.176\) & \(-0.549\) & \(-3.841\) \\ \hline Erica & \(21.424\) & \(-8.579\) & \(0.103\) & \(0.008\) \\ \hline Thyme & \(0.918\) & \(7.740\) & \(2.879\) & \(4.136\) \\ \hline Cotton & \(-19.655\) & \(-14.369\) & \(8.287\) & \(0.265\) \\ \hline Eigenvalue & \(574.123\) & \(255.991\) & \(42.905\) & \(24.068\) \\ \hline \% Variation & \(58.9\) & \(25.5\) & \(10.8\) & \(4.8\) \\ \hline \% Cumulative variation & \(58.9\) & \(84.4\) & \(95.2\) & \(100.0\) \\ \hline \end{tabular}
\end{table} 
Table 2: Eigenvalues, variation (%), cumulative variation and functions at group centroids exported by SLDA. Figure 4: Discrimination of monoflorl honey types based on their volatile compound participation, after applying discriminant analysis. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Botanical**} & \multicolumn{5}{c}{**Predicted Group Membership**} \\ \cline{3-8}  & **Origin** & **Fir** & **Pine** & **Erica** & **Thyme** & **Cotton** & **Total** \\ \hline \multirow{8}{*}{Original (\%)} & Fir & 100.0 & 0 & 0 & 0 & 0 & 100.0 \\ \cline{2-8}  & Pine & 10.5 & 84.2 & 0 & 0 & 0 & 100.0 \\ \cline{2-8}  & Erica & 0 & 0 & 100.0 & 0 & 0 & 100.0 \\ \cline{2-8}  & Thyme & 0 & 0 & 0 & 100.0 & 0 & 100.0 \\ \cline{2-8}  & Cotton & 0 & 0 & 0 & 0 & 100.0 & 100.0 \\ \hline \multirow{8}{*}{
\begin{tabular}{c} Cross-validated \\ (\%) \\ \end{tabular} } & Fir & 83.3 & 16.7 & 0 & 0 & 0 & 100.0 \\ \cline{2-8}  & Pine & 10.5 & 84.2 & 0 & 5.3 & 0 & 100.0 \\ \cline{2-8}  & Erica & 0 & 0 & 100.0 & 0 & 0 & 100.0 \\ \cline{2-8}  & Thyme & 0 & 0 & 0 & 100.0 & 0 & 100.0 \\ \cline{2-8}  & Cotton & 0 & 0 & 0 & 0 & 100.0 & 100.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Classification results (original and cross-validated) extracted from the prediction model after applying SLDA analysis.
## 5 Approaches to Improve Biofilm-Based Wastewater Treatment
### Enhanced Biofilm Adhesion and Performance by Exploiting EPSs  
There are different properties of biofilms that are currently exploited for the enhancement of biofilm technology in WWTPs, such as EPSs. The compositions of EPSs differ depending on the medium that the biomass grows into. The EPS is normally made up of exopolysaccharides, DNA, and proteins. The microorganisms that grow in the center of the biofilm tend to be the microorganisms that are anaerobic, while the ones that grow on the outer surface are aerobic microorganisms [65]. The biofilm is normally enhanced by modifying the surfaces such that they are ideal for biomass attachment. When the microbes grow into a biofilm, they produce a complex high-molecular-weight protective layer known as an EPS. Microorganisms in biological wastewater treatment grow as biofilms, sludge flocs, and granules, and are protected by an EPS that forms a three-dimensional defensive layer against external stresses. Usually, the EPS forms 50-80% of the overall biomass weight. The EPS is a mixture of polymers, made up of polysaccharides, uronic acids, nucleic acids, proteins, humic acids, and lipids. The EPS accumulates through different mechanisms, comprising excretion, secretion, cell lysis, and sorption [66].  
EPSs have been shown to enhance biofilms; thus, some studies have used them as coatings for carriers to improve the biofilm attachment, thereby enhancing the efficiency of the biological wastewater treatment [6]. The film coating of carriers has been carried out using molecules that are similar to EPS molecules, such as glucuronic acid. Dextran has also been shown to be great for coating, particularly for the promotion of nitrifying bacteria such as _Bacillus subtilis_. Pre-seeding has also been said to enhance the attachment of certain anammox microorganisms. Furthermore, the carrier topography has been shown to play an important role in biofilm adhesion and formation. Thus, there have been researchers that have investigated the use of rough materials to coat carriers. The materials such as activated carbon, silica, and charcoal have been shown to increase the surface area for the attachment of anammox bacteria [9].
