esa-sceva/satcom-chunk-collection huggingface dataset:
###### Abstract  
Lattice-based workpieces contain patterned repetition of individuals of a basic topology (Schwarz, ortho-walls, gyroid, etc.) with each individual having distinct geometric grading. In the context of the design, analysis and manufacturing of lattice workpieces, the problem of rapidly assessing the mechanical behavior of large domains is relevant for pre-evaluation of designs. In this realm, two approaches can be identified: (1) numerical simulations which usually bring accuracy but limit the size of the domains that can be studied due to intractable data sizes, and (2) material homogenization strategies that sacrifice precision to favor efficiency and allow for simulations of large domains. Material homogenization synthesizes diluted material properties in a lattice, according to the volume occupancy factor of such a lattice. Preliminary publications show that material homogenization is reasonable in predicting displacements, but is not in predicting stresses (highly sensitive to local geometry). As a response to such shortcomings, this paper presents a methodology that systematically uses design of experiments (DOE) to produce simple mathematical expressions (meta-models) that relate the stress-strain behavior of the lattice domain and the displacements of the homogeneous domain. The implementation in this paper estimates the von Mises stress in large Schwarz primitive lattice domains under compressive loads. The results of our experiments show that (1) material homogenization can efficiently and accurately approximate the displacements field, even in complex lattice domains, and (2) material homogenization and DOE can produce rough estimations of the von Mises stress in large domains (more than 100 cells). The errors in the von Mises stress estimations reach 42% for domains of up to 24 cells. This result means that _coarse_ stress-strain estimations may be possible in lattice domains by combining DOE and homogenized material properties. This option is not suitable for _precise_ stress prediction in sensitive contexts wherein high accuracy is needed. Future work is required to refine the meta-models to improve the accuracies of the estimations.  
design of experiments; lattice structures; homogenization; schwarz primitive; mechanical characterization; modeling and simulation 2020_0
## 2 Results
### Advanced Frontiers Molecular Orbitals (FMOs)
This classification is based on a quantum chemical scale where electrophiles with \(\omega<1.5\) eV are considered weak, those with \(1.5\) eV \(\leq\)\(\omega\)\(\leq\) 2.5 eV are moderate, and those with \(\omega>2.5\) eV are strong with a value within the moderate range; apigenin demonstrates a balanced capacity to accept electrons during interactions with nucleophiles, such as key residues in the Kaep1 protein. This property is crucial in enabling apigenin to disrupt the Kaep1\(-\)Nrf2 interaction, facilitating the activation of antioxidant pathways [46]. The moderate electrophilicity of apigenin highlights its therapeutic relevance, particularly in oxidative stress-related conditions, as it indicates an optimal reactivity that can be further harnessed in biological systems. Additionally, the nucleophilicity index, calculated as 2.95 eV, suggests that the molecule is a moderate nucleophile. This classification is derived from quantum chemical principles, where nucleophilicity measures a molecule's ability to donate electrons to an electrophilic center during a chemical reaction. On a relative scale, molecules with a nu \begin{table}
\begin{tabular}{c c c} \hline \hline
**Molecular Properties** & **Definition** & **Apigenin** \\ \hline E\_HOMO (eV) (Highest Occupied & – & \(-\)0.21421 \\ Molecular Orbital) & & \\ E\_LUMO (eV) (Lowest Unoccupied & – & \(-\)0.05084 \\ Molecular Orbital) & & \\ \(\Delta\)E\_g (eV) (Energy Gap) & E\_LUMO \(-\) E\_HOMO & 0.16336 \\ \(\eta\) (eV) (Chemical Hardness) & E\_L \(-\) E\_H & 4.42 \\ S (eV\({}^{-1}\)) (Chemical Softness) & 1/\(\eta\) & 0.226 \\ \(\chi\) (eV) (Electronegativity) & \(-\)(E\_H + E\_L)/2 & 4.33 \\ \(\omega\) (eV) (Electrophilicity Index) & \(\chi^{2}/2\eta\) & 2.12 \\ N (eV) (Nucleophilicity Index) & (E\_H \(-\) E\_H(TCE))/2 & 0.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Computed quantum chemical properties for the apigenin molecule. cleophilicity index less than 2.5 eV are considered weak nucleophiles, those between 2.5 and 4.0 eV are classified as moderate nucleophiles, and those greater than 4.0 eV are strong nucleophiles [47]. These findings, supported by previous studies on chalcone derivatives, indicate that the studied molecule demonstrates high chemical reactivity. The comparison with similar compounds shows that apigenin has a relatively high electronegativity and electrophilicity index, contributing to its notable reactivity. These descriptors further affirm that the molecule is an active participant in electron transfer processes, confirming its high reactivity in chemical interactions.
