esa-sceva/satcom-chunk-collection huggingface dataset:
## 4 Computational complexity  
This section analyses the SSOR-CRZF precoder's computational complexity as well as that of a few other precoders that are already in use. The comparative analysis of the computational complexity is presented in Table 1. For ZF, RZF, CRZF, and SSOR-ZF, it is necessary for computing \(\mathbf{HH}^{H}\), and it is additionally feasible for computing the complexity beyond \(\mathbf{HH}^{H}\). Therefore, the complexity of the computation for ZF can be written as \(\mathcal{O}(2(N_{RF})^{3}+(N_{RF})^{2})\). Similarly, the complexity of RZF can be written as \(\mathcal{O}(2(N_{RF})^{3}+3(N_{RF})^{2})\). The Kalman filter (KF)-based HP algorithm is also taken into account for the comparison. As far as the KF is concerned, the calculation of the KF gain at the \(n^{th}\) iteration, \(\mathbf{K_{k\!f}}(n)\)\((=\mathbf{R}(n|n-1)\tilde{\mathbf{H}}^{H}\big{[}\tilde{\mathbf{R}}(n|n-1)\tilde{ \mathbf{H}}^{H}+\mathbf{Q}_{n}\big{]}^{-1})\), results in the computational complexity \(\mathcal{O}(2(N_{RF})^{3}+3(N_{RF})^{2})\). Here, the covariance matrix \(\mathbf{R}(n|n)=E\big{[}\mathbf{F}^{BB}(n)(\mathbf{F}^{BB}(n))^{*}\big{]}\) as well as \(\mathbf{Q}_{n}\) has been the covariance matrix corresponding to the noise vector (\(\mathbf{n}\)).  
In the proposed SSOR-CRZF precoder, \(\mathbf{P}_{crzf}\), and the iteration can be written as (as in [40])  
\[t_{n}^{i+1/2}=t_{n}^{i}+\frac{\omega}{p_{ii}}\left(s_{i}-\sum_{j=1}^{n-1}p_{nj }t_{j}^{n+1/2}+\sum_{j=n}^{N_{RF}}p_{nj}t_{j}^{(n)}\right), \tag{36}\]  
where the subscript \(n\) designates the \(n^{th}\) element in a vector, and \(P_{nn}(n=1,\ldots,N_{RF})\) represents the diagonal elements of \(\mathbf{P}_{crzf}\). The initial section of the complexity is mostly caused by Equation (36), and after \(i\) iterations, the computational complexity is \(i2(N_{RF})^{2}\)[42]. Additionally, the multiplication \(\mathbf{H}^{H}\mathbf{t}\) cost an additional level of computational complexity of \((N_{RF})^{2}\). The final part produces a computational complexity of \((N_{RF})\) when \(\beta_{CRZF}\) is multiplied by \(\mathbf{H}^{H}\mathbf{t}\). Therefore, it can be inferred from the above study that the proposed SSOR-CRZF precoder has an overall computational complexity of \(\mathcal{O}(N_{RF}+(N_{RF})^{2}+i2(N_{RF})^{2})\).  
Furthermore, to strengthen the arguments, we explore the computational time corresponding to each of the precoding schemes. For this exploration, we consider the following parameters: \(N_{T}=16\), \(N_{RF}=8\), \(K=10\), \(\mathcal{L}=10\), and \(B=4\). For SSOR and SSOR-CRZF, we consider the number of iterations to be 4. From the perspective of the system configuration, the simulation is carried out using an HP laptop with the following specifications: processor: \(11\)th Gen Intel(R) Core(TM) i5-1135G7 @ 2.40 GHz;RAM: 8 GB; 64-bit operating system. Based on the simulation, the computational times corresponding to the RZ, CRZ, SSOR-ZF, and Kalman schemes are 1.732 ms, 1.347 ms, 1.113 ms, and 2.134 ms, respectively. This shows that the SSOR-ZF scheme produces a relatively small computational load compared to the other schemes.
