esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Geometrical Configuration of the CDCHM  
In this section, the design method for the CDCHM, together with the geometric structure characteristics of the CDCHM and DHM, are explained. Moreover, the geometric parameters and assembly methods of the metamaterials with different configurations are discussed.  
As shown in Figure 1a, the traditional DHM is completely connected by a straight rod, which has a very small stiffness and is easy to deform, so its carrying capacity is very weak. The DHM was improved to the CDCHM, as shown in Figure 1b, by embedding the chiral structure into the traditional configuration, and the chiral structure acted as an internal support to improve the stiffness of the metamaterial. In order to further obtain the low-frequency vibration-suppression ability, metal pins were added to the chiral structure to make a further improvement, as shown in Figure 1c, achieving the collaborative optimization of a high-load-bearing capacity and an excellent vibration-isolation performance.  
Figure 1: Structure diagrams of the (**a**) DHM; (**b**) CDCHM; (**c**) CDCHM with mental pins; (**d**) schematic diagram of the geometric parameters of the CDCHM.  
When the unit cell size is small, there are the problems of high difficulty and large errors in processing and manufacturing. Moreover, when the unit size is large, the overall size of the periodically arranged metamaterial may exceed the height and width of the testing machine, which makes it difficult to conduct experiments. Therefore, considering the limitations of the machining accuracy and test equipment, and combining the number of unit cells arranged in the horizontal and vertical directions, the parameters of the CDCHM are designed using the values listed in Table 1 to ensure the accuracy and convenience of the experiments. The parameters of the CDCHM are shown in Figure 1d, where \(L_{1}\) is length of the entire unit, \(L_{2}\) denotes the distance between two adjacent circles of an embedded chiral structure, \(R\) represents inner diameter of the ring, \(d_{1}\) stands for the width of the wall and \(t\) is the thickness of the unit cell. The overall dimensions of the unit cell of the DHM and CDCHM are the same.
## 3 Results
### EAT Histopathological, Immunohistochemical and Morphometrical Analysis  
EAT thickness, macrophage infiltration (Figure 1a,b), and capillary network (Figure 2a,b) were identified within RAA specimens.  
The EAT thickness (185.8 \(\upmu\)m) was non-significantly lower (\(p\) = 0.07) in CAD patients with CHF, as compared to the ones without CHF (217.2 \(\upmu\)m).  
EAT macrophage infiltration was more extensive in CAD patients with CHF than in those without CHF (Figure 1a,b). The mean value of CD68 positive count in CAD patients with CHF (325.78\(\upmu\)m\({}^{2}\)) was significantly higher (\(p\) < 0.001) than in CAD patients without CHF (244.9\(\upmu\)m\({}^{2}\)). EAT angiogenesis was less extensive in patients with CHF than in those without CHF (Figure 2a,b). The mean value of CD34 positive count in CAD patients with CHF (22.83\(\upmu\)m\({}^{2}\)) was significantly lower (\(p\) < 0.001) than in CAD patients without CHF (65.2\(\upmu\)m\({}^{2}\)).  
The relationship between the accumulative number of risk factors and histological EAT labels is shown in Table 2.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Patients**} & **EAT thickness** & **CD68** & **CD34** \\  & **(\(\upmu\)m)** & **(No/\(\upmu\)m\({}^{2}\))** & **(No/\(\upmu\)m\({}^{2}\))** \\ \hline Without CHF & 217.1 \(\pm\) 21.3 & 244.9 \(\pm\) 5.5 & 65.2 \(\pm\) 1.7 \\ With CHF & 185.8 \(\pm\) 27.9 & 325.7 \(\pm\) 16.1 & 22.7 \(\pm\) 3.8 \\ \(p\)-value & 0.07 & \textless{}0.001 & \textless{}0.001 \\ \hline \hline \end{tabular} \(p\)-value \(\textless{}0.05\) was considered significant, CAD, coronary artery disease; CHF, chronic heart failure.  
\end{table}
Table 2: Mean EAT thickness and IHC markers of macrophages accumulation and angiogenesis in peri-atrial EAT samples from CAD patients.  
Figure 1: Immunohistochemical EAT analysis of the macrophages (CD68 200\(\times\)) in CAD patients without CHF (**a**) and CAD patients with CHF (**b**).  