## 5 Results and Analysis
### Different Model Results and Comparison  
Table 9 presents the modelling results of the impact of the built environment on inbound and outbound ridership during weekday peak hours. In this study, various models including OLS, GWR, MGWR, and GBDT were employed to fit the ridership data. The performance of these models was evaluated and compared using metrics such as R\({}^{2}\) and Adjusted R\({}^{2}\)[12].  
The GWR model, an extension of traditional OLS regression, accounts for spatial non-stationarity by allowing regression coefficients to vary across geographical locations. Both R\({}^{2}\) and Adjusted R\({}^{2}\) of the GWR model are higher than those of the OLS model.  
The MGWR model further extends the GWR model by allowing each explanatory variable to have its own bandwidth at different scales, thus capturing more refined spatial heterogeneity and complex multiscale effects. Consequently, the R\({}^{2}\) and Adjusted R\({}^{2}\) of the MGWR model are higher than those of the GWR model.  
The GBDT model, with the highest fit among the four models, outperforms the MGWR model, highlighting the fitting advantages of machine learning models represented by GBDT in handling high-dimensional and complex data. The established literature [PERSON] et al. (2021) [13] used the GBDT model to study the nonlinear characteristics of the commuter flow in Chengdu metro, and the R\({}^{2}\) reached 0.714. Compared with it, the R\({}^{2}\) obtained in this paper using the GBDT model (0.877 for inbound and 0.908 for outbound) are larger than those of their study.  
Therefore, this study utilises the machine learning model GBDT to analyse the impact of built environment factors on rail transit ridership.
## 3 Results and Discussion
### Adsorption of 4-Ethylphenol and 4-Ethylguaiacol
#### 3.2.4 Joint Removal of 4-Ethylphenol and 4-Ethylguaiacol from Like-Wine Solutions  
When 4-EP and 4-EG were present in the same solution, significant differences were observed, as shown in Figures 2 and 4. The sequence of both phenolic compounds' absorption was similar to that obtained with the individual compound, even though the preferential adsorption of 4-EG, compared to 4-EP, was now more obvious. The sum of the maximum adsorption capacity of both compounds was similar to that obtained for 4-EG when it was alone in the solution. When the adsorption of both compounds was performed in a wine-like solution, with 13% \(v/v\) of ethanol, their respective maximum adsorption capacity was inferior to that found when they were alone in the solution (Figures 3 and 5). The sum of 4-EP and 4-EG was higher than the amount of 4-EG adsorbed on the respective AC when it was alone in the solution. Ethanol seems to promote a cooperative effect that favours the adsorption of both compounds when they are mixed. These outcomes are very promising, as it is expected that with real wine, the results obtained will be similar or even better. The comparison between the 4-EP and 4-EG isotherms obtained in different media is presented in Figure S5 (Supplementary Information). Figure 4: Adsorption isotherms of 4-EG and 4-EP obtained on different ACs, from solutions where both compounds were present, without ethanol. Figure 5: Adsorption isotherms of 4-EG and 4-EP were obtained on different ACs, from solutions where both compounds were present, in the presence of 13% \(v/v\) of ethanol. The 4-EP and 4-EG isotherms were adjusted with Langmuir and Freundlich equations. These equations allow us to obtain some of the most common parameters used to evaluate the performance of ACs against adsorptives [27; 35]. Table 4 shows all of the parameters obtained for 4-EP and 4-EG when they were alone or mixed in solution, in the absence or presence of 13% \(v/v\) of ethanol, applying the Langmuir and Freundlich models. The values of the monolayer capacity (n\({}_{\text{mL}}\)) were very similar to the experimental maximum adsorption capacities for both compounds. However, the adjustment to the Langmuir equation was less consistent in the region of high concentrations. From the
## 3 Protein Enrichment Methods  
Using seaweed as a protein resource requires the processing of biomass to deliver a concentrated form of high-quality protein. The protein concentration from plant materials has traditionally been achieved directly by extracting and isolating the protein, or indirectly by extracting the non-protein components. In contrast with other plant materials, isolating and concentrating proteins from seaweed is a relatively unexplored domain and most protocols tend to focus solely on the initial extraction methods [102]. Purification of the extracted proteins represents a challenge, especially for novel proteins because of their unknown physicochemical properties. The selection of the method also depends on the final application of the product and the scale of production. The extraction method used also influences the purification method chosen. For example, reducing agents, such as N-acetyl-L-cysteine, which are used to improve cell wall-associated protein extraction, might have to be avoided, depending on the applications of the extracted proteins.  
