esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Methodology  
### Bayesian Framework for Parameter Estimation of Structural System  
It is assumed that the numerical model of the structural system is predefined and fixed. The functional form, here the multiple-degree-of-freedom (MDOF) structural model \(\eta\), is used to relate system response with unknown quantities and can be written as  
\[\hat{\textbf{y}}=\eta(\boldsymbol{\upxi}|\boldsymbol{\uptheta})+\textbf{e}, \tag{1}\]  
where \(\hat{\textbf{y}}=(\textbf{y}_{1}\textbf{y}_{2},\cdots\textbf{y}_{\textbf{ny} })^{T}\) is the vector of model outputs, such as displacement, velocity or acceleration; \(\boldsymbol{\uptheta}=(\theta_{1},\theta_{2},\cdots,\theta_{n})\) is a vector of \(n\) structural model parameters to be estimated, and \(\boldsymbol{\upxi}\) is the input values to the structural model. Finally, **e** represents modeling residuals, which consists of various sources of prediction errors. However, it has been observed that many parameter sets close to the global optimum within the feasible parameter space show similar performances of reproducing the observed data [17; 29].  
In Bayesian inference, the uncertainties of the random parameter variables \(\boldsymbol{\uptheta}\) before any data are collected, are described by its probability density functions (pdf), denoted as prior \(p(\boldsymbol{\uptheta})\). The posterior pdf, \(p(\boldsymbol{\uptheta}|\textbf{y})\), confirms the parameters functions given as the observed measurements **y**, and is proportional to the product of the prior pdf and the likelihood function. The posterior distribution is the final goal of the statistical inversion approach, i.e., the solution of the inverse problem. Notably, once a prior probability distribution has been defined, it is possible to weigh its influence over posterior density outcomes based on the initial state of knowledge about the parameters. If the prior information is insufficient or not reliable, a non-informative prior density should be employed (for instance, a uniform distribution); consequently, the information contained in the data has a predominant effect on the inverse solution in the Bayesian inference scheme.  
Typically, for complex structural models, the joint posterior pdf \(p(\boldsymbol{\uptheta}|\textbf{y})\) is multidimensional, complex, and usually unknown, with strong interdependences of nonlinear parameter. \(p(\boldsymbol{\uptheta}|\textbf{y})\) is thereby difficult for direct sampling or analytical integration. The prior information is usually defined by the feasible parameter space, \(\boldsymbol{\uptheta}\in\Theta\in R^{n}\), consisting of lower and upper bounds on uniform distribution (non-informative) of each parameter. The uniform assignment is chosen mostly for its simplicity to encode a lot of initial ignorance about the parameters. In this research, the authors employ the SCEM-UA algorithm to tune a sequence of parameter sets \(\boldsymbol{\uptheta}=(\theta_{1},\theta_{2},\cdots,\theta_{n})\) to the target posterior distribution.
# Primary User Localization Algorithm Based on Compressive Sensing in Cognitive Radio Networks
## 6 Conclusions  
The localization for source signal plays a significant role in resisting PUEA in CRN. This paper put forward a brand new primary user localization algorithm based on compressive sensing in cognitive radio networks (PU-CSL). PU-CSL considers received source signal strength as source fingerprints, using compression sensing to obtain correlation between SUs and source signal, constructing weighted coefficients of SUs based on the relevant information, and, finally, estimating source location by the weighted centroid algorithm. Experimental results show that the proposed PU-CSL scheme outperforms the RR-WCL scheme on localization and anti-noise performance. As PU-CSL integrally explores the geographical correlation between source signal and SUs using CS, the source signal is preferably described by SUs and the localization of the source node becomes more accurate.  
This paper is funded by the National Natural Science Foundation of China (Grant NO. 61301095, NO. 51374099), the Natural Science Foundation of Hei-longjiang Province, China (Grant No. F201345) and the Fundamental Research Funds for the Central Universities of Ministry of Education of China (Grant No. HEUCF150812).  
[PERSON] and [PERSON] proposed the idea of this work and prepared the manuscript. [PERSON] and [PERSON] assisted in the research work.  
The authors declare no conflict of interest.
