esa-sceva/satcom-chunk-collection huggingface dataset:
# Performance Analysis and Parameter Optimization of the Optimal Fixed-Point Quantum Search
## Appendix C Proof of the Optimal Parameter \(\delta_{opt}\) of Equation (24)
\] (A23)  
Note that for \(0<\lambda_{0}\leq 4/5\),  
\[\delta_{min}^{left,\approx}\geq\delta_{0} \Leftrightarrow \lambda_{0,0}^{\prime}\leq\lambda_{0}\leq 4/5,\] (A24) \[\delta_{k}\leq\delta_{min}^{left,\approx}<\delta_{k-1} \Leftrightarrow \lambda_{0,k}^{\prime}\leq\lambda_{0}<\lambda_{0,k-1}^{\prime},\] (A25)  
where  
\[\lambda_{0,k}^{\prime}=1-T_{\frac{1}{2k+1}}^{-2}\left(1/\delta_{min}^{left, \approx}\right),\,k\geq 0.\] (A26)  
Define  
\[L_{E,left}^{Up,\Delta}\left(\lambda_{0}\right)=L_{E,left}^{Up}\left(\delta_ {k}\right)-L_{E,left}^{Up}\left(\delta_{k-1}\right),k\geq 1.\] (A27)  
Then, through further analysis about \(L_{E,left}^{Up,\Delta}\), we can find the following two results: (1) On the range \(\lambda_{0}\in\left[\lambda_{0,k}^{\prime},\lambda_{0,k-1}^{\prime}\right)\) (\(k\geq 1\)), there is a solution for \(\lambda_{0}\) of equation \(L_{E,left}^{Up,\Delta}=0\), denoted by \(\lambda_{0,k-1}\). (2) \(L_{E,left}^{Up,\Delta}<0\) for \(\lambda_{0,k}^{\prime}\leq\lambda_{0}<\lambda_{0,k-1}\), and \(L_{E,left}^{Up,\Delta}>0\) for \(\lambda_{0,k-1}<\lambda_{0}<\lambda_{0,k-1}^{\prime}\). Corresponding reasons are given as follows:  
(1) From Equations (A15) and (A27) it follows that  
\[L_{E,left}^{Up,\Delta} = \frac{2k+1}{1-\delta_{k}^{2}}-\frac{2k-1}{1-\delta_{k-1}^{2}}\] (A28) \[= \frac{T_{2k-1}^{-2}\left(\delta_{0}\right)T_{2k+1}^{-2}\left( \delta_{0}\right)}{2\left(1-\delta_{k}^{2}\right)\left(1-\delta_{k-1}^{2} \right)}h_{k}\left(y\right),\]  
where  
\[y=\text{arcosh}\left(1/\sqrt{1-\lambda_{0}}\right),\] (A29)  
and  
\[h_{k}\left(y\right)=\sinh^{2}(4 ky)+\sinh^{2}(2y)-4k\sinh\left(4 ky\right)\sinh \left(2y\right).\] (A30)  
Note that \(y\) increases as \(\lambda_{0}\) grows, and according to Equations (A22), (A26), and (A29), \(y=\frac{x}{4k+2}\equiv y_{k}^{\prime}\) for \(\lambda_{0}=\lambda_{0,k}^{\prime}\), and \(y=\frac{x}{4k-2}\equiv y_{k-1}^{\prime}\) for \(\lambda_{0}=\lambda_{0,k-1}^{\prime}\). When \(k\) is sufficiently large, i.e., \(k\rightarrow+\infty\), \(y_{k}^{\prime},y_{k-1}^{\prime}\to 0\), then simple algebra shows that,  
\[h_{k}\left(y_{k}^{\prime}\right) \approx \frac{2x^{2}}{2k+1}\left[2-\cosh\left(x\right)\right]<0,\] (A31) \[h_{k}\left(y_{k-1}^{\prime}\right) \approx \frac{2x^{2}}{2k-1}\left[\cosh\left(x\right)-2\right]>0,\] (A32)  
which can also be numerically proven for finite \(k\), for example \(1\leq k\leq 10^{5}\). Therefore, based on the intermediate value theorem (See p. 271 of [24]), we confirm that there exists a solution of \(h_{k}\left(y\right)=0\) between \(y_{k}^{\prime}\) and \(y_{k-1}^{\prime}\), denoted by \(y_{k-1}\). Correspondingly, from Equation (A29), the solution of \(L_{E,left}^{Up,\Delta}=0\) for \(\lambda_{0}\), denoted by \(\lambda_{0,k-1}\), can be finally obtained as defined in Equation (26). (2) Based on Equation (29), we can see that \(L_{E,left}^{Up,\Delta}\) and \(h_{k}\left(y\right)\) have the same sign.
