esa-sceva/satcom-chunk-collection huggingface dataset:
# A Generic Block-Level Error Confinement Technique for Memory Based on Principal Component Analysis
## 3 PCA-Based Error Confinement Technique
### Applying PCA to Memory Elements  
This section we explain the procedures of applying PCA for dimension reduction of the data under protection. The block diagram is shown in Figure 3. The specific steps are as follows:  
1. Prepare the data to be stored as X\(\in R_{m\times n}\) as Equation (1).
2. Center the input data at the mean value of zero to remove the noise during sensing. The normalized data is updated as X = X - \(\overline{\text{X}}\) according to Equation (2)-(4).
3. Calculate the covariance matrix S according to Equation (5).
4. Obtain the eigenvalues and corresponding eigenvectors of S by the Eigen decomposition: S = \(V\wedge V^{T}\), where V is the orthogonal matrix, and its columns are the corresponding unit eigenvectors V = \(\left(\text{v }\text{1},\text{v }\text{2},...,\text{v }\text{n}\right)\). \(\wedge\) is the diagonal matrix consisting of the eigenvalues \(\lambda\text{ 1},\lambda\text{ 2 },...,\lambda\text{  n}\) of the covariance matrix. Sort the eigenvalues in descending order (\(\lambda\text{ 1}\text{ 2}\text{ 2}\text{ }...\text{ 2}\text{ }\lambda\text{  n}\)) as well as reorder their corresponding eigenvectors. The reordered eigenvectors are called the principal components (PCs) of the data X.
5. Project the data X to the orthogonal space defined by the matrix V according to Equation (6). V\({}_{K}\) is the first \(k\) columns of V, and k is the number of PCs reserved. The dimension of projection data Y is \(k\times m\) (\(k<<n\)). The contribution rate (CR) of PCs to the original data is expressed as: \[\text{CR}=\frac{\int_{i=1}^{k}\lambda_{i}}{\int_{i=1}^{n}\lambda_{i}}\] (12) High contribution rate leads to accurate reconstructed data, however increase extra storage and computational efforts. We explore the tradeoff between CR and physical overhead in the experiment section and generalize the empirical suggestions.
6. Encode each element of the projection data \(Y\), mean vector \(\overline{\text{X}}\), and eigenvectors \(V_{k}\)with a single parity for error detection (refer to III.D.1 for details).
7. Write \(Y\), \(\overline{\text{X}}\) and \(V_{k}\) as well as their parity encodings into the memory. The dimension of such extracted features is far smaller than the original data, which dramatically reduces the storage space.  
Noted that PCA is not the only candidate to realize the error confinement technique. We illustrate the flow by using PCA since it is more straightforward and generic than other candidates, such as Singular Value Decomposition (SVD).
# Influence of Electrohydrodynamics on the Drying Characteristics and Volatile Components of Ginger
## 3 Results and Discussion
### Color Difference Analysis  
The color of a product is a key parameter that reflects its overall characteristics and significantly influences consumer perception. Color is an important quality in evaluating the merit of a food product and influences consumer choice and the value of the product [33]. Figure 4 shows how electrohydrodynamic drying affects the surface color of ginger, with significant differences seen at different voltage levels (\(p<0.05\)). After electrohydrodynamic drying, the brightness value of ginger increases with voltage, reaching a maximum of 11.85 \(\pm\) 0.96 at 30 kV. Ginger has a maximum redness value of 6.23 \(\pm\) 0.41 at 20 kV and a maximum yellowness value of 10.12 \(\pm\) 1.37 at 30 kV. Electrohydrodynamic drying (EHD) has higher brightness and yellowness because electrohydrodynamic drying (EHD) is a low-temperature drying process. The color change is caused by enzymatic browning, which is the main influential factor [34]. In addition, the changes in the volume and density of ginger slices before and after drying can also cause differences in color difference measurement results. The lesser color difference in EHD compared to the control group could be attributed to the faster drying rate, which results in a rapid evaporation of water [35]. In conclusion, EHD provides distinct advantages in maintaining the color of ginger. According to [PERSON] et al. [36], an increase in \(\Delta\)E with increasing temperature was observed in the combined EHD-hot air and hot air methods. In the EHD-only method, \(\Delta\)E value did not change significantly with a change in the kV value but, in our study, \(\Delta\)E value decreased with an increase in the kV value. The relationship between color difference and voltage varies with different materials and is not fixed.