## 2 Related Work and Background
### Related Work  
DNN watermarking methods can be classified into black-box (BBx) and white-box (WBx) schemes [14; 15; 23; 24; 25; 26]. By definition, a black-box watermark can be extracted by querying only the model's outputs. The watermarked message is retrieved by examining the outputs of the watermarked model for carefully designed and crafted inputs referred to as the \"trigger set\" [27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44]. These methods have zero-bit capacity, as they can only detect the presence of a given watermark in a protected model. This is equivalent to extracting a message \(b\) of one bit equal to \"1\" if the watermark is detected or \"0\" otherwise.  
In contrast, white-box (WBx) watermarking schemes [45; 46; 47; 48; 49; 50; 51; 52] require access to the complete model parameters to extract the watermark. These schemes have multi-bit capacity, allowing the encoding of messages containing several bits of information. In other words, the message \(b=\{m_{i}\}_{i=1..N}\), with \(m_{i}\in\{0,1\}\), can be chosen by the user. WBx schemes can be further differentiated based on whether the watermark is read directly from the network parameters (called \"static watermarking\" schemes) or by examining the values of the intermediate activation maps for specific inputs (called \"dynamic watermarking\" schemes) [51].  
WBx watermarking schemes can be further classified based on their embedding methodology. The first category involves modifying secretly selected model parameters through classical multimedia watermarking modulation techniques. To maintain model accuracy, these approaches fine-tune the network by updating non-watermarked parameters until the original performance is restored. The second category alters the model's training process by incorporating regularization terms into the loss function, enabling watermark insertion into weights, activation maps, or passport layers.  
Figure 1: CNN architecture for image classification using the MNIST dataset [22], with two convolutional layers, two max-pooling layers, and two fully connected layers.
## Materials and Methods
### Rock Mass Quality and Tunnel Support
#### 2.6.1 Determination of Tunnel Support from Rock Mass Quality
The suggested spacing of rock bolts is the result of a considerably crude correlation between \(Q\) and rock bolt spacing [9], which is usually employed in practice along with a quantitative classification system for supports [40]. The shotcrete thickness for tunnel spans with D\({}_{\rm e}<\) 3 m is simply assumed and is not based on empirical data [11]. The \(Q\) system works best for \(Q\) values ranging from 0.1 to 40 and D\({}_{\rm e}\) values ranging from 2.5 to 30 m [40]. Although a normalized factor has been included in the \(Q\) system, the support chart is not updated for it [36]. Similar to that in \(RMR\), the effects of D\({}_{\rm e}\) and rock mass quality on shotcrete thickness are not equal and constant. Instead, the thickness depends on the value of both.
## 2 Background Principle
### Principle of Erasure Coding  
The typical method of data storage in a distributed file system is to divide the original data into blocks of data of a certain size using replication techniques, and to replicate the divided blocks of n and store them separately on multiple nodes. However, traditional replication technique-based distributed file systems store replicated blocks of data, resulting in an n-fold increase in spatial efficiency. Therefore, to improve this, a recent erasure coding technology-based distributed file system that has been extended from existing replication technique-based distributed file systems is being utilized. Erasure coding is represented in Figure 1 as a technique for storing data through the encoding and recovery of the decoding data, unlike how data blocks are divided into constant sizes, replicated, and stored [10; 11; 12].  
Figure 1 shows a structure in which a Reed-Solomon (RS) code (6, 3) is used to construct six data blocks and three parity blocks generated through encoding. That is, when the original data are entered, they are divided by the RS erasure coding (6, 3) using as many blocks of data. In addition, each data block generates parity blocks through an encoding matrix and calculations, and thus all blocks (data blocks and parity blocks) are distributed and stored for each disk or network environment they use, as shown in Equation (1).  
\[P_{i}=\sum_{j=1}^{k}\alpha_{i,j}D_{j} \tag{1}\]  
The parity block \(P_{i}\) is generated by multiplying the data block \(D_{j}\) by the encoding matrix coefficient \(\alpha_{i,j}(i=row,\ j=column)\) in Figure 1; although the decoding operations have been expressed through multiplication, they are actually computed through various algorithms, such as the RS erasure coding, liberation, AVX-CRS, and XOR algorithms.  
