esa-sceva/satcom-chunk-collection huggingface dataset:
## 6 Security Analysis  
### Correctness  
**Theorem 1**.: _If the server faithfully executes the aggregation protocol, it is easy to aggregate the global gradients._  
Proof of Theorem 1.: Given the encrypted gradients \(\{C_{i}\}_{i\in\mathbb{U}_{2}}\), the server can aggregate the global gradients \(W_{t}\) with the auxiliary information \(Au_{t}^{FN}\) sent by the FN. The server first computes  
\[C_{t} =\left(\prod_{i=1}^{n}C_{i,t}\right)^{sk_{CS}}\pmod{p^{2}}\] \[=\left(1+p\cdot\sum_{i=1}^{n}w_{i,t}\right)^{sk_{CS}}\cdot\left(g _{1}^{0}\right)^{sk_{CS}}\cdot\left(H_{0}(t)^{sk_{FN}\sum_{i=1}^{n}sk_{i}} \right)^{sk_{CS}}\pmod{p^{2}}\] \[=\left(1+sk_{CS}\cdot p\cdot\sum_{i=1}^{n}w_{i,t}\right)\cdot H_{ 0}(t)^{sk_{FN}sk_{CS}\sum_{i=1}^{n}sk_{i}}\pmod{p^{2}}\]  
and obtains the global gradient \(W_{t}\) of current epoch \(t\) by  
\[W_{t} =\frac{\frac{C_{t}}{Au_{t}^{FN}}-1}{p\cdot sk_{CS}}\pmod{p^{2}}\] \[=\frac{\frac{(1+sk_{CS}\cdot p\cdot\sum_{i=1}^{n}w_{i,t})-H_{0}(t )^{sk_{FN}sk_{CS}\sum_{i=1}^{n}sk_{i}}}{H_{0}(t)^{sk_{FN}sk_{CS}\sum_{i=1}^{n} sk_{i}}}-1}{p\cdot sk_{CS}}\pmod{p^{2}}\] \[=\frac{(1+sk_{CS}\cdot p\cdot\sum_{i=1}^{n}w_{i,t})-1}{p\cdot sk_ {CS}}\pmod{p^{2}}\] \[=\sum_{i=1}^{n}w_{i,t}\pmod{p^{2}}\]  
That is, if the server faithfully executes the aggregation protocol, it is easy to aggregate the global gradients.  
**Theorem 2**.: _If the server faithfully executes the aggregation protocol, the aggregated global gradients are able to pass the verification of users._  
Proof of Theorem 2.: Given the encrypted gradients \(\{C_{i}\}_{i\in[1,n]}\), the server can aggregate the global gradients \(W_{t}\) with the auxiliary information \(Au_{t}^{FN}\) sent by the FN. Then, it can compute the proof \(Au_{t}^{2}\). After that, it sends the global gradients \(W_{t}\) and the proof \(Au_{t}^{2}\) to users.  
Based on the global gradients \(W_{t}\), the proof \(Au_{t}^{2}\) and \(Au_{t}^{3}\), Each user can use bilinear pairing to verify the correctness of \(W_{t}\) with Equation (11).  
The validity of Equation (11) can be derived as follows:\[e(Au_{t}^{2},h_{2}) =e(H_{1}(t)^{sk_{CS}\sum_{t=1}^{m}k_{i}}\cdot g_{1}^{sk_{CS}\sum_{t=1} ^{m}w_{t,t}},g_{2}^{x})\] \[=e(H_{1}(t)^{sk_{CS}\sum_{t=1}^{m}k_{i}},g_{2}^{x})\cdot e(g_{1}^{ xsk_{CS}\sum_{t=1}^{m}w_{t,t}},g_{2}^{x})\] \[=e(H_{1}(t),g_{2}^{sk_{CS}\sum_{t=1}^{m}k_{i}})\cdot e(g_{1}^{xK \sum_{t=1}^{m}w_{t,t}},g_{2}^{sk_{CS}})\] \[=e(H_{1}(t),Au_{t}^{3})\cdot e(h_{1}^{W_{t}},h_{2}^{sk_{CS}})\]  
If the Equation (11) holds, the aggregated global gradients are able to pass the verification of users.
