esa-sceva/satcom-chunk-collection huggingface dataset:
# REDUCE--A Tool Supporting Inconsistencies Reduction in the Decision-Making Process
## 2 Overall Structure and Features of the Application
### Analysis of the Application Structure
#### 2.1.4 Comparison of Inconsistency Reduction Algorithms in REDUCE  
In the REDUCE application, two algorithms are available for reducing inconsistencies in pairwise comparison matrices: the **Xu & Wei algorithm**[60] and the **Szybowski algorithm**[61]--the tool is designed to help users improve the consistency of pairwise comparison matrices (PC matrices) by offering these two algorithms, each with distinct characteristics. The Xu & Wei algorithm is an iterative method integrated into REDUCE to reduce inconsistency while balancing the preservation of the original preference values. This method uses a regulatory parameter \(\alpha\) to control the adjustment intensity. For instance, in REDUCE, with \(\alpha=0.5\), the algorithm makes moderate adjustments to achieve a higher consistency level without excessively altering the original matrix. Consider the matrix  
\[A=\begin{bmatrix}1&3&2&4\\ 1/3&1&4&2\\ 1/2&1/4&1&5\\ 1/4&1/2&1/5&1\end{bmatrix}\]  
with \(CR=0.2425\).  
In REDUCE, applying the Xu & Wei algorithm with \(\alpha=0.5\) results in  
\[A_{\text{Xu \& Wei}}=\begin{bmatrix}1&2.1088&2.1366&4.6456\\ 0.4742&1&2.4817&2.6980\\ 0.4680&0.4029&1&3.4379\\ 0.2153&0.3706&0.2909&1\end{bmatrix}\]  
This adjusted matrix has a significantly lower consistency ratio (\(CR=0.0574\)), making it suitable for cases where reducing inconsistency is crucial.  
The Szybowski algorithm, also integrated into REDUCE, focuses on minimizing deviations while preserving the original reciprocal values. This method is intuitive and user friendly, making it ideal for users who prioritize maintaining the integrity of their original inputs. Applying the Szybowski algorithm in REDUCE to the same initial matrix results in  
\[A_{\text{Szybowski}}=\begin{bmatrix}1&3&2&4\\ 0.3333&1&1.4372&2\\ 0.5000&0.6958&1&5\\ 0.2500&0.5000&0.2000&1\end{bmatrix}\]  
with \(CR=0.0781\).  
The Szybowski method preserves original preferences more closely while still achieving a reasonable level of consistency. The Xu & Wei algorithm is best used when aiming for a higher consistency level, even if moderate changes to the original values are necessary--the Szybowski algorithm is recommended when preserving the original preferences is a priority, especially if only minor reductions in inconsistency are needed [87].
# Variable Multiple Interleaved Bi-Directional DC/DC Converter with Current Ripple Optimization
## 3 The Model of Variable Multiplicity Interleaving Bidirectional DC/DC Power Converter
### The Mean Value Model
\tag{17}\]  
Figure 6: The topology of variable multiplicity bidirectional DC/DC power converter. According to the volt-ampere characteristics of the capacitor and [PERSON]'s current law, the average current flowing through the load capacitor in a switching cycle can be obtained. \[\left\langle i_{\text{Load}}(t)\right\rangle_{T_{\text{s}}} =C\frac{d\left\langle\tau_{\text{Load}}(t)\right\rangle_{T_{\text{ s}}}}{dt} \tag{18}\] \[=\left\langle i_{\text{L1}}(t)\right\rangle_{T_{\text{s}}}+ \left\langle i_{\text{L2}}(t)\right\rangle_{T_{\text{s}}}+\cdots+\left\langle i _{\text{Ln}}(t)\right\rangle_{T_{\text{s}}}\]  
The characteristic equation of inductance after averaging treatment is. \[\left\{ \begin{aligned} \left\langle v_{\text{L1}}(t)\right\rangle_{T_{ \text{s}}}&=L_{1}\frac{d\left\langle\tau_{\text{L1}}(t)\right\rangle _{T_{\text{s}}}}{dt}\\ \left\langle v_{\text{L2}}(t)\right\rangle_{T_{\text{s}}}& =L_{2}\frac{d\left\langle\tau_{\text{L2}}(t)\right\rangle_{T_{ \text{s}}}}{dt}\\ \vdots\\ \left\langle v_{\text{Ln}}(t)\right\rangle_{T_{\text{s}}}& =L_{\text{n}}\frac{d\left\langle\tau_{\text{Ln}}(t)\right\rangle_{T_{\text{ s}}}}{dt}\end{aligned} \right. \tag{19}\]  
Substitute Equation (19) into Equation (17), and the following Equation (20) can be obtained. \[\left\{ \begin{aligned} L_{1}\frac{d\left\langle\