Figure 2 shows the behavioral process of the decoding operations in which nodes possessing data block 2 and parity block 1 fail owing to factors such as a network connectivity delay or a natural disaster and do not respond. However, a failure is recoverable by decoding the parity block and the original data block generated through encoding. The number of blocks that can be decoded and recovered reaches only up to three, which is the number of parity blocks, when configured in an RS code (6, 3). In other words, three out of nine blocks can be recovered during a failure, as shown in Equation (2).  
\[d^{*}=(\beta_{1},\beta_{2},\beta_{3},\ldots,\beta_{i})\times\left(\begin{array} []{c}P_{1}\\ P_{2}\\ P_{3}\\ \ldots\\ P_{4}\end{array}\right)=\sum_{i=1}^{k}\beta_{i}P_{i} \tag{2}\]  
Figure 1: Encoding process of erasure coding.  
Blocks d\({}^{*}\) that require recovery are regenerated into new nodes by decoding the decoding matrix coefficients \((\beta_{1},\beta_{2},\beta_{3},\ldots,\beta_{i})\) and the generated parity blocks \((P_{1},P_{2},P_{3},\ldots,P_{i})\).
## 2 Viscoelastic Parameter Model of the Multi-Layered CGS  
### Structure Model of the Multi-Layered CGS  
Figure 1 shows a diagrammatic sketch of three-layered CGS composite structures with solid phase (pebble, sand-clay matrix) and gas phase (pore) of different gradations, where \(H\) is one-layered CGS height, and \(h_{1}\) and \(h_{2}\) are interface-layer height. For determining its macroscopic viscoelastic parameters, its macroscopic elastic parameters need to be firstly obtained based on homogenization principle. This includes four steps: (1) consider the solid phase (sand and clay as matrix, pebble as inclusion) for homogenizing the one-layer CGS without consideration of gas phase (pore), in order to obtain the effective elastic parameters (bulk and shear modulus) of the solid phase, (2) consider both the solid phase (as matrix) and the gas phase (pore as inclusion) for homogenization in order to obtain the elastic parameters (bulk and shear modulus) of the one-layered CGS, (3) consider the interface-layer as two one-layers with different gradations of the solid phase and the gas phase for homogenization, in order to obtain the elastic parameters (bulk and shear modulus) of the interface-layer, (4) superimpose the results of steps (2) and (3) to obtain the effective elastic modulus of multi-layered CGS. Then, apply the elastic-viscoelastic corresponding principle to obtain the viscoelastic parameters of multi-layered CGS, details as follows.
# Dependence of PV Module Temperature on Incident Time-Dependent Solar Spectrum
###### Abstract  
The operating temperature of photovoltaic (PV) modules affects the photovoltaic conversion process. The operating temperature depends on various environmental conditions and on material-dependent properties of the PV modules. Many expressions for the operating temperature have been proposed in the literatures, some are simplified working Equation as NOCT (Nominal Operating Cell Temperature), and others are more complex, being based on a combination of the energy balance Equation and NOCT. The present study offers a new approach (model) for determining the PV module temperature based on the energy balance Equation and on the solar spectrum irradiance. While using the new model, the operating temperature has been determined for four module technologies: c-Si, a-Si/\(\mu\)c-Si, CdTe, and CIGS and it shows that the operating temperatures for the different cell types are close to the manufacturers' NOCT data-sheet temperatures. For c-Si technology, for example, the simulation resulted in 43.2\({}^{\circ}\) and 46\({}^{\circ}\) for the spectrum and NOCT models, respectively. The proposed new model offers a new approach for determining the operating temperature of PV modules.  
PV module temperature; solar spectrum; energy balance Equation; Nominal Operating Cell Temperature; SPECTRAL(2) +
Footnote †: journal: Applied Sciences
## 4 Discussion
### Different TPS Expression Profiles during Flower Developmental Stages  
Some _RcTPS_ genes exhibited peak expressions in fresh flowers or buds that are about to open. In most plants producing floral scents, volatile emission peaks when the flowers are ready for pollination and decreases afterwards [69]. Corresponding to this phenomenon, the TPS genes encoding scent biosynthetic enzymes typically peak 1-2 days ahead of emission of the corresponding compound, and the related TPS expression decreases during petal senescence stages when scent emission declines, such as the _LoTPS1_ and _LoTPS2_ in _Lilium_ 'Siberia' [70; 71; 72]. Previous studies have reported that germacrene D emitted from the petals of _Rosa_ 'Fragrant Cloud' reached a maximum value in mature petals and then decreased [17; 20], which is similar to the _RcGDS_ expression pattern observed in the present study.  
