esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Materials and Methods
### Postprocessing  
Gamma correction serves as a data augmentation technique involving the adjustment of the gamma value to modify the image intensity. Gamma, a non-linear function, is employed for encoding and decoding an image's intensity or brightness. The gamma ratio is modified in gamma correction to change the overall illumination of the image. This method proves highly beneficial when dealing with images exhibiting minimal contrast or suboptimal lighting conditions [25]. Gaussian noise, a distortion introduced into the image through random numbers from a Gaussian distribution, is another approach. As it increases, the noise introduced during image acquisition and preprocessing can help the model become less susceptible to variations in image quality. The extent of noise applied to the image can be adjusted by altering the standard deviation of the Gaussian distribution. A higher standard deviation implies that more noise can be incorporated into the image [26]. In our study, we propose these two methods as postprocessing techniques for the dataset, addressing issues of lost contrast and brightness. Additionally, they introduce a subtle blurring factor to smooth pixel value changes and soften the image edges. The optimal coefficients and filter kernel size for gamma correction, which were utilized to achieve optimal segmentation results, are as follows: a gamma value of 2 and an alpha value of 0.5. Additionally, a Gaussian kernel with a size of 3 and a sigma value of 0.2 were employed. Figure 4 visually represents the final segmentation map generated using our method, showcasing the effectiveness of these parameters in the segmentation process, postprocessing techniques including gamma correction and Gaussian blur are applied to enhance the images, as illustrated in Figure 4.  
Figure 4: Final segmentation map.  
Figure 3: Watershed segmentation.
# Wavelet-Based Estimation of Damping from Multi-Sensor, Multi-Impact Data
## 3 Damping Extraction Methods
### Frequency-Domain Damping Extraction Methods
#### 3.1.4 Bertocco-Yoshida  
The Bertocco-Yoshida (BY) family of algorithms is developed based on discrete Fourier transform (DFT) [23]. The DFT of finite length sequence signal \(x_{n}\) is expressed as  
\[X_{k}=\sum_{n=0}^{L-1}x_{n}e^{-i\omega_{k}n}, \tag{12}\]  
where \(L\) is the length of the signal, \(\omega_{k}\) is \((\frac{2\pi}{L})k\), and \(k=0,1,\ldots,L-1\). Let us rewrite Equation (2) in the discrete form by replacing \(t\) with \(\frac{\mu}{\kappa}\).  
\[x_{n}=A_{0}e^{-\zeta\omega_{n}^{\prime}n}\cos(\omega_{d}^{\prime}n+\phi_{0})=\frac{ A_{0}}{2}\left(e^{-\zeta\omega_{n}^{\prime}n}e^{i(\omega_{d}^{\prime}n+\phi_{0})}+e^{- \zeta\omega_{n}^{\prime}n}e^{-i(\omega_{d}^{\prime}n+\phi_{0})}\right), \tag{13}\]  
where \(n\) is the sample number, Fs is the sampling frequency, \(\omega_{n}^{\prime}=\omega_{n}/\)Fs, and \(\omega_{d}^{\prime}=\omega_{d}/\)Fs.  
Based on the definition of the DFT and utilizing the sum of the geometrical sequence, the discrete Fourier transform of \(x_{n}\), as explained in [23], can be expressed as follows:  
\[X_{k}=\frac{A_{0}}{2}\left(e^{i\phi_{0}}\frac{1-\alpha^{L}}{1-\alpha e^{-i \omega_{k}}}+e^{-i\phi_{0}}\frac{1-\alpha^{*L}}{1-\alpha^{*}e^{-i\omega_{k}} }\right), \tag{14}\]  
where \(\alpha=e^{-\zeta\omega_{n}^{\prime}+i\omega_{d}^{\prime}}\) and \({}^{*}\) denotes complex conjugate. This equation always holds, except for \(\zeta\omega_{n}^{\prime}=0\) and \(\omega_{d}^{\prime}=\omega_{k}\). In this case,  
\[X_{k}=A_{0}\frac{L}{2}e^{i\phi_{0}}. \tag{15}\]  
The damped frequency, denoted as \(\omega_{d}^{\prime}\), can be derived from the highest frequency bin. However, to calculate all three unknown parameters for each mode--amplitude, frequency, and damping--at least three complex bins are necessary. Therefore, following the Bertocco algorithm, a ratio \(R\) is introduced and approximated as follows:  
\[R=\frac{X_{k+1}}{X_{k}}\approx\frac{1-\alpha e^{-i\omega_{k}}}{1-\alpha e^{-i \omega_{k+1}}}, \tag{16}\]  
where \(k\) is the bin with the highest amplitude. As a result, given \(R\), \(\alpha\) is calculated by the following:  
\[\alpha=e^{i\omega_{k}}\frac{1-R}{1-Re^{-i2\pi/L}}. \tag{17}\]  
Then, one can find the damping coefficient (\(\lambda^{\prime}=\zeta\omega_{n}^{\prime}\)) and damping frequency (\(\omega_{d}^{\prime}\)).  