# Optimization of Chinese Chive Juice as a Functional Feed Additive
## 2 Materials and Methods
### Antioxidant Activity and Antioxidant Compound Contents of CC Juice  
#### 2.3.1 DPPH Free Radical Scavenging Assay  
DPPH (2-diphenyl-2-picrylhydrazyl) radical scavenging activity was determined according to a previous method with some modifications [20]. The fresh and heated CC juice (100 \(\mu\)L) were mixed with 500 \(\mu\)L of DPPH (0.06 mg/mL, _w/v_) in ethanol solution. The mixture was kept in a dark place for 15 min and gently agitated. The absorbance was measured using a microplate reader (Synergy 2, BioTek, USA) at 515 nm using ethanol (99.99%, _v/v_) as a blank. The DPPH radical scavenging activity was expressed as the inhibition percentage (%) and calculated using the following Equation (1).  
DPPH free radical scavenging activity \[(\%)\ =\ (\mathrm{Abs\ control\ -\ Abs\ sample})/(\mathrm{Abs\ control})\times 100\] (1)  
Total antioxidant compounds (\(\mu\)g/mL) in 100 \(\mu\)L of the fresh and heated CC juice was expressed as the ascorbic acid equivalent antioxidant content (AEAC) as well as the quercetin equivalent antioxidant content (QEAC). The AEAC and QEAC were determined via measuring the DPPH free radical scavenging activity of ascorbic acid (0-40 \(\mu\)g/mL) or quercetin (0-15 \(\mu\)g/mL) using the calculation y = 2.0234x - 1.986 or y = 5.2237x - 0.3673, respectively (y is the scavenging activity, and x is the concentration). The CC equivalents were converted based on the DPPH scavenging activity.
# Digital Mapping of Soil Organic Matter in Northern Iraq: Machine Learning Approach
## 5 Conclusions  
A study was conducted in the Batifa region to spatially map soil organic matter using ML models based on remotely sensed data. These findings indicate that this approach  
Figure 7: Variable importance of two models: (**a**) XGBoost model and (**b**) RF model.  
yields significant insights into the soil management and agricultural planning within the region. Two ML models, XGBoost and RF, were evaluated, and it was found that XGBoost performed better at predicting changes in soil organic matter. This study produced the following key findings:  
* XGBoost exhibited the best performance (R\({}^{2}\) = 0.92) compared to RF (R\({}^{2}\) = 0.77).
* The RMSE value of the XGBoost model for SOM (RMSE = 0.62) was lower than that of the RF model (RMSE = 0.96), indicating that XGBoost could estimate SOM levels more accurately.
* In XGBoost, Band 10 was found to be the most important variable for predicting SOM, whereas in RF, DEM was the most significant variable.
* The application of our ML model to the entire study area revealed that the SOM's spatial distribution indicated higher predicted values predominantly in the central and southern regions, despite the field survey not encompassing the northern region.  
The XGBoost method is advantageous because it can be easily implemented and modelled using the R software (v. 4.2). This makes it highly useful for handling large amounts of data, as it can produce more accurate estimates while reducing errors and preventing misleading results.  
Conceptualization, H.S.K., Y.T.M., and M.A.F.; methodology, H.S.K. and Y.T.M.; software, Y.T.M.; validation, H.S.K., Y.T.M., and M.A.F.; formal analysis, H.S.K.; investigation, H.S.K. and Y.T.M.; resources, H.S.K.; data curation, H.S.K.; writing--original draft preparation, H.S.K. and Y.T.M.; writing--reviewing, and editing, Y.T.M. and M.A.F.; visualization, H.S.K., Y.T.M., and M.A.F.; supervision, Y.T.M. and M.A.F.; project administration, Y.T.M. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The data presented in this study are available upon request from the corresponding author. The data were not publicly available owing to privacy restrictions.  