Notably, some _RcTPSs_ exhibited increased expression in late stage of flowers. In _Osmanthus fragrans_ flowers, the expression of _OfTPS2_ that exclusively produced linalool increased from the full flowering stage to the late full flowering stage [73]. Only a small amount of linalool and its oxides were released at the late full flowering stage, whereas more glycosylated linalool and its oxides were accumulated in the flower [73]. Some other plants also released or accumulated higher terpenoids in old flowers. For example, higher levels of 1,8-cineole and \(\beta\)-ocimene were emitted from senescent ginger (_Hedychium coronarium_) flowers, and maximum monoterepenes accumulated in old flowers of some wild _Rosa_ species [24; 74]. Additionally, higher levels of caryophyllene and \(\beta\)-cubebene were released in old flowers of _Rosa_ 'Honesty' [19]. Since glycosylation is involved in regulating the release of volatile terpen, the correlation between increased _TPS_ gene expression and terpene emission in senescent petals needs further research.
## 4 Blending Ensemble Learning-Based Landslide Susceptibility Mapping and Risk Assessment
### Optimization Method Based on Blending Ensemble Learning
#### 4.1.3 CatBoost  
CatBoost is a high-performance open-source machine learning library developed by Yandex, primarily designed for handling categorical data. It particularly excels in processing datasets with a large number of categorical features.  
Innovatively employing ordered boosting techniques, CatBoost addresses the common prediction bias issues in gradient boosting frameworks. It effectively prevents data leakage and model overfitting while significantly reducing the need for hyperparameter tuning. Compared to traditional machine learning algorithms, CatBoost can handle high-cardinality categorical variables [35]. It utilizes gradient boosting for regression trees [36] and constructs models in a phased manner through progressively refined approximations, thereby achieving more accurate predictive performance. The CatBoost algorithm demonstrates outstanding capabilities in both classification and regression tasks.  
For geospatial factors in landslide susceptibility assessment (e.g., spatial distance parameters such as water systems, faults, and roads), CatBoost's built-in target statistics technology automatically performs feature preprocessing. This feature eliminates the need for manual data normalization during modeling, allowing raw spatial database data to be directly used for constructing landslide hazard prediction models.  
As a cutting-edge algorithm in ensemble learning, the innovation of CatBoost is manifested in its symmetric tree architecture. During leaf node splitting, the algorithm quantitatively evaluates feature contributions and integrates an innovative auto-encoding mechanism for categorical variables. By introducing a feature combination strategy, it effectively captures multi-dimensional feature interactions, enhancing the model's ability to recognize complex data patterns.
# Broadcasting in Stars of Cliques and Path-Connected Cliques +
## 1 Introduction
This result was subsequently improved, showing that the problem remains NP-Hard to approximate within a factor of \(3-\epsilon\). Additionally, an approximation algorithm was introduced, capable of building a broadcast scheme in \(O(\frac{\log(|V|)}{\log\log(|V|)}b(G))\) rounds [7]. The study of exact algorithms for specific graph families was initiated through the development of a linear-time algorithms for trees [2]. This was later extended to include exact algorithms for grids, tori [8], cube-connected cycles [9], and the shuffle exchange graph [10]. Further advancements addressed more complex graph families, such as fully connected trees [11], \(k\)-cacti with constant \(k\)[12], Harary-like graphs [13], and Unicyclic graphs [14]. For a comprehensive overview of broadcasting and related problems, we direct the reader to the survey papers [1; 10; 15; 16] as well as more recent papers [12; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27]. This paper is a study of the broadcasting problem in graph families consisting of blocks which are cliques. We start with the windmill graph \(Wd_{k,l}\), which is a graph with \(n\) vertices consisting of \(k\) cliques of size \(l\) and a universal vertex. This paper also introduces star of cliques, a generalization of the windmill graph where cliques can have arbitrary sizes. In addition, we analyze the topology of path-connected cliques, which consists of a sequence of cliques arranged along a path, where each pair of adjacent cliques is connected by a single edge. The windmill graph \(Wd_{k,2}\), also known as the Friendship graph, serves as a solution to [PERSON] et al. 's Friendship Theorem [28]. The family of graphs has also been studied in the context of graceful and harmonious graph labeling, as well as in the movable antennae problem [29], with particular attention given to variations such as the Dutch windmill and the French windmill. We propose \(O(1)\) algorithms for windmill graphs and path-connected cliques, and demonstrate how the latter serves as a model for optimizing message dissemination in topologies, such as block graphs, where connectivity is path-dependent. Further, we propose an \(O(n\cdot\log n)\) algorithm to compute the broadcast time of any vertex in an arbitrary star of cliques and analyze the optimality of our approach. We skip all proofs in Sections 2-4 since they are discussed in our conference paper [30]. However, we present the details of the algorithms for completeness.
