esa-sceva/satcom-chunk-collection huggingface dataset:
# Development of a Holographic Waveguide with Thermal Compensation for Augmented Reality Devices
## 5 Conclusions  
The research analyzes, selects and calculates the main parameters of a holographic waveguide, taking into account the issue of thermal compensation when the wavelength of the radiation source changes in order to preserve the position of the optical axis and minimize the possible angular displacement of the augmented reality image.  
Figure 16: A graph of the dependence of the angular displacement of the output image on the change in the wavelength of radiation. (**a**) A circuit with thermal compensation. (**b**) A circuit without thermal compensation.  
The waveguide structure is proposed in the form of four DOEs with the same periods: the input DOE1 and the relay DOE2 and DOE3 superimposed on it have angles of inclination of 60\({}^{\circ}\) and 120\({}^{\circ}\), the output DOE4 is located at an angle of 180\({}^{\circ}\), which makes it possible to compensate for the displacement of \(\lambda\) within \(\pm\)20 nm.  
This study is useful for augmented reality systems, in which a clear positioning of models and output information about real-world objects should be provided, for example, in the field of medicine for surgical operations, for displaying contextual prompts during assembly and repair of complex products, for displaying navigation labels and arrows.  
Conceptualization, A.S. and O.A.; methodology, A.S., O.A. and V.N.; verification, A.S., O.A., V.N. and A.K.; formal analysis, A.S.; research, A.S. and O.A.; resources, V.N. and A.K.; writing--preparation of the original project, A.S., O.A. and V.N.; writing--review and editing, A.S. and O.A.; visualization, A.S.; supervision, V.N.; project administration, A.K. and A.S.; fundraising, A.K. All authors have read and agreed to the published version of the manuscript. This research was funded by the Priority 2030 program at the Bauman Moscow State Technical University.  
Not applicable.  
Data availability StatementData are available from the authors upon request.  
Not applicable.  
The authors declare no conflict of interest.
## Appendix A Framework for Physital Cultural Heritage Tourism Application Development
### Applying the Framework to the Fountain of the Lions Application
* Enhance 3D and AR features with accurate textures, lighting, and motion-capture animations. Iterative Development:
* Test prototypes with diverse user groups, including tourists, students, and cultural enthusiasts, to refine usability and engagement. Marketing Strategy:
* Promote the app through social media campaigns and partnerships with educational institutions, emphasizing its cultural and educational value. Functional Testing:
* Validate the usability of 3D and AR interactions across devices, including touch-screen monitors and VR headsets. * Test NFT integration, ensuring accessibility and seamless transactions. User Feedback:
* Conduct surveys and interviews to evaluate user satisfaction and learning outcomes. * Address feedback, such as simplifying navigation or improving instructional clarity. Compliance Check:
* Ensure alignment with cultural preservation standards and accessibility guidelines. Stage 7: Deployment and Support Launch Strategy:
* Roll out the app with targeted campaigns aimed at tourists, educators, and cultural heritage enthusiasts. * Provide on-site support to help visitors engage with the app and its features. NFT Placement and Accessibility:
* Offer NFTs through the app's marketplace or as rewards for completing tasks. * Use QR codes at the site to link visitors to relevant digital collectibles. Compatibility and Maintenance:
* Regularly update the app with new features, such as additional restoration phases or AR/VR enhancements. Stage 8: Evaluation and Iteration Performance Metrics:
* Monitor engagement through metrics like NFT redemptions, task completion rates, and time spent interacting with the app. * Assess the app's impact on user satisfaction and cultural understanding. Long-Term Improvements:
* Expand content to include other sections of the Alhambra or related historical artifacts. * Use analytics to refine gamified elements and introduce new interactive features. Applying the framework to the Fountain of the Lions application enhances its potential as a tool for cultural preservation and interactive learning. By integrating gamified storytelling, NFTs, and immersive AR/VR features, the app can offer richer and more personalized experiences for users. These enhancements not only deepen engagement but also support sustainable tourism and the preservation of this UNESCO World Heritage Site.