###### Abstract  
There have been many studies on the effect of durability and compressive strength on the increase of the mixing rate of admixtures. However, there is no research that can provide a guide on the optimal mixture proportions for maintaining compressive strength and secure durability properties when using local materials. Therefore, the purpose of this article is to assess the durability and engineering performances of concrete based on local fly ash (FA), as well as to derive the optimum CaO content scope for ensuring durability. The results of this study were compared with the results of the previous study of high-volume ground-granulated blast-furnace slag (GGBFS) concrete. To achieve this, tests were carried out by increasing the admixture mixing rate in 10% increments from 0% to 70%. The unit water was set at 175 kg/m\({}^{3}\) and the amount of binder was set at 330 kg/m\({}^{3}\). It was found that the overall compressive strength of the hardened concrete decreased when the admixture mixing rate increased. In addition, the compressive strength of specimens tended to improve as all the CaO contents of the admixture types increased. When the durability properties were examined, it was found that the relative dynamic elasticity modulus and carbonation depth decreased, and the chloride penetration depth increased as the CaO content increased for both GGBFS and FA. The weight loss rate, however, remained similar. Based on the results of this study, the optimal CaO content that achieved satisfactory engineering and durability properties was found to be between 39% and 48% for FA. The results of this study will be able to offer guidelines for the mixture rates of FA when mixing durable concrete for use in the field. Additionally, these results are expected to be utilized as a basis for determining instructions relating to chemical composition in order to develop binders with improved durability.  
durability properties; ordinary Portland cement (OPC); ground-granulated blast-furnace slag (GGBFS); fly ash (FA) +
Footnote †: journal: Applied Sciences
# MADDPG-Based Offloading Strategy for Timing-Dependent Tasks in Edge Computing
## 4 User-Prediction-Based Timing-Dependent Task Offloading Algorithm
### Timing-Dependent Task Offloading Algorithm
\(RL\) is a preprocessed task-scheduling sequence, in which the correct ordering among the tasks guarantees the success rate of the agent's task offloading. \(D_{j}\) denotes the size of the data of the current computational task \(j\) and the size of its return data. **Action**: Use \(a_{t}\) to represent actions and define action sets as agents that issue service requests globally, as well as optional task-offloading locations, including local UE and MEC servers. Evaluate the effectiveness of different offloading strategies by calculating the overall task offloading delay and learn the optimal action plan to minimize the total offloading delay while maximizing the resource utilization of global nodes. **Reward**: A reward function is a mechanism for measuring behavioral performance in a given environment. The agent uses the immediate reward value to evaluate the effectiveness of its actions, thereby prompting it to learn the optimal task-offloading strategy. This paper considers the comprehensive impact of the time overhead of task offloading and the resource utilization efficiency in the process to define the reward \(r\). The agents use the reward values from the previous step to evaluate the effectiveness of their actions, and after weighing the summed benefits of the current task offloading latency and server resource utilization, the offloading strategy with the optimal value of the summed benefits is used as the learning objective to train all the agents' network parameters. The specific expressions of the reward function and resource utilization as shown in Equations (18) and (19), respectively:  
\[r(j,k)=w_{1}*T^{sum\_inv}_{d,j}+w_{2}*u^{util}_{j,k}\,w_{1}+w_{2}=1\,, \tag{18}\]  
\[\alpha^{util}_{j,k}=\frac{\alpha^{util}_{j}}{\alpha^{util}_{k}}\,, \tag{19}\]  
where \(w_{1}\), \(w_{2}\) denotes the weights in the definition of the reward function. \(T^{sum\_inv}_{d,j}\) denotes the reciprocal of the processing delay of the \(j\)th task of the \(d\)th application. If a task is offloaded to one of the edge nodes, the offloading process includes transmission latency, execution latency, and result return latency. In the case of local task processing, only the local execution delay is considered. In order to allocate enough space for computing resources to the remaining tasks, the reward function aims to guide the agents to prioritize the offloading of tasks to nodes with less available resources.