\[\lambda^{\prime}=-\Re[\ln(\alpha)],\quad\omega_{d}^{\prime}=\Im[\ln(\alpha)]. \tag{18}\]  
On the other hand, the Yoshida algorithm suggests using four bins, which leads to a smaller systematic error [23]. Hence, \(R\) is expressed as  
\[R=\frac{X_{k-2}-2X_{k-1}+X_{k}}{X_{k-1}-2X_{k}+X_{k+1}}. \tag{19}\]  
Then, the damping coefficient and damped frequency are computed as  
\[\lambda^{\prime}=\frac{2\pi}{L}\Im[-\frac{3}{R-1}],\quad\omega_{d}^{\prime}= \frac{2\pi}{L}\Re[k-\frac{3}{R-1}]. \tag{20}\]  
Similar to the peak-picking method, BY algorithms assume that MDOF systems behave similarly to SDOF systems close to each peak.
## 3 Overview of UHS Globally and in the Baltics
### UHS Aspects in Lithuania
#### 3.1.2 Storage Capacity Estimation  
The volumetric approach has been extensively used to estimate the CO\({}_{2}\) and H\({}_{2}\) storage in literature [94; 95]. For instance, [PERSON] [95] applied volumetric approach to calculate the H\({}_{2}\) storage capacity on the European scale. He reported that Germany, Norway, and the UK have the highest capacities, surpassing 1000 TWh, with Norway utilizing significant offshore depleted gas field (DGF) storage. Moderate capacities (10-100 TWh) are seen in countries like France, Poland, and Romania, with a mix of onshore and offshore UHS. Reference [95] does not detail how these estimates were calculated and for which geological reservoirs they were calculated, particularly for Lithuanian reservoirs. [PERSON] et al. [96]  
Figure 10: The plots of the total volume (in Sm\({}^{3}\)) of H\({}_{2}\) in place during a 10-year cycle (**a**) for homogeneous and (**b**) for heterogeneous geological settings.  
Figure 9: The total H\({}_{2}\) injection volume (in Standard m\({}^{3}\), Sm\({}^{3}\)) (in red) and production volume (Sm\({}^{3}\)) (in green) plots for (**a**) homogeneous and (**b**) heterogeneous models.  
have also estimated the storage capacity of 12 oil fields, 3 aquifer structures in Cambrian deimena formation sandstone, and one upper Permian salt dome for H\({}_{2}\) storage in Lithuania. This suggests a total storage volume capacity of 486 Gg (gigagram) H\({}_{2}\), out of which around 121 Gg H\({}_{2}\) for the oil fields, 363 Gg H\({}_{2}\) for the three aquifer structures, and 1.9 Gg H\({}_{2}\) for the Upper Permian salt dome. Figure 11 presents a comparison of working storage resources in Lithuania, Latvia, and Poland using literature data [95]. In the present study, Equation (1) [95,97] has been used to calculate the volumetric H\({}_{2}\) storage capacity for Syderai and Vaskai fields saline aquifers. In Equation (1), \(A_{t}\) is area of the trap (km\({}^{2}\)), \(h_{g}\) is gross thickness (m), \(NTG\) is net-to-gross ratio (i.e., a fraction of porous and permeable formation in a given volume), \(\phi_{t}\) is a volumetric fraction of total porosity, \(\rho_{H_{2}}\) is the density of hydrogen at reservoir depth, and \(S_{eff}\) is sweep efficiency.  
\[Sc=A_{t}*h_{g}*\phi_{t}*NTG*\rho_{H_{2}}*S_{eff} \tag{1}\]  
Volumetric computation shows a combined storage capacity of \(\sim\)898.5 Gg H\({}_{2}\) (\(\sim\)11 TWh), with Syderai contributing 611.4 Gg H\({}_{2}\) and Vaskai 287.1 Gg H\({}_{2}\). This significantly exceeds earlier estimates by [PERSON] et al. [96], which reported a total capacity of \(\sim\)487 Gg H\({}_{2}\) for Lithuanian reservoirs, including oil fields, aquifer structures, and a salt dome. These findings highlight the potential of Syderai and Vaskai aquifers to strengthen Lithuania's energy security and seasonal hydrogen storage, especially during high-demand periods like winter. The study underscores the importance of precise geological data in improving storage capacity estimates.