u_{\text{L1}}(t) \right\rangle_{T_{\text{s}}}}{dt}&=D_{1}\left\langle V_{\text{ DC}}\right\rangle_{T_{\text{s}}}-\left\langle V_{\text{Load}}\right\rangle_{T_{\text{s}}}- \left\langle i_{\text{L1}}\right\rangle_{T_{\text{s}}}R_{1}\\ L_{2}\frac{d\left\langle\
u_{\text{L2}}(t)\right\rangle_{T_{\text{s}} }}{dt}&=D_{2}\left\langle V_{\text{DC}}\right\rangle_{T_{\text{s}} }-\left\langle V_{\text{Load}}\right\rangle_{T_{\text{s}}}-\left\langle i_{ \text{L2}}\right\rangle_{T_{\text{s}}}R_{2}\\ &\vdots\\ L_{\text{n}}\frac{d\left\langle\tau_{\text{Ln}}(t)\right\rangle_{T_{ \text{s}}}}{dt}&=D_{\text{n}}\left\langle V_{\text{DC}}\right\rangle _{T_{\text{s}}}-\left\langle V_{\text{Load}}\right\rangle_{T_{\text{s}}}- \left\langle i_{\text{Ln}}\right\rangle_{T_{\text{s}}}R_{\text{n}}\end{aligned} \right. \tag{20}\]  
According to Equations (18) and (20), the average value model of the variable multiplicity bidirectional DC/DC power converter in Buck mode can be obtained, as shown in Figure 7.
## 7 Experiments
### Dataset Splitting at a 5:5 Ratio
#### 7.4.1 Convergence Results  
Figure 12 reveals that a larger batch size was beneficial to the convergence rate and system stability, whereas enlarging some kernels hindered NN stability. In addition, networks concatenated with a 3D structure were faster and more stable in terms of convergence. However, among the networks concatenated with a 3D structure, the model that did not remove the original first layer of the 2D convolution layer (WRN_ex3D) was faster in terms of convergence than was the model that removed the 2D convolution layer and widened the channel (WRN_ex3D_v2). Moreover, the model that replaced the mean compression method with a convolution layer with learnable parameters (WRN_ex3D_v3) was even more stable, and the convergence rate was faster than that of model WRN_ex3D.  
As shown in Figure 13, enlarging the batch size could stabilize the model. However, ultimate loss stopped at approximately 0.0043 and was unable to be lowered further, even if the learning rate was lowered. In addition, employing a batch size of 128 resulted  
Figure 12: Convergence results of average loss under the condition where the samples were randomly distributed between training and testing sets at a 5:5 ratio.  
in instability in the terminal stage; however, ultimate loss reached approximately 0.001, whereas that of model WRN_kernel5 was approximately 0.0026.  
With respect to the 3D convolution layer concatenation structure, the original WRN_ex3D model was the most stable and its loss reached the lowest at approximately 0.006. Although model WRN_ex3D_v2 was slow, it was stable in the terminal stage, with an ultimate loss at 0.0014. However, the loss of model WRN_ex3D_v3, which had a 3D convolution layer with learnable parameters, was prone to a sudden rise in the terminal stage. Because of this instability, a less inclined curve for reducing the learning rate was required. The ultimate loss achieved was approximately 0.000448.
# Privacy-Preserving Handover Optimization Using Federated Learning and LSTM Networks
## 4 Results
### Dynamic Handover Algorithm Performance
The Dynamic algorithm exhibited the lowest HOPP probability at 0.0333, demonstrating its effectiveness in reducing unnecessary handovers. This indicates a more conservative approach, resulting in fewer handovers and a more stable connection. In contrast, the A3_Event algorithm showed a HOPP probability of 0.0606, and the Greedy algorithm had the highest HOPP probability at 0.1348. The lower HOPP probability of the Dynamic algorithm highlights its success in optimizing handovers, making it particularly suitable for environments with varying signal conditions and mobility patterns. This result underscores the Dynamic algorithm's ability to maintain a balance between handover frequency and connection quality, enhancing overall network performance. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **HSPA+/LTE/5G** & **LTE/5G** & **5G** \\ \hline Hete\_FL 1 & 0.9531 & 0.9677 & 0.9940 \\ Homo\_FL 2 & 0.9460 & 0.9638 & 0.9901 \\ Cen\_LSTM 3 & 0.9458 & 0.9647 & 0.9433 \\ \hline \hline \end{tabular}  
* Heterogeneous federated learning. 2 Homogeneous federated learning. 3 Centralized LSTM Model.  
