esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 The Christoffel Equation and the Use of Slowness Curves  
The Christoffel equation is critical to the flexibility and strength of the partial-wave method. The Christoffel equation can be derived by assuming a plane wave (Equation (4)) propagating in a solid elastic media (Equations (1)-(3)).  
\[\sigma_{ij,j}=\rho u_{i,tt} \tag{1}\]  
\[\sigma_{ij}=C_{ijkl}\epsilon_{kl} \tag{2}\]  
\[\epsilon_{ij}=\frac{1}{2}\big{(}u_{i,j}+u_{j,i}\big{)} \tag{3}\]\[u_{i}(x,y,z,t)=U_{i}e^{i(-k_{j}r_{j}+\omega t)} \tag{4}\]  
Here \(\sigma_{ij}\), \(\epsilon_{ij}\), and \(u_{i}\) are the stress, strain, and displacement; \(\rho\) and \(C_{ijkl}\) are the mass density and elastic stiffness; \(k_{j}\) and \(\omega\) are the wave vector and angular frequency; \(i,j,k,l=x,y,z\), and \(t\) is the time variable. When combined, Equations (1)-(4) yield the Christoffel equation:  
\[C_{ijkl}k_{k}U_{l}k_{j}-\rho\omega^{2}U_{i}=0 \tag{5}\]  
When Equation (5) is solved, a slowness curve/surface can be calculated and plotted in an inverse phase velocity space.
## 4 Experimental Results
### The Effect of the Number of Inputs Shared by Adjacent Submodules on the DNFS  
The target of this section is to explore the performance of the DNFS with different shared inputs on the first three datasets.  
As shown in Tables 5-7, DNFS5-2 had the minimum MAE, RMSE, and SMAPE on the three test datasets, which indicated that the best prediction accuracy can be achieved by DNFS5-2. As shown in Figure 4, it can be seen obviously that DNFS5-2 achieved the best fitting effect on the three test datasets among the three cases.  
Based on the experimental results obtained, it also can be found that the structures of DNFS5-0 and DNFS5-1 were simpler than DNFS5-2. There is no doubt that the more shared inputs there are, the more layers and submodules will be under the same submodule inputs. Consequently, DNFS5-2 had the most layers, submodules, and parameters on average, which led to its poor AIC value.  
On average, DNFS5-0, DNFS5-1, and DNFS5-2 spent 60.02 s, 49.93 s, and 70.84 s on the three test datasets. Therefore, DNFS5-1 is the most efficient method, followed by DNFS5-0 and DNFS5-2.  
As the comprehensive performance was taken into consideration, the superiority of DNFS5-2 is shown obviously. The score of DNFS5-2 was the highest among the three DNFSs, which can resolve the high-dimensional data within a valid period of time. On the whole, DNFS without shared input had a simpler structure, and that with two shared inputs had better prediction accuracy.
## 5 Results and Discussion
### Patch-Level Interpolation Performance  
We first evaluate the patch-level interpolation performance of the proposed scheme for four patches corresponding to different dynamical modes as illustrated in Figure 2 located in the area (5\({}^{\circ}\) E to 75\({}^{\circ}\) E and latitude 25\({}^{\circ}\) S to 55\({}^{\circ}\) S). In Table 1, we report the interpolation performance in terms of root mean square error (RMSE) for the proposed EOF NN-based scheme (NNKF-EOF) and include a comparison to the local analog data assimilation (LAF-EnKF). With a view to specifically analyzing the relevance of NN-based parametric covariance model, we also apply an ensemble Kalman filter with the trained dynamical model \(\mathcal{F}^{\mathcal{P}_{s}}\). The reported results clearly illustrate the relevance of the proposed NN-based scheme for the assimilation of a single patch. The proposed NN-based scheme, which combines a NN-based formulation of the mean forecasting operator and of the associated covariance pattern, slightly outperforms the ensemble Kalman filters, while also significantly reducing the computational complexity induced by the generation of ensembles of size 500.