Figure 2: Immunohistochemical EAT analysis of the vessels (CD34 200\(\times\)) in CAD patients without CHF (**a**) and CAD patients with CHF (**b**).
## 2 Materials and Methods  
### Study Area  
The study area is located at the United States Department of Agriculture-Agricultural Research Service (USDA-ARS), Oklahoma and Central Plains Agricultural Research Center (OCPARC) in El Reno, Oklahoma (Figure 1). It consists of two adjoining pastures: (1) a native pasture (NP) with big bluestem (_Androposon gerardi_ VITman) and little bluestem (_Schiazchyrium halapense_ (Michx.) Nash.) as the dominant species [50] and (2) an introduced (managed) pasture (IP) dominated by old world bluestem (_Bothriochloa caucasica_ [PERSON].) [37]. The Oklahoma Mesonet El Reno weather station is located within the NP, which provides quality-controlled measurements of several meteorological variables, including precipitation, air temperature, solar radiation, soil moisture, and so on [51] ([[http://www.Mesonet.org/](http://www.Mesonet.org/)]([http://www.Mesonet.org/](http://www.Mesonet.org/)), accessed on 30 June 2020). Each field is equipped with an eddy covariance (EC) system to measure CO\({}_{2}\) and H\({}_{2}\)O fluxes. Four MODIS pixels with the majority of them overlapped with the study area are presented in Figure 1. In this study, we focus on the two MODIS pixels having EC towers where modeled GPP and EC-derived GPP have already been compared [37; 52].  
Figure 1: Location of the study area overlapping with MODIS pixels (red lines). Locations of the Oklahoma Mesonet El Reno site (yellow point) and two eddy covariance towers (35.54865\({}^{\circ}\) N, 98.03759\({}^{\circ}\) W in native pasture and 35.54679\({}^{\circ}\) N, 98.04529\({}^{\circ}\) W in introduced pasture) are also shown (red diamonds). Yellow rectangle is the boundary of the native pasture and green rectangle is the boundary of the introduced pasture.
## 2 Results and Discussion
### Optimization of the Magnetic Solid-Phase Extraction (MSPE) Procedure
#### 2.4.2 Optimization of Solution pH and Adsorption Mechanism Investigation  
In this study, the pH effect was measured by applying the fruit extracts spiked with nine fungicides at 5.0 \(\upmu\)g\(\cdot\)kg\({}^{-1}\) over the pH region of 2.0 to 9.0. As shown in Figure 4c, it was easy to observe that the optimal adsorption efficiency for the nine fungicides was obtained under pH 6.0 to 8.0. To increase or decrease the solutions' pH values, the adsorption efficiency of DETA-MPs-GO toward fungicides decreased. This phenomenon could be explained by a synergistic adsorption mechanism. Firstly, the structures of the nine fungicides all have a benzene ring; hence \(\pi\)-\(\pi\) stacking would occur between the fungicide molecule and the GO sheet of DETA-MPs-GO. The adsorption behavior could be observed all over the pH region (Figure 4c). Secondly, all the fungicide molecules have nitrogen or oxygen atoms, which easily form hydrogen bonds with -NH\({}_{2}\) (-NH-) groups in DETA-MPs-GO (including -O\(\cdots\)H-N- and -N\(\cdots\)H-N-). However, when the solution's pH is less than 6.0, the main formation of the amino groups in DETA-MPs-GO is positive -NH\({}_{3}\)\({}^{+}\), while N and O atoms in fungicide molecules are also easy to protonate. Therefore, electrostatic repulsion easily occurs between positive adsorbents and fungicides, leading to poor adsorption recoveries toward target fungicides at pH is less than 6.0. When pH is greater than 8.0, alkaline conditions could easily destroy the formation of hydrogen bonds, also resulting in low adsorption recoveries. When 6.0 \(\leq\) pH \(\leq\) 8.0, the main formation of an amino group on DETA-MPs-GO adsorbent is -NH\({}_{2}\), and it was beneficial for the adsorption of target fungicides via hydrogen bonds. In summary, a solution pH of 7.0 was chosen for subsequent tests.