\end{table} 
Table 3: Model prediction accuracy in different datasets. The training time refers to the duration of the model training process. The execution time is the duration from loading the trained model to the completion of the prediction, while the prediction time is the time taken for the model to forecast future RSRP values. As shown in Table 4, the differences in execution and prediction times among the three model architectures are minimal. The centralized LSTM model has the shortest time since it does not involve model aggregation and transmission across multiple devices. However, in terms of training time, heterogeneous federated learning takes longer due to the clients' computational capabilities and the overhead of weight transmission. In our study, the proposed model architecture achieves an execution and prediction time of less than 1 s, with the LSTM prediction time step set to 200 (each data interval is 10 ms). This performance is sufficient to meet most real-time application requirements in practical environments, demonstrating its feasibility. Figure 11: Comparison of Algorithm and HOPP Probability. Figure 10: 95% Confidence Interval for RSRP Prediction.
## 3 Methodology
### Communication Platform Based on Modbus for Temperature Control
The AI controller dynamically adjusts HVAC operation by modifying holding registers (function code 0x03), which control heating and cooling parameters. A typical adjustment of the cooling setpoint is performed using the Write Single Register (0x06) command:  
[0x01] [0x06] [0x00] [0x14] [0x00] [0x05] [CRC]  
This command architecture enables accurate and real-time temperature control within smart buildings, as well as local control of environments such as small rooms. The integration of Modbus TCP into the AI-driven HVAC system provides several technical advantages: seamless interoperability with industrial control systems, responsive temperature adjustment facilitated by low-latency TCP communication, easy system expansion through a modular design, and cost-effective implementation on a large scale with minimal hardware requirements.
## 3 Non-Linear Load Effect on Operation of Low-Power Synchronous Generator
At \(k_{Ua}=3.5\%\), the average excitation current increased by 2.5% compared with the load flow when there was no rectifier load, and at \(k_{Ua}=15.6\%\) (rectifier load was 25% of the generator rated power), the average excitation current increased by 20%. This fact is due to improper operation of the ARE under such conditions, which requires the use of harmonic filters and excitation current limitation in the ARE. 2. The amplitude of the forced oscillations of the generator excitation current at a frequency multiple of 300 Hz increased. For example, at \(k_{Ua}=15.6\%\), the amplitude of the forced oscillations was 5% of the effective signal. This led to additional losses and extra heating. Figure 11: Waveforms of the turbogenerator rotor speed deviation when additional load was connected: 1—linear load; 2—non-linear load. 3. There were additional mechanical vibrations of the rotor with a frequency of 300 Hz. As the deviation from the sine waveform increased, the amplitude of these oscillations increased as well, which can lead to excessive runout during operation, rapid wear of the generator, and loss of stability.
# Efficient Semantic Segmentation Using Multi-Path Decoder
## 4 Results
### Ade20k
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c c c} \hline \hline  & **Road** & **Swalk** & **Build.** & **Wall** & **Fence** & **Pole** & **Tlight** & **Sign** & **veg.** & **Terrain** & **Sky** & **Person** & **Rider** & **Car** & **Truck** & **Bus** & **Train** & **mbike** & **Bike** & **mIoU** \\ \hline BL & 98.3 & 84.8 & 92.2 & 50.6 & 52.6 & 63.0 & 68.6 & 74.1 & 92.2 & 71.8 & 94.3 & 84.4 & 66.2 & 95.1 & 60.4 & 72.4 & 59.5 & 61.8 & 72.4 & 74.5 \\ +RB & 98.3 & 84.2 & 92.0 & 53.4 & 53.5 & 62.6 & 68.1 & 73.0 & 92.4 & 71.8 & 94.6 & 83.1 & 65.6 & 94.7 & 65.0 & 77.5 & 69.0 & 59.8 & 71.2 & 75.2 \\ +ED & 98.4 & 84.2 & 92.1 & 57.0 & 55.6 & 60.0 & 60.5 & 72.2 & 92.8 & 69.6 & 95.2 & 83.4 & 65.4 & 95.1 & 70.7 & 84.7 & 82.0 & 58.3 & 71.5 & 76.3 \\ +MPD & 98.5 & 85.4 & 92.3 & 51.9 & 56.1 & 61.2 & 67.6 & 74.4 & 92.9 & 71.2 & 95.2 & 83.9 & 66.7 & 95.4 & 72.7 & 83.0 & 76.0 & 62.8 & 72.6 & 76.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Per-class results on Cityscapes validation set. Training is done using the finely annotated train set. Scores are measured by %. ’BL’ denotes baseline. ’ED’ denotes edge decoder. ’MPD’ denotes multi-path decoder.
