esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Materials and Methods
The simplified block diagram of the BESS model is proposed in Figure 2.  
A set of simulations performs the FCR provision on the same frequency trend (see Figure 3) and on the same Li-ion BESS whose main sizing data are reported in Table 2. Frequency data are from system frequency in Continental Europe Synchronous Area (CESA) for the year 2016 [27], with 1 s sampling rate and a resolution of 0.1 MHz. The regulating power for FCR provision is equal to the nominal power of BESS. The difference between the simulations only relates to the SoC restoration mechanism in place. Each SoC restoration mechanism is suitable for exploiting different DoF, and therefore, it could be possibly applied in different regulatory frameworks. The SoC restoration strategies tested are listed here below and described in the following. * The Base case implements no SoC restoration strategy. * The No DoF case implements a SoC restoration strategy based on the interruption in service provision. * The Over/Under-regulation case implements a SoC restoration strategy based on variable droop. Figure 1: Droop control curve based on the Italian Grid Code implemented in the battery energy storage system (BESS) model for Frequency Containment Reserve (FCR) provision. Figure 2: Simplified block diagram of the Simulink tool for the FCR provided by BESS. * The Dead-band case implements a SoC restoration strategy based on dead-band strategy. * Available energy case implements a SoC restoration strategy based on offsetting the regulating power when SoC is outside a window of acceptability. * The Hybrid case implements a SoC restoration strategy based on offsetting the regulation when SoC is outside the window of acceptability and dF is inside dead-band. This set of active strategies presented are designed to be as coherent as possible with the ones adopted in the European experiences already mentioned. Except for the Base case, the other simulations feature a SoC restoration strategy conveniently exploiting the DoF that we assume are granted by the regulation. SoC restoration aims to bring back SoC towards a SoC\({}_{\text{target}}\) equal to 55%. SoC\({}_{\text{target}}\) is selected based on the assumption of symmetric provision of reserves for FCR. At SoC\({}_{\text{target}}\), energy content available (net of the efficiency) is approximately equal for upward and downward reserve. \[(\text{SoC}_{\text{target}}-\text{SoC}_{\text{min}})\times\eta_{\text{avg}} \cong(\text{SoC}_{\text{max}}-\text{SoC}_{\text{target}})/\eta_{\text{avg}}, \tag{3}\]  
where SoC\({}_{\text{min}}\) is the minimum SoC of the battery, \(\eta_{\text{avg}}\) is the average efficiency of the battery equal to 92% based on [23].
# A Unified Vendor-Agnostic Solution for Big Data Stream Processing in a Multi-Cloud Environment
## 3 MC-BDP Reference Architecture
### MC-BDP Architectural Layers
#### 3.4.4 The Networking Layer  
The networking layer represents a network which allows containers deployed to different nodes at different locations to communicate seamlessly. As MC-BDP is a container-based reference architecture, it departs from the traditional approach of networking machines to that of networking containers. Since containers are standalone abstractions decoupled from the environment where they run, it is a sensible design decision to network at the container, rather than the node level.  
There are different ways in which networking can be implemented at the container level, and MC-BDP is agnostic in this regard. Some examples are:  
* Pipework, a legacy networking tool based on Linux's cgroups and namespaces [76].
* Flannel, a virtual network that provides a subnet to each host to use with container runtimes [77].
* Open vSwitch, which creates either an underlay or overlay network to connect containers running on multiple hosts [78].
* Weave Net, a Docker plugin that creates a virtual network to connect Docker containers across multiple hosts and enable their automatic discovery [79].  
Although some container orchestrators claim to offer out-of-the-box networking [80], when building a prototype for MC-BDP using Docker swarms, it was observed that only containers deployed to machines in the same cloud could communicate with each other. In order to achieve inter-cloud networking, the Weave Net plugin had to be installed [81]. The Weave Net plugin is built around the concept of an overlay network, defined as an abstract network built on top of an existing physical network. The plugin deploys a router container and creates a network bridge on each host. The router uses TCP and UDP connections to transfer packets to other routers in the network, connected via the network bridges. Packets destined for containers located within the same host are handled by the kernel directly without going through the network [82]. In the context of the proposed reference architecture, this feature is particularly desirable since commercial cloud consumers are charged for the number of packets transferred over the network. The overlay network provided by the Weave Net plugin is thus a suitable technology for the implementation of container-to-container networking in the context of the reference architecture proposed. Nevertheless, MC-BDP remains agnostic in terms of the technology or approach selected for network containers hosted in different clouds.