Single or combined enrichment methods can be employed. These methods include precipitation, membrane technologies and chromatography [14]. A combination of membrane technologies could be used to isolate seaweed proteins using the same principles used to obtain protein isolates in the dairy industry. Microfiltration (MF) could be used to remove the cell wall components, ultrafiltration (UF) could be used to isolate proteins with a molecular weight between 1 and 200 kDa, nanofiltration (NF) could be used to remove monovalent salts and reverse osmosis (RO) to reduce the final volume [103]. Ultrafiltration has been applied after supercritical CO2 and ultrasonic-assisted extraction to isolate polysaccharides from _Sargassum pallidum_[25] and after hot water extraction in _Ulva fasciata_[104]. Most protocols reported in the literature often describe methods for the purification and isolation of specific proteins, namely, R-PE. Some examples are presented in Table 4.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Aim** & **Extraction Method** & **Enrichment Method** & **Conditions** & **Species** & **Results** & **Ref.** \\ \hline Concentrate & & & & & 100\% of R-PE \\ R-PE; pre-purify by eliminating proteins other & Centrifugation & & PES membrane; MWCO of & & recovered; \\  & of algal powder & & 25–30 kDa; surface area of & & 32.9\% of other \\  & after & Ultrafiltration & 0.033 m\({}^{2}\); 20 °C; 4 bar; & _trututuru_ & & proteins and \\  & than R-PE and & suspension in & & volumetric concentration & 64.6\% of sugars \\  & polysacha- & distilled water. & & factor of 5. & passed through \\  & rides. & & & & the membrane. \\ \hline \hline \end{tabular}
\end{table}
Table 4: Examples of proteins from algae species and the methods tested for their purification.
# A Two-Stage Routing Protocol for Partitioned Underwater Wireless Sensor Networks
## 4 Results and Discussion
### Network without Partitions
#### 4.1.2 Death Ratio  
Figure 12a-d show the number of dead nodes for 25, 50, 75 and 100 nodes, respectively, over the routing cycles intervals of 1-20, 21-40 and 41-50. In all four cases, PH shows a smaller number of dead nodes in each interval. This is due to the residual energy threshold policy which prevents early death of nodes by allowing highly burdened nodes to deny relay service upon reaching their residual energy threshold and by rerouting traffic through other nodes having enough residual energy. (It is important to note that the last interval is only 10 routing cycles as compared to 20 routing cycles in the first two intervals. Therefore, our graphs show smaller number of dead nodes in the last interval). The number of dead nodes increases with increasing routing cycles as nodes run out of their energy due to transmission (mostly relay transmissions) in previous routing cycles. Overall, the number of dead nodes in each interval increases with the increasing number of nodes. The reason for the increase is that higher number of nodes increases load on the nodes nearer to the sink node. However, the rise is not too high due to the following two reasons. Firstly, a higher number of nodes inherently distributes load by offering multiple relay options. Secondly, our link condition criteria for selecting the next hop node improves successful reception of packets which consequently reduces unnecessary transmissions and energy consumption.
# An Automatic Navigation System for Unmanned Surface Vehicles in Realistic Sea Environments
## 4 Collision Avoidance System
### Dynamic Target  
For the above four subfunctions, we can adjust their weights according to their importance. The system selects the optimal control command \(S_{o}\) in the range that the predicted trajectory can cover. However, when there is a concave obstacle, the algorithm can easily to fall into the local optimum, as shown in Figure 11. A dynamic target method is introduced to solve the problem.  
Considering that the path planning system can generate the global optimal path point, if its path point closest to the prediction range is selected as a dynamic target (DT), the USV can be far away from the local optimal area, as verified in Section 6. Because the path planning process requires a certain computation time which results in an information updating delay, the update time \(T_{upd}\) should be considered. The distance \(d_{DT}\) of DT on the optimal path is  
\[d_{DT}=U_{\max}\times t_{p}+U\times T_{upd} \tag{21}\]  
Using this method, the USV can not only follow the global optimal path point, but also have the local collision avoidance functionality.  
Figure 11: The unmanned surface vehicle falling into the local optimum in a static simulation environment.
## 2 Fundamental Theories
### Improved Decision Strategy  
SVDD with relative distance decision strategy (RD-SVDD) is commonly applied for pattern recognition. However, it is difficult for relative distance decision strategy to achieve precise identification, especially for unknown samples within overlap regions of the hyperspheres and regions outside all the hyperspheres. The schematic diagram of positional relationship between samples and hyperspheres is shown in Figure 1. Therefore, further development of decision strategy is required. To this end, SVDD with improved decision strategy (ID-SVDD) that fuses with the k-nearest neighbor (KNN) method is proposed in this research.  
