esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Formulation in Banach Space
### Polynomial Approximation  
An important and at same time one of the simplest methods to construct degenerate kernels approximating given continuous ones is via interpolation. From the several kinds of interpolation and the many interpolation basis functions, we choose here the polynomial interpolation and in particular the Lagrange formula.  
Let the \(n+1\) distinct ordered points \(a=t_{1}<t_{2}<\ldots<t_{n}<t_{n+1}=b\) in the interval \([a,b]\). The continuous kernel \(K(x,t)\) can be approximated by a polynomial degree \(\leq n\) of the form  
\[K_{n}(x,t)=\sum_{j=1}^{n+1}\ell_{j}(t)K(x,t_{j}), \tag{23}\]  
where  
\[\ell_{j}(t)=\prod_{\begin{subarray}{c}i=1\\ i\
eq j\end{subarray}}^{n+1}\left(\frac{t-t_{i}}{t_{j}-t_{i}}\right)\]  
are known as Lagrange basis functions. By putting (23) into (1) in the place of the kernel \(K(x,t)\), we obtain  
\[\tilde{u}_{n}(x)-\lambda\sum_{j=1}^{n+1}K(x,t_{j})\int_{a}^{b}\ell_{j}(t) \tilde{u}_{n}(t)dt=f(x),\quad x\in[a,b]. \tag{24}\]  
Specifying the vectors  
\[G=\lambda\big{(}\begin{array}{ccccc}g_{1}&g_{2}&\ldots&g_{n+1}\end{array} \big{)}=\lambda\big{(}\begin{array}{ccccc}K(x,t_{1})&K(x,t_{2})&\ldots&K(x,t _{n+1})\end{array}\big{)},\]  
and  
\[\Psi(\bar{a}_{n})=\left(\begin{array}{c}\Psi_{1}(\tilde{u}_{n})\\ \bar{\Psi}_{2}(\tilde{u}_{n})\\ \vdots\\ \Psi_{n+1}(\tilde{a}_{n})\end{array}\right),\quad\Psi_{j}(\bar{a}_{n})=\int_{ a}^{b}\ell_{j}(t)\tilde{u}_{n}(t)dt,\quad j=1,2,\ldots,n+1,\]  
Equation (24) may be written in the symbolic form  
\[T_{p}\bar{a}_{n}=\bar{a}_{n}-G\Psi(\bar{a}_{n})=f, \tag{25}\]  
where the operator \(T_{p}:X\to X\) and \(X=C[a,b]\).  
In (25) the computation of \(\Psi(G)\) and \(\Psi(f)\), except in some special cases, has to be performed numerically. To avoid the numerical integration, we may approximate the functions \(\{g_{j}(x)\}\) and \(f(x)\) by polynomials of degree \(\leq r\), which interpolate these functions at the \(r+1\) points \(a=x_{1}<x_{2}<\ldots<x_{r}<x_{r+1}=b\), namely  
\[f_{r}(x)=\sum_{l=1}^{r+1}\ell_{l}(x)f(x_{l}), \tag{26}\]  
and  
\[g_{jr}(x)=\sum_{l=1}^{r+1}\ell_{l}(x)g_{j}(x_{l}),\quad j=1,2,\ldots,n+1. \tag{27}\]  
Then, we can substitute (26) into (25) to obtain  
\[T_{p}\tilde{a}_{n}=\tilde{a}_{n}-G\Psi(\tilde{a}_{n})=f_{r}. \tag{28}\]  
In addition, we may use (27) to set up the vector  
\[G_{r}=\lambda\big{(}\begin{array}{cccc}g_{1r}&g_{2r}&\ldots&g_{(n+1)r}\end{array} \big{)}, \tag{29}\]  
and then by substituting into (28) to have  
\[T_{pp}\tilde{a}_{n}=\tilde{a}_{n}-G_{r}\Psi(\tilde{a}_{n})=f_{r}, \tag{30}\]  
where the operator \(T_{pp}:X\to X\) and \(X=C[a,b]\).  
Note that we will arrive at an analogous equation to (30) if bilinear interpolation is used for interpolating the kernel \(K(x,t)\) at the Cartesian mesh nodes \((x_{l},t_{j})\), where \(l\) varies from \(1\) to \(r+1\) and \(j\) varies from \(1\) to \(n+1\).  
All three Equations (25), (28) and (30) are of the type (3), and thus their unique solutions may obtained through Theorem 1.
