esa-sceva/satcom-chunk-collection huggingface dataset:
# An Improved Jacobi-Based Detector for Massive MIMO Systems
## 1 Introduction
As the SD method provides an efficient searching direction, the combined SD and Jacobi algorithm is capable of satisfying the convergence condition. Furthermore, compared to the conventional Jacobi algorithm, the combined algorithm is more efficient to accommodate a different number of users. (2) Note that, when the iterative approximate solution is close to the exact solution, the SD method will no longer provide an efficient searching direction, and the whole-correction method [21] is employed to improve the convergence. By exploiting the obtained, the more accurate solution can be attained by the whole-correction method. The remainder of the paper is structured as follows. We briefly introduce the system model and present a review of previously proposed approaches in Section 2. In Section 3, a hybrid Jacobi-based iterative method is proposed, where the analysis of convergence and computational complexity of the proposed Jacobi iterative method are presented. In Section 4, numerous simulation results are demonstrated. Finally, the entire paper is concluded in Section 5. Notation: In this paper, bold-face, lower-case letters represent the column vectors (e.g., **a**), while the bold-face, upper-case letters refer to the matrices (e.g., **A**). The superscript of matrix **A**, **A\({}^{T}\)**, **A\({}^{H}\)**, **A\({}^{-1}\)** and **A\({}^{+}\)** indicate the transpose, the Hermitian transpose, the inverse and the Moore-Penrose inverse of **A**, respectively. Furthermore, **I\({}_{K}\)** denotes the \(K\times K\) identify matrix, [**a b**] denotes the inner product of the vectors, and \(\|\cdot\|\) stands for the Euclidean norm of a vector.
# OCT Capillary Depth Measurement in Copper Micro Welding Using Green Lasers
## 2 Materials and Methods  
The experimental investigations were carried out using a scanner based optical setup. A detailed schematic illustration of the setup used in the experiments is displayed in Figure 1.  
A frequency doubled Disk Laser (TruDisk Pulse 421, Trumpf) emitting green light (\(\lambda=515\) nm) was used as laser source. The laser system has an average power of 400 W with pulse durations ranging from 0.3 ms to 50 ms. A fiber core diameter of 150 \(\upmu\)m combined with the optical setup results in a focal diameter of 300 \(\upmu\)m. A laser scanner was used to move the processing beam (green beam, Figure 1) relative to the sample surface in a linear motion. Each weld was carried out within a single pulse. Pure copper (Cu-ETP) with dimensions of 40 mm \(\times\) 20 mm \(\times\) 2 mm was used as sample. No shielding gas was used on the material.  
Optical coherence tomography (OCT) was used for coaxial inline monitoring of the welding process. An additional laser scanning system is provided with the OCT System and allows for easy adjustment of the OCT beam (light red beam, Figure 1) position, as well as super positioning the welding motion with a custom OCT beam movement during the weld. The OCT System (LDD-600; IPG Photonics, formerly Laser Depth Dynamics) uses a measuring wavelength of 840 nm. The acquisition rate in the conducted experiments was set to 200 kHz. The focal diameter on the surface sample was measured to be \(\sim\)33 nm.  
Additionally, coaxial high-speed imaging was used to determine the process regime, as well as the weld process stability. In Figure 1, the imaging beam path is represented by a grey beam. Using a high-speed camera (Phantom VEO1310, Vision Research) allowed recording the welding process with a framerate of 50 kHz at a resolution of 640 \(\times\) 240 pixels, resulting in an observed area of 8000 \(\upmu\)m \(\times\) 3000 \(\upmu\)m. The exposure time was set to 1 \(\upmu\)s. No additional illumination was used. A notch filter with a center wavelength of 514 \(\pm\) 2 nm, as well as a shortpass filter with a cut-off wavelength of 750 nm, was used to block the processing laser, as well as the measuring laser of the OCT System.  
The selection of the process parameters was based on the investigations in Reference [5] to achieve welding depths of up to 1 mm as used in typical copper micro welding applications in different weld regimes. The focal position of the processing beam was set to be on the sample surface. The laser power was varied in the range from 1000 W to 3000 W, while the welding speed was varied from 250 \(\frac{\mathrm{mm}}{\mathrm{s}}\) to 750 \(\frac{\mathrm{mm}}{\mathrm{s}}\). Both parameters remained at a constant value during each welding process. The weld length in the experiments was set to 5 mm. Due to the limitation of the laser with a maximum pulse energy of 40 J, the weld length for the experiments with a welding speed of 250 \(\frac{\mathrm{mm}}{\mathrm{s}}\) was set to 2.5 mm.