## 2 Materials and Methods
### Data Analysis Methods  
To test whether or not the average frequencies of the performed tasks varied significantly between participants, a repeated-measures ANOVA was performed. Paired-samples \(t\)-tests were used to test for differences in average frequencies between the familiar and the unfamiliar car.  
To test if the distribution of tasks that were performed while driving versus standing still was the same for different categories of tasks, a chi-square test was performed. The test hypothesis was that tasks that were more typically performed while standing still could be interpreted as less dangerous compared to tasks that were typically performed while driving. To meet the requirements of a chi-square test, only tasks or task categories that had enough observations were tested for differences in distribution.  
The dependent variable was the number of times that a task was performed adjusted by the driving time for each participant. This type of data can be considered as count data, which is why Poisson regressions were performed to investigate which factors influenced these frequencies. The natural log of the trip durations was used as the offset (exposure) variable, in order to take into account the fact that the trip durations varied across participants. The formula for the Poisson regressions, in which \(\mathrm{x_{i}}\) stands for independent variable \(\mathrm{i}\) and \(\mathrm{\epsilon_{i}}\) stands for the random error in observations (assumed to be Poisson-distributed), is the following: \(\mathrm{ln}(\mathrm{count})=\mathrm{ln}(\mathrm{exposure})+\beta_{0}+\beta_{1 }\mathrm{x_{1}}+\beta_{2}\mathrm{x_{2}}\dots\beta_{1}\mathrm{x_{i}}+\mathrm{ \epsilon_{i}}\).  
Multiple models were constructed with two different types of dependent variables: the total number of tasks performed per hour and the total number of tasks per category performed per hour. The Poisson models were eventually only constructed using the data from the trips with each participant's own car, because the unfamiliar car data had almost no variety in car types, as 28 out of the 30 participants drove the same unfamiliar car. To obtain the final Poisson models, first, separate models were created with only one independent variable. The independent variables with best interpretability and highest statistical significance were then combined in a single model.  
All data were manually entered into Excel, after which the calculations were performed using the statistical software SPSS Statistics 25.
# Turbulence: A Significant Role in Clear-Air Echoes of CINRAD/SA at Night
## 2 Concepts and Theory
### Bragg Scattering  
Bragg scattering is caused by turbulent inhomogeneities with sizes around one-half of the transmitted wavelength of a radar [29]. Technically, the atmospheric turbulence with refractivity gradients is essentially a dipole and causes scattering. [PERSON] provides the radar reflectivity's relationship with the atmospheric structure constant of the refractive index \(C_{n}^{2}\) and the radar wavelength \(\lambda\)[8]. The radar reflectivity \(\eta\) (or radar cross-section per unit volume) is given in Equation (6):  
\[\eta=0.38C_{n}^{2}\lambda^{-1/3} \tag{6}\]  
According to Equation (4), the reflectivity factor \(Z\) is given in Equation (7):  
\[Z=\frac{0.38C_{n}^{2}\lambda^{11/3}}{\pi^{5}K^{2}} \tag{7}\]  
Therefore, the differential reflectivity \(Z_{DR}\) can be equated to \(C_{n}^{2}\) as  
\[Z_{DR}=\frac{Z_{H}}{Z_{V}}=\frac{C_{nH}^{2}}{C_{nV}^{2}} \tag{8}\]Based on isotropic turbulence, \(C_{n}^{2}\) is equal in the horizontal and vertical directions, and the value of \(Z_{DR}\) will be zero in conventional dB form. Additionally, the ratio of the \(Z\) values for two radar wavelengths (also called dual-wavelength ratio, DWR) is  
\[\frac{Z_{1}}{Z_{2}}=\left(\frac{\lambda_{1}}{\lambda_{2}}\right)^{11/3} \tag{9}\]  
[PERSON] used Equation (9) to study clear-air echoes over Florida and Colorado and concluded that the clear-air echoes over these areas were caused by living creatures [3].  
