esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Finite Element Analysis of Knee Integration Model
### Material Properties and Boundary and Load Condition
These included binding relationships between the cartilage and bone, as well as between each ligament's origin and bone, and the meniscus's origin and bone [26; 36; 43]. Meniscus and cartilage interfaces, along with the femoral and tibial cartilage, were treated as frictionless limited-slip contacts, reflecting the presence of synovial fluid in the joint cavity and the low friction typically observed in such structures. [11; 44]. The upper surface of the femur was coupled into a single point to streamline the analysis, while the distal tibia and fibula were fully constrained. The femur was constrained only during flexion activities, allowing for the accurate simulation of the relative positions of the femur and tibia in an extended position. Prior to the simulation, the knee joint was preset in a neutral condition, establishing a baseline for the placement and orientation of the knee model. A brief analysis step at the beginning of the simulation adjusted the angles between the femoral axis in the sagittal plane, the tibial axis, and the longitudinal axis of the foot to determine the knee joint angle [11; 45]. Kinetic data corresponding to three different foot progression angles were then applied to the three adjusted models (see Figure 3A, Table 2). Participants successfully completed seven trials for each of the three scenarios. The kinematic and muscle force data corresponding to the peak ground reaction forces were averaged across trials for each scenario and subsequently used as loading conditions in the finite element model (Table 2). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Component** & **Elastic Modules (MPa): E** & **Poisson’s Ratio: v** & **Destiny (kg/m3)** & **Ref.** \\ \hline Skin & \begin{tabular}{c} Hyperelastic (first-order Ogden model, \\ \(\mu=0.122\) kPa, \(\alpha=18\)) \\ \end{tabular} & N/A & 950 & [39] \\ \hline Bulk soft tissue & \begin{tabular}{c} Hyperelastic (second-order polynomial strain, \\ C10 = 0.8556, C01 = 0.05841, C20 = 0.03900, \\ C11 = 0.02319, C02 = 0.00851, DI = 3.65273) \\ \end{tabular} & N/A & 950 & [24] \\ \hline Anterior cruciate ligament & \
\begin{tabular}{c} Hyperelastic (first-order polynomial strain, \\ C1 = 1.95, D = 0.00683) \\ \end{tabular} & N/A & 1000 & [40] \\ \hline Posterior cruciate ligament &
\begin{tabular}{c} Hyperelastic (first-order polynomial strain, \\ C1 = 3.25, D = 0.0041) \\ \end{tabular} & N/A & 1000 & [40] \\ \hline Fibula, tibia, femur, and patella & 14,220 & 0.3 & 1990 & [22] \\ \hline Cartilage & 20 & 0.46 & 1000 & [24] \\ \hline Medial and lateral collateral & 467 & 0.46 & 1000 & [41] \\ ligament & 59 & 0.49 & 2000 & [42] \\ \hline Meniscus & 59 & 0.49 & 2000 & [42] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material parameters for each structure.
## 2 Mathematical Formulation
On inverting Fourier transform over \(\beta^{{}^{\prime}}\) for Equation (25), we obtain  
\[\frac{\partial^{2}\varphi_{t}}{\partial x^{\prime 2}}+\frac{\partial^{2} \varphi_{t}}{\partial y^{\prime 2}}-\frac{1}{c^{*2}}\frac{\partial^{2} \varphi_{t}}{\partial t^{2}}=\delta^{*}(x^{{}^{\prime}}-x_{0}^{{}^{\prime}}) \delta^{*}(y^{{}^{\prime}}-y_{0}^{{}^{\prime}})e^{-i\omega_{1}^{{}^{\prime}}t ^{{}^{\prime}}}, \tag{3}\]2  
Letting  
\[\frac{\partial^{2}\varphi_{t}}{\partial x^{\prime 2}}+\frac{\partial^{2} \varphi_{t}}{\partial y^{\prime 2}}-\frac{1}{c^{*2}}\frac{\partial^{2} \varphi_{t}}{\partial t^{2}}=\delta^{*}(x^{{}^{\prime}}-x_{0}^{{}^{\prime}}) \delta^{*}(y^{{}^{\prime}}-y_{0}^{{}^{\prime}})e^{-i\omega_{1}^{{}^{\prime}}t ^{{}^{\prime}}}, \tag{3}\]3  
\[\frac{\partial^{2}\varphi_{t}}{\partial x^{\prime 2}}+\frac{\partial^{2} \varphi_{t}}{\partial y^{\prime 2}}-\frac{1}{c^{*2}}\frac{\partial^{2} \varphi_{t}}{\partial t^{2}}=\delta^{*}(x^{{}^{\prime}}-x_{0}^{{}^{\prime}}) \delta^{*}(y^{{}^{\prime}}-y_{0}^{{}^{\prime}})e^{-i\omega_{1}^{{}^{\prime}}t ^{{}^{\prime}}}, \tag{3}\]4  
in Equation (26) we arrive at  
\[\frac{\partial^{2}\varphi_{t}}{\partial x^{\prime 2}}+\frac{\partial^{2} \varphi_{t}}{\partial y^{\prime 2}}-\frac{1}{c^{*2}}\frac{\partial^{2} \varphi_{t}}{\partial t^{2}}=\delta^{*}(x^{{}^{\prime}}-x_{0}^{{}^{\prime}}) \delta^{*}(y^{{}^{\prime}}-y_{0}^{{}^{\prime}})e^{-i\omega_{1}^{{}^{\prime}}t ^{{}^{\prime}}}, \tag{3}\]5  
The above expression (28), after substituting \(x^{{}^{\prime}}_{0}=r_{0}\cos\vartheta_{0}\), \(y^{{}^{\prime}}_{0}=r_{0}\sin\vartheta_{0}\) and for large value of \(r_{0}\) simplifies as  