# Limit Equilibrium Analysis of Landfill Instability Based on Actual Failure Surface
## 2 Theoretical Model and Analysis Method  
### Basic Theory  
A waste body without a dam is vulnerable to an integral slope failure as the water level increases. Engineered dams are crucial in preventing the waste from sliding along the liner interface and causing a catastrophic event. For a general landfill with a garbage dam, due to the continuous decomposition of solid waste during the landfill process, the body will undergo large deformation over time, and the dam can significantly improve the stability of the slope at this time. Due to the limitation of the displacement of the bottom of the waste body by the garbage dam, when the critical water level is reached, there is no obvious overall slip along the liner interface. Initially, cracks emerged at the base of the landfill, with minimal displacement of the lower portion. No failure surface was observed inside the waste body but the displacement of the upper portion continued to increase. Consequently, the cracks advanced and penetrated the top of the landfill. This damage was accompanied by significant horizontal displacement.  
Under the failure condition without the garbage dam, the assumptions are similar to the two-wedge model from [8; 9]. The sliding blocks can be divided into active wedges and passive wedges (Figure 2a); when there is an overall instability with a garbage dam, the limit equilibrium analysis of the three-wedge body by [PERSON] and [PERSON] [11] can be used to calculate the slope stability, and the waste body can be divided into active wedge, passive wedge, and block wedge (Figure 2c). The difference between the actual slip failure process of the landfill slope and the assumption of the traditional wedge limit equilibrium analysis is that the interfaces of the active wedge, passive wedge, and block wedge are not vertical. This is related to the characteristics of solid waste and the geometry of the slope. Here, we consider the actual failure process of the unstable waste body, improve the limit equilibrium analysis of the traditional wedge, set the wedge interface as the actual failure surface according to the results of the previous centrifugal tests, and consider the effect of the water level; we propose the limit equilibrium analysis method of two-wedge and three-wedge based on the actual failure surface.  
Figure 2: Schematic diagram of the two-wedge and three-wedge division of the waste body slope: (**a**) traditional method, two-wedge model; (**b**) based on failure surface, two-wedge model; (**c**) traditional method, three-wedge model; (**d**) based on failure surface, three-wedge model.
## 3 Results and Discussion
### Spatio-Temporal Evolution of SPEI
Despite these limitations, the CHIRPS data's extensive spatial coverage remains invaluable for filling the data gaps in understudied regions. To enhance the accuracy of the SPEI index, researchers should focus on increasing the station density and refining the interpolation and modeling techniques in complex terrains. Additionally, integrating the satellite data with local observations will be crucial in addressing these challenges and providing more accurate drought assessments.
