esa-sceva/satcom-chunk-collection huggingface dataset:
# Departure from Flux-Gradient Relation in the Planetary Boundary Layer
## Appendix B Derivation of Equation (5)  
The lidar measures in the direction  
\[\mathbf{n}=(\sin\!\phi\cos\!\theta,\sin\!\phi\sin\!\theta,\cos\!\phi) \tag{1}\]  
where \(\phi\) is the constant half-opening angle and \(\theta\) is the variable azimuth angle. The line-of-sight velocity measured (positive away from the instrument) is \(\mathbf{n}\cdot\mathbf{u}\) where \(\mathbf{u}=(u,v,w)\) is the instantaneous wind vector at the position of measurement with, as mentioned in the main text, \(u\) is the East component of the velocity vector, \(v\) the North, and \(w\) the vertical. Usinq Equation (1) the line-of-sight speed in the principle geographical directions (since \(\theta\) is using the mathematical convention \(E=0^{\circ}\), \(N=90^{\circ}\), \(N=180^{\circ}\), and \(S=270^{\circ}\)) we get  
\[v_{r,E} =u\sin\!\phi+w\cos\!\phi \tag{2}\] \[v_{r,W} =-u\sin\!\phi+w\cos\!\phi\] (3) \[v_{r,N} =v\sin\!\phi+w\cos\!\phi\] (4) \[v_{r,S} =-v\sin\!\phi+w\cos\!\phi\ . \tag{5}\]  
Suppose that the turbulence at measurement height is statistically homogeneous in the horizontal directions, then the variance of the East and West beams can be written as  
\[\sigma^{2}(v_{r,E}) =\sigma_{u}^{2}\sin^{2}\!\phi+\sigma_{w}^{2}\cos^{2}\!\phi+2\! \left\langle u^{\prime}w^{\prime}\right\rangle\sin\!\phi\cos\!\phi \tag{6}\] \[\sigma^{2}(v_{r,W}) =\sigma_{u}^{2}\sin^{2}\!\phi+\sigma_{w}^{2}\cos^{2}\!\phi-2\! \left\langle u^{\prime}w^{\prime}\right\rangle\sin\!\phi\cos\!\phi \tag{7}\]where \(\mathrm{a^{\prime}}\) indicates the fluctuations around the mean. Subtracting these equations and using the trigonometric relation \(2\sin\!\phi\cos\!\phi=\sin 2\phi\) one gets  
\[\left\langle u^{\prime}w^{\prime}\right\rangle=\frac{\sigma^{2}(v_{r,E})-\sigma^ {2}(v_{r,W})}{2\sin 2\phi}\ \ . \tag{10}\]  
Similarly, using the North and South beams the equation for \(\left\langle v^{\prime}w^{\prime}\right\rangle\) can be obtained. If the beams are not perfectly aligned with the principal geographical directions but deviates with an angle \(\delta\) then the wind in the East-North coordinate system can be expressed as  
\[\left(\begin{matrix}\tilde{u}\\ \tilde{v}\end{matrix}\right)=\begin{pmatrix}\cos\!\delta&-\sin\!\delta\\ \sin\!\delta&\cos\!\delta\end{pmatrix}\begin{pmatrix}u\\ v\end{pmatrix} \tag{11}\]  
Taking the fluctuations on both sides, multiplying with \(w^{\prime}\) and averaging we get a relation between the fluxes in the two systems. Combining that equation with Equation (10) and the corrospending equation for \(\left\langle v^{\prime}w^{\prime}\right\rangle\) we finally get Equation (5).
## 2 Experiment and Methods
### Data Processing  
The discharge voltage and current waveforms are shown in Figure 4a. There were many micro discharge channels in the gas gap of the DBD reactor. It is difficult to measure the discharge power using the integral of voltage and current product; therefore, the discharge power in DBD reactors is usually measured using the Q-V Lissajous figure, which requires a capacitor (\(C_{m}\)) in series in the DBD circuit. Figure 4b shows the Lissajous figure measured during the experiment. The discharge power is calculated by:  
\[P=fC_{m}K_{x}K_{y}KA \tag{1}\]  
where \(f\) is the discharge frequency in Hz; \(K_{x}\) is the X-axis sensitivity, V/grid; \(K_{y}\) is the Y-axis sensitivity, V/grid; \(K\) is the voltage decrease ratio, 1000:1; \(A\) is the area enclosed by the Lissajous figure.  