## 2 Materials and Methods
### Characterization
#### 2.3.3 Chlorine Content  
Chloride concentration was measured using a chloride ion-selective electrode with the Oakton Ion 700 Cl-meter, calibrated using 1, 10, and 100 ppm dilutions from a 1000 ppm Cl' standard solution. For this study, all chlorine originated from the solid phase, and the sample to be measured was prepared in accordance with ASTM standard D4208-18. After the combustion was complete, the bomb was opened, and the pressure was then released at a steady rate, taking at least 2 min to avoid disturbing the contents. After the bomb was opened, all interior parts were washed thoroughly with distilled water and collected in a 140 mL beaker for testing. The total volume of liquid was kept between 80 and 90 mL. Liquid mass was next taken on an A&D EK-15 KL scale (readability of 0.1 g). Finally, prior to measuring the chlorine content, two milliliters of 5M NaNO\({}_{3}\) ionic strength adjustor (ISA) were added to the solution.  
The Oakton Cl-meter determined the chloride concentration by measuring electric potential across a liquid and converting it to a concentration value in ppm. During measurements, a magnetic stirrer was used to keep the solution homogeneous, and ambient temperature was maintained for each test. Since the aqueous chloride concentration provided by the measurement was given with respect to the mass, the chlorine concentration of the original solid could be calculated according to Equation (3),  
\[C_{Cl,\ sample}=\frac{C_{Cl,\ aq}M_{aq}}{M_{sample}}. \tag{2}\]  
where \(C_{Cl,\ sample}\). and \(C_{Cl,\ aq}\) are the chlorine/chloride concentrations in ppm of the material sample and aqueous solution, respectively. \(M_{sample}\). and \(M_{aq}\). are the respective masses of the material sample and aqueous solution.
###### Abstract  
This study analyzed the result of parameter optimization using the digital elevation model (DEM) resolution in the TOPography-based hydrological MODEL (TOPMODEL). Also, this study investigated the sensitivity of the TOPMODEL efficiency by applying the varying resolution of the DEM grid cell size. This work applied TOPMODEL to two mountainous watersheds in South Korea: the Dongkok watershed in the Wicheon river basin and the leemokjung watershed in the Pyeongchang river basin. The DEM grid cell sizes were 5, 10, 20, 40, 80, 160, and 300 m. The effect of DEM grid cell size on the runoff was investigated by using the DEM grid cell size resolution to optimize the parameter sets. As the DEM grid cell size increased, the estimated peak discharge was found to increase based on different parameter sets. In addition, this study investigated the DEM grid cell size that was most reliable for use in runoff simulations with various parameter sets in the experimental watersheds. The results demonstrated that the TOPMODEL efficiencies in both the Dongkok and leemokjung watersheds rarely changed up to a DEM grid-size resolution of about 40 m, but the TOPMODEL efficiencies changed with the coarse resolution as the parameter sets were changed. This study is important for understanding and quantifying the modeling behaviors of TOPMODEL under the influence of DEM resolution based on different parameter sets.  