## 3 Models and Methods
### Spatial Autocorrelation Model  
Neglecting spatial autocorrelation problems may lead to errors in the estimation of convergence analysis considering spatial effects [52]. Therefore, it is necessary for us first to use the [PERSON]'s I index to test the spatial autocorrelation of the integrated transport efficiency of China's provinces.  
Global spatial autocorrelation mainly reflects the overall similarity of spatially adjacent units in the entire research area [53]. In this study, [PERSON]'s I index was used to analyze the spatial autocorrelation of integrated transport efficiency among 31 provinces in China. It was also used to measure whether there exists a related influence on integrated transport efficiency between neighboring provinces. The range of [PERSON]'s I value is \([-1,1]\). The closer the value of the index is to \(1\), the greater the positive spatial autocorrelation is. Conversely, when the [PERSON]'s I index is closer to \(-1\), it indicates a spatial negative autocorrelation. When the [PERSON]'s I index is close to \(0\), it shows that the subjects may be randomly distributed in space [54]. The specific calculation method used was as follows:  
\[\begin{split} I_{ITE}=\frac{n\sum\limits_{i}\sum\limits_{j}w_{ ij}(ITE-\overline{ITE})(ITE_{j}-\overline{ITE})}{\left(\sum\limits_{i}\sum \limits_{j}w_{ij})\sum\limits_{i}\left(ITE_{i}-\overline{ITE}\right)^{2}}\quad \quad(i,j=1,2,\ldots,31)\end{split} \tag{2}\]  
where \(ITE_{i}\) and \(ITE_{j}\) represent transport efficiency in regions \(i\) and \(j\), respectively; \(\overline{ITE}\) represents the average value of regional integrated transport efficiency; \(n\) represents the number of regional units; and \(W\) is the space weight matrix, reflecting the spatial adjacency of regions \(i\) and \(j\). Due to the irregularity of the boundaries of each provincial unit, we chose the \"queen\" adjacency method to set the spatial weight matrix. In other words, there is a shared edge or a shared point in the adjacent area. Using binary weights, when \(i\) and \(j\) regions are adjacent, the weight of \(w_{ij}\) is \(1\); otherwise, it is \(0\). The specific formula applied was as follows:\[W=\left[\begin{array}{cccc}w_{11}&w_{12}&\cdots&w_{1n}\\ w_{21}&w_{22}&\cdots&w_{2n}\\ \cdots&\cdots&\cdots&\cdots\\ w_{n1}&w_{n2}&\cdots&w_{nn}\end{array}\right] \tag{3}\]  
\[w_{ij}=\left\{\begin{array}{ll}1,&\mbox{ {\it region i} and region j are adjacent}\\ 0,&\mbox{ {\it region i} and region j are not adjacent}\end{array}\right. \tag{4}\]  
To ensure the accuracy of the global [PERSON]'s I index, it is necessary to apply the \(Z\)-test to further test the significance of the spatial autocorrelation. The test formula is as follows:  
\[Z_{ITE}=\frac{I-E(I_{ITE})}{\sqrt{V(I_{ITE})}} \tag{5}\]  
where \(E(I_{ITE})=1/(n-1)\) indicates the expected value; \(V(I_{ITE})=E(I_{ITE}^{2})-E(I_{ITE})^{2}\) represents the standard deviation.
# An Improved Convergence Analysis of a Multi-Step Method with High-Efficiency Indices
## 4 Numerical Examples  
In this section, we examine two examples to calculate the parameters we have discussed in our theoretical part.  