The authors declare no conflict of interest.
# A Supervised Neural Network Control for Magnetorheological Damper in an Aircraft Landing Gear
## 1 Introduction
However, existing techniques using neural nets use optimization or reinforcement learning schemes, so a large amount of data is required for sufficient learning. A sufficient amount of data can be given in a numerical simulation environment, and thus a neural net controller shows good performance. On the other hand, sufficient learning could be challenging to achieve with actual drop test experiments because only a limited number of drop tests are performed due to cost and time limitations. Neural nets that are not sufficiently learned not only degrade the performance but can also cause unpredictable behavior. A supervised learning approach with a proven controller as a target can be a solution to this problem. This enables a controller to show adaptability in various landing conditions without relying on models and parameter estimations, with a relatively small number of experiments. This paper presents an intelligent controller based on supervised learning for a landing gear equipped with an MR damper adaptively operating in various landing conditions, without any online knowledge or estimates of mass and forces. To this end, the hybrid control is applied to the MR damper in a drop test environment with a dSPACE platform for generating training data for a neural network controller. The hybrid control [11; 17] utilizes exact values of test mass and data from a load cell for measuring the ground reaction force, which is, of course, ideal because it is not possible in the actual operating environment of aircraft landing gears. The hybrid controller is also well tuned for each landing condition to maintain high landing performance. The inputs of the neural net are the state variables of the damper, and thus the presented controller trained with the hybrid control in the ideal environment is also applicable in landing conditions other than where it is trained. Comparative experiments are conducted to verify the effectiveness of the presented intelligent controller against a passive damper and existing controllers, i.e., skyhook controller and hybrid controller in differing landing conditions of aircraft mass and sink speeds. In the comparative experiments, the skyhook and hybrid controllers use the estimates of aircraft mass and strut force with a mathematical model for emulating a realistic operating environment. The structure of the paper is as follows: Section 2 describes the environment of the drop test experiments for an MR damper landing gear; Section 3 explains the performance measure of the drop tests; Section 4 details the principles and experimental results of the hybrid controller; Section 5 describes the structure and training of the neural network controller; Section 6 presents the comparative experimental results; the conclusions are presented in Section 7.
# Removal of Color-Document Image Show-Through Based on Self-Supervised Learning
## 4 Experimental Results and Analysis
### Analysis of Ablation-Experiment Results  
To evaluate the effectiveness of the method proposed in this paper, we conducted ablation studies using the S-color0.5 dataset. Specifically, we periodically removed a component from the overall architecture. To ensure fair comparison, all models tested were trained under the same training settings, except for the modifications shown in Table 4. Additionally, the effectiveness of cycle consistency loss 2 (\(\mathcal{L}_{cycle2}\)) and pseudo-similarity loss (\(\mathcal{L}_{ps}\)) was further investigated.  
From observations of the last three columns of Table 4, it can be seen that there is a decline in performance when the \(\mathcal{L}_{cycle2}\) and \(\mathcal{L}_{ps}\) are replaced. This confirms their advantages in improving the quality of restoration results. By combining all the aforementioned components, our proposed method achieved the best performance, with a PSNR of  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Index**} & \multicolumn{6}{c}{**Methods**} \\ \cline{2-7}  & **w/o \(\mathbf{D}_{\text{predict}}\)** & **w/o \(\mathbf{D}_{\text{remove}}\)** & **w/o \(\mathbf{R}_{\text{predict}}\)** & **w/o \(\mathbf{S}\)** & **w/o CAB** & **w/o \(\mathbf{\mathcal{L}}_{ps}\)** & **w/o \(\mathbf{\mathcal{L}}_{cycle2}\)** & **CDSR- CycleGAN** \\ \hline PSNR & 32.52 & 33.73 & 29.87 & 33.75 & 32.94 & 30.45 & 33.71 & **33.79** \\ \hline SSIM & 0.978 & 0.981 & 0.969 & 0.983 & 0.982 & 0.974 & 0.983 & **0.984** \\ \hline \hline \end{tabular}
\end{table}
Table 4: Analysis of ablation experiments on different components on the S-color0.5 dataset.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Index**} & \multicolumn{3}{c}{**Methods**} \\ \cline{2-4}  & **Hua** & **Mog** & **Ro2** & **Ours** \\ \hline FgError & 0.2308 & 0.0746 & 0.0696 & 0.0633 \\ \hline BgError & 0.0012 & 0.0148 & 0.0085 & 0.0008 \\ \hline TotError & 0.0413 & 0.0244 & 0.0196 & 0.0160 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Analysis of mean error probabilities for the entire BTD dataset.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Methods** & **Framework** & **Time (s)** \\ \hline DAD & PyTorch & 0.4649 \\ DeepOtsu & TensorFlow & 1.3982 \\ Uformer & PyTorch & 0.5203 \\ MPRNet & PyTorch & 0.1363 \\ VDIR & TensorFlow & 0.5729 \\ S-CycleGAN & PyTorch & 0.2438 \\ YMT & PyTorch & 0.2134 \\ CDSR-CycleGAN & PyTorch & **0.1303** \\ \hline \hline \end{tabular}
\end{table}
Table 3: Analysis of average runtime (seconds) using images sized 256 \(\times\) 256.  