# A Predictive Model of Chlorophyll a in Western Lake Erie Based on Artificial Neural Network
## 2 Materials and Methods
### Modeling Methodology  
#### 2.2.1 GLM-AED Description  
The one-dimensional model GLM-AED (General Lake Model-Aquatic Ecosystem Dynamics module library) is open-source [37], and it has been applied to various water bodies, such as temperate lakes [19] and reservoirs [38]. The advantage of computational requirements makes it a common tool for long-term simulations. The hydrodynamic model GLM assumes there is no horizontal variability and adopts a flexible Lagrangian structure, making it possible to adjust the vertical layer thicknesses dynamically to resolve the water column structure. The module solves the turbulent kinetic energy balance to model the surface heat and momentum budgets. The biogeochemical module AED can simulate nutrients, phytoplankton, and oxygen. In this module, 15 state variables were applied to model Chl-a, including dissolved oxygen (DO), four dissolved inorganic groups (dissolved reactive phosphorus (PO\({}_{4}\)), nitrate (NO\({}_{3}\)), ammonium (NH\({}_{4}\)), and reactive silica [39]), three dissolved organic groups (dissolved organic nitrogen (DON), dissolved organic phosphorus (DOP), and dissolved organic carbon (DOC)), and three particulate detrital organic groups (particulate organic nitrogen (PON), particulate organic phosphorus (POP), and particulate organic carbon (POC)), diatoms (DIAT), chlorophytes (CHLOR), cryptophytes (CRYPT), and cyanobacteria (CYANO). Given the difficulties in simulating the changes in the associated population dynamics, we neglected to model dreissenid  
Figure 1: Map of Lake Erie and data sites. Detail of western basin shoreline showing the Detroit River (A), Maumee River (B), NOAA (red dots), and GLENDA (black dots).  
mussels and zooplankton, subsuming the related mortality and nutrient cycling into the respiration parameter [40].  
GLM-AED was initialized on 1 May 2002. The mean daily meteorological forcing data included air temperature, wind speed, relative humidity, precipitation, shortwave solar radiation, and cloud cover. Mean daily boundary conditions included flow rates and water quality state variables for the Detroit River and Maumee River (flow, temperature, and the water quality state variables). The boundary of outflow was specified as the central basin, and the flow rate was calculated based on water balance from the flow rates of the Detroit River and Maumee River, evaporation, and the observed water levels [41; 42]. The model was calibrated to the observed surface water temperature and Chl-a concentrations from 2002 to 2015.
## 3 Results
### Example 2. Luus-Tassone Nonseparable Control Problem  
The behavior of the control object is described by the system of difference equations:  
\[x_{1}(t+1)=\frac{x_{1}(t)}{1+0.01u_{1}(t)(3+u_{2}(t))};\] \[x_{2}(t+1)=\frac{x_{2}(t)+u_{1}(t)(1)x_{1}(t+1)}{1+u_{1}(t)(1)+u_ {2}(t)};\] \[x_{3}(t+1)=\frac{x_{3}(t)}{1+0.01u_{2}(t)(1+u_{3}(t))},\]  
where \(x\in\mathbf{R}^{3}\), \(t=0,\ldots,N-1\), and \(u\in\mathbf{R}^{3}\).  