## 2 Methodology
### Case Study: St. Cristov\(\ddot{\text{a}}\)o Church  
The simulations presented in this paper are based on a case study, i.e., St. Cristov\(\ddot{\text{a}}\)o church, which is a 13 th-century church that is located in the vicinity of St. Jorge Castle in Lisbon (Figure 1). The church has thick, mortared limestone walls, single-glazed windows, and a ceramic tile roof, and it does not have any type of climate control system [17]. The church, which is naturally ventilated, has several compartments, with the largest ones being the naive, the mortuary, and the sacristy. Overall, the church has a volume of 5250 m\({}^{3}\), and the window (45 m\({}^{2}\)) per wall area (800 m\({}^{2}\)) ratio is 0.056 [35]. St. Cristov\(\ddot{\text{a}}\)o church has a large variety of artifacts, among which sculptures and panel paintings [36].  
The church was subjected to a long-term monitoring campaign from November 2011 to August 2013 that used several sensors to later on determine the quality of the indoor climate in terms of artifacts conservation [17]. Subsequently, the recorded data were used in the calibration process of computational models of the church [16; 37]. The outdoor temperature and relative humidity in the vicinity of the church were monitored to build an outdoor weather file, which was then used to run the church models [16].  
St. Cristov\(\ddot{\text{a}}\)o model was calibrated using four statistical indices, and the measured temperature (T) and water-vapor pressure (Pu), namely [16]: coefficient of determination (R2--0.99 for T and 0.97 for Pu), normalized mean bias error (NMBE--2.7% for T and 3.4% for Pu), coefficient of variation of the root mean square error (CV(RMSE)--3.2% for T and 4.4% for Pu), and goodness-of-fit (fit--84.8% for T and 81.7% for Pu). Considering the values that exist in the models published in the literature and the limits that exist in the specifications/guidelines [38], the obtained values for the St. Cristov\(\ddot{\text{a}}\)o model are quite suitable, which validates this model [16]. The results of this validation can be seen in Figure 2, which presents the measured and simulated indoor temperature and water-vapor  
Figure 1: Location (a) and facade (b) of St. Cristov\(\ddot{\text{a}}\)o Church, Lisbon.  
pressure for St. Cristovano. A detailed explanation of the performed monitoring campaign in St. Cristovano church can be found in Ref. [17], while Ref. [16] thoroughly describes the development and validation procedure of the whole-building hygothermal model used in this study.  
Several types of retrofit measures were tested individually (Table 1), i.e., installation of internal insulation thermal systems and application of an external thermal insulation system (to the exterior walls), replacement of the existing windows systems by more energy efficient ones, and installation of a thermal insulation system in the ceiling/roof [39]. The materials used are included in the WUFI database [8].
## 4 Results and Validation  
The control strategies use specific configurations regarding the size of the photovoltaic system and TES size based on the energy demands. The photovoltaic system tested is 8 kW, a medium-sized system compared to other neighboring buildings in the community. The storage volume consisted of 1.0 m\({}^{3}\).  
The results achieved have been compared at this level, similar to those performed by Equation (14), considering a conventional control system and a system without photovoltaic energy as analysis cases. These include the building's electrical system and heating. Figure 4 presents the values of the energy supplied to the heating circuit and the electricity provided by the utility, which is also considered a positive photovoltaic energy input. The energy values of the thermal component are also shown, which includes those provided by the heat pump, whether supplied by the utility or by the solar photovoltaic system. Approximately two-thirds of the medical center's 125 kWh electrical demand can be guaranteed to be powered by the electricity provided by the solar panels. Figure 4 below shows the energy production under different conditions and the demand of the subsystems.  
The economic analysis that allowed us to evaluate the efficiency of the HP system with the photovoltaic system and the impact of the control strategies and PV system sizing was assessed by comparing the configuration--including the photovoltaic supply and additional thermal energy storage (TES)--against a baseline system without PV, equipped with an 800 L TES and operated under standard control conditions, as defined by Equation (17).  
As the size of the photovoltaic system increases, as shown in Figure 5a, assuming a constant TES size, \(W_{el,grid}\) and \(W_{el,sys,grid}\) decrease, while \(W_{el,feedin}\) tends to increase. There is a tendency to further decrease consumption from the public electricity grid. Furthermore, in good proportions, it is possible to inject the energy produced by the eco-friendly home where the photovoltaic solar panels are installed into the electricity grid. This dynamic occurs in both the fully integrated and standard scenarios.  