33.79 dB. Therefore, each key component considered during the ablation process has made its own contribution.
## 2 Materials and Methods
### Sample Preparation and Generation of MALDI-TOF Mass Spectra  
Four samples of collagen hydrolysate were prepared for analysis using matrix-assisted laser desorption/ionization time-of-flight (MALDI-TOF) mass spectrometry. The samples included collagen hydrolysate before and after sterilization with beta radiation, gamma radiation, and ethylene oxide. Each sample was dissolved in 1 mL of methanol and thoroughly mixed by vortex for 5 min at room temperature to ensure homogeneity. Following the preparation, the solution samples were individually subjected to MALDI-TOF analysis to characterize the collagen hydrolysate and assess the impact of different sterilization methods on its composition.  
Figure 1: The area (yellow box) of the collagen hydrolysate sample that was used to measure the histogram of the physical appearance image and the red frame was used as the outer edge where the tip of the arrow cross cursor met for measurement accuracy.  
A 0.5 \(\mu\)L volume of each of the solution-sample-containing sterile peptide synthesis (see above) was spotted onto a clean ground steel target plate (Bruker Daltonics, Bremen, Germany) in 8 replicates (for generating a MALDI-TOF MS mass spectrum profile), air-dried at room temperature, and then overlaid with 0.5 \(\mu\)L of the matrix solution (4 mg/mL 4 chloro-\(\alpha\)-cyanocinnamic acid in 70% Methanol and 0.1% trifluoroacetic acid. After the matrix solution was air-dried at room temperature, the sample was promptly analyzed using an ultrafineXtreme mass spectrometer and FlexControl software version 3.0 (Bruker Daltonics, Germany), with the following settings: spectrum recording mode, positive linear; mass range (\(m/z\)), 700-3500 Da; laser frequency, 60 Hz; ion source-1 voltage, 25 kV; ion source-2 voltage, 24 kV; and lens voltage, 7.0 kV. With the automatic mode and default setting, 50 sets of 500 laser shots were applied in different positions within one sample spot, and the generated mass spectra were accumulated for MALDI-TOF MS analysis. In each experiment, the peptide calibration standard II (Bruker Daltonics, Germany) was used to calibrate the mass spectrometer according to the manufacturer's instructions.  
Next, all \(m/z\) values for each sample were calculated using Equation (1). The values for each sample group were then compared to the non-sterile group to determine the percentage difference from the control group:  
\[\%\;\text{Difference from control group}\;=\;\frac{\text{B}-\text{A}}{\left( \frac{\text{B}+\text{A}}{2}\right)}\times 100 \tag{1}\]  
where:  
A is the sum of \(m/z\) value from the control group or non-sterile;  
B represents the sum of \(m/z\) from the comparison group (ethylene oxide, beta, and gamma).