The removal efficiency of NO\({}_{x}\) is calculated using the following formula:  
\[\text{Removal efficiency of NO}_{x}=\frac{\left[\text{NO}_{x}\right]_{ \text{inlet}}-\left[\text{NO}_{x}\right]_{\text{outlet}}}{\left[\text{NO}_{x }\right]_{\text{inlet}}}\times 100\% \tag{2}\]  
where \(\left[\text{NO}_{x}\right]_{\text{inlet}}\) and \(\left[\text{NO}_{x}\right]_{\text{outlet}}\) are the concentrations of NO\({}_{x}\) (ppm) measured at the inlet and outlet of the DBD reactor, respectively.  
The removal efficiency of SO\({}_{2}\) is calculated using the following formula:  
\[\text{Removal efficiency of SO}_{2}=\frac{\left[\text{SO}_{2}\right]_{ \text{inlet}}-\left[\text{SO}_{2}\right]_{\text{outlet}}}{\left[\text{SO}_{2 }\right]_{\text{inlet}}}\times 100\% \tag{3}\]  
Figure 4: The current and voltage waveforms for the DBD reactor: (**a**) the voltage and current waveforms; (**b**) the Lissajous figure.  
where \(\left[\text{SO}_{2}\right]_{\text{inlet}}\) and \(\left[\text{SO}_{2}\right]_{\text{outlet}}\) are the concentrations of SO\({}_{2}\) (ppm) at the inlet and outlet of the DBD reactor, respectively.  
The oxidation degree of NO\({}_{x}\) is defined as follows:  
\[\alpha_{0}=\frac{\varphi(\text{NO}_{2})}{\varphi(\text{NO}_{x})}\times 100\% \tag{4}\]  
where \(\alpha_{0}\) is the oxidation degree of NO\({}_{x}\); \(\varphi(\text{NO}_{2})\) is the concentration of NO\({}_{2}\) in ppm; \(\varphi(\text{NO}_{x})\) is the concentration of NO\({}_{x}\)(NO + NO\({}_{2}\)) in ppm.
# Impedance Modeling Based Method for Sub/Supsynchronous Oscillation Analysis of D-PMSG Wind Farm
## 2 Impedance Characteristics Analysis of D-PMSG  
This section constructs the impedance model of grid-connected D-PMSG based wind farm. The structure diagram of the wind farm integrated in weak AC grid is presented first. Secondly, two assumptions are adopted to simplify the D-PMSG to a grid-connected converter. Then, the small-signal model of PLL considering frequency coupling is proposed, which is a key step to apply the harmonic linearization in different reference frame. Based on the PLL model, harmonic components in current control loop could be further obtained. Another simplification is about the PWM converter model. Finally, the impedance of D-PMSG is calculated and the relationship between coupled currents is analyzed.
## 3 Results
### Assessment of Volumetric Dentin Removal  
When the mean values of volumetric dentin removal data were analyzed across all groups, the ProTaper Gold rotary system (2.015 \(\pm\) 0.074) again exhibited the significantly highest value of dentin removal as compared, volumetrically, to the RaceEvo, R-Motion and Manual instrumentation groups (0.4629 \(\pm\) 0.018; 0.4957 \(\pm\) 0.018; 0.8427 \(\pm\) 0.12, respectively/\(p\) = 0.000 for all comparisons), whereas no statistical difference was observed in the  
Figure 3: Multiplanar images of a single primary root canal.  
Figure 2: Thresholding for segmentation of the primary root canal. (**A**) Active contour “Snake” segmentation window; (**B**) Pre-segmentation speed image of a single primary root canal with threshold between \(-\)1024 and 1200 GV; (**C**) Bubble placement to initialize the contour with 1.20 mm radius red bubbles; (**D**) Post-execution speed image of the root canal (red areas); (**E**) Final image of the primary root canal.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Multiple Comparisons of Volumetric Dentin Removal across Experimental Groups** & & _p-Value_ \\ \hline Race Evo vs. R-Motion & 0.4629 \(\pm\) 0.018 & 0.4957 \(\pm\) 0.017 & 0.679 \\ Race Evo vs. ProTaper Gold & 0.4629 \(\pm\) 0.019 & 2.015 \(\pm\) 0.074 & 0.000 *** \\ Race Evo vs. Manual & 0.4629 \(\pm\) 0.020 & 0.8427 \(\pm\) 0.11 & 0.014 * \\ R-Motion vs. ProTaper Gold & 0.4957 \(\pm\) 0.017 & 2.015 \(\pm\) 0.074 & 0.000 *** \\ R-Motion vs. Manual & 0.4957 \(\pm\) 0.018 & 0.8427 \(\pm\) 0.11 & 0.027 * \\ ProTaper Gold vs. Manual & 2.015 \(\pm\) 0.074 & 0.8427 \(\pm\) 0.12 & 0.000 *** \\ \hline \hline \end{tabular}
\end{table}
Table 2: Multiple comparisons of volumetric dentin removal across experimental groups. (Results are given as mean values \(\pm\) SEM). (*** \(p\) < 0.001, * \(p\) < 0.1).  