# Large Constellations of Small Satellites: A Survey of Near Future Challenges and Missions
## 3 Future Challenges
### Space Traffic Management
Thanks to the global situational awareness of the service, such a maneuver can ensure minimum fuel consumption while avoiding \"cascade maneuvers.\" Moreover, after suggesting the maneuver directly to the involved spacecraft operators, it can update its database and inform the other operators when the maneuver is accomplished. Another interesting attempt is discussed in [48], wherein the Australian Government is financing a conjunction assessment service featuring a ground-based laser \"deviator.\" The aim is to maneuver small uncooperative objects remotely from ground using a laser beam, which is theoretically feasible but with great technical challenges due to the laser power needed.
## 3 System Development
### Design Parameters of Telepresence Robot  
The design parameters of our telepresence robot are triggered by a wheeled motion of a vehicle, such as turning angle, velocity, and angular momentum. The telepresence robot's parameters are chosen after an analysis of the kinematic motion of the robot, as shown in Table 2.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Technical Specification** & **Unit** & **Min–Max Value** \\ \hline Robot speed & m/s & 0–3.25 \\ Robot momentum & N.m & 0–0.93 \\ Robot height & ft & 5\({}^{\prime}\)3\({}^{\prime\prime}\) \\ Robot width & ft & 1\({}^{\prime}\)5\({}^{\prime\prime}\) \\ Robot breadth & ft & 0\({}^{\prime}\)6\({}^{\prime\prime}\) \\ Robot weight & kg & 14 \\ Robot battery & Ah & 35 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Telepresence robot parameters.  
Figure 7: Manufactured Working Telepresence Robot Prototype. Our telepresence robot prototype is a robotic platform designed to facilitate remote communication and control in real-time. The proposed approach of the hybrid of DDQN and GRU can be implemented and tested on our manufactured robot to gather data and compare its performance with other approaches. The telepresence robot typically includes cameras, sensors, and actuators that allow a remote user to view and interact with the physical environment. The robot’s movement and actions can be controlled through a user interface, such as a joystick, keyboard, or touch screen.
# Blockchain-Based Federated Learning: A Survey and New Perspectives
## 4 Blockchain-Based Federated Learning: State-of-the-Art
### Application Direction of Blockchain-Enabled Federated Learning
#### 4.2.7 Audit Mechanisms  
Audit mechanisms perform transparent review of the source of the data and assess the traceability of the data on the chain. The distributed ledger feature of the blockchain ensures the consistency of model parameter data among multiple participants in federated learning, and the synchronization and sharing of model parameter data is safe and reliable, which can save node data. Moreover, the tamper-resistant nature of blockchain guarantees data transparency and traceability. Due to these two characteristics of blockchain, the censorship of blockchain-based federated learning data is realized.  
[PERSON] et al. proposed a verifiable and auditable federated learning framework named VFCChain based on blockchain system [103]. Main process: First, the blockchain selects a committee to collectively aggregate models and record verifiable proofs in the blockchain, achieving verifiability. Then, a novel authentication data structure is proposed for blockchain to improve the search efficiency of verifiable proof and further enhance the auditability of the model.
# Characterization of Chromatic Dispersion and
## 3 Experimental Set-Up
On the other hand, we were able to carry out Raman measurements by using a confocal Raman spectrometer (InVia, Renishaw, Wotton-under-Edge, UK) at room temperature. The source in this case was a 532 nm laser operated at only 1% of the maximum emitting power in order to avoid any damage on the sample material. The spectra of the fiber cores can be measured by placing each of the samples parallel to the laser beams on the excitation plane, thus allowing us to visualize the core end-face in the Raman microscope and to excite the core material alone. On the other hand, the Raman bands of each of the claddings can be obtained by placing the sample perpendicular to the laser beams. However, due to the small thickness of the cladding, about 10 \(\upmu\)m, the Raman equipment had to be set in its high-confocality mode before the experiment in order to excite the cladding material alone. In all cases, a 50\(\times\) objective was employed and the acquisition time was 30 s.