# A Computational Platform for Automatic Signal Processing for Bender Element Sensors +
## 3 Description of the GeoHyTE Platform
### Theoretical Fundamentals
#### 3.1.1 Material Model  
In this beta version, GeoHyTE offers material models based on the \(u-w\) variant of the [PERSON]'s theory of porous media [29], in which the displacements in the solid phase and the fluid seepage are the main variables. The biphasic medium is modelled as a homogeneous combination of an elastic solid phase and a Darcy-compliant fluid phase. The motion of the two phases is coupled through the constitutive laws. Both phases are assumed compressible.  
[PERSON]'s mathematical model is chosen due to its effectiveness in modelling the transient wave propagation through dry sands [14], as is the case of the International Parallel Test benchmark. Also, note that the biphasic formulation can be used to model both dry and saturated geomaterials by simply specifying distinct properties for the fluid phase.  
The mathematical model assumes that the medium is piece-wise isotropic and homogeneous. This means that different finite elements may have distinct mechanical properties, but they must be constant within each element. The displacements and strains are assumed small and the material is linear elastic. The flow of the fluid through the pores is laminar, meaning that it complies with [PERSON]'s law. Although soils typically exhibit non-linear behaviour, physical and geometrical linearity assumptions are adequate for bender element experiments, which take place at very small strains.  
The beta version of GeoHyTE only accommodates two-dimensional models under plane strain conditions. Although the vibration of the bender element does occur in a plane, the propagation of the waves is a complex phenomenon of a three-dimensional nature. Therefore, a plane strain model may fail to consider the complex interaction between the propagating wave and the container, especially after the occurrence of multiple reflections. However, according to the authors' experience [14], plane strain models are a good trade-off between the need for accuracy and the need for computational efficiency.  
Another GeoHyTE-specific limitation is that the initial conditions (displacement, velocity, acceleration) are implicitly set to zero. In hybrid-Trefftz finite elements, non-null initial conditions cause the governing differential equations in the domain to become non-homogeneous. The effect of the source terms is typically accounted for by the Dual Reciprocity Method, but it comes at a higher computational price. Since non-null initial conditions are not of interest in the modelling of bender element experiments, only trivial initial conditions are accommodated.
###### Abstract  
In this paper, we present a novel passive dual-tuned magnetic metasurface, which can enhance the field distribution produced by a closely placed radio-frequency coil for both \({}^{1}\)H and \({}^{23}\)Na 1.5 T MRI imaging. In particular, the proposed solution comprises a \(5\times 5\) capacitively loaded array, in which each unit-cell is composed of two concentric spiral coils. Specifically, the unit-cell internal spiral coil operates at the proton Larmor frequency (64 MHz), whereas the external is at the sodium one (17 MHz). Therefore, the paper aims to demonstrate the possibility of enhancing the magnetic field distribution in transmission and reception for 1.5 T MRI scanners by using the same metasurface configuration for imaging both nuclei, thus drastically simplifying the required instrumentation. We first describe the theoretical model used to design and synthetize the dual-tuned magnetic metasurface. Next, full-wave simulations are carried out to validate the approach. Finally, we report the experimental results acquired by testing the fabricated prototype at the workbench, observing a good agreement with the theoretical design and the numerical simulations. In particular, the metasurface increases the transmission efficiency \(T_{x}\) in presence of a biological phantom by a factor 3.5 at 17 MHz and by a factor 5 at 64 MHz, respectively. The proposed solution can pave the way for MRI multi-nuclei diagnostic technique with better images quality, simultaneously reducing the scanning time, the invasiveness on the patient and the overall costs.  