In the integral process, increasing the size of the photovoltaic system produces an increase in \(SPF_{sys,grid}\); however, it reduces the \(SPF_{sys}\). For the standard strategy, the \(SPF_{sys}\) is the same for all photovoltaic system sizes since the system will always operate with energy regardless of whether it is supplied with power from the photovoltaic system or the public electricity grid. In this context, the size of the photovoltaic system has a more significant influence on the fully integrated control system than on the standard control system. The self-consumption ratio (SCR) tends to increase as the PV system size decreases, reaching a maximum value of 75% with a capacity of 65 kWh in both scenarios.  
Figure 4: Power production and demand of the subsystems.  
Figure 5: _Cont._
## 3 Results  
To gain a comprehensive understanding of the issue, Figure 2 illustrates the daily NO\({}_{2}\) averages along with the daily TBM ring production. A clear relationship can be observed between the TBM's production and an increase in NO\({}_{2}\) levels in the TBM. As the TBM production increases, the number of locomotives required for transporting rings, grout, and other materials also increases, leading to higher NO\({}_{2}\) emissions in the TBM. Additionally, Figure 2 shows a correlation between the tunnel length and NO\({}_{2}\) levels. As the tunnel length increases, the TBM's performance improves, but this improvement is accompanied by an increase in NOx levels. Furthermore, the reduction of airflow at the tunnel face due to the expansion of the tunnel length also contributes to the higher concentration of NOx.  
The average NO\({}_{2}\)/NO ratio is 0.70 ppm NO\({}_{2}\)/ppm NO. This ratio provides important insight into the composition of NOx emissions in the tunnel and can be valuable for further analysis and mitigation strategies.  
Overall, there were a total of 4640 NO\({}_{2}\) readings collected throughout the 349-day construction period of the tunnel. The following section will analyze these data comprehensively, including individual data points and daily averages.  
Figure 2: Daily NO\({}_{2}\) averages and daily TBM ring production.  
There is a clear relationship between the number of rings installed per day and the concentration of NO\({}_{2}\) in the air. As seen in the graph in Figure 3A, the NO\({}_{2}\) concentration increases as the number of rings increases. Although there is some dispersion in the results, a linear relationship can be established, with a correlation coefficient of \(r^{2}=0.78\). This is logical because the more rings are installed in a day, the more times locomotives have to enter the tunnel on that day, and therefore, the higher the amount of NO\({}_{2}\) they have emitted inside the tunnel. However, this relationship becomes much more evident when representing the total volume of NO\({}_{2}\) emitted inside the tunnel as a function of the total number of rings installed up to that point. As shown in Figure 3B, the relationship between these variables is much clearer. It should be noted that if the number of locomotives was continuously increased as the tunnel progressed, the relationship between these variables would be parabolic, as seen in the first part of the graph. In this case, beyond a certain tunnel length, the number of California crossings and, consequently, the number of locomotives inside the tunnel remains constant. As the decrease in air flow rate is nearly linear for large lengths, the concentration will increase linearly.
# Novel Resource Allocation Techniques for Downlink Non-Orthogonal Multiple Access Systems
## 2 Related Works
In comparison with NOMA-FTPA and OFDMA, the proposed method has the best performance. The difference of convex (DC) programming approach was proposed in [28] as a suboptimal solution to allocate the user's power and subchannel, improving the network energy efficiency and sum rate. The proposed technique showed greater improvement than the OFDMA approach and the equal power allocation method. The aforementioned suboptimal solutions have considered the sum rate and weighted sum rate of the NOMA system without investigating the closed-form solutions for the optimal power allocation. Additionally, the energy efficiency and sum rate of the NOMA system that could achieve the optimal performance are not well studied in the recent works. Our previous conference work [15] investigated the user pairing based on HNG and presented the closed-form optimal user power allocation solution based on PKKT conditions to maximize system sum rate without considering energy efficiency performance and fairness among users.
## 5 Influence Analysis of the Main Structural Parameters on Dynamic Characteristics
### Structural Stiffness  
On the basis of the original structure, the stiffness values of the main girder, bridge tower, cable, and other components are changed, and the stiffness value scaling changes from 0.8 to 1.6. The vibration frequencies of typical vibration modes at different working conditions are compared with those of the original model.  
The results are shown in Figure 7.  
According to Figure 3, the following conclusions can be obtained.  
1. The stiffness variations of bridge tower and stayed cables have little influence on the frequency changes of the first-order torsion.