# Achievable Rate of NOMA-Based Cooperative Spectrum-Sharing CRN over Nakagami-\(m\) Channels
## 4 Achievable Rate Analysis
### Ergodic Achievable Rates
Substituting \(I_{4}\) in (36), we obtain  
\[\bar{R}_{s,k}^{\text{NOMA}} =\frac{\left(\frac{m_{22}}{\overline{\kappa}\,\overline{\gamma}_{ sk}}\right)}{2\text{ln}(2)\Gamma(m_{22})}\frac{1}{\left(2\pi\iota\right)^{2}} \int_{\mathfrak{L}_{1}}\int_{\mathfrak{L}_{2}}\frac{\Gamma(1+s)\Gamma(-s)^{2}} {\Gamma(1-s)}\] \[\quad\times\Gamma(m_{22}-1+t)\Gamma(-1+t)\Gamma(1-s-t)\] \[\quad\times\left(\frac{\alpha_{k}}{\bar{\pi}}\right)^{-s}\bigg{(} \frac{m_{22}}{\bar{\kappa}\overline{\gamma}_{sk}}\bigg{)}^{-t}ds\,dt. \tag{38}\]  
It is now convenient to represent the above expression in terms of a bivariate Fox's H-function \(H_{E,(A;C),F,(B;D)}^{L,N,N_{1},M,M_{1}}[\cdot]\) as ([25], Equation (2.2.1))  
\[\bar{R}_{s,k}^{\text{NOMA}}=\frac{\left(\frac{m_{22}}{\bar{\kappa}\, \overline{\gamma}_{sk}}\right)}{2\text{ln}(2)\Gamma(m_{22})}\] \[\quad\times\,H_{1,(0,0),0,(2;2)}^{1,1,0,1,2}\hskip-14.226378 pt \left[ \begin{array}{c}(1,1)\\ \frac{m_{22}}{\overline{\kappa}\,\overline{\gamma}_{sk}}\end{array} \right] \hskip-14.226378 pt\left[ \begin{array}{c}(1,1)\\ (1,1),(0,1)\end{array} \hskip-14.226378 pt\underbrace{\hskip 14.226378 pt(1,1), \hskip-14.226378 pt\hskip 14.226378 pt\hskip 14.226378 pt\hskip 14.226378 pt\hskip 14.226378 pt \hskip 14. \[\bar{R}_{s,K}^{\text{NOMA}} = \frac{\left(\frac{m_{22}}{k^{7}\gamma_{sk}}\right)}{2\ln(2)\Gamma(m_ {22})} \tag{40}\] \[\times \ G_{1,(0,0),0,(2;2}^{1,1,0,1,2}\left(\frac{\frac{\alpha_{k}}{k}}{ \frac{m_{22}}{k\gamma_{sk}}}\left| \begin{array}{c}1;\dfrac{1}{1}\\ 1,0;-1,m_{22}-1\end{array} \right.\right).\]  
The bivariate Meijer's G-function can be evaluated by expressing it in the form of double Mellin-Barnes-type integrals by selecting suitable contours in the complex planes. For the \(k^{\text{th}}\) SR having an instantaneous rate given by (8), we follow the same steps using (20) and (21) to obtain the ergodic achievable rate \(\bar{R}_{s,K}^{\text{NOMA}}=\mathbb{E}\{R_{s,K}^{\text{NOMA}}\}\) as  
\[\bar{R}_{s,K}^{\text{NOMA}}=\frac{1}{\ln(2)\Gamma(m_{22})}G_{3,2}^{1,3}\left( \frac{\overline{\gamma}_{sk}}{m_{22}}\left| \begin{array}{cc}1,&1,&1-m_{22} \\ 1,&0\end{array} \right.\right). \tag{41}\]  
**Ergodic Achievable Rate at the PR when ST is silent**: The ergodic achievable data rate at the PR, denoted by \(\bar{R}_{p}^{\text{ST-silent}}=\mathbb{E}\{R_{p}^{\text{ST-silent}}\}\), during the silent mode can be determined using (9) and following the same steps using (20) and (21) to obtain  
\[R_{p}^{\text{ST-silent}}=\frac{1}{\ln(2)\Gamma(m_{0})}G_{3,2}^{1,3}\left( \frac{\overline{\gamma}_{p}}{m_{0}}\left| \begin{array}{cc}1,&1,&1-m_{0}\\ 1,&0\end{array} \right.\right). \tag{42}\]  
Note that when the ST is silent, we have \(R_{s,k}^{\text{ST-silent}}=0\ \forall k\).