magnetic metasurface; magnetic resonance imaging; multi-nuclei imaging; signal-to-noise; transmission efficiency Article
## 3 Results  
The computations were carried out for the Reynolds number \(\text{Re}=U_{0}D/\
u=5000\) for which the jet dynamics significantly depends both on the variation of the Reynolds number and the velocity parameters at the nozzle exit [23]. The momentum thickness of the velocity profile \(\theta=\int_{0}^{\infty}U/U_{0}(1-U/U_{0})\text{d}r\) was equal to \(\theta=D/40\), whereas the shape factors (\(H\)), computed as \(H=\delta/\theta\) (\(\delta=\int_{0}^{\infty}(1-U/U_{0})\text{d}r\)--the displacement thickness), was equal to \(H=1.38\), which indicates the velocity profile typical for a turbulent flow. The turbulence intensity was assumed at the levels \(Ti=u_{x}/U_{0}=0.01\%,0.1\%\) and \(1.0\%\) (\(u_{x}\)--RMS of the axial velocity fluctuation). The following analysis is divided into two parts:  
1. Non-excited jets, where the influence of the coordinate system (Cartesian vs. cylindrical) on an evolution of the natural free jet and analysis of how it changes with the turbulence intensity level is presented;
2. Excited jets, where an attempt was made to explain and demonstrate the mechanism of side-jet formation and to show differences in their occurrence when the jets are modelled applying the Cartesian and cylindrical coordinate systems at different turbulence intensity levels.  
In all analysed cases, the simulations began from a quiescent flow in the domain. The jet and co-flowing stream started flowing impulsively and freely evolved in space. After an initial transient time (\(t=100D/U_{0}\)), the flow was fully developed, and the time-averaging procedure was turned on. It lasted for \(t=300D/U_{0}\), after which the obtained  
Figure 2: Computational meshes: Cartesian (**a**) and cylindrical (**b**).  
time-averaged solutions were statistically steady, and further computations practically did not change them. To make the presentation of the results and their discussion clear, the particular cases are denoted as: \(E/NE-Car/Cyl-Ti_{Ti}\), where \(E\) means excited jets, \(NE\) stands for non-excited jets, and the abbreviations \(Car\) and \(Cyl\) represent Cartesian and cylindrical coordinate systems, respectively. For example, the case \(E-Car-Ti_{0.01}\) refers to an excited jet with a turbulence level \(Ti=0.01\%\) predicted on the Cartesian mesh.
# Evaluation of Forward Models for GNSS Radio Occultation Data Processing and Assimilation
### FM Algorithm in Data Assimilation and RO Data Processing  
(1) FM in RO data assimilation. In terms of the RO data assimilation, two options, the bending angle (BA) or refractivity, are used for variational assimilation [15; 16]. The option of forward modeled BA is convenient and concise. During assimilation, atmospheric parameters are firstly transformed to refractivity (\(N\))  
\[N=77.6\frac{p}{T}+3.73\times 10^{5}\frac{e}{T^{2}} \tag{1}\]  
where \(T\) is temperature, \(e\) is water vapor partial pressure, and \(p\) is pressure. Then the refractivity is inverted to BA (\(\alpha\)) by the Abel integral, a core part of FM  
\[\alpha(a)=-2a\int_{a}^{\infty}\frac{d\ln(n)}{dx}\frac{dx}{\sqrt{x^{2}-a^{2}}} \tag{2}\]  
where \(a\) is impact parameter, refractive index \(n=10^{-6}N+1\). Hence, the accuracy of BA is strongly affected by n and the FM. This BA is then assimilated into the NWP data assimilation system. Therefore, the FM is critical for RO data assimilation.  
(2) FM in RO data processing. The FM is employed to correct the ionospheric error to BA during RO data processing by the method of statistical optimization. The ionosphere frequently interferes with GPS signals [17]. There are several approaches for ionospheric calibration: the linear combination of two frequencies corrects the first order; the K-correction corrects the higher-order [18]; the statistical optimization corrects all the ionospheric error [19]. The last one is based on background climatological models such as MSIS-90 (mass spectrometer and incoherent scatter radar in 1990) [20], BAROCLIM (the bending angle radio occultation climatology) based on Formosat-3/COSMIC data [21], and CIRA (the 1986 COSPAR International Reference Atmosphere) [21]. Most data in these background climatological models are stored as refractivity. Therefore, we need to invert them to BA via FM. Therefore, the accuracy of the FM is important.  