2. The changes in the stiffness of the bridge tower make the frequency change rate of the first-order vertical bending negative. When the scaling ratio is 1.2 times, the frequency change rate reaches the minimum, approximately \(-17\%\). Therefore, the overall stiffness of the bridge can be increased by adding auxiliary piers or auxiliary cables during the construction stage.
3. Changes in the stiffness of the main girder can induce, accordingly, the frequency change rate of the first-order torsion, the coupling of the first vertical bending and the lateral bending torsion can change basically linearly, and gradually increase.
4. The frequency change rates of the lateral bending torsion coupling are approximately linear, but the frequency variation rate of the pylon stiffness is the maximum. When the scaling ratio is 1.6, the frequency change rate is close to 90%.
## 4 Model Verification Using the Real Data
### Practical Results  
The measurement results from 10-times average values using the real bike frame are concluded in Table 1. Based on the same bike frame, the error between the proposed model and the Vernier caliper is below 0.05 mm, and the repeatability is at the range of 0.1 mm. This verifies that the proposed model presents both robust and stable performance. Nevertheless, the measured data reveals that the tested frame has some defects occurred in the center plane offset, parallelism and verticality.  
To clarify the uncertainty of the measurement, the estimated standard deviation for a series of \(n\) measurements is expressed mathematically as:  
\[s=\sqrt{\frac{\sum\limits_{i=1}^{n}(x_{i}-\overline{x})^{2}}{n-1}} \tag{32}\]  
where \(x_{i}\) is the result of the \(i\)th measurement and \(\overline{x}\) is the arithmetic mean of the \(n\) measurement results.  
When a set of several repeated readings has been taken, the mean, \(\overline{x}\), and estimated standard deviation, \(s\), can be calculated. The measurement uncertainty, \(u\), of the mean is therefore defined as:  
\[u=\frac{s}{\sqrt{n}} \tag{33}\]  
where \(n\) is the number of measurements in the set.  
The estimated standard deviation and measurement uncertainty based on 10 measurements for S/T rotating shaft, T/T rotating shaft, and H/T rotating shaft is shown in Tables 2-4, respectively. From the statistics, it is obvious that both standard deviation (\(s\)) and measurement uncertainty (\(u\)) for all shaft measurements present a very low value no more than 0.018. Thus, accuracy and robustness of the proposed model is thus confirmed.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Check Item Check Point** & **T/T Rotating Shaft** & **H/T Rotating Shaft** \\ \hline Center plane offset & \(-\)2.71 mm & Not applicable \\ \hline Parallelism & 8.2\({}^{\circ}\) & Not applicable \\ \hline Verticality & Not applicable & 114.65\({}^{\circ}\) \\ \hline Internal diameter & 14.86 mm & Not applicable \\ \hline Length & Not applicable & 109.89 mm \\ \hline \hline \end{tabular}
\end{table}
Table 1: Measured values using the proposed model.  
Figure 15: GUI of verticality: (**a**) synchronous action; (**b**) GUI result.
# Quadratic Multilinear Discriminant Analysis for Tensorial Data Classification
## Appendix A  
This appendix deals with the exact solution of the optimization problem from Section 3 in the case of vector data, and it contains proofs of Propositions 1 and 2.  
Consider vector data \(x_{1},\ldots,x_{m}\in\mathbb{R}^{n}\), with \(n<m\), and concatenate them as columns of a matrix \(X\) of size \(n\times m\). Consider the group \(\mathrm{SL}_{n}\) acting on the columns of \(X\). We wish to minimize the squared norm of \(AX\) over all \(A\in\mathrm{SL}_{n}\). Since the squared norm of a matrix \(Y\) equals \(\mathrm{Tr}(Y^{t}Y)\), this optimization problem amounts to minimizing \(\mathrm{Tr}((AX)^{t}AX)\) over all \(A\in\mathrm{SL}_{n}\).  
By Kempf-Ness Theorem, we are looking for critical points of the function \(\mathrm{Tr}(Y^{t}Y)\), whose gradient is \(2Y\). A convenient way to find critical points is using the language of Lie groups (i.e., groups that are also differentiable manifolds). In our setting, we are interested in the Lie groups \(\mathrm{SL}_{n}\) and \(\mathrm{T}_{n}\). Let \(G\) be one of these two groups. The Lie algebra \(\mathfrak{g}\) of \(G\) is the tangent space to \(G\) at the identity, and the tangent space of the orbit \(G\cdot X\) at \(AX\) for some \(A\in G\) equals \(\mathfrak{g}AX\). Therefore \(AX\) is a critical point of \(GX\) for the squared norm if and only if the gradient of the squared norm at \(AX\) is perpendicular to \(\mathfrak{g}AX\); equivalently, if and only if \(\mathrm{Tr}(2 AX\cdot BAX)=0\) for all \(B\in\mathfrak{g}\).  