## 5 BER and Data Rate Calculation of the Proposed Network
### The DSCA-MC-CR Synchronous Model  
In the expression of the SINR term of the synchronous models at the subscriber receiver antenna, the MAI term vanishes due to the synchronization process. Then, the SINR becomes \(SINR_{u}=\frac{P_{u}}{\sigma_{u}^{2}}\). Thus,  
\[SINR_{u}=\frac{\alpha_{u}^{2}\frac{E_{u}T_{h}}{2}}{\frac{\eta_{u}T_{h}}{4}}\,. \tag{19}\]  
The probability of error in the synchronization models for both the \(PU_{i}\) and the \(SU_{j}\) systems, when incentivizing the PU system and using the QPSK-OFDM modulation scheme within the proposed DSCA-MC-CR system, becomes  
\[P^{p}_{e_{\textit{DSCA-MC}}} = \mathcal{Q}\Bigg{(}\sqrt{\frac{\alpha_{u}^{2}\frac{E_{u}T_{h}}{2} (1+K)}{\frac{\eta_{u}T_{h}}{4}}}\Bigg{)}\,, \tag{20}\] \[P^{s}_{e_{\textit{DSCA-MC}}} = \mathcal{Q}\Bigg{(}\sqrt{\frac{\alpha_{u}^{2}\frac{E_{u}T_{h}}{2} (1-\gamma)}{\frac{\eta_{u}T_{h}}{4}}}\Bigg{)}\,. \tag{21}\]  
The maximum data rates of the synchronous PU system and the SU system within the proposed DSCA-MC-CR system are  
\[R^{p}_{\textit{DSCA-MC}} = \frac{1}{2}\Bigg{(}1+\frac{\alpha_{u}^{2}\frac{E_{u}T_{h}}{2}(1+ K)}{\frac{\eta_{u}T_{h}}{4}}\Bigg{)}\,, \tag{22}\] \[R^{s}_{\textit{DSCA-MC}} = \frac{1}{2}\Bigg{(}1+\frac{\alpha_{u}^{2}\frac{E_{u}T_{h}}{2}(1- \gamma)}{\frac{\eta_{u}T_{h}}{4}}\Bigg{)}\,. \tag{23}\]
## 3 System Architecture
### Virtual Vehicular Server
#### 3.3.1 Hierarchical Partitioning  
The busiest intersection near the center of the city map is chosen as the highest level VVS (denoted as L1 in Figure 2), level 1 server covers the whole map. The map is divided into four regions, in each region, there is level-two server (denoted as L2 in Figure 2), level-two server is responsible only for that region, not the whole map. Each level-two region is further divided into four level-three regions, and so on and so forth. In Figure 2 we have used three levels hierarchy just as an example; the number of hierarchy levels can be adjusted according to the size of the city. To avoid overloading the upper levels servers, each path request is treated based on its scope, more specifically it is treated at the lowest level server that covers the source and destination positions, thus short paths that are within the scope of level 3 or level 2 servers are treated locally.
## 3 Numerical Examples
### Influences of Various Construction Factors of the Unit Cell on the Band Structures
#### 3.4.1 Effect of the Geometrical Parameters of Constituent Beams on the Band Structures  
The involved geometrical parameters of the constituent beams are the cross-sectional area and the cross-sectional inertia moment. The cross-sectional area or the cross-sectional inertia moment of the altered beam is changing independently on each other. The ratio of cross-sectional area \(\gamma_{A}\) has been specified as three values 0.25, 1 and 4. Similarly, the ratio of cross-sectional inertia moment are specified as the same three values \(\gamma_{I}=0.25\), \(\gamma_{I}=1\) and \(\gamma_{I}=4\). Figures 9 and 10 depict respectively the phase/attenuation constant spectra of the resulting periodic beams with Ternary-I unit cell as the cross-sectional area and the cross-sectional inertia moment change independently.  
Figures 9 and 10 indicate that both the phase and the attenuation constant spectra are sensitive to the variation of the cross-sectional area and the cross-sectional inertia moment. From Figure 9, it can be noticed that the band structures generally move to the lower frequency side with the increase of the cross-sectional area. As the cross-sectional inertia moment decreases, Figure 10 shows the same phenomena. The highlighted regions of phase constant spectra in Figures 9 and 10 indicate that with the alterations of \(\gamma_{A}\) or \(\gamma_{I}\), the novel dispersion property, i.e., the feature that the frequencies corresponding to the Brillouin zone boundaries may not be the demarcation between pass-bands and stop-bands, will probably disappear or re-occur. It seems that there is not a general rule for this phenomenon.