# Urban CO2 Budget: Spatial and Seasonal Variability of CO2 Emissions in Krakow, Poland
## 3 Results and Discussion  
### Soil Emissions of CO\({}_{2}\)  
The seasonal variability of CO\({}_{2}\) emissions from soils reflects changes in soil respiration intensity throughout a year. The highest fluxes of CO\({}_{2}\) from the soil were recorded at all four sites during summer (Figure 4). In winter, emissions were substantially lower, indicating that processes of CO\({}_{2}\) production in the soil were slowed down but not completely stopped. The highest emissions of CO\({}_{2}\) were recorded at site S2 (large meadow in the city center), which is consistent with the highest carbon concentration in the soil at this site. As expected, no significant difference was observed in the recorded emissions from soils within the city and at suburban site. The soil CO\({}_{2}\) emissions depend on soil type and its respiration intensity, and are not directly related to the extent of urbanization. Changes of respiration intensity are mostly driven by two factors: soil temperature and its water content [11]. The exponential dependence of CO\({}_{2}\) flux on the soil temperature has been confirmed, with strongest soil temperature sensitivity (Q\({}_{10}\) coefficient) found for the S2 site. The Q\({}_{10}\) values varied from 1.59 \(\pm\) 0.36 for S1 site (lawn separating two traffic lanes of the busy street), to 1.96 \(\pm\) 0.35 for S2 site, within the range reported in the literature [11]. Among the sites studied in Krakow, the only one with undisturbed soil is S2, where the highest carbon content was measured. The effect of soil moisture content on soil respiration intensity has been observed at all sites, with maximum CO\({}_{2}\) fluxes measured for soil water contents varying between 27% and 32%.  
The seasonal variability of soil CO\({}_{2}\) emissions has been widely studied in various climatic zones. At mid-latitude areas, the maximum CO\({}_{2}\) emissions occurred during summer, and the minimum during the winter months, reflecting the seasonal changes of the respiration activity of the biosphere. This general trend was confirmed in Krakow, with all-sites average CO\({}_{2}\) efflux equal to \(7.51\pm 071\) umol m\({}^{-2}\) s\({}^{-1}\) during summer (June to August) and \(1.77\pm 0.26\) umol m\({}^{-2}\) s\({}^{-1}\) during winter (December to February) (Figure 4). The obtained results are comparable with other studies conducted at mid latitudes: the annual mean flux density from grasslands in the temperate climate was estimated at \(442\pm 78\) gC m\({}^{-2}\)[11], to be compared with the mean value obtained in this study equal \(424\pm 43\) gC m\({}^{-2}\) per year.
# Renyi Entropy-Based Adaptive Integration Method for 5G-Based Passive Radar Drone Detection
## 4 Practical Challenge--Content Dependency and Possible Approaches to Its Analysis
### Root-Mean-Square Signal Bandwidth  
A slightly different approach than the one presented in Section 4.1 is to determine the effective operating bandwidth based on the power spectral density (PSD) of the signal [21]. In the cited work, this method was used to analyze the root mean square (RMS) of an FM signal, which has a different nature than a 5G signal but is content-dependent as well. The calculation uses the following formula:  
\[B\cdot A_{\mathrm{max}}=\int A(f)\mathrm{d}f, \tag{4}\]  
where \(B\) is the effective signal bandwidth, \(A(f)\) is the PSD and \(A_{\mathrm{max}}\) is its maximum value. Based on (4), the effective bandwidth was calculated for several fragments of real-life data, with different data link occupation. Periodograms, along with spectrograms of signal samples, are shown in Figure 11. The results presented here show that effective bandwidth can even decrease with an increase in link occupancy.  
The bandwidth of the 5G signal, in the analyzed example, is 38.16 MHz, but the values calculated using the discussed method are much lower. A small effect of data link occupancy on the determined effective bandwidth can also be observed here. The method is sensitive to the presence of peaks and PSD distortions, hence the results obtained may be  
Figure 11: Evaluation of RMS effective bandwidth method. Spectrograms and PSD plots for different amount of content in real-life 5G signal. (**a**) Spectrogram for almost no content. (**b**) PSD for almost no content. (**c**) Spectrogram for medium amount of content. (**d**) PSD for medium amount of content. (**e**) Spectrogram for large amount of content. (**f**) PSD for large amount of content.  
ambiguous. Another limitation of the analyzed method is the fact that 5G signal generation is based on the OFDM technique, which in this case provides a rectangular shape of the signal spectrum envelope. This is a definite difference compared with FM modulation. Another problem in the application of this method is the large bandwidth of the 5G signal and the vulnerability of the shape of its spectrum to distortion due to radio propagation. In order to eliminate the impact of these phenomena, it would be necessary to equalize the channel in all OFDM symbols, which is impossible to implement in practice. Hence, the possibility of using a method based on estimating the effective bandwidth of the signal to select time moments for PCL processing is marginal.