## 6 Conclusions  
In this case study, six landslide susceptibility evaluation methods, namely, the FR, IoE, FR_SysFor, IoE_SysFor, FR_LR, and IoE_LR models, were systematically analyzed and compared as part of landslide susceptibility research in Nanzheng Country (China). Based on previous research and the geological environmental characteristics in the study area, 16 conditioning factors were selected for the research: elevation, profile curvature, plan curvature, slope angle, slope aspect, SPI, TWI, SPI, distance to roads, distance to rivers, distance to faults, lithology, rainfall, soil, NDVI, and land use. These models were applied to the calculation of landslide occurrence probability for the first time. Finally, the model performances were compared by the statistical parameters of ROC curves, AUC values, SE and 95% CI. The results show that all the models perform well. Compared with other models, the prediction capability of the FR_SysFor model is the highest, with a success rate of 0.940 and prediction rate of 0.831. Hence, the FR_SysFor model is considered the most promising technique in this study. The results can provide a reference for land-use planning and decision-making in the study area.  
[PERSON], [PERSON], [PERSON], and [PERSON] contributed equally to the work. [PERSON] collected field data and conducted the landslide susceptibility mapping and analysis. [PERSON] wrote and revised the manuscript. [PERSON], [PERSON], and [PERSON] edited the manuscript. All the authors discussed the results and edited the manuscript. All authors have read and agreed to the published version of the manuscript.  
This research was funded by Key Laboratory of Mine Geological Hazard Mechanism and Control, Shaanxi Provincial Natural Resources Department (Program No. KF2018-05), the National Natural Science Foundation of China (41807192), Natural Science Basic Research Program of Shaanxi (Program No. 2019 ILM-7, Program No. 2019Q-094), China Postdoctoral Science Foundation (Grant No. 2018T111084, 2017M613168), and Project funded by Shaanxi Province Postdoctoral Science Foundation (Grant No. 2017 BSHYDZZ07).  
The authors declare no conflict of interest.
# Comparing the Reasoning Capabilities of Equilibrium Theories and Answer Set Programs
## 4 Relativised Equivalence  
As usual, we consider theories \(\Pi_{1}\), \(\Pi_{2}\), etc. and now make explicit languages \(\mathcal{L}\), \(\mathcal{L}^{\prime}\), etc. As before, we view a language as a set of atoms. A theory is said to be _in_ the language \(\mathcal{L}\) if all its atomic formulas belong to \(\mathcal{L}\).  
Definition 6: Let \(\Pi_{1}\) and \(\Pi_{2}\) be theories.  
(i): \(\Pi_{1}\) _and_ \(\Pi_{2}\) _are_ strongly equivalent relative to \(\mathcal{L}\)_, in symbols_ \(\Pi_{1}\equiv^{\mathcal{L}}\Pi_{2}\)_, iff for any (empty or non-empty) set_ \(\Sigma\) _of_ \(\mathcal{L}\) _formulas_,_ \(\Pi_{1}\cup\Sigma\) _and_ \(\Pi_{2}\cup\Sigma\) _are equivalent, i.e., have the same equilibrium models. (ii): \(\Pi_{1}\) _and_ \(\Pi_{2}\) _are_ uniformly equivalent relative to \(\mathcal{L}\)_, in symbols_ \(\Pi_{1}\equiv^{u\mathcal{L}}\Pi_{2}\)_, iff for any (empty or non-empty) set_ \(X\) _of_ \(\mathcal{L}\) _literals_,_ \(\Pi_{1}\cup X\) _and_ \(\Pi_{2}\cup X\) _are equivalent, i.e., have the same equilibrium models._  
We can now apply these definitions to different relativised versions of strong and uniform equivalence.  
Definition 7: Let \(\Pi_{1}\) and \(\Pi_{2}\) be theories and \(\alpha\in\{c,s,p\}\). Then,  
* we write \(\Pi_{1}\equiv^{s,\mathcal{L}}_{\alpha}\Pi_{2}\) if for any further theory \(\Pi\) in \(\mathcal{L}\), \((\Pi_{1}\cup\Pi)\equiv_{\alpha}(\Pi_{2}\cup\Pi)\);
* we write \(\Pi_{1}\equiv^{u,\mathcal{L}}_{\alpha}\Pi_{2}\) if for any set \(X\) of \(\mathcal{L}\) atoms, \((\Pi_{1}\cup X)\equiv_{\alpha}(\Pi_{2}\cup X)\).  