# Application and Assessment of Cooperative Localization in Three-Dimensional Vehicle Networks
## 5 Vehicle Model
### Vehicle State Equations  
Considering the single vehicle shown in Figure 1 and as described in the previous section, the pose of the vehicle can be represented by \(r_{0}^{v}=[x_{0}^{v}\ \ y_{0}^{v}\ \ z_{0}^{v}]^{\top}\) and \(\dot{q}^{v}\). For a kinematic model, we may choose the state vector as a collection of the seven pose variables:  
\[x^{v}=\begin{bmatrix}r_{0}^{v}\\ \dot{q}^{v}\end{bmatrix} \tag{6}\]  
Using (4) and (5), the driftless state equations may be written as:  
\[\dot{x}^{v}=g^{v}(x^{v})u^{v} \tag{7}\]  
where  
\[g^{v}=\begin{bmatrix}R_{0}^{v}&0_{3\times 4}\\ 0_{3\times 3}&\frac{1}{2}G^{v^{\top}}\end{bmatrix},\quad u^{v}=\begin{bmatrix}v^{v }\\ \omega^{v}\end{bmatrix} \tag{8}\]  
where \(0_{n\times m}\) represents the \(n\times m\) zero matrix and the vehicle input vector consists of the body-fixed velocities \(v^{v}\) and \(\omega^{v}\).  
The \(7\times 7\) Jacobian matrix of state equations, \(J^{v}\), necessary for EKF linearization is calculated as:  
\[J^{v}=\frac{\partial(g^{v}(x^{v})u^{v})}{\partial x^{v}}=\begin{bmatrix}0_{3 \times 3}&\frac{\partial\dot{q}^{v}_{0}}{\partial\dot{q}^{v}}\\ 0_{4\times 3}&\frac{\partial\dot{q}^{v}}{\partial\dot{q}^{v}}\end{bmatrix} \tag{9}\]  
where the nonzero components are:  
\[\frac{\partial\dot{r}_{0}^{v}}{\partial\dot{q}^{v}} =\begin{bmatrix}\frac{\partial r_{0}^{v}}{\partial q_{0}^{v}}& \frac{\partial\dot{r}_{0}^{v}}{\partial q^{v}}\end{bmatrix} \tag{10a}\] \[\frac{\partial\dot{q}^{v}}{\partial\dot{q}^{v}} =\frac{1}{2}\begin{bmatrix}0&-\omega^{v^{\top}}\\ \omega^{v}&-S(\omega^{v})\end{bmatrix} \tag{10b}\]  
and  
\[\frac{\partial\dot{r}_{0}^{v}}{\partial q_{0}^{v}} =[(4q_{0}^{v})I_{3}+2S(q^{v})]v^{v} \tag{11a}\] \[\frac{\partial\dot{r}_{0}^{v}}{\partial q^{v}} =2q^{v}v^{v^{\top}}+2(q^{v^{\top}}v^{v})I_{3}-2q_{0}^{v}S(v^{v}) \tag{11b}\]  
It is important to note that several approaches have been proposed to adhere to the unit quaternion constraint during the integration of the state equations [50, 51, 52].
## 4 Results: Proof of Concept
### Identity Management Implementation
#### 4.1.2 Issuance of Verifiable Credentials (VCs)
```
1 Credential:{
2\"#context\":'[[https://www.w3.org/2018/credentials/v1](https://www.w3.org/2018/credentials/v1)]([https://www.w3.org/2018/credentials/v1](https://www.w3.org/2018/credentials/v1))\",
3\"id\":'[[http://example.edu/credentials/1872](http://example.edu/credentials/1872)]([http://example.edu/credentials/1872](http://example.edu/credentials/1872))\",
4\"type\":[
5\"VerifiableCredential\",
6\"IoTDeviceCredential\"
7],
8
9\"credentialSubject\":{
10\"id\":'did:'id:'4 Yes3 JS4 gSevichGuuw7 TXg52474 SkuwHGBiGSFsp5 iH\",
11\"firmwareVerizon\":\"1.2.3\",
12\"mackdress\":\"00::11::22::33:44:55\",
13\"model\":\"Raspberry Pi 4\",
14\"name\":\"rpi\",
15\"serialNumber\":\"123456789\"
16},
17\"issuer\":\"did:iota:9 FJX2 qG2 EYeJsB5 JTVWZBpD3 LtMyMH3 wOffHashJypc3s\",
18\"issuanceDate\":\"2023-03-31T11::17:422\",
19\"expirationDate\":\"2023-03-31T11::22:422\",
20\"credentialStatus\":{
21\"id\":'did:'9 FJX2 qG2 EYeJsB5 JTVWZBpD3 LtMyMH3 wOffHashJypc3s#rev-service\",
22\"type\":\"ReveconBitmap2022\",
23\"revocationBitmapIndex\":\"2\"
24},
25\"proof\":{
26\"type\":\"JcsEd25S19 Signature2020\",
27\"verificationMethod\":
28\"did:iota:9 FJX2 qG2 EYeJsB6 JTVWZBpD3 LtMyMH3 wOffHashJypc3s#key-issuer\",
29\"signatureValue\":
30\(\sim\) \"2 AltmXUPEC1 GGbptL1 ZBRtYDdiDARRHrvvbBsSMHRES97 tN@myrprPkjB4 MNhybM7 nLk...him8 RoIgAUcpcSUALLeg\",
31\"proofPurpose\":\"assertionMethod\"
32}
```  
Listing 4: Semantic structure of the Raspberry Pi Verifiable Credential.