DEM grid cell size; efficiency; mountainous watersheds; optimized parameter set; TOPMODEL +
Footnote †: journal: Applied Sciences  
Article
## 3 Numerical Analyses
### Fiber Model
Only the modal distribution was considered because, in the case of the uniform acceleration profile, the intersection between the capacity curve and the capacity spectrum occurs in the elastic branch for both the X and Y directions. The obtained values of the behavior factor for the modal distribution are q = 1.37 (X direction) and q = 1.39 (Y direction). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Direction** & **d*u** & **d*y** & **F*y** & **T* \\
**[-]** & **[mm]** & **[mm]** & **[kN]** & **[s]** \\ \hline X & 34.27 & 24.10 & 3340 & 0.59 \\ Y & 34.48 & 22.59 & 3472 & 0.57 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameters obtained from the bilinearization of the capacity curves with modal distribution. Figure 8: Site response spectrum according to NTC18. Figure 9: Capacity curves in the X (**a**) and Y (**b**) loading directions. As alternative to the N2 method, the Capacity Spectrum Method (CSM) proposed in [53] was also used to evaluate the behavior factor q, adopting the procedure A of [54]. A comparison of the results is reported in Table 5, where S\({}_{\text{a}}\) is the spectral acceleration evaluated in correspondence to the performance point, S\({}_{\text{d}}\) is the related spectral displacement, V is the base shear of the inelastic structure evaluated considering the performance point, and d is the related maximum displacement of the inelastic structure. It has to be noted that the values of V and d obtained with the CSM method are related to the MDOF structure system, while those obtained by the N2 method consider a SDOF system. For this reason, to make a comparison possible, it was necessary to convert the results of the N2 method from SDOF to MDOF systems. The values obtained with the two different methods are comparable. As an example, considering the value of the base shear obtained for the modal load distribution, the difference between the CSM and the N2 method is about 8.2% and 7.65% in the X and Y direction, respectively. The CSM confirms the results predicted by the N2 method: the tower does not collapse due to a soft story mechanism because, under the uniform acceleration profile, the structure remains in the elastic range (q = 1). In fact, the shear capacity associated to the modal load distribution is always lower than the uniform acceleration one.
## 2 Methodology & Case Study
### Slope Stability Analysis  
For transient infiltration conditions, the factor of safety \(F\)s (-) at a depth \(Z\) (m) below the ground surface at time \(t\) (day) is given by the following equation:  
\[F\textit{s}(Z,t)=\ \frac{\tan\varphi^{\prime}}{\tan\beta}+\frac{c^{\prime}- \sigma^{\textit{s}}(Z,t)\ \tan\ \varphi^{\prime}}{(\gamma_{\textit{s}}+\gamma_{\textit{w}} \ast\theta(Z,t)Z\ \sin\ \beta\cos\ \beta)} \tag{1}\]  
where \(\varphi^{\prime}\) (\(\circ\)) is the angle of internal friction for effective stress, \(\beta\) (\(\circ\)) is the slope angle, \(c^{\prime}\) (kPa) is the effective cohesion, \(\gamma_{\textit{s}}\) (N/m\({}^{3}\)) is the soil unit weight, \(\gamma_{\textit{w}}\) (N/m\({}^{3}\)) is the water unit weight, \(\theta\) (-) is soil moisture content, and \(\sigma^{\textit{s}}\) (kPa) is the suction stress defined by [PERSON] and [PERSON] [6]:  
\[\sigma^{\textit{s}}=S_{\textit{e}}\psi \tag{2}\]  
where \(S_{\textit{e}}\) (-) is the effective degree of saturation, \(\psi\) (kPa) is the matric suction. The hydro-mechanical infinite-slope stability analysis is based on the factor of safety approach coupling the Brooks-Corey equations [18] and suction stress [6] in variably saturated soils.  
\[S_{\textit{e}}=\left\{\begin{array}{ll}|\alpha\psi|^{-n},&\alpha\psi<-1\\ 1,&\alpha\psi>-1\end{array}\right. \tag{3}\]  
and \(a\) (kPa\({}^{-1}\)), \(l\) (-), \(n\) (-), are fitting parameters.  
The soil parameters for the slope stability analysis from the topsoil of the slope and parameterization of soil hydraulic properties for the hydro-mechanical models [19] are based on the soil water characteristic curves (SWCC). Its parameters of hydrology are presented in Table 1.
## 5 Performance Evaluation  
### Real Dataset  
The experiment dataset plays an important role in the simulation and implementation of the structure fidelity data collection framework. Thus, we used the real world dataset from the Intel Berkeley Research lab [36] as the evaluation object. The data set including humidity, temperature, light, and voltage values is collected from 54 Mica2 Dot sensor nodes deployed in the lab layout for a period of one-month. In the publicly available data set, we selected the temperature readings sampled every thirty one seconds for all nodes to perform a data analysis. Since 2 sensor nodes are without data available for a long period of observation in the dataset, only 52 nodes are used in our experiment. As shown in Figure 1, the location information of all nodes is fixed at configuration time and hence the distance between nodes can be calculated. The \(X\) and \(Y\) axis in Figure 1 represent coordinates of sensors in meters relative to the lower left corner of the lab.