# Scheduling Optimization of Prefabricated Construction Projects by Genetic Algorithm
## 4 The Proposed Genetic Algorithm
### Genetic Algorithm Design for Scheduling Problem of Prefabricated Building
#### 4.2.3 Selection Operator  
The selection operation of GA generally has several methods such as proportional selection, ranking selection, and elite selection [67]. Roulette is the most commonly used method among the proportional selection strategies. The idea of the roulette method is to determine the individual's choice based on the proportion of each individual's fitness value in the population fitness value. The method requires multiple rounds of random numbers between [0, 1]. The larger the individual's fitness value is, the more likely it will be retained under roulette selection. Due to the uncertainty brought by random operation, the individual with the highest fitness only can be easily eliminated by roulette selection method. The elite selection method can ensure that the best individuals that have appeared to date will not be eliminated or destroyed during the algorithm evolution due to  
Figure 3: Distribution of random priority of activities.  
Figure 2: DSM.  
selection, crossover, and mutation operations. In order to select a better project scheduling scheme, this study adopts the combination of roulette and elite selection methods for the design of GA selection operator, as shown in Figure 4. The algorithm divides the current population individuals (scheduling solution) into two parts. One part directly copies the contemporary individuals with the highest fitness (current optimal scheduling solution) to the next generation through elite selection. In the other part, some individuals were selected by roulette selection method to produce new individuals through crossover and mutation. The newly generated individuals and the copied individuals form a new offspring population. The new generation will repeat the selection and iterate until it reaches the stop standard. The combination of roulette and elite selection methods plays an important role in enhancing the global convergence ability of traditional GA.
# Analyzing Zone-Based Registration under 2-Step Paging in Mobile Communication Network
## 2 Zone-Based Registration and 2-Step Paging
### Mobility Model for Movement among the Cells in a Zone  
In this study, the movement characteristics between the cells in the zone are assumed to be as follows: In 1 ZR, we assume that the UE in any cell enters the cell in the direction of the zone visited immediately before with probability \(q\), and that it equally enters the remaining cells with probability \(r=(1-q)/3\), which is very similar to the movement characteristics between zones in 2 ZR [9; 12; 13]. Note that \(q\) and \(\theta\) have essentially the same properties and that \(q\) is just a cell version of \(\theta\). For example, in Figure 5, assuming that a UE enters a new zone from the left zone, the UE in cell a returns to cell \(\mathbf{p}\) with probability \(q\), and it enters the remaining adjacent cells with equal probability \(r=(1-q)/3\). Similarly, the UE in cell b enters cell a with probability \(q\), and it enters the remaining adjacent cells with equal probability \(r=(1-q)/3\).  
In Figure 5, assuming that the UE enters a new zone out of the left zone, the state of two cells adjacent to the zone visited just before is defined as \(1\). These two cells are defined in a similar manner to state \(1\) because the probabilistic characteristics are the same regardless of whether the cell is above or below. A UE belonging to state \(1\) enters the cell of the zone visited immediately before with probability \(q\) and enters the remaining cells with probability \(r=(1-q)/3\) in the same way. Even when the UE stays in a cell and is not in contact with the zone visited immediately before (state \(2\)) and enters a neighboring cell, it enters the cell (state \(1\) cell) in the direction of the zone visited immediately before with probability \(q\), or it enters the remaining cells with probability \(r=(1-q)/3\) in the same way. Two cells that are not in contact with the zone visited immediately before are defined as the same state \(2\) because the probabilistic characteristics are the same regardless of whether the cell is above or below.  
Likewise, even when the total number of cells is \(9\) (\(n=9\)), it is assumed that all cells enter the cell in the direction of the zone visited immediately before with probability \(q\) and enter the remaining cells with probability \(r=(1-q)/3\). Among the three cells in contact with the zone visited immediately before, the upper and lower cells have the same  
Figure 5: Inter-cell mobility model in a zone in 1 ZR when a UE moves from the zone in the left (\(n=4\)).  
probabilistic characteristics, so they can be defined as the same state 1. However, the middle cell has different probabilistic characteristics from the cells above and below it, so it becomes a new state 2; this is also true for state 4 cell and state 6 cell. As a result, as shown in Figure 6, the cells are classified into six states.  
In the case of \(n=4^{2}=16\), \(n=5^{2}=25\),..., the state can be defined to analyze the performance similarly.