## 3 Results
This is mainly due to the small refractive index difference between Si\({}_{3}\)N\({}_{4}\) and gain polymer materials, thus resulting in a smaller overlapping integration factor than the SOI slot waveguide. While the main advantage of preparing EYCDWA using a Si\({}_{3}\)N\({}_{4}\) slot waveguide was the small transmission loss of the waveguide, a long waveguide could be used to improve the gain. At present, the minimum loss of the Si\({}_{3}\)N\({}_{4}\) slot waveguide measured was approximately 3 dB/cm, the optimized length of the device was 6 cm, and the net gain obtained was approximately 8.2 dB. The doped Er\({}^{3+}\) concentration will be further improved, and the optimum length of the waveguide will be shortened. Under the optimized conditions above, we simulated the gain characteristics of Si\({}_{3}\)N\({}_{4}\) slot waveguide amplifiers with different slot widths, as shown in Figure 9c. The figure shows that the smaller the slot width, the smaller the pump threshold power is, which was associated with the A\({}_{\text{eff}}\) of the waveguide. When the pump power was less than 300 mW, the gain increased with W\({}_{\text{S}}\). Additionally, the gain values corresponding to each slot width were nearly overlapped as the pump power continued to increase. Therefore, the optimized range of W\({}_{\text{S}}\) was relatively larger. In this paper, considering polymer packing and transmission loss, the W\({}_{\text{S}}\) with 200 nm was selected as the optimized width. Figure 9d shows the gain versus pump power for different W\({}_{\text{r}}\)s. Within this width range, the gain curves of each device almost completely coincided, mainly due to W\({}_{\text{r}}\) not having direct effects on the light field. Within the W\({}_{\text{r}}\) range of 300 nm to 450 nm, the gain presented minor variations. This feature provides convenient conditions for preparing devices and allows certain process tolerances.
## 2 Input Modalities: CT or X-ray  
### Clinical Perspective  
An early study (March 2020) pointed out that fever, cough, mylalgia, fatigue, expectoration, and dyspnea are the main clinical symptoms of COVID-19 patients [24]. These symptoms can be used to diagnose COVID-19. However, later research shows that many infected patients (estimated as at around 20%) can be asymptomatic, and that those asymptomatic patients play an important role in the transmission of COVID-19 [25; 26; 27]. Real-time RT-PCR has proven to be a much more effective way to diagnose COVID-19, but it still has the risk of false-negative and false-positive results [28].  
To solve this issue, medical imaging (CT or X-ray)-based diagnoses can be used as a complementary method to correct false-negative RT-PCR tests. In February 2020, a group from China [29] found that some patients with positive chest CT findings may present with negative results of RT-PCR tests for COVID-19. CT patterns of COVID-19 includes Ground-Glass Opacities (GGO), vascular enlargement, bilateral abnormalities, lower lobe involvement and posterior predilection [30]. [PERSON] et al. [31] reported that the sensitivity of CT-based diagnosis was greater than that of RT-PCR (98% vs. 71%). Meanwhile, chest X-ray imaging has also proven to be an effective tool for diagnosing COVID-19 [32]. [PERSON] et al. [33] showed that there are several commonly observed features in chest X-ray images, including lung consolidations, GGO, nodules and reticular-nodular opacities. [PERSON] et al. [32] showed that nearly half of COVID-19 patients have abnormal chest X-ray findings, and that GGO in lower lobes is the most common finding. Some typical examples of COVID-19 CT and X-ray features can be found in Figure 2.  
At present, a (repeated) RT-PCR test is the most commonly adopted COVID-19 diagnosing approach due to its scalability and relatively high sensitivity. Medical imaging-based diagnosis is used as a complementary method to the RT-PCR test. Comparing CT and X-ray-based diagnoses, a CT-based diagnoses are much more accurate (and even better than RT-PCR) but much more expensive, whereas X-ray-based diagnoses are less accurate but less expensive [34; 35; 36].