Figure 6: Volumetric dentin removal across experimental groups. Results are given as mean values \(\pm\) SEM. (*** \(p\) < 0.001).  
Figure 7: Buccolingual views of preoperative (red) and postoperative (yellow) root canal three-dimensional (3D) reconstruction images of a primary mandibular molar tooth (reconstructed from an exported surface mesh STL data). (**A**) Preoperative-3D buccolingual view of a root canal; (**B**) Postoperative-3D buccolingual view of a root canal.  
In the present study, the radiographic success of all the tested manual and rotary instrumentation systems was also evaluated. There were four (4) primary root canals were detected with perforations in the ProTaper Gold (PTG) rotary file system and also one (1) case with perforation was observed in the manual instrumentation group while no cement perforation was present in both RaceEvo and R-Motion group after preparation procedure among all tested groups. (Perforated root canals were replaced with new primary root canals and the procedures were repeated).
## 3 Metabolic Responses to Different Antibiotic Classes
### Antimetabolite Antibiotics: Direct Effect and Biosynthetic Compensation
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Antibiotic Class** & **Target Mechanism** & **Metabolic Response** & **References** \\ \hline \multirow{2}{*}{\(\beta\)-lactams} & Inhib PBPs and & Upregulation of peptidoglycan precursor & \\  & peptidoglycan synthesis & pathways, glyoxylate cycle activation, & [6; 35; 36; 37; 38; 39; 40; 41; 42; 43] \\  & & fermentative shift & \\ \hline \multirow{2}{*}{Aminoglycososides} & Bind ribosomal subunits, & \multirow{2}{*}{
\begin{tabular}{c} Fermentative metabolism, reduced \\ respiration, increased glutathione/NADPH \\ pathway activity \\ \end{tabular} } & [6; 7; 12; 44; 45; 46] \\  & & & pathway activity \\ \hline \multirow{2}{*}{Quinolones} & Inhib DNA & Suppression of TCA cycle, activation of \\  & gyrase/topoisomerase, & glyoxylate cycle, reduced ROS via altered \\  & induce ROS & & redox flux \\ \hline \multirow{2}{*}{Glycopeptides} & Bind D-Ala-D-Ala, block & Metabolic quiescence, reorientation of \\  & peptidoglycan cross-linking & carbon metabolism, phosphoenolpyruvate- & [12; 53; 54; 55; 56] \\  & pyruvate-oxaloacetate flux & \\ \hline \multirow{2}{*}{Polymyxins} & Disrupt outer membrane via & Lipid A modification (L-Ara4N, pEtN), \\  & lipid interaction & altered lipid biosynthesis, activation of \\  & & two-component systems & \\ \hline \multirow{2}{*}{Antimetabolites} & Block nucleotide or cell wall & Uptake of purines, derepression of purine \\  & precursor biosynthesis & synthesis, activation of pentose & [64; 65; 66; 67; 68] \\ \hline \multirow{6}{*}{PBBPs: penicillin-binding proteins; TCA: tricarboxylic acid; ROS: reactive oxygen species; L-Ara4N: 4-amino-4-deoxy-L-arabinose; pEN: phosphoethanolamine.} & \\  & & & \\ \end{tabular}
\end{table} 
Table 3: Metabolic adaptations to different classes of antibiotics.