Proposition 5: For any theories \(\Pi_{1},\Pi_{2}\) and \(\alpha\in\{c,s\}\), \(\Pi_{1}\equiv^{s,\mathcal{L}}_{\alpha}\Pi_{2}\) iff \(\Pi_{1}\equiv^{s\mathcal{L}}\Pi_{2}\); similarly \(\Pi_{1}\equiv^{u,\mathcal{L}}_{\alpha}\Pi_{2}\) iff \(\Pi_{1}\equiv^{u\mathcal{L}}\Pi_{2}\).  
Proof: The right to left directions are obvious. For the other direction, suppose for instance that \(\Pi_{1}\) and \(\Pi_{2}\) are not strongly equivalent relative to \(\mathcal{L}\). Then, for some set of \(\mathcal{L}\) formulas \(\Pi\), \(\Pi_{1}\cup\Pi\) and \(\Pi_{2}\cup\Pi\) have different sets of equilibrium models. We can apply Lemma 1 again to conclude that \(\Pi_{1}\cup\Pi\) and \(\Pi_{2}\cup\Pi\) can be separated by different queries, both in the sceptical and in the credulous sense, i.e., that \(\Pi_{1}\cup\Pi\
ot\equiv_{s}\Pi_{2}\cup\Pi\) and \(\Pi_{1}\cup\Pi\
ot\equiv_{c}\Pi_{2}\cup\Pi\). The uniform case follows the same pattern.  
\[\Pi_{1}\equiv^{s,\mathcal{L}}_{\alpha}\Pi_{2} \Leftrightarrow \forall\Pi\in\mathcal{L},\,\Pi_{1}\cup\Pi\equiv_{\alpha}\Pi_{2}\cup\Pi\] \[\Leftrightarrow \forall\Pi\in\mathcal{L},\,E(\Pi_{1}\cup\Pi)=E(\Pi_{2}\cup\Pi) \text{by Proposition \ref{prop:
# Optimization of Microalgae-Bacteria Consortium in the Treatment of Paper Pulp Wastewater
## 3 Results and Discussion
### Influence of the microalgae-Bacteria Inoculation Ratio on the Growth and Formation of Biomass
PBR3, PBR4, and PBR5 with bacteria and microalgae inoculation had chlorophyll (a + b) values around 0.50 mg/L, indicating that even with a high concentration of suspended solids, there was good algal biomass productivity. The lowest total chlorophyll productivity was observed in PBR2 with an average of 0.30 mg/L, which is related to the high concentration of suspended solids in the water column, which hinders light penetration and thus limits the growth of  
Figure 5: Variation of the concentration of (**a**) chlorophyll-a and (**b**) chlorophyll-b during the operational period. photoautotrophic organisms. It is also worth noting that there was no initial inoculation of microalgae in PBR2. Flocculation efficiencies (FE) were calculated trough Equation (3) for the biomass generated in the photobioreactors. The average values obtained during the 14 days were \(55.65\pm 7.40\%\), \(82.49\pm 9.70\%\), \(82.06\pm 8.95\%\), \(94.23\pm 2.92\%\), \(94.89\pm 1.57\%\), and \(91.15\pm 3.30\%\) for PBR1, PBR2, PBR3, PBR4, PBR5, and PBR6, respectively. PBR4, PBR5, and PBR6 worked with a higher concentration and inoculation ratio of microalgae: bacteria, respectively, 1:3, 1:5, and 3:1, having presented a FE above 90% (i.e., a high biomass sedimentation capacity). This may indicate a more stable microalgae-bacteria consortium development with good biofloculation, producing a biomass with greater potential as well as efficiency of the possibility of harvesting for resource recovery [27]. In similar work, [PERSON] et al. [26] reported a FE of 42.37 \(\pm\) 0.25%, which is lower than the values found in this study, but for domestic wastewater treatment and an inoculation ratio of 1:0.75. The PBR1, with only microalgae inoculation (_Scendesmus_ sp. ), produced a sinuous behavior with a lack of linearity in the biomass generated. As a result, the sedimentation process was impacted by cell wall properties as well as aspects related to the microscopic nature of microalgae. In this way, the satisfactory flocculation and sedimentation of biomass using the microalgae-bacteria consortium can be attributed to the start of the system with aerobic sludge inoculation. The good sedimentability of these reactors is typical of the aerobic processes of activated sludge, which, in turn, present more stable microbial aggregates allowing larger and denser sizes of granules.