esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Basic theory
### An Introduction to Copulas
#### Sklar's Theorem  
First, let us define a copula in \(\mathbb{R}^{d}\).  
**Definition 2.1**.: _A \(d\)-dimensional copula is a joint cumulative distribution function \(C\) defined on \([0,1]^{d}\), with uniform margins._  
The following theorem explains in what extent a copula does describe the dependency between two or more random variables.  
**Theorem 2.1** ([PERSON] [1]).: _Let \(F\) be a joint multivariate distribution with margins \(F_{1}\),..., \(F_{d}\), then, there exists a copula \(C\) such that_  
\[F(x_{1},...,x_{d})=C(F_{1}(x_{1}),...,F_{d}(x_{d})) \tag{2.1}\]  
_If marginal cumulative distributions are continuous, then the copula is unique. Otherwise, the copula is unique on the range of values of the marginal cumulative distributions._  
\(\mathcal{R}emark\) **2.1**.: _First, for any copula \(C\) and any \(u_{i}\) in \([0,1]\), \(1\leq i\leq d\), we have_  
\[W(u_{1},\ldots,u_{d})=\max\left\{1-d+\sum_{i=1}^{d}u_{i},0\right\}\leq C(u_{1},\ldots,u_{d})\leq\min_{j\in\{1,\ldots,d\}}u_{j}=M(u_{1},\ldots,u_{d})\]  
_where \(W\) and \(M\) are called the Frechet-Hoeffding copula boundaries and are also copulas._  
_We set the independent copula \(\Pi\) as \(\Pi(u_{1},\ldots,u_{d})=\Pi_{i=1}^{d}u_{i}\), for any \(u_{i}\) in \([0,1]\), \(1\leq i\leq d\)._  
Moreover, we define the density of a copula as the density associated with the cdf \(C\), which we will name as \(c\):  
**Definition 2.2**.: _Whenever there exists, the density of \(C\) is defined by \(c(u_{1},...,u_{d})=\frac{\partial^{d}}{\partial u_{1}...\partial u_{d}}C(u_{1},...,u_{d})\), for any \(u_{i}\) in \([0,1]\), \(1\leq i\leq d\)._  
Finally, let us present several examples of copulas (see also Appendix A to find an overview).  
\(\mathcal{E}xample\) **2.1**.: _The Gaussian copula \(C_{\rho}\) (in \(\mathbb{R}^{2}\)):_  
_Defining \(\,\Psi_{\rho}\) as the standard bivariate normal cumulative distribution function with \(\rho\) correlation, the Gaussian copula function is_  
\(C_{\rho}(u,v)=\,\Psi_{\rho}\left(\,\Psi^{-1}(u),\,\Psi^{-1}(v)\right)\)__  
_where \(u,v\in[0,1]\) and where \(\,\Psi\) is the standard normal cumulative distribution function._  
_The Student copula \(\mathcal{C}_{\rho}\) (in \(\mathbb{R}^{2}\)):_  
_Defining \(T_{\rho,k}\) as the standard bivariate student cumulative distribution function with \(\rho\) as the correlation coefficient and with \(k\) as the degree of freedom of the distribution, the Student copula function is_  
\(\mathcal{C}_{\rho}(u,v)=T_{\rho,k}\left(T_{k}^{-1}(u),T_{k}^{-1}(v)\right)\)__  
_where \(u,v\in[0,1]\) and where \(T_{k}\) is the standard Student cumulative distribution function._  
_The Elliptical copula :_  
_Similarly as above, elliptical copulas are the copulas of elliptical distributions (an overview is provided in Appendix A)._
## 3 Results
### Realization and Evaluation of the Pre-Test Phase
#### 3.1.4 Results Obtained in the IV Stage of the Pre-Test Phase
For example, the magnitudes of the first singular curve in Figure 13b are much smaller than in the other cases. Moreover, repeated modes appear in the CMIF plot as peaks in multiple singular curves at the same (or very close) frequency, which is not evident in each of the realized cases (see the comparative table of assessed modes presented in Section 3.2). The auto MAC was used to correlate the similarities between the modes with an emphasis on proving that some of the selected modes with closely spaced natural frequencies are the repeated modes. The off-diagonal elements of the MAC matrix shown in Figure 14 include mainly the values from 0 to 0.2 (only one value is approaching 0.3). This indicates that the modes, estimated in one of the IV\({}^{\text{A}}\) stage measurements, share very close frequencies and have distinct mode shapes, i.e., they are repeated. Figure 13: Mean singular curves of the CMIF plots obtained from three measurements in the: (**a**) IV\({}^{\text{A}}\); (**b**) IV\({}^{\text{B}}\); (**c**) IV\({}^{\text{C}}\); and (**d**) IV\({}^{\text{D}}\) stages of the pre-test phase. The mode shapes estimated as repeated modes can be seen in Figure 15 labelled by Greek symbols \(\alpha\) and \(\beta\). Moreover, as the specimen response was captured from multiple points, the obtained singular curves contain richer mode shape information, leading to a more accurate and detailed reconstruction of the mode shapes. In contrast to Figure 13, where the CMIF plots consisted of three and two singular curves, respectively, Figure 16 shows a comparison of the particular mean singular curves of the CMIF plots obtained when evaluating the EMAs conducted with three different locations of the reference degree of freedom, i.e., 49, 50, and 51, respectively. It is obvious that the singular curves obtained in the \(\mathrm{I}^{\mathrm{ref}}\), \(\mathrm{IV}^{\mathrm{E}}\), and \(\mathrm{IV}^{\mathrm{F}}\) stages are significantly different. When using reference degrees of freedom 50 and 51, some modes of the analysed specimen with a honeycomb infill pattern were not found (see the comparative table of estimated modes presented in Section 3.2). Figure 14: Possible modes analysis using auto MAC realized in one of the \(\mathrm{IV}^{\mathrm{A}}\) stage measurements. Figure 15: Mode shapes of the clamped specimen with a honeycomb infill pattern estimated in stage \(\mathrm{IV}^{\mathrm{A}}\) of the pre-test phase. Indices \(\alpha\) and \(\beta\) represent the repeated modes.
# Parameterized Modeling and Planning of Distributed Energy Storage in Active Distribution Networks
## 4 Mixed-Integer Second-Order Cone Programming (MISOCP) Model Conversion
### Planning Results
#### 5.1.2 Power Fluctuation Smoothing  
The planning results are shown in Tables 7 and 8. The coordinated planning results are the same as the planning of only VRB in Table 7. It can be seen that the power fluctuation cost is reduced by $49,902 when a VRB is allocated, a decrease of 68.18%. Considering the investment cost of DES, \(C_{2}\) is reduced by $18,702, a decrease of 25.43%.  
In this case, because of the rapid power fluctuation of renewable DGs, DES needs to charge and discharge frequently to meet the demand for power smoothing. VRB has an exceptionally long lifetime compared with the other two DES types, making it is quite suitable for charging/discharging with high frequency. Although a lead-acid battery has an advantage in investment cost, it is not selected to install owing to its low life cycle.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type** & **Location** & **Power Capacity (kVA)** & **Energy Capacity (kWh)** \\ \hline \multirow{4}{*}{Lead-acid battery} & 14 & 50 & 550 \\  & 17 & 70 & 810 \\  & 31 & 20 & 260 \\  & 32 & 60 & 690 \\ \hline \multirow{2}{*}{Li-ion battery} & 31 & 130 & 1040 \\  & 32 & 80 & 650 \\ \hline VRB & — & — & — \\ \hline Total & 14, 17, 31, 32 & 410 & 4000 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Coordinated planning results of economic benefits improvement in IEEE 33-node system.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type** & **Location** & **Power Capacity (kVA)** & **Energy Capacity (kWh)** \\ \hline \multirow{4}{*}{Only Li-ion battery} & 10 & 260 & 1380 \\  & 16 & 160 & 1240 \\  & 17 & 180 & 540 \\  & 33 & 400 & 840 \\ \hline \multirow{4}{*}{Only VRB} & 10 & 290 & 1450 \\  & 16 & 200 & 1240 \\  & 17 & 160 & 490 \\  & 33 & 350 & 820 \\ \hline Only lead-acid battery & — & — & — \\ \hline \hline \end{tabular}
\end{table}
Table 7: Planning results of power fluctuation smooth in IEEE 33-node system.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type** & **Location** & **Power Capacity (kVA)** & **Energy Capacity (kWh)** \\ \hline \multirow{4}{*}{Only Li-ion battery} & 10 & 260 & 1380 \\  & 16 & 160 & 1240 \\  & 17 & 180 & 540 \\  & 33 & 400 & 840 \\ \hline \multirow{4}{*}{Only VRB} & 10 & 290 & 1450 \\  & 16 & 200 & 1240 \\  & 17 & 160 & 490 \\  & 33 & 350 & 820 \\ \hline Only lead-acid battery & — & — & — \\ \hline \hline \end{tabular}
\end{table}
Table 8: Power smooth results of DES planning in IEEE 33-node system.  