# Machine Learning Methods with Decision Forests for Parkinson's Detection
## 3 Decision Forests
### Decision Forest by Penalizing Attributes (ForestPA)  
Another novel decision forest called Decision Forest by Penalizing Attributes (ForestPA) [28] has been proposed by the same authors of SysFor with a provision for penalizing attributes during the tree building process. Unlike SysFor, which plants C4.5 decision trees in the forest, the ForestPA plants the Classification and Regress Tree (CART) as an effective decision-maker. Like Random Forest, the ForestPA generates a bootstrap sample \(S\) from the original training instances \(D\). The CART decision trees are built upon these samples, where the attributes merit values decide the splitting point. The merit values of an attribute \(M_{A_{i}}\) is calculated as:  
\[M_{A_{i}}=\big{(}C_{A_{i}}\times W_{A_{i}}\big{)} \tag{8}\]  
where \(C_{A_{i}}\) represents the classification capacity and \(W_{A_{i}}\) represents weights of attribute A. The first tree is generated with the default weight \(1\). The weight of the attributes is gradually increased during the tree building process. The level of the tree decides the final weight of the attributes. A weight range function of \(WR_{d}\) for tree level of \(d\) decreases the attribute weight and is represented as:  
\[WR_{d}=\left\{\begin{array}{c}\left[0.0000,\;e^{-1/d}\right]\\ \left[e^{-1/(d-1)}+0.0001,e^{-1/d}\right]\end{array}\right\}\,\ if\ d=1\ \tag{9}\]  
The Equation (9) essentially allocates advantageous weight to the lower level nodes & penalizes to the higher-level nodes. In the other words, the nodes having lower rules in hand have more advantageous weight & nodes having significant values have disadvantageous weights. Moreover, there are incidents where an attribute is tested at the root node, thus, scoring the lowest weight of 0.0000, which results the attribute not to be selected in subsequent trees. Therefore, the authors suggested a dynamic increase in weight on the attributes that are tested at the root node only. The weight increment value \(WA_{i}^{++}\) of such attributes is calculated as:  
\[WA_{i}^{++}\ =\ \frac{1.0\ -\ WA_{i}}{(h\ +\ 1)\ -\ \ell} \tag{10}\]  
where \(WA_{i}\) is the weight of the attribute \(A_{i}\) obtained from a tree at level \(\ell\) and \(h\) is the height of the tree (highest level in the tree). The process of dynamic allocation of weight allows the decision trees to predict the unlabeled instances. The prediction output of the trees is combined and the final decision about the class label of the instance is determined through voting.
# A Dual-Adaptive Approach Based on Discrete Cosine Transform for Removal of ECG Baseline Wander
## 2 Methods
### The Proposed Dual-Adaptive Scheme
#### 2.2.1 Calculating the Cardiac Fundamental Frequency (CFF)  
Common methods to calculate CFF are based on R-wave detection. However, the R-wave detection itself is an awful task in the presence of various artifacts. Moreover, the CFF calculation according to the R-wave occurrence is improper in the case of abnormal ECG records, which is illustrated in Section 3. In this paper, we present a simple and effective method to calculate CFF through DCT domain analysis. It is well known that, for periodic waves, there must be a distinct peak that corresponds to the fundamental frequency in the spectrum domain. ECG signals can roughly be regarded as periodic waves, but their periodic properties are usually destroyed by artifacts. Nevertheless, the periodicity of ECG is well reflected by its QRS-complexes. Based on these ideas, CFF can be calculated by the following three substeps.  
* Extract the QRS-complexes \(x_{QRS}(n)\) from the ECG signal \(x(n)\) by a DCT-based band-pass filter whose passband is [5; 6; 7; 8; 9; 10] Hz.
* Waveform \(\left|x_{QRS}(n)\right|\) in Figure 1c is taken from QRS-complexes to strengthen the periodicity and the DCT coefficients \(\left|y_{QRS}(n)\right|\) (in Figure 1d) of \(\left|x_{QRS}(n)\right|\) are calculated afterward.
* Detect the peak's index \(I_{CFF}\) related to CFF in \(\left|y_{QRS}(n)\right|\). Detecting \(I_{CFF}\) is based on a threshold decision as shown in Figure 1d. The maximum value \(V_{m}\) of \(\left|y_{QRS}(n)\right|\) in the range of 0.2 Hz to 2.5 Hz is detected at first. The index \(I_{m}\) of \(V_{m}\) may be related to CFF but also could be related to the higher harmonics of CFF. In this study, a threshold value of 0.65 was chosen empirically to determine \(I_{CFF}\) which is the first point whose value exceeds \((\theta*V_{m})\).