## 3 Results
### Cross-Validation Analysis (Phase B)  
Results for the cross-validation analysis are presented in Table 2.  
Cross-validation analysis comparing the mean power (MPO) estimated by using the first 15 (WAnT\({}_{15}\)) and 20 (WAnT\({}_{20}\)) seconds of the test, and the 30 s MPO (reference criterion).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & **Variable** & **B** & **B 95\% CI** & \(\beta\) & \(t\) & \(p\) \\ \hline WAnT\({}_{15}\) & & & & & & \\  & Y-Intercept & 114.33 (18.74) & 76.36 to 152.29 & & 6.10 & \textless{}0.001 \\  & MPO & 0.81 (0.019) & 0.77 to 0.85 & 0.94 & 42.27 & \textless{}0.001 \\  & FI & \(-\)205.70 (23.94) & \(-\)254.21 to \(-\)157.20 & \(-\)0.19 & \textless{}8.59 & \textless{}0.001 \\ WAnT\({}_{20}\) & & & & & & \\  & Y-Intercept & 70.43 (15.52) & 38.99 to 101.88 & & 4.54 & \textless{}0.001 \\  & MPO & 0.88 (0.02) & 0.85 to 0.91 & 0.97 & 58.71 & \textless{}0.001 \\  & FI & \(-\)115.10 (19.16) & \(-\)153.91 to \(-\)76.29 & \(-\)0.10 & \textless{}0.001 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Regression models to estimate 30 s mean power output (MPO) using the MPO and the fatigue index (FI) obtained in the first 15 (WAnT\({}_{15}\)) and 20 (WAnT\({}_{20}\)) seconds of the test.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **WAnT\({}_{15}\)** & **WAnT\({}_{20}\)** \\ \hline
**Agreement** & & & \\ r & 0.99 & 0.99 \\ ICC & 0.99 & 0.99 \\ CI-95\% lower & 0.98 & 0.99 \\ CI-95\% upper & 1.00 & 1.00 \\ \(t\)-test (\(p\)-value) & 0.56 & 0.96 \\
**Magnitude of error** & & \\ SEM (W) & 8.0 & 3.3 \\ SDC (W) & 22.2 & 9.3 \\ CV (\%) & 1.2 & 0.5 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Cross-validation analysis comparing the mean power (MPO) estimated by using the first 15 (WAnT\({}_{15}\)) and 20 (WAnT\({}_{20}\)) seconds of the test, and the 30 s MPO (reference criterion).  
MPO estimated by the two models showed a high agreement (r \(\geq\) 0.99, ICC \(\geq\) 0.99) and no significant differences (\(p\) \(>\) 0.05) with the 30 s MPO (reference criterion). Nevertheless, the magnitude of error both in absolute and relative terms was lower for the WAnT\({}_{20}\) (SDC = 9.3 W, CV = 0.5%) than for the WAnT\({}_{15}\) (SDC = 22.2 W, CV = 1.2%). Similarly, Bland-Altman plots (Figure 3) exhibited lower bias for MPO estimated by the WAnT\({}_{20}\) (bias = \(-\)0.1 W) compared to that estimated by the WAnT\({}_{15}\) (bias = 1.8 W).