## 3 Results and Discussion
### Effect of Operating Parameters
Figure 8: \(Cont.\)  
The power transferred by the TES tank during the discharging cycle exhibits a similar type of fluctuation as observed in the charging cycle. This occurred as the hot fluid held inside the TES tank was flushed by the new cold fluid during the discharging cycle. After the hot fluid that was confined in the TES tank was completely removed, the PCM temperature dropped, resulting in reduced variation in power. As can be seen in Figure 8, the TES tank with the HTF mass flow rate of 6 kg/min had the highest power output throughout the phase transition process. This maximum power ranged between 145 W and 185 W during the discharging cycle. The time required for the PCM temperature to drop from 45 \({}^{\circ}\)C to 23.5 \({}^{\circ}\)C is defined as the discharging time. The bio-inspired TES tank with a 3 kg/min HTF flow rate took the least time (1.4 h) to discharge the PCM. However, those with flow rates of 1.5 kg/min and 6 kg/min required 1.6 h to reach 23.5 \({}^{\circ}\)C.
## 2 Materials and Methods  
### Instruments and Reagents  
The morphology of colloidal gold particles and Au NPs-embedded MIHs were observed on a transmission electron microscope (TEM, Tecnai G2 F30 S-Twin, FEI Company, Hillsboro, OR, Netherlands) operating at an acceleration voltage of 300 kV. The TEM was equipped with an energy dispersive X-ray (EDX) analyzer (DPP-II). The zeta potential and the size of Au NPs were measured using dynamic light scattering instrument (DLS, Nano-ZS90, Malvern Instrument, Worcs, UK) equipped with a 628 nm laser source. SERS spectra were collected on a DeltaNu 785 Raman spectrometer (DeltaNu Inc., Laramie, WY, USA). The laser power of the spectrometer is 120 mW with an excitation wavelength at 785 nm and a spectral range of 200 to 2000 cm\({}^{-1}\). The spectra were acquired with baseline off using NuSpec software (Copyright DeltaNu 2009) and analyzed using GRAMS/AI software (Ver 9.1, Thermo Fischer Scientific, Waltham, MA, USA).  
Chloroauric acid (HAuCl\({}_{4}\)4H\({}_{2}\)O, 99%) was purchased from Shanghai Civil Chemical Technology Co., Ltd. (Shanghai, China). Cysteamine (95%), Erythrosin B sodium (85%), and Allura Red (85%) were supplied by Shanghai Macklin Biochemical Co., Ltd. (Shanghai, China). New Red (98%) and Amaranth (98%) were bought from Shanghai Jinpan Biotechnology Co., Ltd. (Shanghai, China). Acrylamide (98%) was obtained from Shanghai Aladdin Bio-Chem Technology Co., Ltd. (Shanghai, China). Sodium borohydride (NaBH\({}_{4}\), 98%) and \(N\),\(N\)'-methylenebis(acrylamide) (97%) were from Shanghai Aladdin Bio-Chem Technology Co., Ltd. (Shanghai, China). Potassium persulfate (AR) was purchased from Sinopharm Chemical Reagent Co., Ltd. (Shanghai, China). Methanol (\(\geq\)99.5%) and acetic acid (\(\geq\)99.5%) were obtained from Shanghai Lingfeng Chemical Reagent Co., Ltd. (Shanghai, China). Distilled water was used throughout the experiments.
# A More Efficient Conditional Private Preservation Scheme in Vehicular Ad Hoc Networks
## 7 Performance Analysis
### Computational Cost Analysis  
We evaluate the computational cost for anonymous certificate and signature verification process with the prior related schemes such as ECPP [10], Boneh Lynn Shacham (BLS) scheme [29], group signature based (GSB) scheme [8], certifiateless aggregate signatures (CAS) [30] and key-insulated pseudonym self delegation (KPSD) scheme [31]. To facilitate analysis, the using notations are given in Table 3, and the result was obtained on a 2.6-GHz computer with 8-GB installed memory, running Cygwin 1.7.35-15 [32] with the gcc version 4.9.2 for the implementations.  
The results of computation cost comparisons with ECPP, BLS, GSB, CAS, KPSD schemes are summarized in Table 4. From Table 4, it can be clearly observed that the proposed MECCP scheme takes less computational cost than others, because it takes only 2\(T_{pair}\), \(T_{exp}\) and \(T_{hash}\) for verifying a certificate and signature. Especially comparing with ECPP, the required execution time has been decreased by about 54%.