# Self-Assembled MoS2/ssDNA Nanostructures for the Capacitive Aptasensing of Acetamiprid Insecticide
## 3 Results and Discussions
### LA-MoS2/SPCE Surface Modification and Characterization  
To build the aptasensing platform, the SPCE surface was modified with LA-MoS2 nano-sheets using an electrochemical deposition method. Indeed, LA-MoS2 was deposited using a continuous cyclic voltammetry sweep (\(n=10\)) from the corresponding aqueous dispersion, which is an excellent general approach that allows modifying carbon surface by 2D nanomaterials through hydrophobic interaction [38]. This approach has several advantages compared to the conventional deposition methods that begin with precursors molecules. The obtained coating conserved the main properties of the deposited nanomaterials and it can be performed in aqueous solutions under mild condition, at moderate potential, and at RT. Using an electrical field, the chemical environment such as pH changes around the electrode surface due to oxidation or reduction of water. This change results on a decrease of the inter-particle repulsive forces by suppression of the nanomaterial net surface charge, which stabilizes the nanomaterial dispersion and causing its aggregation and irreversible deposition on the electrode surface [39].  
The surface morphology before and after SPCE modification was probed using scanning electron microscopy (SEM) to analyze the morphology and energy-dispersive X-ray EDX (EDX) to check the surface composition. SEMs images of bare and LA-MoS2-modified SPCE are presented respectively on Figure 2a,b. The electrodeposition of LA-MoS2 led to the formation of multilayer of MoS2 nano-sheets with aggregates (Figure 2b). The vertical orientation of the MoS2 nano-sheets could be explained by the interaction between different MoS2 islands during electrodeposition. The EDX spectrum confirmed the presence of molybdenum and sulfur (Figure 2c). It also showed the Cl and O provided from ClO4 used in electrochemical deposition process and remaining in the MoS2 modified SPCE.  
Figure 1: Spectroscopic characterization of MoS2 and LA–MoS2: (**a**) Spectrum of MoS2 after hydrothermal synthesis; (**b**) FTIR spectra of MoS2 nanosheets and LA–MoS2 conjugate.
# Modeling Polymer Microencapsulation Processes Using CFD and Population Balance Models
## 2 Materials and Methods
### Experimental Methodology  
In the experimental setup, 1% \(w/v\) polyvinyl alcohol/water solution (PVA) was prepared as the continuous phase, and 20% \(w/v\) polyethyleneimine/dichloromethane solution (PEI) served as the dispersed phase. Table 1 presents the physical properties of the materials used.  
The procedure, illustrated in Figure 1, commenced with placing 90 mL of PVA in a beaker equipped with a high-shear S18N-19G dispersing tool (IKA, Wilmington NC, USA) [50]. Subsequently, 10 mL of PEI was introduced from the top using a syringe, with the agitator impeller initially set to its lowest speed to generate turbulence and prevent the PEI from adhering to the beaker bottom. Once the mixing domain stabilized, the impeller speed was adjusted to the desired test velocity. The flow rate of the dispersed phase was maintained at 0.33 mL/min, taking approximately half an hour to complete the PEI dispersion into PVA, thereby concluding the microencapsulation process. For this study, impeller speeds were set at 5000, 7500, 10,000, 12,000, and 15,000 rpm, which are typical for high-shear agitators in simple emulsion microencapsulation processes [51; 52; 53].  
After completing the emulsification process, the PEI/PVA dispersions obtained at each tested agitator velocity were washed using a Sorvall RC5B Plus refrigerated centrifuge (Thermo Scientific, Waltham, MA, USA) [54] for three cycles. Following centrifugation, the microcapsules were formed through a freeze-drying technique [55]. Drops from each processed sample were placed on aluminum specimen mounts, stored in a box, and subjected to \(-80\)\({}^{\circ}\)C for 24 h before being dried in a LyoQuest apparatus (Telstar, Terrassa, Spain) [56].  
Scanning electron microscopy (SEM) and dynamic scattering light (DSL) techniques were used to obtain qualitative and quantitative data on the morphology and size of the prepared particles. The DSL technique specifically measured the obtained particle sizes at different impeller speeds. The data were then analyzed, plotted, and used to validate the CFD model, as discussed in the following sections. For SEM, a Focus Ion Beam Neon40 Crossbeam workstation (Carl Zeiss, Oberkochen, Germany) [57] was used. For DLS, a NanoBrook 90 Plus Zeta Instrument (Brookhaven Instruments, Holtsville, NY,  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Material** & **Density (kg/m\({}^{3}\))** & **Viscosity (Pa \(\cdot\) s)** \\ \hline PEI & 1332.7 & 3.21 \(\times\) 10\({}^{-1}\) \\ PVA & 998.00 & 1.02 \(\times\) 10\({}^{-3}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Physical properties at 20 \({}^{\circ}\)C and 1 atm.  
Figure 1: Schematic diagram of the experimental setup.  