With the development of DES technology, capital cost will be further reduced, and the economic benefits of DES will become more promising. In addition, DES can also perform the auxiliary service functions such as peak shaving, frequency support, and voltage regulation. Considering the above economic and environmental benefits, the practical value of DES will be further improved.
## 4 Control and Monitoring of MRI-Assisted Interventions
### Compatibility and Control Perturbations
#### 4.2.2 Complexity and Uncertainty Handlings  
As stated previously, the precision implicated in the image-assisted robotic control associated with actuation and window positioning is conditional on troubling dynamics, including the complexity degree of different involved blended components, the related identification uncertainties, and unusual outer threat occurrences. The reduction in such potential troubles as well as the consideration of specific individual process information are indispensable for the correct functioning of the controlled image-guided procedure. Such objectives could be accomplished by monitoring the involved parameters in a matched real-virtual pair by means of a digital twin (DT) tool [66]. A DT is characterized by an integration of data within a pair of a physical event and its digital replica in a two-way manner. Such an approach is practiced for the managing of complexity in controlled procedures [67] and structured as a physical-virtual pair allowing self-adjusting behavior. Thus, the physical side of the pair delivers processed sensed data to the virtual side, while the last transmits control commands to the physical side. This self-adjustment matching helps reduce pair uncertainties and unexpected randomness in process control. It thus clearly appears that the management of complexity, uncertainties, and randomness by DT responds well to the troubling dynamics of image-assisted robotic control mentioned above. Note that, generally, DTs can be planned at the echelons of a structure, a substructure, or  
Figure 2: MRI field components: (**a**) electromagnet B\({}_{0}\), (**b**) gradient coils (one couple for one axis), and (**c**) RF coil (birdcage) B\({}_{1}\).  
a particular component and employed for diagnostics, prediction, procedure condition monitoring, optimization, and risk evaluation [68].  
Recently, DT has been gradually introduced into the health sector, which has allowed its use in different treatments to be gradually explored, thus enabling the renovation of daily life, health, and the connected monitoring and prolonged management of disorders. Many cases have been studied for this purpose; see, for example, the studies of [69; 70; 71; 72; 73; 74; 75; 76; 77; 78; 79], which are mainly general reviews illustrating the abovementioned treatments, monitoring, and managements.