## 4 Discussion
### Numerical Simulation
#### 4.1.3 Effect of Material Inhomogeneities  
Cortical pores result in scattering and subsequent diffusion of the ultrasound waves. This causes local fluctuations of the arrival time of the received backside echoes compared with the reference flat bone plate model. The backside confocal depth, which is required for the simultaneous estimation of both thickness and sound velocity, has been estimated in our previous work by detecting the peak position of the DAS beamformed backside echoes with respect to the focusing depth [19]. Phase aberration induced by cortical pores cause a decrease in the intensity of the beamformed signal. With increasing porosity, the confocal peak arising from the backside reflection becomes less sharp and the peak position is harder to detect; therefore, we have developed another method to extract the confocal backside position by analyzing the curvature of the backside echo wavefront prior to the summation of all receive channels at each focus depth. The curvature of the wavefront was extracted by analyzing the cross correlation of the backside echoes relative to the backside echo with the highest signal amplitude. The change of the wavefront curvature from a convex shape (negative curvature) to a concave shape (positive curvature) was used to extract the focus position. The zero-crossing point was calculated using a linear fit of the retrieved curvature values over the focus depth. Incorporating cross correlation analysis prior to the summation of the beamformed signals improved the accuracy of the estimation of the backside confocal position, as well as precision and accuracy in simulations including pores (Table 5). Moreover, this method improved the backside signal detection rate and the accuracy of the estimation of cortical thickness in the ex-vivo measurement.
# Spatial Assessment and Prediction of Urbanization in Maseru Using Earth Observation Data
## 4 Discussion
### Interannual Changes in LULC Classes  
The highest growth of 73.6% in the bare soil class was observed between 2013 and 2019, whilst the highest decrease (\(-41\%\)) was for areas covered with agricultural fields. This decline in agricultural fields might be a result of an increase in settlements due to a rise in population and road development over the years. This is in line with [PERSON] [21], who highlighted that increased road development and settlements in 2000, 2001, 2005 and 2007 brought LULC changes in Maseru. This is also supported by the World Bank [20], which highlighted that the rise in population led to the building of houses and the construction of roads, resulting in negative effects such as pollution and undesirable LULC changes.  
The decrease in agricultural fields (\(-6.1\%\)) and an increase in bare soil (15.9%) between 1988 and 1993 (Figure 3) could also be attributed to poor farming methods and the 1992 severe drought which faced all Southern African countries. During this drought period, there was low rainfall and high temperatures, which reduced agriarian produce, where most agricultural fields had no crops, leading to a food security crisis in Southern Africa [61]. [PERSON] supports this, and [PERSON] [62] highlighted that similar to other Southern African countries, Lesotho faced a food crisis and land degradation due to population growth in the country over the years and during extreme drought events such as the severe 1992 and 2015 drought. The population in Maseru was estimated to be around 150,000 in 1989, which rose to approximately 519,186 in 2016 [63].  
During the study period, the amount of land covered by built-up structures increased from 15.3% in 1988 to 48% in 2019 (Table 3). This increase in the built-up area could be attributed to the internal migration of people from rural areas to Maseru and from nearby South Africa. People migrated to Maseru for jobs in textile factories, local income-earning opportunities in the informal sector, and a decline in the South African demand for unskilled labor [64]. The rising population in Maseru has resulted in urban expansion and in-filling, where agricultural farmlands have been converted into residential development [53]. This urbanization process also led to a decrease in areas covered by grasslands, water bodies and woody vegetation (Figure 3).
_Sustainability_**2015**, \(7\), 13055-13072; doi:10.3390/su71013055  
_Article_  
Assessing the Atmospheric Oxygen Balance in a Region of Rapid Urbanization: A Case Study in the Pearl River Delta, China  
**[PERSON] 1,*, [PERSON] 2, [PERSON] 1 and [PERSON] 3**  
1 Laboratory for Earth Surface Processes, Ministry of Education, College of Urban and Environmental Sciences, Peking University, Beijing 100871, China; E-Mail: [EMAIL_ADDRESS]  
2 Key Laboratory for Environmental and Urban Sciences, School of Urban Planning and Design, Shenzhen Graduate School, Peking University, Shenzhen 518055, China; E-Mail: [PERSON]IL_ADDRESS]  
3 Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China; E-Mail: [EMAIL_ADDRESS]  
* Author to whom correspondence should be addressed; E-Mail: [EMAIL_ADDRESS]; Tel./Fax: +86-10-6275-0926.  
Academic Editor: [PERSON]  
_Received: 25 June 2015 / Accepted: 17 September 2015 / Published: 24 September 2015_  
**Abstract:** Oxygen is a product of photosynthesis and is essential for human survival. It also has a profound effect on ecosystems as the atmospheric oxygen balance is the basis for regional ecological sustainability. The Pearl River Delta (PRD) has experienced rapid urbanization and has become one of China's three major urban agglomerations. This study focused on the oxygen balance of the PRD in 2011, and established a model to calculate the oxygen balance that was suitable for a region of rapid urbanization by applying remote sensing gross primary production data via the C-Fix model. The influencing factors for the oxygen imbalance were analyzed and it was suggested that more attention be paid to the management of oxygen emissions than oxygen consumption. The results indicated that the oxygen balance capacity of the PRD was weak, with an oxygen consumption 9.37 times that of its oxygen emission. Zhaoqing and Huizhou are the main sources of oxygen in the PRD, with an oxygen emission density more than 4.67 times that of Dongguan or Zhuhai. Guangzhou and Shenzhen are the main oxygen sinks, with a total oxygen consumption more than 5.49 times that of Zhaoqing. Moreover, the oxygen balance of the PRD is more sensitive to oxygen emissions than consumption. Therefore, it could be inferred that the land urbanization has a stronger influence on the oxygen balance than the population urbanization.  