## 3 Optically Pumped Probe Design
### Electronics Unit Design
#### 3.2.3 RF Excitation Circuit  
The light source of the optically pumped probe is an electrodeless cesium discharge lamp, which is ignited by a high-frequency excitation source provided by the excitation circuit. This circuit must satisfy the requirements of the excitation frequency and maintain stable output power. A schematic diagram of the circuit is shown in Figure 11. The circuit primarily consists of a voltage-controlled oscillator and an RF power amplifier. The voltage-controlled oscillator can change the operating frequency by controlling the voltage, and the RF power amplifier can adjust the RF output power through gate voltage.
## 7 Discussion
### Contribution Benefits and Implications  
In the final segment of this discussion, it's essential to focus on the myriad of contributions, benefits, and implications of AR in various sectors, given the technological advancements and emerging trends in the short term. One of the key contributions of AR is its potential to revolutionize education and training. Through active learning experiences, AR can help students and professionals better visualize and understand complex concepts, enhancing engagement and retention. Moreover, AR facilitates remote learning and training, which is particularly significant in the current global context.  
In the healthcare sector, AR brings substantial benefits ranging from improved patient education, where patients can better comprehend their medical conditions, to advanced surgical procedures, where doctors can overlay patient-specific data onto their field of view during surgeries. The implications are profound, potentially improving health outcomes and patient satisfaction. On the other hand, manufacturing and industrial processes stand to gain significantly from AR applications. AR can improve safety and efficiency in these productive sectors by providing workers with real-time information and instructions overlaid in their work environment. It also opens avenues for remote maintenance and inspections, significantly reducing downtime and operational costs. In addition, retail and marketing sectors are leveraging AR to create innovative customer experiences, contributing to enhanced customer engagement and increased sales. By overlaying additional product information or virtual fitting rooms, AR can drastically transform the shopping experience, bridging the gap between online and offline retail. In urban planning and smart cities, AR can facilitate better visualization of proposed architectural designs and infrastructural changes. It can contribute to more inclusive urban development by facilitating citizens' understanding of proposed plans and promoting greater involvement in decision-making processes.  
The advancements in AR devices are pushing the boundaries of user experience, improving comfort, and enhancing immersion. However, these advancements also bring with them important implications to consider, such as privacy and ethical concerns. As AR becomes more prevalent, ensuring user data security and privacy is paramount. We also need to address the ethical implications, such as potential over-reliance on AR and the societal impacts of widespread AR adoption. AR, with its numerous contributions and benefits across various sectors, has a profound potential impact on society. It presents a promising future, brimming with opportunities, but also challenges that require thoughtful consideration. This balance of understanding both the potential benefits and implications will be crucial as the whole of society continues to explore and leverage the full potential of AR.
## 1 Introduction  
Rainbow Subgraph  
**Instance:** An undirected graph \(G=(V,E)\), an edge coloring \(\chi:E\rightarrow\{1,\ldots,p\}\) for some \(p\geq 1\), and an integer \(k\geq 0\).  
**Question:** Is there a subgraph \(G^{\prime}\) of \(G\) that contains each edge color exactly once and has at most \(k\) vertices?  
We call a subgraph \(G^{\prime}\) with these properties a _solution_ of order at most \(k\). In the problem name, the term _rainbow_ refers to the fact that all edges of \(G^{\prime}\) have a different color. For convenience, we define a _rainbow cover_ as a subgraph where every color occurs at least once; these definitions are illustrated in Figure 1. Note that every rainbow cover \(G^{\prime}\) of order at most \(k\) has a subgraph that is a solution: Simply remove any edge whose color appears more than once in \(G^{\prime}\). Repeating this operation as long as possible yields a solution of the same order as \(G^{\prime}\).  
Rainbow Subgraph arises in bioinformatics: there is a natural reduction from the (Population) Parsimony Haplotyping problem to Rainbow Subgraph[1, 2]. In Parsimony Haplotyping, one aims to reconstruct a set of chromosome types, called haplotypes, from an observed set of genotypes. Each genotype consists of exactly two haplotypes; these haplotypes _explain_ the observed genotype. There can be, however, more than one possibility of explaining a genotype by two haplotypes. In the reduction to Rainbow Subgraph, the approach is to first compute all possible explanations for each genotype. Then, each haplotype that occurs in at least one possible explanation becomes a vertex of the graph. Each pair of haplotypes that explains one of the input genotypes is connected by an edge, and this edge receives the label of the genotype as edge color. Selecting a minimum number of haplotypes that explains all genotypes is now equivalent to finding a minimum-size vertex set that induces a graph containing all edge colors. Note that in the worst case, this reduction might not produce a polynomial-size instance, as the number of possible explanations of each genotype may become exponential. Another bioinformatics application appears in the context of PCR primer set design [1, 3].