In another aspect, the RO data are also used in commercial companies or civilian industries, wherein they might consider using some analysis data sets to assimilate RO data in their assimilation systems or develop their own RO data processing program. Generally, widely used and free analysis data sets are considered. However, some of those data sets have limited vertical and horizontal resolution. Therefore, how many biases the forward modeling results contain is open to debate. The biases are generated by not only forward models but also the level resolution of the analysis data. Therefore, the level resolution of the original data should also be under consideration for evaluating the error of FMs.
## 2 Materials and Methods
### Statistical Analysis  
The qualitative analysis of VOCs was carried out using MS combined with the retention index. The NIST 14 database was used for MS to identify unknown compounds. The compound's retention index (RI) was determined by measuring the retention time of C7-C40 n-alkanes. RI calculation is shown in Equation (1). The internal standard method was used for quantitative analysis of VOCs. One-way ANOVA (\(p<\) 0.05) was performed using SAS 9.2. Principal component analysis (PCA) and orthogonal partial least squares-discriminant analysis (OPLS-DA) were performed using SIMCA 14 software, PCA analysis was performed to select the principal components that could explain 80% of the total variance, and the input matrix was not automatically scaled. Origin 2018. [[https://www.omicstudio.cn/tool](https://www.omicstudio.cn/tool)]([https://www.omicstudio.cn/tool](https://www.omicstudio.cn/tool)) (accessed on 29 December 2022) was used for the Spearman correlation analysis.  
\[\text{RI}=100\text{Z}+\frac{100\times[\text{TR}_{\text{x}}-\text{TR}_{\text{Z} }]}{\text{TR}_{\text{Z+1}}-\text{TR}_{\text{Z}}} \tag{1}\]  
where TR is the retention time, X is the compound to be analyzed, and Z and Z + 1 are the number of carbon atoms of the two n-alkanes before and after the compound to be analyzed, i.e., \(\text{TR}_{\text{Z}}<\text{TR}_{\text{X}}<\text{TR}_{\text{Z+1}}\).
# Removal of Metal Ions in Spin-on Hardmask Using Functionalized Porous Silica Adsorbents
## 2 Experimental
### Preparation of Metal Ion Solutions  
To prepare the metal ion solutions used in the adsorption experiments, three different solution systems were prepared: a solvent-only solution, a monomer-dispersed solution, and a polymer-dispersed solution. In all cases, the final total metal ion concentration was adjusted to 100 ppm.  
For the solvent-only system, a stock solution was prepared by dissolving Al(NO\({}_{3}\))\({}_{3}\): 9H\({}_{2}\)O (183.53 mg), Cr(NO\({}_{3}\))\({}_{3}\cdot\)9H\({}_{2}\)O (101.57 mg), Cu(NO\({}_{3}\))\({}_{2}\cdot\)3H\({}_{2}\)O (50.18 mg), Fe(NO\({}_{3}\))\({}_{3}\cdot\)9H\({}_{2}\)O (95.48 mg), Ni(NO\({}_{3}\))\({}_{2}\cdot\)6H\({}_{2}\)O (65.40 mg), and TiCl\({}_{4}\) solution (275.75 \(\mu\)L, 1 M) in 10 mL of methanol. This stock solution, corresponding to a 10 wt% metal ion concentration, was diluted 100-fold with methanol to yield a 100 ppm working solution.  
For the monomer-dispersed system, phenol (186.92 mL) and formaldehyde (181.92 mL) were mixed with methanol (749.47 mL) at a mass ratio of 1:1:3. The same amount of metal salts used in the solvent-only system was dissolved in 10 mL of this monomer mixture to prepare a stock solution containing 10 wt% total metal ions. Thisstock solution was then diluted 100-fold with the same monomer mixture to obtain the final solution at 100 ppm.  