# Transient Analysis of a Selective Partial-Update LMS Algorithm
## 3 Stochastic Modelling of the Proposed Algorithm  
### First-Order Analysis  
Note that Equation (12) can be rewritten as  
\[\mathbf{w}(k+1)=\mathbf{w}(k)+\beta\mathbf{\Gamma}(k)\mathbf{x}(k)e(k), \tag{16}\]  
where \(\mathbf{\Gamma}(k)\) is an \(N\times N\) diagonal matrix, with each element of its main diagonal denoted as \(\gamma_{i}(k)\), where \(i\) is the associated block index. The main diagonal elements of \(\mathbf{\Gamma}(k)\) are obtained by  
\[\gamma_{i}(k)=\left\{\begin{array}{ll}0,&\text{ if }i\
otin\mathcal{I}_{B} \\ 1,&\text{ if }i\in\mathcal{I}_{B}\end{array}\right.. \tag{17}\]  
Consider that reference signal \(d(k)\) is generated by the following affine regression model:  
\[d(k)=[\mathbf{w}^{\star}]^{T}\mathbf{x}(k)+\
u(k), \tag{18}\]  
where \(\mathbf{w}^{\star}\in\mathbb{R}^{N}\) is a vector that contains the coefficients of the ideal (and unknown) plant and \(\
u(k)\) is an additive noise. Defining the deviation coefficient vector as \(\tilde{\mathbf{w}}(k)\triangleq\mathbf{w}^{\star}-\mathbf{w}(k)\), the following recursion can be obtained from Equation (16):  
\[\tilde{\mathbf{w}}(k+1)=\Big{(}\mathbf{I}-\beta\mathbf{\Gamma}(k)\mathbf{x}(k)\mathbf{x}^{T}(k) \Big{)}\tilde{\mathbf{w}}(k)-\beta\mathbf{\Gamma}(k)\mathbf{x}(k)\
u(k), \tag{19}\]  
which is a non-homogeneous stochastic difference equation, where \(-\beta\mathbf{\Gamma}(k)\mathbf{x}(k)\
u(k)\) acts as a driving force that avoids the asymptotic convergence of the deviation vector energy to zero. A first-order stochastic analysis of the SPU-LMS-M-min algorithm can be performed by applying the expectation operator in \(\mathbb{E}[\cdot]\) in (19), which leads (using the popular _independence assumption_-IA [4]) to  
\[\mathbb{E}[\tilde{\mathbf{w}}(k+1)]=(\mathbf{I}-\beta\mathbf{R_{\Gamma}})\mathbb{E}[ \tilde{\mathbf{w}}(k)], \tag{20}\]  
where \(\mathbf{R_{\Gamma}}\triangleq\mathbb{E}[\mathbf{\Gamma}(k)\mathbf{x}(k)\mathbf{x}^{T}(k)]\).  
**Remark 3**.: _Note that Equation (20) implies that the SPU-LMS-M-min, under a sufficient excitation condition, performs an asymptotically unbiased estimation [20]. Furthermore, the maximum step size that guarantees mean-weight convergence can be obtained by assuming_  
\[\beta<\frac{2}{\rho[\mathbf{R_{\Gamma}}]}, \tag{21}\]  
_where \(\rho[\mathbf{R_{\Gamma}}]\) denotes the spectral radius of \(\mathbf{R_{\Gamma}}\), i.e., \(\rho[\mathbf{R_{\Gamma}}]\triangleq\max_{i}|\lambda_{i}(\mathbf{R_{\Gamma}})|\), where \(\lambda_{i}\) is the \(i\)-th eigenvalue of \(\mathbf{R_{\Gamma}}\). Unfortunately, a stable-in-the-mean adaptive filter may perform an estimation with unbounded variance, so that a second-order stochastic analysis is necessary in order to achieve proper performance guarantees [20]. In the derivation of Equation (20), the statistically strong (but physically plausible) assumption that the additive noise is white and statistically independent from the remaining random variables is employed. Such a noise assumption (IA) is almost ubiquitous and is utilized henceforth._
# Cyclic Elasto-Plastic Behaviour of 51 CrV4 Steel for Railway Parabolic Leaf Spring Design
###### Abstract  
Parabolic leaf springs are components typically found in suspensions of freight railway rolling stock. These components are produced in high-strength alloyed steel, DIN 51 CrV4, to resist severe loading and environmental conditions. Despite the material's good mechanical characteristics, the geometric notches and high surface roughness that features its leaves might raise local stress levels to values above the elastic limit, with cyclic elasto-plastic behaviour models being more appropriate. In this investigation, the parameters of the Chaboche model combining the kinematic and isotropic hardening models are determined using experimental data previously obtained in strain-controlled cyclic tests. Once the parameters of the cyclic hardening model are determined, they are validated using a finite element approach considering the Chaboche cyclic plasticity model. As a result, the material properties specified in this investigation can be used in the fatigue mechanical design of parabolic leaf springs made with 51 CrV4 (local approaches to notches and at surface roughness level) or even in other components produced with the same steel.  