# Performance Analysis of Soft-Switching FSO/THz-RF Dual-Hop AF-NOMA Link Based on Cognitive Radio
## 3 Performance Analysis
### Outage Probability  
Hence, a user achieves successful signal reception by decoding and eliminating the signal from users with higher PAC and successfully decoding its own signal. Based on this, the OP can be derived as \[P_{OUT}^{n}=1-\Pr\Big{(}\gamma_{j\to n}>\gamma_{th,j}\Big{)} \tag{20}\] \[=1-\Pr\left(\frac{a_{j}P_{S}P_{R}|h_{SR}|^{2}|h_{RUu}|^{2}}{P_{S}P_{R }|h_{SR}|^{2}|h_{RUu}|^{2}\sum\limits_{i=j+1}^{M}a_{i}+P_{S}|h_{SR}|^{2}+P_{R}|h _{RUu}|^{2}+1}>\gamma_{th,j}\right)\] \[=1-\Pr\Bigg{(}\Bigg{[}P_{S}P_{R}\bigg{(}a_{j}-\gamma_{th,j}\sum \limits_{i=j+1}^{M}a_{i}\bigg{)}|h_{RUu}|^{2}-P_{S}\gamma_{th,j}\Bigg{]}|h_{SR}| ^{2}>\gamma_{th,j}\Big{(}P_{R}|h_{RUu}|^{2}+1\Big{)}\Bigg{)}\] \[=1-\Pr\left(|h_{RUu}|^{2}>\frac{\gamma_{th,j}}{P_{R}\bigg{(}a_{j} -\gamma_{th,j}\sum\limits_{i=j+1}^{M}a_{i}\bigg{)}}\triangleq\theta_{j},|h_{ SR}|^{2}>\frac{\theta_{j}\Big{(}1+P_{R}|h_{RUu}|^{2}\Big{)}}{P_{S}\Big{(}|h_{ RUu}|^{2}-\theta_{j}\Big{)}}\right),\]  
where \(\gamma_{th,j}\) denotes the threshold of the \(j\)th user and \(\theta_{j}\) is some constant product of the \(j\)th user.  
After some algebraic manipulations, the expression can be written as  
\[P_{OUT}^{n}=\int_{0}^{\theta_{n}^{*}}f_{|h_{RUu}|^{2}}(x)dx+\int_{\theta_{n}^{ *}}^{\infty}f_{|h_{RUu}|^{2}}(x)F_{|h_{SR}|^{2}}\Bigg{(}\frac{\theta_{n}^{*} \Big{(}1+P_{R}|h_{RUu}|^{2}\Big{)}}{P_{S}\Big{(}|h_{RUu}|^{2}-\theta_{n}^{*} \Big{)}}\Bigg{)}dx, \tag{21}\]  
where \(\theta_{n}^{*}=\max\big{(}\theta_{j},\cdots,\theta_{n}\big{)}\). Substituting (7), (12), and (15) into (21) yields the OP for the corresponding user.
# System for Evaluation and Compensation of Leg Length Discrepancy for Human Body Balancing
## 2 Problem Description  
### Anthropometric Human Body Model  
An anthropometric human body model with variable leg length and scoliosis is shown in Figure 2. For the purpose of this research, LLD evaluation and compensation were done only for subjects with structural LLD (Figure 2b,c) and persons who developed scoliosis of the spine as a consequence of structural LLD (Figure 2e). The percentage of mass and the length of individual segments of the human body in Figure 2 are calculated according to [20; 21].  
Figure 2: 12-segment anthropometric human body model with variable leg length and scoliosis (RF, Right Foot; LF, Left Foot; RLL, Right Lower Leg; LLL, Left Lower Leg; RUL, Right Upper Leg; LUL, Left Upper Leg; PEL, Pelvis; LT, Lower Trunk; UT, Upper Trunk; H, Head; RTA, Right Total Arm; LTA, Left Total Arm). Left leg length is given as \(l_{L}\), right leg length is \(l_{R}\), and the angle of scoliosis is \(\phi\): (**a**) human body without LLD and scoliosis (\(l_{R}=l_{L},\phi=0\)); (**b**) human body with LLD (\(l_{R}<l_{L},\phi=0\)); (**c**) human body with LLD (\(l_{R}>l_{L},\phi=0\)); (**d**) human body with scoliosis (\(l_{R}=l_{L},\phi>0\)); and (**e**) human body with LLD and scoliosis (\(l_{R}>l_{L},\phi>0\)).