USA) [58] was used. Figure 2 shows examples of the SEM images obtained for each tested agitator speed.
# Experimental Assessment of the Spatial and Temporal Distribution of Non-Contact Tonometer Airflows
## 3 Results
### CorvisST Airflow Pressure  
#### 3.2.1 Spatial Distribution  
The maximum pressure at the central measurement point was found to be 96.4 \(\pm\) 142 mmHg (95%CI 96.1 to 96.6 mmHg). The airflow pressure could be distinguished from the sensor noise within an area of 45.2 mm\({}^{2}\), Figure 5a-c and Table 1. The airflow pressure was highly repeatable within the area affected (CoV 4.2%; 95%CI 3.9% to 4.4%).
# Measurement-Device-Independent Two-Party Cryptography with Error Estimation
## 3 Weak String Erasure
### Definition  
Before introducing our redesigned WSE protocol, we first introduce its definition. WSE is a basic two-party cryptographic protocol between [PERSON] and [PERSON] that can be used to construct other two-party cryptographic protocols, such as bit commitment, oblivious transfer, etc. The ideal functionality of WSE is shown in Figure 3[2].  
The process of WSE can be seen as a black box, with no inputs from [PERSON] and [PERSON]. As outputs, [PERSON] gets a randomly chosen bits string \(X^{n}\) and [PERSON] obtains a randomly chosen subset of indices \(I\subseteq[n]\) and the bits \(X_{I}\in\{0,1\}^{|I|}\). Next, we denote \(A\) and \(B\) as honest [PERSON] and [PERSON], and \(A^{\prime}\) and \(B^{\prime}\) as dishonest [PERSON] and [PERSON]. \(\rho\) represents the joint state generated in the actual protocol operation, and \(\sigma\) represents the state generated in the ideal protocol operation.  
The specific definition of WSE is as follows [2]:  
**Definition 3** (Weak string erasure [2]).: _A \((n,\lambda,\varepsilon)\)-weak string erasure (WSE) scheme is a protocol between [PERSON] and [PERSON] satisfying the following properties:_  
1. _Correctness: If both parties are honest, then for any attack strategy of the third-party attacker, [PERSON] always gets a uniformly distributed string_ \(X^{n}\in_{R}\{0,1\}^{n}\)_and [PERSON] will get an index_ \(I\in[n]\) _and_ \(X_{I}\in\{0,1\}^{|I|}\)_;_
2. _Security for [PERSON]: If [PERSON] is honest, then for any attack strategy of dishonest [PERSON], we have:_ \[\frac{1}{n}H_{\min}^{\varepsilon}(X^{n}|B^{\prime})\geq\lambda.\]  
Figure 3: The ideal functionality of weak string erasure (WSE).  
Security for [PERSON]: If [PERSON] is honest, then for any attack strategy of dishonest [PERSON], there exists \(\alpha\geq 0\):  
\[\mathrm{H_{min}}(I|A^{\prime})\geq\alpha.\]
## 6 Experimental Results
### Performance Metrics  
The comparison study considers four performance metrics: success ratio, number of executors, execution time, and average response time.  
**Success ratio:**: Consider a set \(\Sigma=\{\Delta_{1},\Delta_{2},\ldots,\Delta_{i},\ldots,\Delta_{N}\}\) composed of \(N\) subsets of callbacks \(\Delta_{i}\), and \(A\) as a scheduling algorithm. We say that \(\Delta_{i}\) can be scheduled by the scheduling algorithm \(A\) if all callbacks from \(\Delta_{i}\) meet their deadlines, denoted by \(A(\Delta_{i})=1\), and if not, we denote it by \(A(\Delta_{i})=0\). As a result, the success rate \(SR\) of the scheduling algorithm \(A\) on \(\Sigma\) is defined by the following:  
\[SR=100*\frac{\sum_{i=1}^{N}A(\Delta_{i})}{N} \tag{15}\]  
**Number of executors:**: This metric represents the number of executors provided by the algorithm to schedule all callbacks while meeting real-time constraints. We try to minimize this metric.
**Runtime:**: This metric measures the time it takes the algorithm to obtain a solution.
**Average response time:**: Average response time is the time elapsed between the activation and completion of a callback. The following equation is defined to calculate the average response time rate \(TRm\) for a set of callbacks with cardinality \(n\):  
\[TRm=100*\frac{\sum_{i=1}^{n}\frac{\frac{\Delta_{i}}{d_{i}}}{n} \tag{16}\]