# Analysis of Cement Sheath-Rock Damage Mechanism--A Case Study on Water Injection Wells
## 1 Introduction
Regarding damage to the cement-rock interface, notable scholars such as [PERSON] et al. [18], [PERSON] et al. [19], and others have designed concrete-rock models to analyze shear-induced interface damage through controlled laboratory experiments, thus revealing the framework of damage models. Despite extensive research on water injection, water breakthrough, casing damage, and concrete-rock models, there are still limitations in directly applying these findings to understand water breakthrough outside the casing of water injection wells. [PERSON] et al. [20] and [PERSON] et al. [21] have explored the mechanisms of cement sheath damage by examining the parameters relating to cement slurry performance. In the field of numerical simulation, [PERSON] et al. [22] implemented a three-dimensional finite element model to analyze well integrity, investigating the plastic deformation of wellbore cement and the utilization of the von Mises yield criterion under different stress scenarios. The study also examined the mechanical properties of the formation. [PERSON] and [PERSON] [23] (2018)developed a hydro-mechanical coupling dynamic model (PD) to derive the mechanical behavior of rock damage under coupled effects. [PERSON] et al. [24] utilized the ABAQUS software to perform three-dimensional simulation analysis, incorporating geological mechanics modeling data and taking into account the wells' environmental conditions, while examining the effect of casing spacing on cement integrity through sensitivity analysis and parameter testing. To comprehend the current production status of water injection wells in area Y, a geometric model of the cement sheath-rock bonding surface is established. An improved bonding force formula is utilized to enhance the accuracy of the shear stress model, thereby revealing the damage characteristics supporting these interfaces. The damage process of the rock at the bonding surface encompasses shear cracking damage and elastoplastic damage, where the elastoplastic damage model adopts a statistical damage model, and the elemental strength adheres to the Mohr-Coulomb criterion [17]. Drawing upon this foundation, a coupled damage model has been devised to accurately characterize the attributes of the rock outside the casing in water injection wells. The evolution process of damage in the cemented rock under fluid-solid coupling is studied through numerical simulation. This study provides a theoretical roadmap to enhance understanding and develop prevention strategies for water breakthrough in water injection wells in area Y.
# Applications of Satellite Radar Imagery for Hazard Monitoring: Insights from Australia
###### Abstract  
Earth observation (EO) satellites facilitate hazard monitoring and mapping over large-scale and remote areas. Despite Synthetic Aperture Radar (SAR) satellites being well-documented as a hazard monitoring tool, the uptake of these data is geographically variable, with the Australian continent being one example where the use of SAR data is limited. Consequently, less is known about how these data apply in the Australian context, how they could aid national hazard monitoring and assessment, and what new insights could be gleaned for the benefit of the international disaster risk reduction community. The European Space Agency Sentinel-1 satellite mission now provides the first spatially and temporally complete global SAR dataset and the first opportunity to use these data to systematically assess hazards in new locations. Using the example of Australia, where floods and uncontrolled bushfires, earthquakes, resource extraction (groundwater, mining, hydrocarbons) and geomorphological changes each pose potential risks to communities, we review past usage of EO for hazard monitoring and present a suite of new case studies that demonstrate the potential added benefits of SAR. The outcomes provide a baseline understanding of the potential role of SAR in national hazard monitoring and assessment in an Australian context. Future opportunities to improve national hazard identification will arise from: new SAR sensing capabilities, which for Australia includes a first-ever civilian EO capability, NovaSAR-1; the integration of Sentinel-1 SAR with other EO datasets; and the provision of standardised SAR products via Analysis Ready Data and Open Data Cubes to support operational applications.  