**Example 1**.: _Let \(X=\mathbb{R}^{3}\) with \(\Omega=\tilde{U}(0,1)\). \(F:\Omega\subset X\to X\) is defined for \(\omega=(\omega_{1},\omega_{2},\omega_{3})\) by_  
\[\mathcal{E}(\omega)=\left(\frac{1}{3}sin\omega_{1},\frac{\omega_{2}^{2}}{15}+ \frac{\omega_{2}}{3},\frac{\omega_{3}}{3}\right)\]  
_The first derivative will be_  
\[\mathcal{E}^{\prime}(\omega)=\left[\begin{array}{ccc|ccc}\frac{cos\omega_{1 }}{3}&0&0\\ 0&\frac{2\omega_{2}}{15}+\frac{1}{3}&0\\ 0&0&\frac{1}{3}\end{array}\right],\]  
_and the second derivative will be_  
\[\mathcal{E}^{\prime\prime}(w)=\left[\begin{array}{cccc|ccc|ccc}\frac{-sin \omega_{1}}{3}&0&0&0&0&0&0&0&0\\ 0&0&0&0&\frac{2}{15}&0&0&0&0\\ 0&0&0&0&0&0&0&0\end{array}\right].\]  
_Consider the solution \(s^{*}=(0,0,0)\). Start with the initial point \((0,0,\frac{1}{3})\). Choosing \(G=I\), we have our solution \(s^{*}\in U((0,0,\frac{1}{3}),\frac{1}{2})\). By comparing with the assumptions \((a_{2})-(a_{3})\) and \((a_{6})-(a_{8})\), the constants can be found to be \(L_{0}=L_{1}=L_{2}=K_{1}=K_{1}=\frac{1}{3}\). Then the parameters are \(p_{1}=0.7780542\), \(\rho_{2}=0.8549823\), and \(\rho=0.588058733\). Thus, \(r=0.588058733\)._  
**Example 2**.: _Let us consider the trajectory of an electron in the air gap between two parallel plates, described by the expression_  
\[\mathcal{E}(s)=\frac{\pi}{4}-\frac{1}{2}cos(s)+s.\]  
_Let the domain be \(\Omega=[-1,1]\) and take the initial point \(s_{0}=0\). Choosing \(\mathcal{G}=I\), the iterated solution is found to be \(s^{*}=0.30909327\)[21]. By comparing with the assumptions \((a_{2})-(a_{3})\) and \((a_{6})-(a_{8})\), the constants can be found to be \(L_{0}=L_{1}=L_{2}=K_{1}=K_{1}=\frac{1}{2}\). Then the parameters are \(\rho_{1}=0.53918887\), \(\rho_{2}=0.60668011\), and \(\rho=0.38631554\). Thus \(r=0.38631554\)._
# Through-Life Maintenance Cost of Digital Avionics
## 7 Results and Discussion
### Warranty Maintenance
In general, analyzing Figures 6-8, we can state that an increase in the conditional probability of in-flight false-positive, or the rate of intermittent faults or permanent failures leads to the rise of corresponding a posterior probability and decrease of two other a posterior probabilities. Figure 9 shows the dependences of the mean waiting time (\(t_{spare}\)) on the number of spare LRU (\(PS\)) for the second WM option when \(N_{W}=10\), \(\lambda=10^{-4}\)h\({}^{-1}\), \(t_{TE}^{I-level}=2\) h, \(E\big{(}T_{repair}\big{)}=72\) h (red circles), \(E\big{(}T_{repair}\big{)}=26.5\) h (black squares), \(E\big{(}T_{repair}\big{)}=12.7\) h (red triangles), and the rest of data the same as in Figure 3.  
We calculated the mean time of LRU repairing \(E\big{(}T_{repair}\big{)}\) by Equation (24). As we can see in Figure 9a,b, the mean waiting time \(t_{spare}\) has a much weaker dependence on the conditional probability of the in-flight false-positive and intermittent fault rate in comparison with the same dependence for the first WM option shown in Figure 3a,b. Figure 10 shows the dependency of the optimal quantity of spare LRU on the quantity of aircraft for the second WM option when \(t_{TE}^{I-level}=2\) h and the rest of data the same as in Figure 4. Figure 10a corresponds to the case when \(P_{flight}^{FP}=1\times 10^{-4}\) and \(E\big{(}T_{repair}\big{)}=72\) h (red circles), \(P_{flight}^{FP}=1\times 10^{-3}\), \(E\big{(}T_{repair}\big{)}=26.5\) h (black squares), and \(\theta=1\times 10^{-4}\) h\({}^{-1}\)  
Figure 8: Dependences of the posterior probabilities of dismounting the LRU due to the in-flight false-positive (red curve), intermittent fault (black curve), and permanent failure (blue curve) on the permanent failure rate when \(\theta=10^{-4}\) h\({}^{-1}\); (a) \(P_{flight}^{FP}=1\times 10^{-3}\); (b) \(P_{flight}^{FP}=1\times 10^{-4}\). We plotted Figure 10b when \(\theta\ =\ 1\ \times\ 10^{-4}\ \mathrm{h}^{-1}\), \(E\big{(}T_{repair}\ \big{)}\ =\ 72\ \mathrm{h}\) (red circles), \(\theta\ =\ 1\ \times\ 10^{-3}\ \mathrm{h}^{-1}\), \(E\big{(}T_{repair}\big{)}\ =\ 12.7\ \mathrm{h}\) (black squares), and \(P_{flight}^{\mathrm{FP}}\ =\ 1\times 10^{-4}\). Comparing the plots in Figure 10a,b, we can observe that the results are different only for \(N_{W}=15\). For all other values of \(N_{W}\), the optimal number of spare LRU is the same. Thus, the optimal amount of spare LRU almost does not depend on the conditional probability of in-flight false-positive and intermittent fault rate. Essentially, the second option is resistant to the negative influence of false-positives and intermittent faults.