For the polymer-dispersed system, novolac resin (112.47 mL) and PGMEA (528.50 mL) were mixed with cyclohexanone (359.03 mL) to form a solution with a mass ratio of 15:51:34. Due to the poor metal salt solubility in the polymer solution, a stock solution with a metal ion concentration 20 times lower than that of the other stock solutions was prepared and subsequently diluted 5-fold with the same polymer mixture to yield a final total metal ion concentration of 100 ppm.
# A Review of Geometry, Construction and Modelling for Carbon Nanotori
## 3 Lennard-Jones Potential and Continuum Approximation
### Interaction Energy of Offset Molecule and Torus  
To calculate the interaction energy between an offset atom inside a carbon nanotorus, the atom is assumed to be located inside the nanotorus at a distance \(\mu\) from the cross-sectional centre of the torus as illustrated in Figure 11. Therefore, this point has Cartesian coordinates  
\[(x,y,z)=\big{(}(R+r\cos\phi_{1})\cos\theta_{1},(R+r\cos\phi_{1})\sin\theta_{1}, r\sin\phi_{1}\big{)},\]  
and the torus is parameterised by the toroidal coordinated defined in (7), so the distance between the point and an arbitrary point on the toroidal surface is  
\[\rho^{2}=(r-\mu)^{2}+4(R+r\cos\phi)(R+\mu\cos\phi_{1})\sin^{2}[(\theta-\theta_ {1})/2]+4r\mu\sin^{2}[(\phi-\phi_{1})/2].\]  
Substituting into (3) and (2) results in the interaction energy between an offset atom and a torus, denoted by \(E^{\text{(tp)}}\), which is expressible as  
\[E^{\text{(tp)}} = \frac{3\eta_{t}\pi^{2}rR^{1/2}}{4(R+\mu)^{1/2}}\left[-\frac{A}{(r^ {2}-\mu^{2})^{5/2}}P_{3/2}\left(\frac{r^{2}+\mu^{2}}{r^{2}-\mu^{2}}\right)\right. \tag{16}\] \[\left.+\frac{21B}{32(r^{2}-\mu^{2})^{11/2}}P_{9/2}\left(\frac{r^{ 2}+\mu^{2}}{r^{2}-\mu^{2}}\right)\right].\]  
For the interaction energy between a torus and an offset fullerene of radius \(a\) and offset distance \(\mu\) from the cross-sectional centre of the torus as shown in Figure 12. Such an interaction can be evaluated using the same technique as previously described. Finally, the interaction energy of an offset and a torus, denoted by \(E^{\text{(ft)}}\), is derived as  
\[E^{\text{(ft)}} = 256\eta_{t}\eta_{t}\pi^{3}arR\left[-\frac{5 Aa^{3}R^{3}(R+\mu)^{3} }{2[4 Rx(R+\mu)+\kappa^{2}]^{2/2}}F_{1}\left(1/2;7/2,7/2;1;\alpha,\beta\right)\right. \tag{17}\] \[+\left.\frac{155584 Ba^{9}R^{9}(R+\mu)^{9}}{[4 Rx(R+\mu)+\kappa^{2} ]^{19/2}}F_{1}\left(1/2;19/2,19/2;1;\alpha,\beta\right)\right],\]  
where \(\kappa=(r+\mu)^{2}-a^{2},\alpha=4r\mu/\kappa,\beta=4r\mu/\big{[}4R(R+\mu+ \kappa)\big{]}\), \(\eta_{t}\) and \(\eta_{t}\) are the mean atomic densities for the fullerene and the torus, \(F_{1}(a;b,b_{1};c;x,y)\) is the Appell hypergeometric function of the first kind and the full derivation of (17) is detailed in [46].  
Figure 11: Schematic showing offset atom within nanotorus.