Keywords:railway; rolling stock; parabolic leaf springs; cyclic plasticity; finite element analysis; numerical optimisation Article
###### Abstract  
The effect of high volume fraction of magnetic nanoparticles (MNP) on Magnetic Resonance Imaging (MRI) transverse relaxation rates (\(R_{2}=1/T_{2}\) and \(R_{2}{}^{*}=1/T_{2}\)*) is investigated using Monte Carlo (MC) simulations. Theoretical models assume that particles occupy a small volume fraction of the sample space. Results presented in this work show that models based on both motional averaged (MAR) and static dephasing (SDR) regimes respectively underestimate and overestimate relaxation rates at large volume fractions. Furthermore, both \(R_{2}{}^{*}\) and \(R_{2}{}^{*}\) become echo-time dependent. This suggests that diffusion is involved with larger echo-times producing smaller relaxation rates due to better averaging of the magnetic field gradients. Findings emphasize the need for the models to be modified to take account of high particle concentration especially important for application involving clustering and trapping of nanoparticles inside cells. This is important in order to improve the design process of MNP Contrast Agents.  
magnetic nanoparticles; MRI; T2; Monte Carlo; contrast agent; SDR; MAR Article
# Hybrid Particle Swarm Optimization-Jaya Algorithm for Team Formation
## 6 Experimental Results
### Convergence Analysis  
**Convergence of I-PSO-Jaya**: From Tables 8 and 9, it can be seen that I-PSO-Jaya takes at most 30 iterations to arrive at a better solution than that achieved by the other methods. Thereafter, when the number of iterations is increased, the value does not change significantly.  
To assess the convergence of the I-PSO-Jaya algorithm, we conducted experiments with a population size of 100 across 10 different skills. The algorithm was tested with iterations of 5, 10, 15, 20, 25, 30, 35, 40, and 45, utilizing datasets from Academia Stack Exchange and ACM. As shown in Tables 13 and 14, the I-PSO-Jaya algorithm converges to an acceptable solution within 30 iterations. Beyond this point, additional iterations result in only marginal improvements, suggesting that the algorithm has stabilized and that further iterations do not significantly enhance the solution quality.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Exp. No.**} & \multirow{2}{*}{**Iterations**} & \multicolumn{2}{c}{**Std**} & \multicolumn{2}{c}{**Mean**} & \multirow{2}{*}{**Computing Time**} & \multirow{2}{*}{**Communication Cost**} \\  & & **Communication Cost** & & & & **Cost** \\ \hline
1 & 5 & 0.3885 & 2.052 & 4.7207 & 1.49 \\ \hline
2 & 10 & 0.4792 & 1.8391 & 165.6379 & 0.54 \\ \hline
3 & 15 & 0.5496 & 1.831 & 232.6655 & 0.52 \\ \hline
4 & 20 & 0.5881 & 1.8391 & 311.2419 & 0.50 \\ \hline
5 & 25 & 0.5881 & 1.776 & 405.4156 & 0.44 \\ \hline
6 & 30 & 0.6092 & 1.7731 & 459.3279 & 0.37 \\ \hline
7 & 35 & 0.6193 & 1.7554 & 528.184 & 0.37 \\ \hline
8 & 40 & 0.6366 & 1.7566 & 640.1597 & 0.37 \\ \hline
9 & 45 & 0.6466 & 1.708 & 734.5202 & 0.37 \\ \hline \hline \end{tabular}
\end{table}
Table 13: Convergence analysis of the I-PSO-Jaya algorithm for the Academia Stack Exchange dataset.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Exp. No.**} & \multirow{2}{*}{**No. of Skill**} & \multirow{2}{*}{**Iterations**} & \multirow{2}{*}{**JAYA**} & \multirow{2}{*}{**I-JMSO**} & \multirow{2}{*}{**GWO**} & \multirow{2}{*}{**I-GWO**} & \multirow{2}{*}{**I-PSONSO**} & \multicolumn{2}{c}{**I-PSO-Jaya**} \\ \hline
1 & 2 & 5 & 0.02 & 0.07 & 0.005 & 3.69 & 1.36 & 2.91 \\ \hline
2 & 3 & 10 & 0.05 & 0.35 & 0.006 & 7.30 & 5.09 & 10.0 \\ \hline
3 & 4 & 15 & 0.09 & 0.65 & 0.009 & 10.77 & 11.86 & 22.66 \\ \hline
4 & 5 & 20 & 0.29 & 0.30 & 0.01 & 14.86 & 23.45 & 44.54 \\ \hline
5 & 6 & 25 & 0.36 & 2.35 & 0.03 & 21.36 & 42.54 & 79.96 \\ \hline
6 & 7 & 30 & 0.10 & 20.30 & 0.04 & 23.16 & 60.23 & 127.08 \\ \hline
7 & 8 & 30 & 0.12 & 23.16 & 0.06 & 24.93 & 75.80 & 131.71 \\ \hline
8 & 9 & 30 & 0.16 & 24.93 & 0.07 & 24.80 & 106.34 & 202.67 \\ \hline
9 & 10 & 30 & 0.20 & 25.80 & 0.11 & 26.30 & 115.23 & 236.11 \\ \hline \hline \end{tabular}
\end{table}
Table 12: Computing time of I-PSO-Jaya and existing methods for the ACM dataset.