The cost functional on the feasible set of processes is:  
\[I=x_{1}{}^{2}(N)+x_{2}^{2}(N)+x_{3}^{2}(N)+\] \[+\bigg{[}\bigg{(}\sum_{k=1}^{N}x_{1}^{2}(k-1)+x_{2}^{2}(k-1)+2u_{ 3}^{2}(k-1)\bigg{)}\bigg{(}\sum_{k=1}^{N}x_{3}^{2}(k-1)+2u_{1}^{2}(k-1)+2u_{2} ^{2}(k-1)\bigg{)}\bigg{]}^{\frac{1}{2}}.\]  
The problem is to find the minimum value of the cost functional and optimal process \((x^{*}(\cdot),\ u^{*}(\cdot))\).  
Initial state vector \(x(0)=(2;\ 5;\ 7)^{T}\); control constraints: \(0\leq u_{1}(t)\leq 4\); \(0\leq u_{2}(t)\leq 4\); \(0\leq u_{3}(t)\leq 0.5\). Number of stages: \(N=20\).  
The best known value of the cost functional obtained for this problem is \(\min I=209.26937\)[1].  
The obtained approximate value of the functional was \(I^{*}=209.429533683522\), and the runtime was \(49.92\) s. Table 3 shows the parameters of the method for solving this problem. Figures 5 and 6 show the obtained control and corresponding trajectory.  
where \(x\in\mathbf{R}\), \(t=0,1,2\), and \(u\in\mathbf{R}\).  
The cost functional on the feasible set of processes is:  
\[I=\big{[}x^{2}(0)+x^{2}(1)+(2x^{2}(2)+x^{2}(3))\exp(x^{2}(1))\big{]}\times\big{[} 50+u^{2}(0)+(u^{2}(1)+u^{2}(2))\exp(u^{2}(0))\big{]}^{1/2}.\]  
The problem is to find the minimum value of the cost functional and optimal process \((x^{*}(\cdot),\ u^{*}(\cdot))\).  
Initial condition: \(x(0)=15\); control constraint: \(-1\leq u(t)\leq 1,\ t=0,1,2\). Number of stages: \(N=3\). The best known value of the cost functional obtained for this nonseparable control problem is \(\min I=1596.4796778\)[1].  
The obtained approximate value of the functional was \(I^{*}=1596.47967783389\), with a runtime of 00.19 s. Table 4 shows the parameters of the method for solving this problem. Figure 7 shows the obtained control and corresponding trajectory; the numerical solution of the problem is presented in Table 5.  
Examples 2 and 3 are devoted to solving a class of optimal control problems with nonseparable cost functionals, for which it is difficult to apply necessary and sufficient optimality conditions for discrete deterministic dynamical systems.
# Research on Passive Ranging Technology of Moving Ship Based on Vertical Hydrophone Array
## 4 Experimental Analysis
### Results Analysis
In this paper, we are more concerned about the accuracy of the estimation results near the CPA point, because the range, time and radial velocity of the CPA point determine the total estimated range. Therefore, we choose the estimation results of the first 300 s of Figure 14 for statistical calculations. Table 1 gives the RMSE of each hydrophone and the RMSE after the 16-element fusion. From this table, we can see that the RMSEs of the 16 elements are slightly different. The RMSEs of the 7 th, 10 th and 13 th element are significantly higher than those of the other elements, which is consistent with the curves in Figure 14. Moreover, the RMSE of the fusion results is \(4.9\times 10^{-4}\), which is lower than the RMSE of most elements. Hydrophones at different depths receive signals with different SNRs. Inaccurate range estimation results can be obtained by a low SNR signal, as shown in the 7 th, 10 th and 13 th element, because the sound signals at different depths go through different paths, undergoing different reflections and scattering. The signals reaching the receivers are attenuated differently, and the SNRs are also various. The performance evaluation of the algorithm proposed in our paper is based on a comparison with real GPS data and the range estimation results obtained by a single hydrophone element. The comparison of these three results infer that this method can improve the estimation accuracy effectively and obtain a more accurate range estimation result than a single hydrophone. It should be noted that the target and array should avoid being located in the shadow zone. In the shadow zone, the sound field is mainly composed of bottom-reflected rays rather than direct rays. The sound rays reflected by the sea bottom are greatly attenuated, and the SNRs of the signal received by the hydrophones are low. Thus, the range localization performance may be inaccurate.