However, Equation (6) is not the only relation between the radar reflectivity and the radar wavelength. The value of the radar reflectivity is variable based on the different applied turbulence theories, and Equation (4) is based on the Kolmogorov-Obukhov theory. According to the Villars-Weisskopf theory, the radar reflectivity's relation is given in Equation (10) [30]:  
\[\eta=C\lambda^{1/3} \tag{10}\]  
where \(C\) is constant. Researchers hold different views regarding the relationship, which changes from \(\eta\propto\lambda^{-1/3}\) to \(\eta\propto\lambda\), and the ratio of the \(Z\) values for the two radar wavelengths changes according to the researcher's view.
## 2 Proposed Method
### Validation of the Proposed Method through Approximation Error  
We outlined a few things here to ensure that the proposed method was giving a precise approximated histogram to the original histogram of the infrared image. To validate the approximation, the approximation errors or relative errors \(\left(e_{Approx}\right)\) between the original histogram and the approximated histogram were calculated for the second part of the histogram shown in Figure 2c. The approximation error is defined as [40].  
\[e_{Approx}=\left|\frac{\hat{h}(i)-h(i)}{\hat{h}(i)}\right| \tag{24}\]  
where \(h(i)\) is the grayscale frequency at the intensity level \(i\) of the original histogram and \(\hat{h}(i)\) is the grayscale frequency at the intensity level \(i\) of the approximated histogram.  
The approximation error compares the approximated histogram against the original histogram at different intensity levels. As shown in Figure 2, the second part of the histogram contains the grayscale intensities ranging from 72 to 255. To reveal the test results regarding the approximation error, we provided the values obtained for the approximation error over the duration of 6 grayscale intensities and the list of approximation errors obtained at different grayscale intensities is shown in Table 1. Since the number of pixels present at the intensities corresponding to the zero grayscale frequency is zero, we omitted the approximation error calculation for these grayscale intensities. According to Table 1, the highest deviation of the approximated histogram from the original histogram is obtained at the intensity level 114. At this intensity level, the number of pixels corresponding to the original histogram is 52 however the number of pixels related to the approximated histogram using Equation (10) is 609. The lowest deviation of the approximated histogram from the original histogram is obtained at the grayscale intensity level 216. At this intensity level, the number of pixels corresponding to the original histogram is 40, however, the number of pixels related to the approximated histogram using Equation (10) is 38. The approximation error with a very low value at the grayscale intensity indicates that the grayscale frequency obtained from the approximation histogram has a value very close to the grayscale frequency of the original histogram. We observe from Table 1 that the approximation error is less than what it is for most grayscale intensities. The results of this paper finding the approximation errors imply that the approximated histogram follows the original histogram. These results further strengthened our conviction that the proposed method can generate an accurate approximation histogram to the original histogram of an infrared image. Further analyses were carried out in the next section to analyze the working performance of the proposed method by conducting experiments on infrared images collected from the standard infrared image databases.
## 2 Preliminaries
### Packing  
This section introduces the batch technology that we will use, the packing technology of the polynomial Chinese remainder theorem, so that each ciphertext can correspond to multiple independent plaintexts and improve the encryption efficiency.  