# Short-Term Power Forecasting Framework for Microgrids Using Combined Baseline and Regression Models
## 3 Methodology
### Rule-Based Baseline Prediction
Therefore, the _baseline_s1_ method can be considered equivalent to the naive method in this methodology, with day-ahead forecasting being the objective. This method is applied in [43, 56, 57], where forecasting performed simply by using the measurements of the previous day was called the \"persistence method\". Other authors propose the use of other methods, such as the autoregressive moving average (ARMA) [43] or the autoregressive integrated moving average (ARIMA) models [58], as references in their case studies. In the proposed methodology, the _baseline_s1_ method is preferred because of its simplicity, as it avoids a more complex parameter adjustment process which would be required for other models such as ARMA or ARIMA (which would be computationally expensive due to the high orders of the models with data aggregations of 1 h or 15 min). Figure 1: Method of rule-based baseline forecasting. Once the rules are defined, their application can be classified into the \"strict\" and \"non-strict\" types. The \"strict application of a rule\" implies that a baseline for a certain day is considered valid only if the available number of days in the set \(n\) is the maximum number defined by the rule. If there are any missing data in the needed days according to the rule, this baseline is discarded and not considered valid. In contrast, the \"non-strict application of a rule\", does not necessarily require a specified number of days. The baseline is considered valid if there is at least one day available for the calculation. As will be seen in the case study, the evaluation of baselines will be performed under the criterion of strict application. Notwithstanding, some non-strict results will also be shown for illustrative purposes.
## 2 Study Area and Data  
### Study Area  
This research focuses on Changsha City, Hunan Province, China, representing a critical case for investigating aging society challenges. As a megacity, Changsha faces intensifying population aging pressures [63]. According to Changsha Municipal Government statistics [64], by the end of 2023, the permanent population aged 60 and above in Changsha reached 1.8946 million, accounting for 18.02% of the total permanent population; the permanent population aged 65 and above was 1.1992 million, accounting for 11.41% of the total permanent population. Both indicators exceed the World Health Organization's aging society baseline [3] thresholds by a substantial margin, indicating that Changsha has fully entered an aging society. Notably, the age structure of the elderly population in the city shows a trend of gradual upward shift, with the proportion of the oldest-old population continuously increasing [4]. This demographic shift has had a profound impact on the economic and social development of Changsha and poses serious challenges to the pension security system, urgently requiring collaborative efforts from the government and various sectors of society to explore effective coping strategies.  
In the face of the severe situation of population aging, the contradiction between the supply and demand of elderly care services in Changsha has become increasingly prominent. According to data from the Hunan Provincial Bureau of Statistics [65], the aging rates in the five central urban districts with higher urbanization rates (Furong District 15.8%, Kaifu District 14.8%, Tianxin District 14.7%, Yuelu District 13.2%, and Yuhua District 12.7%) are all lower than the city's average (16.8%). In contrast, the aging rates in suburban counties (21.4%), Wangcheng District (20.1%), and Liuyang City (19.3%) are substantially higher than the city's average. There are also considerable disparities between urban and rural areas in terms of infrastructure, public services, social security, industrial development, and resident income. The economic gravitational effect of the urban areas continues to attract the working-age population to migrate in, resulting in relatively lower levels of population aging in the urban districts.
###### Abstract
Moreover, gold nanoparticles conjugated with VEGF exhibit a surface carrying negative charges, which is ideal for VEGF transdermal delivery efficacy in wound repair [25]. Recently, AuNP functionalized with VEGF165 and (11-mercaptoethanol)-\(N\),\(N\),\(N\)-trimethyl-ammonium bromide showed pro-angiogenic and anti-microbial activity in wound healing process [22]. The use of the whole protein can have drawbacks in the immune response and in the higher costs [26], for this reason new nanoparticles were synthesized and functionalized using biomimetic peptide fragments [27; 28]. A relevant issue in the use of AuNPs for peptide delivery is to avoid toxicity in normal cells. NPs functionalized with peptides containing RGD sequence showed to increase uptake by HUVEC cells, while the nanoparticles were not toxic for these cells [29]. In the present work, we studied the immobilization of a peptide, VEGF\({}_{73-101}\), encompassing a recognition domain of VEGF [30; 31], labelled with 5,6-carboxy fluorescein (VEGF-FAM) on AuNPs through (_i_) indirect physisorption of the VEGF\({}_{73-101}\) peptide (VEGF-FAM/Au) and (_ii_) a direct chemisorption mediated by the mutated residue 88 with a cysteine (Cys) instead of the Glycine (Gly) in the VEGF\({}_{73-101}\) peptide (VEGF\({}_{\text{Cys}}\)FAM/Au)(Scheme 1). The promising potentialities in the nanoparticle-driven cellular uptake of the peptide were tested on human umbilical vein endothelial cells (HUVEC).