# Biogas Production Enhancement through Chicken Manure Co-Digestion with Pig Fat
## 2 Materials and Methods
### Biogas Production at Different OLRs  
Biogas production at different OLRs was performed in four experiments (OLR3.0, OLR3.5, OLR4.0, and OLR4.5). Each experiment has been named as a stage (Stage I, Stage II, Stage III, and Stage IV) of the entire research. The first research stage was dedicated to digestate preparation, starting the digestion process and biogas production from raw, diluted chicken manure. The further three stages were dedicated to biogas production from raw, diluted chicken manure co-digestion with pig fat. In the first research stage, the reactor was fed with chicken manure at an OLR of 3.0 kg VS-(m\({}^{3}\cdot\)day)\({}^{-1}\). This OLR value was selected based on results and suggestions of an earlier study reported in [27, 30]. In this case, the daily feeding input of the reactor consisted of 158.7 g of chicken manure and 240.7 g of hot tap water, setting up the total solids of feeding material of 10.5% and ensuring efficient substrate mixing and the appropriate distribution of organic matter inside the digester. The fat was used and added to the reactor in the further stages. The research with fat addition was conducted at three organic load rates: 3.5, 4.0, and 4.5 kg VS-(m\({}^{3}\cdot\)day)\({}^{-1}\). When biogas production had been stable for ten days, as suggested by [31], the composition of drained digestate was analysed for total solids (TS) and volatile solids (VS) determination. Such measurements of VS and TS allowed finding the OLR value when the increase of biogas production stopped [27], and further increasing of OLR would be less effective.
## 3 The Proposed HSTMAC Framework and System Model
### Foundation of the HSTMAC Protocol
#### 3.1.3 Packet Size Threshold  
Solving the equation \(C_{S-ALOHA}=C_{TDMA}\), we can get the packet size threshold:  
\[\overline{\delta}=\frac{1}{1-e^{-1}}.\frac{1}{\gamma} \tag{6}\]  
**Remark 1**. _According to Equations (2) and (5), the S-ALOHA system is superior to the TDMA system if \(\delta<\overline{\delta}\). On the contrary, the TDMA system is superior to the S-ALOHA system if \(\delta>\overline{\delta}\) Considering that M2M traffic is usually in a small packet size while traditional H2H traffic is in a large packet size, it would be a feasible idea to design a hybrid S-ALOHA/TDMA MAC protocol for M2M and H2H coexisting scenario._
## 3 Results
### Segmentation Result Visualization  
Figure 12 presents a visual comparison of five models--UNet, DeepLabv3+, HRNet, PSPNet, and MHC-PSPNet--for image segmentation tasks. MHC-PSPNet shows more precise segmentation boundaries and richer details than UNet, demonstrating superior performance in complex scenarios. Compared to DeepLabv3+ and HRNet, which excel at integrating global and local information, MHC-PSPNet outperforms in detail capturing and accuracy, particularly in the fine segmentation of object contours. PSPNet, on the other hand, struggles with high background complexity or poor lighting, whereas MHC-PSPNet maintains high segmentation quality and clarity even under challenging conditions, providing more accurate and comprehensive results [27]. This underscores the effectiveness  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Modelling** & **IoU\%** & **Accuracy/\%** & **F1 Score/\%** & **Total Params/M** \\ \hline PSPNet+Mobilenetv2(ReLU) & 81.29 & 96.72 & 89.03 & 2.38 \\ PSPNet+Mobilenetv2(H-Swish) & 81.55 & 96.89 & 89.54 & 2.38 \\ PSPNet+Mobilenetv2(ReLU)+CBAM & 83.43 & 97.09 & 91.31 & 2.38 \\ MHC-PSPNet & 83.82 & 97.15 & 92.17 & 2.38 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparison experiments of H-Swish and ReLU activation functions.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Mobilenetv2** & **H-Swish** & **CBAM** & **IoU/\%** & **Accuracy/\%** & **F1 Score/\%** & **Total Params/M** \\ \hline \(\surd\) & & & 79.74 & 96.07 & 87.23 & 2.38 \\ \(\surd\) & \(\surd\) & & 81.55 & 96.89 & 89.54 & 2.38 \\ \(\surd\) & & \(\surd\) & 82.94 & 97.07 & 91.23 & 2.38 \\ \(\surd\) & \(\surd\) & \(\surd\) & 83.82 & 97.15 & 92.17 & 2.38 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Ablation results of different modules.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Feature Extractors** & **Attention Mechanism** & **IoU\%** & **Accuracy/\%** & **F1-Score/\%** \\ \hline \multirow{3}{*}{MobileNetV2} & CA & 82.84 & 96.98 & 91.08 \\  & GAM & 82.37 & 96.89 & 90.02 \\ \cline{1-1}  & CBAM & 82.94 & 97.07 & 91.23 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Performance comparison of different attention mechanisms.  