**Definition 3** (Polynomial Chinese Remainder Theorem): _[_20_]__. Let \(f_{1}(x),\cdots,f_{n}(x)\) be \(n\geq 2\) pairwise coprime polynomials. For arbitrary \(n\) polynomials \(g_{1}(x),\cdots,g_{n}(x)\), there is a unique polynomial \(G(x)\), such that \(G(x)\equiv g_{i}(x)(\text{mod }f_{i}(x))\) and \(G(x)=\sum_{i=1}^{n}g_{i}(x)H_{i}(x)M_{i}(x)(\text{mod }F(x))\), where \(H_{i}(x)=\frac{F(x)}{f_{i}(x)},\ M_{i}(x)=1/H_{i}(x)(\text{mod }f_{i}(x))\),\(i\in[n]\)._  
Our scheme is based on the algebraic structure \(R_{2}=R/2R=\mathbb{Z}_{2}[x]/f(x)\). In practical applications, \(f(x)\) is generally set as the cyclotomic polynomial \(\Phi_{m}(x)\) with degree \(\varphi(m)=d\), while \(\varphi(\cdot)\) represents the Euler function. The cyclotomic polynomial \(\Phi_{m}(x)\) can be decomposed into \(n\) factors \(f_{i}(x)\) with degree \(d^{\prime}\) under module 2, namely \(\Phi_{m}(x)=\prod\limits_{i=1}^{n}f_{i}(x)\ mod\ 2\), which satisfies \(2^{d^{\prime}}\equiv 1(\text{mod }m)\) and \(n\cdot d^{\prime}=\varphi(m)\). \(\mathbb{F}_{p}\) represents the finite field. According to the polynomial CRT in Definition 3, there is the following isomorphism relationship:  
\[R_{2}\cong\mathbb{Z}_{2}[x]/f_{0}(x) \times\mathbb{Z}_{2}[x]/f_{1}(x)\times\cdots\times\mathbb{Z}_{2} [x]/f_{n-1}(x)\] \[\cong\mathbb{F}_{2^{d^{\prime}}}\times\cdots\times\mathbb{F}_{2^ {d}}\]  
Namely, the elements on \(R_{2}\) have a mapping relationship with \(n\) elements in \(\mathbb{F}_{2^{d^{\prime}}}\cong\mathbb{Z}_{2}[x]/f_{i}(x)\). If we set \(T_{i}=\mathbb{Z}_{2}[x]/f_{i}(x),i\in[n]\), it holds that:  
\[\Gamma:\left\{\begin{array}{c}\mathbb{F}_{2^{d^{\prime}}}\to T_{i}\\ m_{i}\mapsto\Gamma_{i}(m_{i})\end{array}\right.\]  
where \(H(x)=\Phi_{m}(x)/f_{i}(x),M_{i}(x)=1/H_{i}(x)(\text{mod }f_{i}(x))\). The mapping of \(\Gamma_{i}\) is isomorphic from \(\mathbb{F}_{2^{d^{\prime}}}\) to \(\mathbb{Z}_{p}[x]/f_{i}(x),i\in[n]\) and the mapping of \(CRT(X)=\Gamma\circ\Psi\) is isomorphic from \(\mathbb{F}_{2^{d^{\prime}}}^{n}\) to \(R_{2}\).  
Here, we set polynomial vectors \(\mathbf{a},\mathbf{b}\in R_{2}^{n}\), and according to the above isomorphism relationship we get:  
\[CRT^{-1}(CRT(\mathbf{a})+CRT(\mathbf{b})) =\mathbf{a}+\mathbf{b}\ mod\ 2,\] \[CRT^{-1}(CRT(\mathbf{a})\times CRT(\mathbf{b})) =\mathbf{a}\times\mathbf{b}\ mod\ 2.\]
# Fuzzy-Based Dynamic Time Slot Allocation for Wireless Body Area Networks
## 5 Fuzzy-Based Dynamic Time Slot Allocation
### Comparison of Time Slot Allocation  
Consider the tree structure shown in Figure 4. The tree structure has 15 nodes and a root node. The number of nodes are selected in random manner. The root node has three direct children node 1, 2, and 3. The whole tree can be divided into three branches. The branch I include nodes 1, 4, 9, and 10. Branch II has nodes 2, 5, 6, and 11. Nodes 3, 7, 8, 12, 15, 13, and 14 constitute branch III. Any node in the tree can be a child node, a relay node, or a leaf node (which does not have any child). For example, node 3 has direct children 7 and 8; the leaf nodes are 7, 13, 14, and 15; the relay nodes are 3, 8, and 12. Assume that the total transmission time for all nodes is 1 s. With a total of 15 nodes, the equal slot duration for each node is 0.0666 s (1/15). Hence, the total slot duration for nodes 1, 2, and 3 are  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**ER** & **BMR** & **PAR** & **Required Time Slots** \\ \hline Low & High & Low & Rather low \\ Low & High & Medium & Medium \\ Low & High & High & Rather high \\ Low & Medium & Low & Low \\ Low & Medium & Medium & Rather low \\ Low & Low & Low & Low \\ Low & Low & Medium & Low \\ Low & Low & High & Rather low \\ Medium & High & Low & Medium \\ Medium & High & High & High \\ Medium & Medium & Low & Rather low \\ Medium & Medium & Medium & Medium \\ Medium & Medium & High & Rather high \\ Medium & Low & Low & Low \\ Medium & Low & Medium & Rather low \\ Medium & Low & High & Medium \\ High & High & Low & Rather high \\ High & High & Medium & High \\ High & Medium & Low & Medium \\ High & Medium & Medium & Rather high \\ High & Medium & High & High \\ High & Medium & High & Right \\ High & Medium & High & Right \\ High & Low & Low & Rather low \\ High & Low & Medium & Medium \\ High & Low & High & Rather high \\ \hline \hline \end{tabular}
\end{table}
Table 1: Fuzzy inference rules.  
0.266 s, 0.266 s, and 0.466 s respectively. This equal slot allocation is used for the conventional sensor networks. The proposed DTS method uses dynamic slot allocation to enhance network performance. The slot allocation to each node depends on the relay nodes, child nodes, and the leaf nodes. In the conventional method of equal slot allocation, each parent node must be active during the entire time duration of its child and leaf nodes. This leads to higher energy consumption. Hence, the dynamic slot allocation method is adopted in the DTS scheme such that the parent needs to be active only during its own and direct child slot duration. This is represented in Figures 5 and 6. It shows the comparison between the two methods with respect to the duration of an active state for parent nodes for the branch III. The branch has nodes 3, 7, 8, 12, 13, 14, and 15. According to the conventional method, the node 3 has to be active for a duration of 0.4662 s and node 8 must remain active for a duration of 0.333 s. The DTS method reduces the active duration of nodes 3 and 8 to 0.1998 s which also results in reduced energy consumption.
## 3 Finite Element Modeling (FEM) of Human-Seat Interactions
### _Material Modeling and Challenges_
#### 3.3.2 Viscoelasticity of the Polyurethane Foam  
This study extended the material modeling by incorporating the time-dependent viscoelastic properties of PU foam. According to [PERSON] [22], viscoelastic behavior is influenced by deformation and deformation rates, exhibiting stress relaxation under constant strain. To investigate this behavior, foam specimens of the same dimensions (100 \(\times\) 100 \(\times\) 80 mm) were compressed to strain levels ranging from 5% to 70% in 5% increments. Each strain level was maintained for 1800 s, and stress relaxation data were recorded (Figure 7).  
A 9 th order Prony series was used to model the viscoelastic behavior:  
\[S(t)=S^{(\infty)}+\sum_{k=1}^{N_{D}}S^{(k)}e^{-\frac{t}{\tau_{k}}} \tag{3}\]  
where:  
\(S(t)\) represents the time-dependent strain energy function;  
\(S^{(\infty)}\) is the infinite relaxation modulus;  
\(N\) denotes the order of the Prony series;  
\(\tau_{k}\) k is the relaxation time for the k-th Prony term;  
Figure 7: Data for foam relaxation from the experiment.  
\(S^{(k)}\) is the Prony coefficients.  
The calibrated Prony coefficients and relaxation times (Table 3) were integrated into the MSC.Marc simulations, successfully modeling the time-dependent material behavior.  
The experimental and simulated force-displacement and stress-strain relationships showed a high degree of agreement (Figure 8), confirming the reliability of the derived material model.  
According to the referenced studies ([16; 19; 20; 21]), polyurethane is a commonly used foam material in the automotive industry. Polyurethane (PU) exhibits strong nonlinear characteristics in both physical and geometric aspects, posing significant challenges for finite element simulation. However, most studies have chosen hyperelastic material models to describe the constitutive relationship of polyurethane.