Proof of Proposition 1.: The Lie algebra of \(SL_{n}\) equals the space of \(n\times n\) matrices with trace zero [36]. Therefore \(AX\) is a critical point if and only if \(\mathrm{Tr}(2 AX\cdot BAX)=0\) for all \(B\) with \(\mathrm{Tr}(B)=0\). This amounts to \(\mathrm{Tr}(BAXX^{t}A^{t})=0\) for all \(B\) with \(\mathrm{Tr}(B)=0\), which is equivalent to having that \(AXX^{t}A^{t}\) is a multiple \(\lambda I_{n}\) of the identity. If \(\lambda=0\), this means that \(AXX^{t}A^{t}=0\), hence that \(X=0\). If \(\lambda=0\), then necessarily \(\lambda>0\) and \(XX^{t}=\lambda(A^{t}A)^{-1}\). Therefore \(XX^{t}\) is invertible and \(X\) has rank \(n\). Furthermore, taking the determinant on both sides we have \(\det(XX^{t})=\lambda^{n}\). Therefore \(\lambda=\det(XX^{t})^{\frac{1}{n}}\) and \(A^{t}A=\det(XX^{t})^{\frac{1}{n}}(XX^{t})^{-1}\). Now one just has to check that the matrix \(A=DU^{t}\) defined in the Proposition satisfies this equation.  
Proof of Proposition 2.: The proof is very similar to the previous one. The Lie algebra of \(T_{n}\) equals the space of \(n\times n\) diagonal matrices with trace zero. Therefore \(AX\) is a critical point if and only if \(\mathrm{Tr}(2 AX\cdot BAX)=0\) for all diagonal matrices \(B\) with \(\mathrm{Tr}(B)=0\). This amounts to \(\mathrm{Tr}(A^{t}BAXX^{t})=0\) for all diagonal matrices \(B\) with \(\mathrm{Tr}(B)=0\). It is now easy to check that the matrix \(A\) defined in the Proposition satisfies this condition.
## 3 Results  
All measurements were performed by one investigator. The intra-observer reliability was assessed by ICC testing on 35% of the samples, with each variable being measured at two time points, and showed excellent reliability (0.995) between the measurements.  
The cortical bone thickness and the cortical bone density were found to increase between the lower and the upper gingival height level, in both the right and left sides of the maxilla. Specifically, as is recorded by the mean values in Table 1, the cortical thickness increased from 0.71 mm at the lower level, to 0.98 mm at the middle, and 1.1 mm at the upper level on the right side, while on the left side, it increased from 0.67 mm, to 0.88 mm and 0.99 mm, respectively. The cortical bone density on the right side increased from 1155.75 HU at the lower level, to 1250.40 HU at the middle, and 1395.10 HU at the upper level, while on the left side, it increased from 995.85 HU, to 1171.20 HU and 1224.30 HU, respectively (mean values in Table 1).  
However, the situation was different for the trabecular density. More specifically, the trabecular density was higher at the middle gingival level, on the right side (732.95 HU), and at the lower level (604.10 HU), on the left side (mean values in Table 1).  
Regarding the correlation between the cortical bone thickness and cortical bone density, we found statistically significant correlation in both sides (\(p\)-value 0.018 for the right side and 0.001 for the left side). The thicker the cortical bone, the bigger the cortical bone density (Table 2).  
Finally, we found a medium association between the gingival height and the cortical bone thickness, a weak association between the gingival height and the cortical bone density, and no association between the gingival height and the trabecular bone density, either for the right or the left side (Table 3).  
Figure 3: (**a**) The region (rectangular shape) in which measurements were performed at the lower, middle, and upper level of the attached gingiva. (**b**) The measurements on the selected coronal slice of the CBCT image, at the middle height level of the attached gingiva, indicated by the blue line, which is in correspondence with the blue line on the left photograph. The same measurements were performed for the lower and upper height levels.