# Fat Graft in Surgical Treatment of Medication-Related Osteonecrosis of the Jaws (MRONJ)
## 4 Discussion
### Findings and Study Limitations  
In this study, fat graft was found to have an influence on the evolution of the disease toward better stages or complete resolution, which is perhaps due to the described effects of the included ASCs. Exciting results have been reported by [PERSON] et al. [21] and [PERSON] et al. [22] using the buccal fat pat to cover the surgical site. In their studies, the complete resolution of the disease was documented over a middle postoperative follow-up for almost all the operated patients. Being a pedicled tissue flap, the optimal results probably may be justified by the preserved vascularization more than their biological properties, or both. The buccal fat pat surely represents an optimal solution in case of small to moderate-sized defects in the oral cavity. However, it is not always available in sufficient volume, or it could not be fully mobilized depending on subjective variabilities. It is also more commonly indicated for maxillary defects, while mandibular ones could be addressed by using a mylohydoid muscle flap [21; 22], which might endanger the lingual nerve causing discomfort or pain [21].  
The knowledge from current literature suggests that ASCs may lead the process of influencing the micromilieu, causing a significative improvement on the vascularization of the residual bone and the overlying mucosa and reducing the inflammation on the surgical site. It should be underlined that the patients included in group A received a fat graft, which do not represent a cellular therapy as well as the local delivery of isolated ASCs. This obviously implies a much lower amount of stem cells introduced in the surgical site, potentially reducing the effects of the ASCs. However, using a purified ASCs population implies complex purification processes that implicate costs, time, expertise, and dedicated materials, which might not be available. Future studies focusing on the comparison between fat grafts, stromal vascular fraction, and ASCs would be of utmost interest.  
Several limitations do not permit defining the reliability of the studied treatment protocol. Firstly, the small sample size precluded a reliable analysis of the retrieved results and a multivariate analysis that would have addressed the potential issues deriving from the existence potential baseline confounding. A more extensive population would have allowed an assessment of the risk of bias by a more complex statistical design. Although in this study, both groups were comparable with respect to diabetes and MRONJ stages, these would represent the most probable sources of bias that should be investigated.  
Another limitation is represented by the relatively short follow-up period considered for the study groups. Part of the included patients was lost after the 12-month follow up, because of the progression of the oncological disease or because they voluntary quit.
# A Novel Method Using 3D Interest Points to Place Markers on a Large Object in Augmented Reality
## 2 Impact of the number of markers
### Discussion  
It was verified that, to determine the position of multiple markers, the proposed method performed better than the conventional method which is subjectively determined by humans.  
The weight determined by the preliminary experiment (\(w\) = 0.75) means that the DoI is more effective than the CSA to minimize the inevitable problems that arise in AR. It was also confirmed that the registration error decreased as the proportion of the DoI increased. This means that the more interest points, the easier for humans or sensors to recognize. However, the registration error increased when the CSA was completely excluded (\(w\) = 1). This means that even a small proportion must be reflected to minimize the geometric discrepancy problem.  
When the minimum number of markers (\(k\) = 4) was used, MREproposed was approximately 59.8% less than MREconventional, and the reduction in error increased as \(k\) increased.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \(k\) & **M (mm)** & **STD (mm)** \\ \hline
4 & 2.184 & 0.662 \\
6 & 1.770 & 0.298 \\
8 & 1.581 & 0.328 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Overall comparison between MREproposed by number of markers \(k\).  
\begin{table}
\begin{tabular}{c c c} \hline \hline \(k\) & **DM (\(p\) = 5.23 \(\times\) 10\({}^{-5}\))** & **DA (\(p\) = 0.393)** \\ \hline
4 & 2.802 \(\pm\) 0.292 & 1.566 \(\pm\) 0.165 \\
6 & 1.966 \(\pm\) 0.258 & 1.573 \(\pm\) 0.185 \\
8 & 1.691 \(\pm\) 0.394 & 1.471 \(\pm\) 0.189 \\ \hline \hline \end{tabular}
\end{table}
Table 11: Individual comparisons between MREproposed by number of markers \(k\) (mean \(\pm\) standard deviation).  