# Thermal Strain-Based Simplified Prediction of Thermal Deformation Caused by Flame Bending
## 2 Prediction of Thermal Deformation
### Material Properties during Cooling Phase  
Predicting thermal deformation requires the material properties of each cycle formed in the heating and cooling process, which can be expressed as a function of temperature, reflecting changes in the material phase according to the thermal analysis procedure. The material properties in the cooling case are defined by Equations (7)-(9) [9; 16].  
\[\alpha_{C}(T)=\left(8e^{k\cdot max[(M_{\mathrm{c}}-T),0]}+13\right)\times 10^{ -6} \tag{7}\]  
\[E_{C}(T)=\left(-3.333 Te^{kmax[Ms-T,0]}-5T+20000\right)\times 0.98 \tag{8}\]  
\[\
u_{C}(T)=-0.2e^{-0.001824T}+0.5 \tag{9}\]  
where \(\
u_{C}\), \(E_{C}\) (\(Kgf/mm^{2}\)), \(\alpha_{C}\)denote [PERSON]'s ratio, Young's modulus, and the thermal expansion coefficient in the cooling cycle, respectively. In the cooling cycle, the yield stress (\(\sigma_{YC}\)) of martensite is larger than that of ferrite because martensite volumetric expansion can relax the tensile stress in the heated region [16]. Therefore, according to the maximum temperature of austenite, the austenite grain size ASTM (American Society of Mechanical Engineers) number and diameter of the average grain of the mild A-grade steel can be obtained from Figure 3 using Equations (10) and (11) [17].  
\[ASTM=-\frac{T_{C}+T_{max}}{1000}+9.2 \tag{10}\]  
\[AGS\left(D\right)=0.359e^{-0.3464 ASTM} \tag{11}\]  
where \(T_{C}\) is the critical temperature which is equal to \(Ac1\) (Equation (3)), \(T_{max}\)is the maximum temperature in the whole process and \(AGS\) is the average grain size \(D\).  
Hence, the yield stress in cooling can be obtained by Equation (12) [18; 19], assuming that the grain is 100% fine-grained. Due to the different temperature in HAZ, the yield stress in cooling is not regarded as a value but as a range [20]. Therefore, the average maximum temperature and critical temperature should be used in Equation (10).  
\[\sigma_{YC}=\left(370+\frac{27.1}{\sqrt{D}}\right)+\left(480-370\right)\frac {\sqrt{C}}{\sqrt{0.2}}\ +\frac{\sqrt{C}}{\sqrt{0.2}}\cdot\frac{48.0-27.1}{\sqrt{D}} \tag{12}\]  
where \(D\) is the average grain size and \(C\) is the content of carbon in steel, as described in Table 1.
## 4 Experiments and Discussion
### Impact of the BFE and DFE Modules  
To verify that the BFE and DFE have an enhancing effect on the classification performance, we conducted the following ablation experiments: removing both the DFE and BFE modules (baseline); removing the DFE module but keeping the BFE module (w/o DFE); removing the BFE module but keeping the DFE module (w/o BFE); and keeping all modules (DCTransformer). The results of the comparison experiments are shown in Table 10.
## 4 Discussion  
With the influence of global climate change, droughs are gradually increasing. Therefore, real-time and accurate monitoring of vegetation drought using satellite-based SIF at a regional scale is of great significance. Firstly, large-scale monitoring of vegetation drought using SIF can provide help for forestry, grassland, and agricultural management. Early detection of drought using SIF can help stakeholders such as herders and farmers in implementing measures to mitigate the impacts appropriately. Moreover, SIF can quantify GPP losses caused by drought and assess the effects of drought on forestry, grassland, and agriculture, which is crucial for food security.