SAR; InSAR; Australia; Earth Observation; hazards +
Footnote †: journal: Applied Optics and Applications of Satellite Radar Imagery for Hazard Monitoring: Insights from Australia
## 1 Introduction
In particular, the SEI layer in LiFTESI-based electrolytes contains an optimum amount of inorganic species (mainly LiF), a prerequisite for a mechanically and electrochemically stable SEI layer [15]. In cells containing a Si anode and a Ni-rich layered oxide cation, the decomposition of the (fluorosulfonyl)(trifluormethanesulfonyl)imide (FTSI) anions leads to a LiF- and Li\({}_{3}\)N-rich SEI [21]. The development of passivation films on LiF was also computationally investigated by [PERSON] et al., because lithium fluoride is one of the main components of the SEI layer on electrodes [23]. Other computational and/or experimental studies regarded the coordination of FTSI-based ILs with Li ions [24; 25; 26; 27], many times in connection with the Raman bands of the aggregates, which were firstly calculated by [PERSON] et al. for pure ionic liquids [28]. In view of the relatively limited studies of ionic liquids based on the FTSI anion compared to the FSI and TFSI, we synthesized two new ILs coupling the FTSI anion with two different quaternary ammonium cations, namely the \(N\)-trimethyl-\(N\)-butyl-ammonium, (N1114)\({}^{+}\), and the \(N\),\(N\)-diethyl-\(N\)-methyl-\(N\)(2-methoxyethyl)-ammonium (N122(20 Cl))\({}^{+}\). The same cations were previously investigated by us in conjunction with the symmetric FSIand TFSI anions [29; 30; 31] and, therefore, a direct comparison of the properties of the derived ionic liquids is feasible. We characterized the new FTSI ILs concerning their thermal, vibrational and electrochemical stability, liquid range and ionic conductivity.
## 2 Materials and Methods  
### Chlorine Kinetic Model  
Chlorine decay in seawater is often modeled using the first-order decay kinetics [20; 29]. However, as this model only contains one parameter and does not consider other reactions potentially occurring in real water, it often fails to make an accurate prediction [20; 30; 31]. In this study, we evaluated in-situ electro-chlorination in a pilot-scale cooling system using a CFD code including the chlorine decay kinetics to predict the behavior of generated chlorine. This model consists of two parts: the first one represents the slow reaction (typically related to the presence of organic matters) while the other concerns the fast reaction (typically related to easily oxidizable matters, such as metals or simple organic chemicals in the water) [20]. The differential form of the model can be expressed as:  
\[\frac{dC}{dt}=-k_{f}C_{f}-k_{s}C_{s} \tag{1}\]  
The integrated form of the model is:  
\[C(t)=C_{0}ze^{-k_{\mathrm{f}}t}+C_{0}(1-z)e^{-k_{\mathrm{f}}t} \tag{2}\]  
where \(C(t)\) is the chlorine concentration (mg L\({}^{-1}\)) at a given time; \(C_{0}\) is the initial chlorine concentration (mg L\({}^{-1}\)); \(z\) is the fraction factor accounting for slow reaction; and \(k_{\mathrm{s}}\) and \(k_{\mathrm{f}}\) are the first-order rate constants (h\({}^{-1}\)) for the slow and fast reactions, respectively [32]. There have been various attempts to estimate these rate constants using water quality parameters such as chemical oxygen demand (COD), total organic carbon (TOC), dissolved organic carbon (DOC), salinity, NH\({}_{4}\)\({}^{+}\), temperature, and pH [22; 33; 34; 35]. Moreover, the initial chlorine concentration is included, since a strong correlation is common between the chlorine decay rate and initial concentration [22; 33]. We use the following equations to estimate the aforementioned model parameters as suggested by [PERSON] et al. [33]:  
\[k_{s}=p_{s}\ C_{0}^{-m_{s}}e^{m_{s}\ TOC} \tag{3}\]  
\[k_{f}=p_{f}\ C_{0}^{-m_{f}}e^{m_{f}\ TOC} \tag{4}\]  
\[z=d_{1}\ C_{0}^{d_{2}}\ TOC^{-d_{3}} \tag{5}\]  
The coefficients, \(p_{s}\), \(p_{f}\), \(m_{s}\), \(m_{f}\), \(n_{s}\), \(n_{f}\), \(d_{1}\), \(d_{2}\), and \(d_{3}\) must be estimated. In Equations (3)-(5), TOC is used as an indicator of the amount or organic matter in the water.