# An Information Theoretic Approach to Privacy-Preserving Interpretable and Transferable Learning
## 5 Information Theoretic Measures for Privacy Leakage, Interpretability, and Transferability  
### Definitions  
To define formally the information theoretic measures for privacy leakage, interpretability, and transferability; a few variables and mappings are introduced in Table 2. Definitions 10-12 provide the mathematical definitions of the information theoretic measures. \begin{table}
\begin{tabular}{c c} \hline \hline
**Symbol/Mapping** & **Definition/Meaning** \\ \hline \(x_{sr}\in\mathbb{R}^{n_{sr}}\) & vector representing private/sensitive variables associated to source domain \\ \hline \(y_{sr}\in\mathbb{R}^{p_{sr}}\) & source domain data vector \\ \hline \(t_{sr}\in\mathbb{R}^{q}\) & vector representing the set of interpretable parameters associated to \\  & non-interpretable data vector \(y_{sr}\) \\ \hline \(y_{sr}^{+}\in\mathbb{R}^{p_{sr}}\) & noise-added data vector (that is either publicly released or used for the training of \\  & source model) obtained from \(y_{sr}\) via Algorithm 5 \\ \hline \(f_{x_{sr}\to y_{sr}^{+}}:\mathbb{R}^{n_{sr}}\to\mathbb{R}^{p_{sr}}\) & mapping from private variables to noise-added data vector, i.e., \(y_{sr}^{+}=f_{x_{sr}\to y_{sr}^{+}}(x_{sr})\) \\ \hline \(f_{t_{sr}\to y_{sr}^{+}}:\mathbb{R}^{q}\to\mathbb{R}^{p_{sr}}\) & mapping from interpretable parameters to noise-added data vector, i.e., \(y_{sr}^{+}=f_{t_{sr}\to y_{sr}^{+}}(t_{sr})\) \\ \hline \(\{\mathcal{P}_{c}^{+sr}\}_{c=1}^{C}\) & differentially private source domain autoencoders, representing data features of \\  & each of \(C\) classes, obtained via Algorithm 6 \\ \hline \(y_{lg}\in\mathbb{R}^{p_{lg}}\) & target domain data vector \\ \hline \(y_{lg\to sr}\in\mathbb{R}^{p_{sr}}\) & representation of target domain data vector \(y_{lg}\) in source domain via transformation (39) \\ \hline \(\{\mathcal{P}_{c}^{lg}\}_{c=1}^{C}\) & target domain autoencoders, representing data features of \\  & each of \(C\) classes, obtained via Algorithm 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Introduced variables and mappings. Figure 3: A comparison of the estimated information leakage values with the theoretically calculated values. **Definition 10** (Privacy Leakage). : _Privacy leakage (by the mapping from private variables to noise-added data vector) is a measure of the amount of information about private/sensitive variable \(x_{sr}\) leaked by the mapping \(f_{x_{sr}\to y_{sr}^{+}}\) and is defined as_  
\[IL_{f_{x_{sr}\to y_{sr}^{+}}} :=I\Big{(}x_{sr};f_{x_{sr}\to y_{sr}^{+}}(x_{sr})\Big{)}-H(x_{sr}) \tag{110}\] \[=I\big{(}x_{sr};y_{sr}^{+}\big{)}-H(x_{sr}). \tag{111}\]  
**Definition 11** (Interpretability Measure). : _Interpretability (of noise-added data vector) is measured as the amount of information about interpretable parameters \(t_{sr}\) leaked by the mapping \(f_{t_{sr}\to y_{sr}^{+}}\) and is defined as_  
\[IL_{f_{t_{sr}\to y_{sr}^{+}}} :=I\Big{(}t_{sr};f_{t_{sr}\to y_{sr}^{+}}(t_{sr})\Big{)}-H(t_{sr}) \tag{112}\] \[=I\big{(}t_{sr};y_{sr}^{+}\big{)}-H(t_{sr}). \tag{113}\]  
**Definition 12** (Transferability Measure).