## 4 Results
#### 4.2.1 Frequency Bands Used in RF Energy Collection
This taxonomy supports the contextual analysis of frequency selection in ambient RF energy harvesting systems. show notable representation, with 14.5% and 8.6%, respectively, emphasizing their role in RFID, IoT, and low-power sensor networks. Other frequency ranges such as C band (8.6%), X band (1.3%), Ku band (0.7%), and HF band (0.7%) appear less frequently, suggesting their use in more specialized or high-frequency harvesting scenarios. Overall, the distribution reflects a strong research focus on frequency bands that balance compact antenna design, high signal availability, and regulatory accessibility. To complement the quantitative distribution shown in Figure 14, Table 15 provides detailed classification of reviewed articles according to the frequency band addressed in each study. This breakdown enables precise traceability of the literature supporting each spectral category and facilitates more granular interpretation of technological focus within the field. By linking each frequency band to its corresponding references, this table strengthens the methodological transparency of the review and supports future comparative or meta-analytical studies.
## 3 Results
### Univariate Analysis
#### 3.1.2 Parametric Analysis  
The results obtained do not correspond to a normal distribution, which rules out the suitability of carrying out a parametric analysis in this case. Examining the linear regressions of all emotional temperature variables, it is evident that the regression line does not adequately fit the totality of the data. The residual normality tests, specifically the skewness and kurtosis tests, indicate, according the chi-square values, that the regression is not correct and the residuals would not follow a normal distribution.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Populations**} \\ \cline{2-10}  & \multicolumn{2}{c}{**HC *} & \multicolumn{2}{c}{**AD1 *} & \multicolumn{2}{c}{**AD2 *} & \multicolumn{2}{c}{**AD (AD1 + AD2)**} \\ \hline
**Variable/** & \begin{tabular}{c} **Human** \\ **Interview** \\ \end{tabular} & \begin{tabular}{c} **Automatic** \\ **\(\mu\)(\(\sigma\))** \\ \end{tabular} & \begin{tabular}{c} **Human** \\ **\(\mu\)(\(\sigma\))** \\ \end{tabular} & \begin{tabular}{c} **Automatic** \\ **\(\mu\)(\(\sigma\))** \\ \end{tabular} & \begin{tabular}{c} **Human** \\ **\(\mu\)(\(\sigma\))** \\ \end{tabular} & \begin{tabular}{c} **Automatic** \\ **\(\mu\)(\(\sigma\))** \\ \end{tabular} & \begin{tabular}{c} **Human** \\ **\(\mu\)(\(\sigma\))** \\ \end{tabular} & \begin{tabular}{c} **Automatic** \\ **\(\mu\)(\(\sigma\))** \\ \end{tabular} & \
\begin{tabular}{c} **Human** \\ **\(\mu\)(\(\sigma\))** \\ \end{tabular} &
\begin{tabular}{c} **Automatic** \\ **\(\mu\)(\(\sigma\))** \\ \end{tabular} \\ \hline \(et_{d}\) & 52.92 (13.79) & 52.68 (14.05) & 57.49 (9.01) & 57.37 (11.94) & 48.91 (8.82) & 57.13 (14.48) & 56.12 (9.37) & 57.29 (12.75) \\ \(\overline{et}_{c}\) & 29.53 (29.4) & 28.42 (27.76) & 23.36 (29.84) & 33.32 (29.84) & 38.16 (26.41) & 34.40 (29.89) & 25.73 (28.47) & 33.67 (29.72) \\ \(\sigma_{dc}^{2}\) & 451.50 (445.2) & 435.72 & 390.53 & 514.74 & 767.26 & 583.80 & 487.93 & 537.14 \\ \(\widetilde{et}_{d_{3}}\) & \(-\)0.12 (0.51) & \(-\)0.12 (0.5) & \(-\)0.19 (0.38) & \(-\)0.29 (0.50) & 0.01 (0.28) & \(-\)0.19 (0.53) & \(-\)0.16 (0.36) & \(-\)0.26 (0.50) \\ \(Kurt_{et_{e}}\) & 2.42 (0.6) & 2.37 (0.73) & 2.23 (0.46) & 2.36 (0.64) & 1.93 (0.19) & 2.24 (0.76) & 2.18 (0.44) & 2.32 (0.68) \\ \hline \hline \end{tabular}  
* HC: healthy control; AD1: mild-grade Alzheimer’s; AD2: moderate-grade Alzheimer’s.  
\end{table}
Table 1: Descriptive statistical values of the emotional temperature measures for each population and for each interviewer: mean value (\(\mu\)) and standard deviation (\(\sigma\)).