# Dental Hydrogels with Essential Oils with Potential Activity in Periodontitis
## Materials and Methods
### The Antimicrobial Effect  
Using agar well-diffusion experiments, the hydrogels' antibacterial efficacy was assessed. Four bacterial reference strains (n = 4 each of _Staphylococcus aureus_ ATCC 25923, _Bacillus cereus_ ATCC 14579, _Enterococcus faecalis_ ATCC 29219, and _Escherichia coli_ ATCC 25922) and two clinical _Staphylococcus aureus_ isolates (n = 2) were used. A concentration of 1 \(\times\) 10\({}^{7}\) colony forming units (CFU)/mL, determined using the McFarland scale, was employed for the 24-h bacterial culture. Flooding was used to inoculate the Muller Hinton agar plates, and then 6 mm diameter wells were cut (in triplicate). As a control, amoxicillin/clavulanic acid (20/10 mg, Oxoid) was used. The widths of the growth inhibition zones were measured following a 24-h incubation period at 37 \({}^{\circ}\)C. In addition, the minimum inhibitory concentrations (MIC) and minimum bactericidal (MBC) concentrations of the hydrogels were established using a broth microdilution method. Serial dilutions were made in 100 \(\mu\)L broths for the selected hydrogels; 5.0 \(\mu\)L of 1 \(\times\) 10\({}^{7}\) CFU/mL bacterial inoculum was added in each well, followed by cultivation at 37 \({}^{\circ}\)C for 24 h.  
The most crucial \"one-number characterization\" of how effective an antimicrobial drug is against a target organism is the minimum inhibitory concentration (MIC).  
The minimum inhibitory concentration assay is one of the main techniques for evaluating the emergence of antibiotic resistance in bacteria. These assays result in censoring, which, as opposed to a precise value, indicates a minimum inhibitory value from an interval of concentrations. The MIC is described as the lowest concentration (in mg L\({}^{-1}\)) of the antibacterial element that impedes the visible growth of a microorganism under defined circumstances noticed with the unaided eye. In clinical application, this in vitro parameter is used to classify the tested microorganism as clinically susceptible, intermediate, or resistant to the tested drug. For new drug candidates, MIC determination is one of the first steps to evaluate the antimicrobial potential [41; 42; 43].  
The quantities of hydrogels were 33.6 mg (50 \(\mu\)L), 16.8 mg (25 \(\mu\)L), 11.15 mg (16.6 \(\mu\)L), 8.4 mg (12.5 \(\mu\)L) and 6.72 mg (10 \(\mu\)L). The amount of pure essential oils was 0.11 \(\mu\)L, 0.055 \(\mu\)L, 0.036 \(\mu\)L, 0.0275 \(\mu\)L, and 0.022 \(\mu\)L. The lowest concentration of hydrogels with growth inhibition potential (the absence of turbidity) of bacteria is considered the MIC.  
For MBC evaluation, 10.0 \(\mu\)L of bacterial culture from each well was added to Muller-Hinton agar plates. After 24 h, the lowest hydrogel concentration that induces bacterial growth inhibition in the agar plate is considered the MBC.  
Three duplicates of each experiment were carried out. The MBC/MIC ratio (bactericidal--MBC/MIC 4 and bacteriostatic--MBC/MIC > 4) was used to express the bactericidal and bacteriostatic potential of the studied hydrogels.