## 3 Operating Principle  
This work considers an approach based on the energy balance between the stacks of the converter. To achieve this balance ac and dc voltages and currents are employed to transfer energy to and from the different stacks. Figure 5 shows a simplified model using dc voltages \(V_{se1,2}\), \(V_{de1,2}\), \(V_{o1,2}\) and ac voltages \(v_{se1,2}\), \(v_{de1,2}\), \(v_{o1,2}\) that are produced by each stack, under steady-state operation. The dc voltages are obtained by applying voltage law to the arms of the topology; their values are \(V_{se1,2}=(V_{i}-V_{o})\) and \(V_{de1,2}=V_{o}\). For control purposes the dc voltages of the _output_ stacks are zero. If \(V_{o1,2}=0\), the energy transferred by the _output_ stacks due to dc components is minimized, and it is associated mainly to ac voltages and currents.  
The ac voltages \(v_{\text{se1},2}\), \(v_{de_{1},2}\), \(v_{o_{1,2}}\) have sinusoidal waveform as \(\pm v_{u}=\pm V_{u}\sin(2\pi f_{c}t)\), where \(f_{c}\) is a fundamental frequency. The sign of \(V_{u}\) depends on the control objective and on the circulating current, in this case \(v_{\text{se1}}=-v_{u}\), \(v_{\text{se2}}=v_{u}\), \(v_{de_{1}}=+v_{u}\), \(v_{de_{2}}=+v_{u}\), \(v_{o_{1}}=+v_{u}\) and \(v_{o_{2}}=-v_{u}\) (see Figure 5). These ac voltages are intended to interact with the circulating ac currents \(i_{u1}\) and \(i_{u2}\) to achieve the energy balance of the converter.  
The ac circulating currents can be expressed as \(i_{u1}=I_{u1}\sin(2\pi f_{c}t)\) and \(i_{u2}=I_{u2}\sin(2\pi f_{c}t)\). These currents are aimed to allow the energy balance of the _derivation_ (\(i_{u1}\)) and _output_ (\(i_{u2}\)) stacks. Additionally, dc currents \(I_{\text{se1},2}\), \(I_{de1,2}\), \(I_{0,1,2}\) circulate in all arms of the topology. The dc currents \(I_{\text{se1},2}\) allow the energy balance of _series_ stacks. Using expressions (1)-(7), neglecting the series equivalent resistance \(R\) of the inductor \(L\) and neglecting the product \(\omega L\) which is comparatively small with respect to the product \(VI\), it is possible to calculate the power equations of each stack as defined in (12)-(17). With the operating principle of the topology and the model defined in Section 2, the control strategy can now be derived as presented in Section 4.  
\[P_{\text{se1}}=\frac{d\overline{W}_{\text{se1}}}{dt}=\int v_{\text{se1}}(t){\cdot }i_{\text{se1}}(t)dt=(V_{i}-V_{o})I_{\text{se1}}-v_{u}\,i_{u1} \tag{12}\]  
\[P_{de_{1}}=\frac{d\overline{W}_{de_{1}}}{dt}=\int v_{de1}(t){\cdot}i_{de1}(t) dt=-V_{o}I_{de_{1}}+v_{u}\,(i_{u1}-i_{u2}) \tag{13}\]  
\[P_{o_{1}}=\frac{d\overline{W}_{o_{1}}}{dt}=\int v_{01}(t){\cdot}i_{o1}(t)dt=v _{u}\,i_{u2} \tag{14}\]  
\[P_{\text{se2}}=\frac{d\overline{W}_{\text{se2}}}{dt}=\int v_{\text{se2}}(t){ \cdot}i_{\text{se2}}(t)dt=(V_{i}-V_{o})I_{\text{se2}}-v_{u}\,i_{u1} \tag{15}\]  
\[P_{de_{2}}=\frac{d\overline{W}_{de_{2}}}{dt}=\int v_{de2}(t){\cdot}i_{de2}(t) dt=-V_{o}I_{de_{2}}-v_{u}\,(-i_{u1}+i_{u2}) \tag{16}\]  
\[P_{o_{2}}=\frac{d\overline{W}_{o_{2}}}{dt}=\int v_{o2}(t){\cdot}i_{o2}(t)dt=v _{u}\,i_{u2} \tag{17}\]
## 3 Results and Discussion
### Analysis of Typical Performances
#### 3.2.2 Resistance Characteristic  
The volumetric resistivity of the polyethylene composite can reflect the overall insulation performance of the material. Volume resistivity refers to the impedance effect of a material per unit of volume to electric current, as shown in formula (2). The volume resistivity is shown in Figure 7.  