The KNN method proposed by [PERSON] et al. [43] is one of the most widely used algorithms for pattern recognition, which is easy to understand and realize. The basic idea of KNN is to measure the differences between samples and their neighbors, and Euclidean and Manhattan distances are usually employed to achieve the measurement. Let \(p\), \(q\) be two samples with \(m\) terms, the distances between them can be defined as:  
\[\text{Euclidean distance}:D(p,q)=\sqrt{\sum
## 3 Results
### Statistical Analysis of the Experimental Data
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \begin{tabular}{c} **Skeletal** \\ **Class** \\ \end{tabular} & **Number** & \begin{tabular}{c} **Mean \(\pm\) Standard** \\ **Deviation** \\ \end{tabular} & \begin{tabular}{c} **Comparison** \\ **between Skeletal** \\ **Classes** \\ \end{tabular} & \
\begin{tabular}{c} **Students \(t\)-Test** \\ **\(p\) Value** \\ \end{tabular} &
\begin{tabular}{c} **ANOVA with** \\ **Bonferroni** \\ **Correction** \\ \end{tabular} \\ \hline \multirow{3}{*}{Length} & Class I & 30 & 8.53 \(\pm\) 0.990 & Class I and Class II & 0.138 & \multirow{3}{*}{1.049 \(\times\) 10\({}^{-10}\)} \\ \cline{2-6}  & Class II & 30 & 8.13 \(\pm\) 1.264 & Class I and Class III & \textless{}0.001 & & (\textless{}0.001) \\ \cline{2-6}  & Class III & 30 & 10.30 \(\pm\) 1.115 & Class II and Class III & \textless{}0.001 & & \\ \hline \multirow{3}{*}{Diameter} & Class I & 30 & 9.96 \(\pm\) 1.008 & Class I and Class II & 0.133 & \multirow{3}{*}{3.89 \(\times\) 10\({}^{-9}\)} \\ \cline{2-6}  & Class II & 30 & 9.56 \(\pm\) 0.980 & Class I and Class III & \textless{}0.001 & & (\textless{}0.001) \\ \cline{2-6}  & Class III & 30 & 11.34 \(\pm\) 1.054 & Class II and Class III & \textless{}0.001 & & \\ \hline \multirow{3}{*}{Depth} & Class I & 30 & 7.68 \(\pm\) 0.934 & Class I and Class II & 0.567 & \multirow{3}{*}{5.24 \(\times\) 10\({}^{-6}\)} \\ \cline{2-6}  & Class II & 30 & 7.55 \(\pm\) 0.669 & Class I and Class III & \textless{}0.001 & & (\textless{}0.001) \\ \cline{2-6}  & Class III & 30 & 8.74 \(\pm\) 1.153 & Class II and Class III & \textless{}0.001 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The \(p\)-values obtained using the Anova test with Bonferroni correction, for all skeletal classes. Figure 7: Q–Q plots for the depth, for each of the classes I, II, and III, respectively.
## 4 Experimental Settings
### Parameter Configuration and Evaluation Metrics  
We used the Python language for program development and built models based on the deep learning frameworks TensorFlow and Keras; we used the Adam optimizer for model training. In the convolutions of Conv1 and L residual units, 64 filters of size 3 \(\times\) 3 were used, while 2 filters of size 3 \(\times\) 3 were used in the convolution of Conv2. All experiments in our research were conducted on a machine equipped with CPU: Intel i9-13900 kf, GPU: GeForce RTX 3080, and OS: Ubuntu 22.04-LTS.  
In order to achieve optimal experimental results, we manually adjusted the training parameters for the experiments. For ease of viewing, we show the finalized parameter configurations in Table 2.  