# A Review on Local Failure Probability Sensitivity Analysis
## 4 Local RSA in the Standard Normal Space
### Sensitivity with Finite Difference Schemes
#### 4.4.1 Expression of the Finite Difference Schemes  
The derivatives of \(P_{f}\) with respect to \(\mathbf{s}\) can be directly based on finite difference schemes [54; 55]. Denoting \(\mathbf{h}_{\ell}\) as the \(p\)-vector whose components equal zero except the \(\ell\)-th component equals to \(h\), with \(h>0\), we recall here the forward formula  
\[\frac{\partial\widehat{P_{f}(\mathbf{s},\mathbf{h}_{\ell})}^{\mathrm{F}}}{ \partial\delta_{\ell}}=\frac{P_{f}(\mathbf{s}+\mathbf{h}_{\ell})-P_{f}( \mathbf{s})}{h}=\frac{\mathbb{E}_{f_{\mathbf{\chi}}}\left[\mathbb{I}_{D_{f}( \mathbf{s}+\mathbf{h}_{\ell})}(\mathbf{X})\right]-\mathbb{E}_{f_{\mathbf{\chi}}} \left[\mathbb{I}_{D_{f}(\mathbf{s})}(\mathbf{X})\right]}{h},\]  
and the central formula  
\[\frac{\partial\widehat{P_{f}(\mathbf{s},\mathbf{h}_{\ell})}^{\mathrm{C}}}{ \partial\delta_{\ell}}=\frac{P_{f}(\mathbf{s}+\mathbf{h}_{\ell})-P_{f}( \mathbf{s}-\mathbf{h}_{\ell})}{2h}=\frac{\mathbb{E}_{f_{\mathbf{\chi}}}\left[ \mathbb{I}_{D_{f}(\mathbf{s}+\mathbf{h}_{\ell})}(\mathbf{X})\right]-\mathbb{E }_{f_{\mathbf{\chi}}}\left[\mathbb{I}_{D_{f}(\mathbf{s}-\mathbf{h}_{\ell})}( \mathbf{X})\right]}{2h}.\]  
The expected values of these formulas can then be estimated with sampling methods. Here, we use the same formulations to present the different approaches as in [50]. The Direct approach consists in employing independent samples for the estimations of \(P_{f}(\mathbf{s}+\mathbf{h}_{\ell})\), \(P_{f}(\mathbf{s})\) and \(P_{f}(\mathbf{s}-\mathbf{h}_{\ell})\). Therefore, in order to obtain the failure probability sensitivity, the simulation budget is multiplied by two with the forward formula and by three with the central formula. In contrast, the Common Random Variable (CRV) approach employs the same sample for the estimations of \(P_{f}(\mathbf{s}+\mathbf{h}_{\ell})\), \(P_{f}(\mathbf{s})\) and \(P_{f}(\mathbf{s}-\mathbf{h}_{\ell})\). However, the limit state functions with parameter \(\mathbf{s}+\mathbf{h}_{\ell}\) and \(\mathbf{s}-\mathbf{h}_{\ell}\) differ from \(g(\mathbf{s},\ \cdot)\). Consequently, the simulation budget is still multiplied by two with the forward formula and by three with the central formula. Using the same sample makes it possible to cancel the noise of the estimates of the expected values, which justifies the CRV approach. Improvements of the finite difference schemes have been recently proposed in [56].