# Hybrid Power System Design for Multifunctional Mini-Loader Vehicles
## 1 Introduction
Despite the fact that the hybrid power can meet the demand of green energy, the mini-loader vehicles and typical hybrid vehicles have large differences includes the structure, transmission, weight range, load, and energy consumption. The mini-loader vehicles use a hydraulic system to drive the working devices, the load varies greatly during working operation, and energy consumption characteristics are more complex. Therefore, the previous researches of typical hybrid vehicles cannot be directly applied to mini-loader vehicles. The multifunctional mini-loader vehicle with a hybrid power system is a feasible solution for the powertrain development with higher fuel efficiency, less energy use, and emissions. However, existing commercial mini-vehicle systems are insufficient to cope with the increasingly demanding multifunctional requirements and high energy efficiency. Most importantly, when power is supplied only by the ICE, not only are the systems prone to generating a large amount of greenhouse gases, but they also cause air pollution in a confined space, which is harmful to the operators. Mini-vehicles are limited to the space requirement of the operation. Not exceeding the volume specification after incorporating the electric motor (EM), battery, and motor module is an important challenge for the machine design. Therefore, considering the need to replaceable tool functions, increase the amount of available energy, reduce greenhouse gas emissions, and create a user-friendly work environment while maintaining a certain volume requirement, the goal of this study was to design a mini-loader vehicle using gas-electric hybrid power system. The three design requirements for the multifunctional mini-loader vehicle are as follows: first, emissions from fossil fuel combustion can cause harmful pollution to the environment, humans, and even crops. Therefore, energy-saving and carbon reduction have become important indices of the power system design of vehicles. Second, with the rise of greenhouse planting and indoor agricultural planting, mini-car bodies are needed to travel through narrow entrances and operate in indoor spaces. Finally, the capabilities of this loader should be extended to disaster relief and civil engineering to clear road obstacles and climb barriers, increasing its value and usage.
# Pollen-Food Allergy Syndrome: Allergens, Clinical Insights, Diagnostic and Therapeutic Challenges
## 2 Food Allergens  
Food allergens are classified into class I and class II allergens based on their stability, source, and immunological properties [40]. Class I allergens are typically heat- and digestion-stable proteins found in foods such as nuts, shellfish, and eggs. These allergens are capable of sensitizing individuals through the gastrointestinal tract and are often associated with systemic and severe allergic reactions, including anaphylaxis. Their resilience to thermal processing and enzymatic digestion allows them to retain their allergic properties even after cooking, making them a significant concern for individuals with food allergies [41].  
In contrast, class II allergens are heat- and digestion-labile proteins that are often homologous to pollen allergens. These allergens, such as PR-10 proteins, profilins, and lipid transfer proteins (LTPs), are the ones commonly implicated in PFAS. They are primarily responsible for localized allergic reactions, which typically manifest as itching or swelling in the mouth and throat after consuming raw plant-based foods. The labile nature of class II allergens means that they generally lose their allergenity when foods are cooked or processed, reducing the risk of severe systemic reactions in most cases [42]. Class II allergens are proteins that typically do not cause primary sensitization through the gastrointestinal tract but instead trigger allergic reactions due to cross-reactivity with aeroallergens (such as pollen) that have already sensitized the immune system. This means that an individual first develops an allergic response to an aeroallergen, such as birch pollen, which contains proteins structurally similar to those found in certain foods [33; 43].  
The distinction between class I and class II allergens is clinically significant, as it informs both the diagnosis and management of food allergies. Class I allergens often necessitate strict avoidance and emergency preparedness for anaphylaxis, while class II allergens may allow for dietary flexibility with processed or cooked forms of the triggering foods [33]. Advances in component-resolved diagnostics have further enhanced the ability to classify allergens accurately, enabling personalized approaches to allergy care that consider the unique properties of these allergenic proteins. Understanding the differences between these allergen classes is crucial for developing targeted therapies and improving the quality of life for individuals with food allergies.