In this study, the mean squared error (MSE) is selected as the loss value. Additionally, root mean squared error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) are set to comprehensively evaluate the predictive capability of the model. The formulas are as follows:  
\[MSE=\frac{1}{m}{\sum\limits_{i=1}^{m}{(y_{i}-\hat{y_{i}})}^{2}} \tag{13}\]  
\[RMSE=\sqrt{\frac{1}{m}{\sum\limits_{i=1}^{m}{(y_{i}-\hat{y_{i}})}^{2}}} \tag{14}\]  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Dataset** & **SubwayBJ** \\ \hline Temperature span/\({}^{\circ}\)C & [\(-\)12, 38] \\ Wind speed span/m/s & [1, 61] \\ \hline \hline \end{tabular}
\end{table}
Table 1: _Cont._  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter Name** & **Parameter Value** \\ \hline length of closeness sequence (c) & 3 \\ length of period sequence (d) & 1 \\ length of trend sequence (w) & 1 \\ learning rate (lr) & 0.002 \\ the number of training sessions (epochs) & 500 \\ batch size (batch\_size) & 32 \\ number of residual units (k) & 3 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameter configurations.  
\[MAE=\frac{1}{m}\sum_{i=1}^{m}\left|\hat{y_{i}}-y_{i}\right| \tag{15}\]  
\[MAPE=\frac{100\%}{m}\sum_{i=1}^{m}\left|\frac{\hat{y_{i}}-y_{i}}{y_{i}}\right| \tag{16}\]  
where \(\hat{y_{i}}\) is the predicted value and \(y_{i}\) is the true value, \(m\) represents the number of the predicted samples.  
Among them, MSE squares the error, making it more sensitive to the degree of deviation in prediction errors and the outliers. RMSE takes the square root of MSE to make the dimension consistent with the true value, making it easier to interpret. MAE is more evenly sensitive to errors and can better reflect prediction errors. The smaller the values of these three metrics, the more accurate the predictive results. MAPE focuses on the percentage of prediction deviation, which has high practicality for the passenger flow prediction problem that needs to consider accuracy in this study. Its range is from 0% to positive infinity, and the closer it is to 0%, the smaller the prediction error.
# Proving Fixed-Point Theorems Employing Fuzzy \((\sigma,\mathcal{Z})\)-Contractive-Type Mappings
## 1 Introduction and Motivation  
In the theory of fuzzy sets and systems, many researchers have attempted to formulate an appropriate definition of fuzzy metric space (e.g., [1; 2; 3]). The most natural and widely acceptable definition is essentially due to [PERSON] and [PERSON] [4]. [PERSON] [5] is one of the earliest mathematicians to study the theory of the fixed point in fuzzy metric spaces. In doing so, he introduced the notions of \(\mathcal{G}\)-Cauchyness and the \(\mathcal{G}\)-completeness of fuzzy metric spaces and extended the fixed-point theorems of [PERSON] and [PERSON] from metric spaces to fuzzy metric spaces introduced by [PERSON] and [PERSON]. It has been observed that the notions of \(\mathcal{G}\)-Cauchy sequences and \(\mathcal{G}\)-completeness are relatively strong. With a view toward having a Hausdorff topology on a fuzzy metric space, [PERSON] and [PERSON] [6] modified the definition of the fuzzy metric space due to [PERSON] and [PERSON] [4] and also established some valuable related results.  
In 2002, [PERSON] and [PERSON] [7] initiated a class of mappings called fuzzy contractive mappings and proved a fuzzy version of the Banach contraction theorem in the sense of [PERSON] and [PERSON]. Thereafter, employing a control function satisfying suitable properties, [PERSON] [8] and [PERSON] [9] generalized the class of fuzzy contractive mappings by introducing the concepts of the fuzzy \(\psi\)-contractive mapping and fuzzy \(\mathcal{H}\)-contractive mappings, respectively. For such kind of work, we refer the reader to [10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25]. Very recently, [PERSON] et al. gave the concept of fuzzy \(\mathcal{Z}\)-contractive mappings (see Definition 4, given later), which unifies all the classes of mappings mentioned earlier.  
On the other hand, the concept of the \(\sigma\)-admissible mappings was introduced by [PERSON] et al. (see [26], Definition 2.2) in metric spaces. In [27], [PERSON] and [PERSON] extended this notion to the setting of fuzzy metric spaces (see Definition 8, given later). Employing this notion, they introduced the concept of \(\sigma\)-\(\psi\)-fuzzy contractive mappings and proved a theorem that ensures the existence of a fixed point for this types of mappings. Their presented theorem extends, generalizes, and improves the corresponding results given in the literature.  
This article aims to enlarge the class of fuzzy \(\mathcal{Z}\)-contractive mappings by introducing the family of fuzzy \((\sigma,\mathcal{Z})\)-contractive mappings to cover all of the concepts introducedin [7; 8; 9; 28; 29], besides extending a result due to [PERSON] and [PERSON] [27]. Our newly introduced notion is utilized to prove some results in \(\mathcal{M}\)-complete fuzzy metric spaces. Finally, some examples are adopted to demonstrate that our newly presented results are a proper extension of [PERSON] et al.'s results [28].