## 2 Sampling and Methodology
### Indoor Water-Immersed Compression Test  
In this test, the collapsibility of loess samples was assessed using the double-line method [29]. The collapsibility test commenced with an initial pressure of 50 kPa, with increments of 50 kPa added at each level. Upon reaching 200 kPa, increments of 100 kPa were subsequently applied until a pressure of 400 kPa was achieved. Two specimens are required for each set of tests, one of which is kept at a certain moisture content and the other is completely submerged under a vertical stress of 25 kPa. As shown in Figure 2. The test concluded when the readings of the two settlements did not exceed 0.01 mm.  
The test soil sample had dimensions of 3000 mm\({}^{2}\) in area and 20 mm in height. Initially, collapsibility tests were conducted on undisturbed loess under natural water content conditions across various regions. Subsequently, four moisture gradients of Malan loess, with water contents of 6.79%, 12.50%, 18.56% and 24.61% were prepared. The soil samples were adjusted to different moisture states using either the titration method or the air-drying method. During the humidification process, the amount of water required to reach a specific water content was calculated. The water was evenly applied to both ends of the soil sample enclosed within the ring knife. The fresh-keeping film was wrapped around the moisturizing cylinder, and after allowing it to stand for three days, both ends were flattened. The water content of the soil sample was measured in accordance with geotechnical testing standards to ensure uniformity across samples used in the test. The prepared soil samples were stored in a humidor as shown in the Figure 3.  
Utilizing the compression curve outlined in the Chinese national standard (GB/T50123-2019) [30], the collapsibility coefficient of each sample group was computed. The formula for the calculation is defined as follows:  
\[\delta_{S}=\frac{h_{P}-h_{P}^{\prime}}{h_{0}}\]  
where \(\delta_{s}\) represents the collapsibility coefficient; \(h_{P}\) denotes the height of the sample following stabilization under a specific stress level; \(h_{P}^{\prime}\) indicates the height after stabilization  
Figure 2: Double-line method.  
of submerged deformation at a particular stress level; and \(h_{0}\) is the original height of the specimen.  
ASTM D2435-03 [31] and D5333-03 [32] can be used to achieve essentially the same test results for the collapsibility test of loess. In the ASTM D2435-03 test standard, the test steps of loess collapsibility are specified in detail. The D5333-03 test method covers the determination of the magnitude of one-dimensional collapse that occurs when loess is inundated with fluid. In the ASTM D5333-03 test method, the formula for determining the coefficient of collapsibility of loess is consistent with that in the Chinese national standard (GB/T50123-2019). The Chinese national standard (GB/T50123-2019) is similar to the American standard (ASTM D2435-03 and D5333-03) in the process of collapsible compression test for loess. Therefore, the results have a certain accuracy.
# A Design Method of Code Correlation Reference Waveform in GNSS Based on Least-Squares Fitting
## 3 Results  
The representative results for BPSK(1), BOC(1,1), BOC(2,1), BOC(6,1) and BOC(7,1) signals are presented and discussed in this section. The process for the BPSK(1) signal can be applied to BPSK(n) signals with the same ratio between the chip rate and the bandwidth. Similarly, the results of BOC(1,1), BOC(2,1), BOC(6,1) and BOC(7,1) can be also applied to BOC(n,n), BOC(2n,n), BOC(6n,n) and BOC(7n,n), respectively. The results of CCRW W2, the double-delta correlator, the BGP waveform and the process in [14] are also simulated as for comparisons.  