## 3 Materials and Methods
### Preliminaries and Notations
#### 3.1.2 Underwater Movement Model  
The movement model is shown in Figure 2. We assume that the moving speed of \(v_{i}\) is denoted as \(SP_{i}(t)\) obeys the normal distribution \(N(\mu_{1},\sigma_{1}^{2})\) and its actual value range is \((0,2\mu_{1})\). \((d\theta_{i}(t),d\phi_{i}(t))\) denotes the movement direction of \(V_{i}\) at time slot \(t\), where \(d\theta_{i}(t)\) and \(d\phi_{i}(t)\) obey uniform distributions \(U(0,\pi)\) and \(U(0,2\pi)\), respectively. The next location of \(v_{i}\) from its current location \(C_{i}(t)=(x_{i}(t),y_{i}(t),z_{i}(t))\) will be:  
\[C_{i}(t+1)=\begin{cases}x_{i}(t)+SP_{i}(t)\sin d\theta_{i}(t)\cos d\phi_{i}(t) \\ y_{i}(t)+SP_{i}(t)\sin d\theta_{i}(t)\sin d\phi_{i}(t)\\ z_{i}(t)+SP_{i}(t)\cos d\theta_{i}(t)\end{cases} \tag{1}\]  
when \(|\mathbf{C_{i}(t+1)}|>R_{i}\), where \(R_{i}\) denotes the length of the tethering wire of \(v_{i}\), the node is held still by its tethered wire and \(C_{i}(t+1)\) can be written as \((R_{i},\theta_{i}(t)+d\theta i(t),\phi_{i}(t)+d\phi i(t))\) in spherical coordinates. Otherwise, \(C_{i}(t+1)\) is defined by Formula (1).
## 4 Orthogonality and Discussions
For the first 10 modes of the DCS, the values from Equations (8) and (9) are within [1.0064, 1.0085] for the identical modes, while the values are within [\(4.945\times 10^{-5}\), 0.00343] for different modes. Therefore, the orthogonal relationships are almost the same when \(\varepsilon_{r,m}\) is \(-14.88\), where an orthogonal set is almost remains. As the relationships of the next 40 DCS modes are considered, the orthogonal properties are maintained. Although the orthogonality for the real metal case is not completely satisfied, it is not enough to affect the accuracy of transmittance. Despite this incomplete orthogonality, the transmission characteristics are mainly determined by the fundamental mode, so that the accurate results can still be maintained. The field profiles by higher-order modes change more, but the higher-order modes do not significantly affect the slit transmission. The guide wavelengths \(\lambda_{g}\) of the DCS, as well as that of the PS modes, are also investigated to allow the transmission fundamentals to be understood. The \(\lambda_{g}\) value of the first PS mode is 4.382, when the gap width \(2g\) is 4 nm and the permittivity of Ag \(\varepsilon_{r,m}\) is \(-14.88\). By contrast, the \(\lambda_{g}\) value of the first DCS mode is purely imaginary and roughly \(-\)3.859 under the same conditions. This is significantly greater than the imaginary parts of the PS listed in Table 2, demonstrating the \(\lambda_{g}\) value of the DCS attenuates significantly and cannot contribute to the transmission. Therefore, the DCS modes do not contribute to the transmission but perform a complete orthogonal set for the MMT [10].