Figure 26: Difference in MRE between the proposed and conventional methods.  
This means that the proposed method can be applied in various ways, from environments using a small number of multiple markers to environments using a large number of multiple markers.  
In the performance comparison analysis of the proposed method using the number of markers, as in results of previous studies, the error decreased significantly as the number of markers increased. However, a significant reduction in the specific object DA was not observed. This means that the using only four markers in DA is no different than using six or eight, so it is not necessary to use many markers; and this result means that there may be an optimal number of markers depending on the geometry of a specific model.  
Lastly, because the proposed method automatically determines the positions of multiple markers used for registration, it can be used as a comparison group in all subsequent and extended experiments to compare registration performance.
# The Impact of Eclipsing GNSS Satellites on the Precise Point Positioning
## 3 Results and Discussion  
### Current GNSS Constellations and the Results of Eclipsing Monitor  
The sun angles and the nominal yaw angles of all GNSS satellites are calculated every 30 s using precise orbit and clock products. After monitoring the sun angles and the orbital angles for all GNSS satellites, it has been found that many satellites are in eclipsing seasons in July 2017 (31 days in total, from DOY 182 to DOY 212 of 2017), as shown in Figure 1. In this month, about 85 GPS/GLONASS/GALILEO/BDS satellites are available, while 18 of them are in eclipse. Therefore, the data of this whole month are selected. During the whole month, 31 GPS satellites are operational (except G04), including eight IIR-A satellites, four IIR-B satellites, seven IIR-M satellites and 12 IIF satellites. There are seven GPS eclipsing satellites, including two IIR satellites (in cyan dots) and five IIF satellites (in red dots). Among them, G01, G02, G06 and G21 have the complete eclipsing period in this month. Due to the smaller threshold value of the sun angle, it is obvious that the number of days influenced by the eclipsing satellites for GPS IIR satellites is significantly shorter than that of the GPS IIF satellites. For GLONASS, the constellation is mainly composed of the GLONASS-M satellites, but also includes two GLONASS-K1 satellites (R09/R26). Since the R26 satellite is in the flight test phase, no precise orbit and clock products are available. Therefore, this satellite will be automatically deleted in the PPP processing. Compared with GPS satellites, the sun angle limit of GLONASS for shadow crossing regime is relatively bigger, and R10, R11, R13, R15 and R16 satellites are always in eclipse in the whole month (in blue dots). The GALILEO system consists of two generations of satellites, namely the IOV and FOC satellites. On 15 December 2016, GALILEO started offering Initial Operational Capability (IOC) with four IOV satellites and 14 FOC satellites ([[https://www.gsc-europa.eu/](https://www.gsc-europa.eu/)]([https://www.gsc-europa.eu/](https://www.gsc-europa.eu/))). Among them, the E20 (IOV) experienced a permanent failure of the E5 and E6 signal transmission and two FOC satellites (E14 and E18) were in the wrong orbits. On July 2017, four FOC satellites are in eclipse (E01/E02/E24/E30, in pink dots). The development of BDS is divided into two stages: the regional system, which was realized at the end of December 2012, and the global system. As of July 2017, five GEO, six IGSO and three MEO satellites are providing valid navigation messages. Even though five BDS-3 satellites are successfully launched into the correct orbit plane, they are still in the phase of the flight test. Therefore, all the results of BDS satellites in this paper are always referred to that of the BDS-2 satellites. The attitude of two IGSO satellites (C07/C10, in green dots) will switch to orbit normal mode.
# An Experimental Survey of Extended Resolution Effects for SAT Solvers on the Pigeonhole Principle
## 2 Preliminaries
### Pigeonhole Principle  
The pigeonhole principle (PHP) [29] is defined as follows.  