\[\rho_{v}=R_{v}\frac{S}{h}, \tag{2}\]  
where \(\rho_{v}\) is the volume resistivity, \(R_{v}\) is the resistance value, \(h\) is the thickness of the sample (i.e., the distance between the electrodes), and \(S\) is the area of the electrode.  
The variation trend of the volume resistivity is consistent with that of the crystallinity (Section 3.2.1). Although the volume resistivity of polyethylene is decreased after changing the preparation technology, the microcapsule can increase its volume resistivity. Moreover, the volume resistivity of the composite is the largest.  
Volume resistivity is a characterization of electrical conductivity that is usually independent of material size [47]. The ionic conductivity is the main conductive form of the polymer. Furthermore, space charge traps can be formed in the interface between the crystal and amorphous regions, whose trapping effect on carriers can reduce the conductivity of the material [37; 47]. In other words, the larger the crystallinity, the smaller the ionic conductivity. In addition, the microstructure in high crystallinity material is more stable and less affected by electric field and injected charge. Thus, the volume resistance of polyethylene is positively correlated with its crystallinity.  
Doping microcapsules can introduce new interface regions, which not only contain many charge traps [37; 46], but also increase the number of crystal grains in the matrix (Section 3.2.1)--that is, increase the interface between the crystal and amorphous regions. Therefore, doping microcapsules can increase the charge traps in polyethylene. Charge traps formed in many interface regions can capture carriers (as shown in Figure 8), reducing their movement rate and shortening their free path, thus increasing the volume resistivity.  
Figure 7: Volume resistivity of the samples.  
In brief, the crystallization characteristics of polyethylene can affect its conductivity by changing its ionic conductivity and carrier transport. Moreover, doping microcapsules can not only increase the crystallinity of polyethylene, but also introduce new charge traps. Furthermore, due to the small doping number of microcapsules, the influence of their resistance characteristics on the polyethylene matrix is not obvious. Therefore, doping 1 wt.% microcapsules can greatly increase the volume resistance of polyethylene. Besides this, the higher volume resistance of the composite can meet the application requirements of polyethylene insulating material.
# A Review of Deep Learning Algorithms and Their Applications in Healthcare
## 3 Artificial Neural Networks
### Autoencoders (AE)  
This is an unsupervised learning algorithm used to efficiently code the dataset for dimensionality reduction. It is a specific type of neural network where the input is the same as the output. In essence, it compresses the input into a lower dimensional code and then reconstructs the output using this representation. The code is a compact way of summarizing or compressing the data, also known as the latent space representation. An autoencoder consists of three components: (1) encoder: this compresses the input; (2) code: this is produced by the encoder; (3) decoder: this reconstructs the input using only the code. To build an autoencoder, the following things are needed: (1) an encoding method, (2) a decoding method, and (3) a loss function to compare the output with the target. The main function of an autoencoder is to reduce dimensionality (or compress) with the following properties: data specific, lossiness, and no supervision [46].
## 2 Security Requirement and S-Box Design Methods
### S-Box Properties
#### 2.1.5 Algebraic Complexity (Alc)  
The Lagrange interpolation polynomial is the polynomial \(P(x)\) of degree \(\leq(n-1)\) that passes through \(n\) points \((x_{1},y_{1}=f(x_{1})),(x_{2},y_{2}=f(x_{2})),\cdots,(x_{n},y_{n}=f(x_{n}))\) and is given by:  
\[P(x)=\sum_{j=1}^{n}P_{j}(x),\]  
where  
\[P_{j}(x)=y_{j}\prod_{k=1,k\
eq j}^{n}\frac{x-x_{k}}{x_{j}-x_{k}}\]  
The number of terms in \(P_{j}(x)\) determines whether an S-box has a simple or complex algebraic expression, thereby classifying whether the S-box has a low or high algebraic complexity. A complex AIC is needed to resist an interpolation attack [6] and other concerning algebraic attacks [7].