keywords:atmospheric oxygen balance assessment; oxygen emission; oxygen consumption; C-Fix model; urban agglomeration; Pearl River Delta; China
# Weight Adjustment Framework for Self-Attention Sequential Recommendation
###### Abstract
However, recent research [15] has revealed that the attention mechanism might suffer from inaccuracies in weight allocation, with noisy data inputs [16; 17] and suboptimal position encoding [18] identified as primary causes. The existing sequential recommendation models typically assume that the target item is related to all historical interaction items. However, in real-world scenarios, this assumption may not always hold true, as users may inadvertently interact with items that deviate from their interests or preferences, leading to noise in the interaction data. These noise sources are difficult to identify, which presents challenges in accurately discerning users' true preferences through the self-attention mechanism, resulting in inaccurate attention weight allocation. Inspired by previous works [15; 19; 20], we address the issue of inaccurate attention weight distribution from two perspectives. (1) We introduce a denoising technique to mitigate the influence of noisy data input on the attention weight distribution. We set up a filter layer to clean the data before it flowed into the self-attention layer, to prevent noise from negatively affecting the model's interpretation of user behavior and the accuracy of its recommendations. (2) We enhanced the model's capability to understand user behavior, thereby refining the attention weight distribution. We enhanced the model's grasp of the logic behind user behavior by introducing a logical representation layer. This logical representation layer enabled the attention mechanism to more effectively identify the user interactions that had the greatest impact on the recommendation outcomes. In summary, our contributions are as follows:  
* We propose a novel sequential recommendation method, WAF-SR, which enhances the accuracy of attention weight allocation by mitigating the interference of noise in the input data;
* We introduce logical representation technology to correct and optimize the allocation of weights by the attention mechanism more precisely;* We have conducted extensive experiments on three public datasets, and the results validate the effectiveness and superiority of our proposed method. The structure of this paper is organized as follows: Section 1 serves as the introduction, presenting the research background, objectives, and significance of the study. Section 2 provides a review of previous work closely related to our research. Section 3 elaborates, in detail, our research methodology, including the formal definition of the problem and key components: the filter layer, self-attention layer, logical representation layer, and prediction layer. Section 4 describes the specific setup and steps of the experiments, covering the selection of datasets, evaluation metrics, choice of baseline models, technical details of implementation, overall performance of the model, ablation studies, and research on hyperparameters. Section 5 summarizes the findings of this study and includes the discussion of the results.
# The DLR FireBIRD Small Satellite Mission: Evaluation of Infrared Data for Wildfire Assessment
## 2 Materials and Methods
\begin{table}
\begin{tabular}{l l l l l l} \hline \multicolumn{2}{c}{**Mission**} & \multicolumn{2}{c}{**Satellite**} & \multicolumn{2}{c}{**Sensor**} \\ \hline Orbit & 560 km & Dimensions & 83 cm \(\times\) 54 cm \(\times\) 62 cm & **Infrared** & mid-infrared: \\  & sun-synchronous & & **Sensor** & 3.400–4.200 \(\upmu\)m (Nadir), \\ Inclination & 97.6 \(\lx@math@degree\) & Total Mass & ca. 130 kg & & thermal infrared: \\  & & & & 8.500–9.300 \(\upmu\)m (Nadir) \\ Mission Operations & German Remote & Payload Mass & ca. 14 kg & Optical & vis green: \\  & Sensing Data Center, & Infrared Sensor & & Sensor & 0.460–0.560 \(\upmu\)m (6\(\lx@math@degree\) forward), \\  & German Space & & & & vis red: \\  & Operations Center & & & 0.565–0.725 \(\upmu\)m (Nadir), \\  & \(<\)1.5 years & Power & 200 W DC & & near infrared: \\ Mission Duration & \(>\)2.5 years & Communications & S-Band, UHF & 0.790–0.930 \(\lx@math@degree\) (6\(\lx@math@degree\) backward) \\ \hline \end{tabular}
\end{table} 
Table 1: Overview of the FireBIRD-mission specifications ([7; 19], ed. ).