and robustness of MHC-PSPNet in complex rescue scenarios. ( The following images are publicly sourced from the internet and have been mosaicked and blurred for privacy).
## 4 Results and Discussion
### Evaluation of Computational Complexity
Figure 8a,b show the results for the SSMF and LEAF study, respectively. In both cases, all NLEs reach their performance limit, at a certain \(N_{FFT}\). Tables 1 and 2 show the \(Q^{2}\)-factor improvement, with respect to the FEC limit, provided by each NLE, at the optimum \(N_{FFT}\) as well as the number of real multiplications required per sample per polarization for these improvements. After SSMF transmission (Table 1), we observe that the 3 rd-order IVSTF-NLE is as good as the DBP-SSF\({}_{8}\) NLE but with the latter being almost eight times more complex. After LEAF transmission (Table 2), we observe that, in the presence of stronger nonlinear effects, the 3 rd-order IVSTF-NLE is as good as the DBP-SSF\({}_{2}\) NLE with the latter requiring \(\sim\)2 times more real multiplications, compared to the former. Finally, the DBP-SSF\({}_{8}\) NLE is only marginally better compared to the IVSTF-NLE. The estimations, summarized in Tables 1 and 2, validate what it was already observed in the experimental and the simulation results, and this is the fact that the performance of the DBP-SSF method saturates with eight-steps-per-span, whereas the improvement it provides is comparable to the improvement provided by the significantly less complex 3 rd-order IVSTF-NLE. Although we understand that the differences from the performances of DBP-SSF\({}_{1,2}\) NLEs might sound modest, we still draw useful conclusions considering the physical limits of the NLEs in the presence of increased nonlinearities.
## 3 Results and Discussion
### Symmetric Spiral Disks
From this viewpoint,  
Figure 5: Sensor parameters for the distantly spaced (\(p=768\)\(\upmu\)m) spiral disks with 90\({}^{\circ}\) C-resonator, evaluated from the transmittance spectra in Figure 4: (**a**) the frequency shifts \(\Delta f\) of resonances at 0.297, 0.339 and 0.372 THz vs. photoresist thickness \(d\) (left—simulations, right—experiments); (**b**) the sensitivity of \(S\) vs. \(d\); (**c**) the full width at the half minimum (_FWHM_) vs. \(d\); (**d**) figure of merit (_FOM_) vs. \(d\). it is preferable to use sensors with higher values of the figure of merit (_FOM_), which is defined as the ratio _FOM_ = _S/FWHM_, with the units of (RIU-mm)\({}^{-1}\). The calculated graphs of the _FOM_ as a function of \(d\) depicted in Figure 5d show that magnetic resonances were more sensitive than electric ones, especially for very thin analyte layers. The highest _FOM_ was attained at \(d\) = 0.3 \(\upmu\)m: _FOM_\(\approx\) 1670 (RIU-mm)\({}^{-1}\). Measurements under the oblique illumination of the samples demonstrated that the main resonances (see Figure 3) had the same sensitivity and _FOM_ to the analyte as at normal incidence.