The simulation parameters are listed in Tables 1-5. The fitting range is the simulation range for the S-curve fitting. The CCRWs are constrained within the waveform range (less than one chip), with base strobe waveform gate width of \(\mu\). \(\mu\) is selected according to the bandwidth. If there is a large front-end bandwidth, \(\mu\) can be a rather small value, since the sampling rate is always greater than the bandwidth. The target S-curve has a linear region around the tracking point and a small offset in the right side to expand the pull-in region and avoid the possible false locking points.
## 4 Development of a New Bubble Size Model
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Mechanism** & **Model** & **Reference** \\ \hline Turbulent impact & \(\phi_{TI}=\frac{\gamma_{\rm{aa}}(1-\alpha)\varepsilon^{1/3}}{D_{b}^{1/3}( \alpha_{\rm{max}}-\alpha)}\exp(-\frac{K_{B}\alpha}{\rho_{c}D_{b}^{3/3} \varepsilon^{1/3}})\) & [PERSON] and [PERSON] [42] \\ Random collision & \(\phi_{RC}=\frac{\gamma_{\rm{OC}}\varepsilon^{2/3}}{D_{b}^{1/3}(\alpha_{\rm{ max}}-\alpha)}\exp(-\frac{K_{C}\rho_{c}^{1/2}D_{b}^{5/6}\varepsilon^{1/3}}{\sigma^{1/2}})\) & [PERSON] [42] \\ Wake entrainment & \(\phi_{WE}=\gamma_{\rm{WBE}}\Big{(}\frac{\xi\Delta\rho(1-\alpha)}{\rho_{c}} \Big{)}^{1/3}\frac{\sigma_{\rm{OC}}^{2}\upsilon_{J}^{1/3}}{D_{b}^{1/3}}\exp(- \frac{K_{C}\rho_{c}^{1/2}D_{b}^{5/6}\varepsilon^{1/3}}{\sigma^{1/2}})\) & [PERSON] et al. [43] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Models for bubble breakup and coalescence. \[D_{b}\approx f(\alpha,\frac{\sigma}{\rho_{c}},\varepsilon,\frac{\rho_{c}-\rho_{d}}{ \rho_{c}},U_{r}) \tag{30}\]  
In an air-water flow under low pressure conditions, the density of the gas is significantly low compared to that of the liquid, thus, \((\rho_{c}-\rho_{d})/\rho_{c}\) can be assumed to be 1. Subsequently, Equation (30) can be non-dimensionalized from the turbulent Reynolds number defined by [PERSON] and [PERSON] [14] (\(\text{Re}_{b}=\epsilon^{1/3}L\sigma^{4/3}/v_{c}\)), Laplace length (\(\text{Lo}=\sqrt{\sigma/g\Delta\rho}\)), and Weber number defined by relative velocity (\(We_{r}=2\rho_{c}U_{r}Lo/\sigma\)) as follows:  
\[\frac{D_{b}}{Lo}=A\alpha^{X}\text{Re}_{b}^{Y}We_{r}^{Z} \tag{31}\]  
Finally, considering the dependency of variables, we proposed the following bubble size correlation for a bubbly flow under a steady-state fully developed condition by applying Equation (31) with the help of the iterative CFD calculation against the experimental database by following the procedure shown in Figure 2.  
\[D_{b}=258.4\alpha^{0.383}\text{Re}_{b}^{-0.562}We_{r}^{-0.443}Lo \tag{32}\]  
The above correlation is a semi-theoretical correlation whose constant and exponents were obtained via multiple linear regression against the experiments by [PERSON] [44], [PERSON] et al. [45], and [PERSON] et al. [46]. The turbulent dissipation rate and relative velocity, which were not measured in the experiments, were obtained through CFD analysis. Equation (32) satisfies the precondition that the bubble size should converge to zero when the void fraction tends toward zero. As the amount of void fraction increases, the random collision and the wake entrainment occur actively compared to the bubble breakup mechanism, and bubble size increases, and thus, the exponent of the void fraction is positive. As the turbulent dissipation rate and relative velocity increase, the turbulent impact for bubble breakup increases, and thus, bubble size decreases. Therefore, the exponent of the turbulent Reynolds numbers has a negative value.