## 2 Materials and Methods
### Chemical Composition Determination  
Moisture content was assessed by drying 1 g of the sample at 105 \({}^{\circ}\)C until a constant weight was achieved, following the procedure outlined in AOAC Method 925.10-1925 [18]. Lipid content was determined via Soxhlet extraction using hexane for 3 h with 3 g of sample, following AOAC Method 948.22 [18]. Crude protein concentration was measured using the Kjeldahl technique (conversion factor N \(\times\) 6.25) on 1 g of sample, based on AOAC Method 978.04 [18]. To quantify the ash content, 2 g of the sample were initially charred for 30 min, followed by incineration in a muffle furnace at 625 \({}^{\circ}\)C for 2 h, in accordance with AOAC Method 930.05 [18]. Total dietary fiber (TDF), including its soluble (SDF) and insoluble (IDF) fractions, was analyzed using the Total Dietary Fiber Assay Kit provided by Megazyme International (Wicklow, Ireland), according to the manufacturer's protocol based on AACC Method 32-07.01 and 991.43 [19]. In brief, 1 g of sample was suspended in 40 mL of 0.05 M MES-Tris buffer (pH 8.2) and subjected to enzymatic digestion. The sample was first treated with \(\alpha\)-amylase (50 \(\mu\)L, 95 \({}^{\circ}\)C, 30 min), followed by protease (100 \(\mu\)L, 60 \({}^{\circ}\)C, 30 min), under continuous agitation at 120 rpm. The pH of the mixture was then adjusted to a range of 4.1-4.8 using 1 N HCl (0.56 mL), after which amyloglucidase (200 \(\mu\)L) was loaded and the hydrolysis continued (60 \({}^{\circ}\)C, 30 min) under the same stirring conditions. Following enzymatic treatment, the mixture was filtered using a Fibertec 1023 E system (Foss System, Hilleroed, Denmark). The solid residue was sequentially rinsed with hot distilled water (10 mL, 70 \({}^{\circ}\)C), then with 95% ethanol (10 mL) and acetone (10 mL), followed by drying at 103 \({}^{\circ}\)C overnight. The resulting dry mass was recorded as the IDF fraction. The filtrate and washings were combined and mixed with four volumes of 95% ethanol for SDF quantification. After standing for one hour at ambient temperature, the mixture was filtered. The collected residue was washed with 78% and 95% ethanol, followed by acetone, then dried and weighed. The protein and ash contents in both the IDF and SDF fractions were determined and subtracted to yield the fibre values. TDF was calculated as the sum of SDF and IDF.
# End-to-End Performance Evaluation of MEC Deployments in 5G Scenarios
## 2 Multi-Access Edge Computing in 4G/5G  
### Background on Multi-Access Edge Computing  
In Figure 1 the MEC architecture, as standardized by ETSI [4], is reported. The MEC architecture allows MEC apps to be executed in a virtualized environment, thus enabling dynamic and on-demand allocation of computational resources in response to users request for a particular task or service. Network operators supervising and managing an instance of a MEC system will be able to optimize resource utilization even dynamically, e.g., by migrating and/or relocating user applications between MEC hosts, following computation and communication requirements.  
At the top of the hierarchy sits the MEC System Level, which maintains a global vision of the state of all the MEC Hosts within the system. The MEC System Level handles several management tasks, including handling MEC Application Instantiation requests coming from user applications, checking application requirements (e.g., MEC-services availability, maximum allowed communication  
Figure 1: Overview of the Multi-access Edge Computing Framework.  
latency, requested computational resources), selecting and configuring the MEC host that will host and execute the MEC application instance. In a MEC host, a MEC platform provides multiple MEC services, as defined in ref. [15]. The latter can be used by MEC apps (acting as clients for the MEC platform), to realize complex context-dependent behaviors. Example of MEC services are: the smart relocation service, which allows MEC apps to migrate among MEC hosts (e.g., to follow the least-latency path when users are mobile); the radio network information service (RNIS), which provides information on the state of the underlying network (e.g., how many users are connected, what is the load at the base station, etc.); the bandwidth manager, which sets data traffic priorities within the MEC host; the location service, that can be queried to get access to the users' position. MEC apps run on the MEC host as virtual machines, and they can communicate both with other entities in the MEC host (e.g., the MEC platform, to use its services) and with the outside world (e.g., users' local applications). This is achieved by the virtualization infrastructure.