Definition 1: (Pigeonhole Principle). The pigeonhole principle asks whether all \(n>1\) pigeons can enter \(n-1\) holes so that one pigeon is at one hole. In other word, there is no injective function mapping from \(\{1,2,\ldots,n\}\) to \(\{1,2,\ldots,n-1\}\) for \(n>1\).  
The answer is clearly no. Thus a SAT instance converted from the pigeonhole principle is unsatisfiable. For each integer \(n>1\), the pigeonhole principle is formulated as follows. A variable \(P_{ij}\) for \(1\leq i\leq n\) and \(i\leq j\leq n-1\) is true when pigeon \(i\) is at hole \(j\). The constraints are described as a set of clauses: one pigeon at least in one hole (at least one constraint) is  
\[(P_{i,1}\lor P_{i,2}\vee\ldots\lor P_{i,n-1})\ for\ 1\leq i\leq n \tag{1}\]  
and one hole containing at most one pigeon (at most one constraint) is  
\[(\
eg P_{i,k}\vee\
eg P_{j,k})\ for\ 1\leq i<j\leq n,1\leq k\leq n-1 \tag{2}\]  
The pigeonhole principle formula \(S_{n}\) constitutes the conjunction of Formulas (1) and (2).  
[PERSON] [10] proved that the PHP can be solved in polynomial steps by using extended resolution [9]. Given a formula \(F\), extended resolution is a proof system to apply the general resolution on the extended formula \(F*\), where \(F*\) is obtained by adding redundant clauses to \(F\). [PERSON] introduced a new variable \(Q_{i,j}\) below:  
\[Q_{i,j}\equiv(P_{i,j}\vee(P_{i,n-1}\wedge P_{n,j}))\ for\ 1\leq i\leq n-1,\ 1 \leq j\leq n-2 \tag{3}\]  
The formula is expressed as the following four clauses:  
\[Q_{i,j}\vee\
eg P_{i,j}\]  
\[Q_{i,j}\vee\
eg P_{i,n-1}\vee\
eg P_{n,j}\]  
\[\
eg Q_{i,j}\lor P_{i,j}\lor P_{i,n-1}\]  
\[\
eg Q_{i,j}\lor P_{i,j}\lor P_{n,j}\]  
The addition of these clauses to the original PHP formula guarantees the satisfiability equivalency. We describe the newly introduced variable \(Q_{i,j}\) as an extended variable and a clause including extended variables as an extended clause. Using \(O(n^{3})\) resolutionson every \(P_{i,j}\) variable, only the extended variables remain. Hence, the formula \(S_{n}\) can be reduced to \(S_{n-1}\). By repeating the same manner, we can derive \(S_{2}=P_{1,1}\wedge P_{2,1}\wedge(\
eg P_{1,1}\vee\
eg P_{2,1})\) that can be easily proved to be unsatisfiable.  
**Example 1**.: _For a case where the number of pigeons is 3 (\(n=3\)), Formula (1) is_  
\((P_{1,1}\lor P_{1,2})\wedge(P_{2,1}\lor P_{2,2})\wedge(P_{3,1}\lor P_{3,2})\)__  
_Formula (2) is_  
\((\
eg P_{1,1}\vee\
eg P_{2,1})\wedge(\
eg P_{1,1}\vee\
eg P_{3,1})\wedge(\
eg P _{2,1}\vee\
eg P_{3,1})\wedge(\
eg P_{1,2}\vee\
eg P_{2,2})\wedge(\
eg P_{1,2 }\vee\
eg P_{3,2})\wedge(\
eg P_{2,2}\vee\
eg P_{3,2})\)__  
_Formula (3) is_  
\(Q_{1,1}\equiv(P_{1,1}\vee(P_{1,2}\wedge P_{3,1}))\wedge Q_{2,1}\equiv(P_{2,1} \vee(P_{2,2}\wedge P_{3,1}))\)__