\[\frac{\partial^{2}\varphi_{t}}{\partial x^{\prime 2}}+\frac{\partial^{2} \varphi_{t}}{\partial y^{\prime 2}}-\frac{1}{c^{*2}}\frac{\partial^{2} \varphi_{t}}{\partial t^{2}}=\delta^{*}(x^{{}^{\prime}}-x_{0}^{{}^{\prime}}) \delta^{*}(y^{{}^{\prime}}-y_{0}^{{}^{\prime}})e^{-i\omega_{1}^{{}^{\prime}}t ^{{}^{\prime}}}, \tag{3}\]6  
with  
\[\frac{\partial^{2}\varphi_{t}}{\partial x^{\prime 2}}+\frac{\partial^{2} \varphi_{t}}{\partial y^{\prime 2}}-\frac{1}{c^{*2}}\frac{\partial^{2} \varphi_{t}}{\partial t^{2}}=\delta^{*}(x^{{}^{\prime}}-x_{0}^{{}^{\prime}}) \delta^{*}(y^{{}^{\prime}}-y_{0}^{{}^{\prime}})e^{-i\omega_{1}^{{}^{\prime}}t ^{{}^{\prime}}}, \tag{3}\]7  
The solution of Equation (21) fulfilling radiation conditions and after utilizing Equations (22)-(24), may be written as  
\[\varkappa(\beta^{{}^{\prime}},y^{{}^{\prime}},\omega^{{}^{\prime}})=\left\{ \begin{array}{cc}A_{1}(\beta^{{}^{\prime}},\omega^{{}^{\prime}})e^{-\gamma y ^{{}^{\prime}}}&y^{{}^{\prime}}\geq 0,\\ -A_{1}(\beta^{{}^{\prime}},\omega^{{}^{\prime}})e^{\gamma y^{{}^{\prime}}}&y^{{}^ {\prime}}\leq 0.\end{array} \right.
## 4 HPS-Based Catalysts for the Synthesis and Transformation of Platform Chemicals
### Hydrolytic Oxidation of Cellobiose to Glucaric Acid
The maximum yield of gluconic acid was observed after 1 h of reaction while the maximum yield of glucaric acid was after 2 h.  
In the process of the conditions optimization for the hydrolytic oxidation of cellobiose, the obtained qualitative and quantitative results were analyzed and allowed to propose  
Figure 7: TEM images of catalysts (**a**) 3% Pt/MN270; (**b**) 3% Pd/MN270; (**c**) 3% Au/MN270; (**d**) 3% Ru/MN270 [170]. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multirow{2}{*}{**Catalyst**} & \multirow{2}{*}{\begin{tabular}{c} **Cellobiose** \\ **Conversion, \%** \\ \end{tabular} } & \multicolumn{6}{c}{**Product Selectivity, \%**} \\ \cline{3-7}  & & **Glucose** & \
\begin{tabular}{c} **Cellobionic** \\ **Acid** \\ \end{tabular} & \multirow{2}{*}{**Gluconic Acid**} & \multirow{2}{*}{**Glucaric Acid**} & \multirow{2}{*}{
\begin{tabular}{c} **\Sigma of** \\ **Byrproducts** \\ \end{tabular} } \\ \hline
3\% Pt/MN270 & 100 & 4.1 & 9.4 & 16.1 & 41.5 & 28.9 \\
3\% Au/MN270 & 86.2 & 24.6 & 50.1 & 12.3 & 0 & 13.0 \\
3\% Pd/MN270 & 53.3 & 24.2 & 40.0 & 2.8 & 0 & 33 \\
3\% Ru/MN270 & 45.4 & 26.4 & 0 & 0 & 0 & 73.6 \\ blank (without catalyst) & 9.5 & 14.7 & 0 & 0 & 0 & 85.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Cellobiose conversion and selectivity to the main reaction products for the catalyst with different active phase. reaction scheme for the conversion of cellobiose into gluconic and glucaric acids in the presence of 3% Pt/MN270 (Figure 8). The study showed that with quadruple use of 3% Pt/MN270, the yields of gluconic and glucaric acids gradually decreased by 5.5 and 11.0%, respectively, which is likely due to the gradual degradation of the HPS polymer as a result of oxidation, as evidenced by the deterioration of porous properties (Table 10). At the same time, TEM results showed that the average size of Pt particles on the used catalyst remained almost unchanged, at 2.9 nm. The results obtained are promising for a technology of the catalytic conversion of plant polysaccharides, primarily cellulose, into aldonic and aldaric acids, which are high value products widely used in the chemical, food, pharmaceutical, and other industries.
## 3 Background
### Counterfactual Baseline  
Firstly, COMA employs a centralized critic. It is important to note that in independent actor-critic (IAC) setups, each actor \(\pi(u^{a}|\tau^{a})\) and each critic \(Q(\tau^{a},u^{a})\) or \(V(\tau^{a})\) conditions solely on the agent's own action-observation history \(\tau^{a}\). However, during learning, only critics are used, while actors are needed solely during execution. Due to the centralized nature of learning, a centralized critic can be assumed to condition on the real global state \(s\) (if available) or the joint action-observation history \(\tau\). Each actor conditions on its own action-observation history \(\tau^{a}\), employing parameter sharing.  
COMA utilizes counterfactual baselines, inspired by the concept of a differential reward ([PERSON] et al., 2019), which is a shaped reward \(D^{a}=r(s,u)-r(s,(u^{-a},c^{a}))\). The global reward is compared with the reward obtained when agent \(a\)'s action is replaced with a default action \(c^{a}\). Any improvement \(D^{a}\) in \(a\)'s action also enhances the actual global reward \(r(s,\mathbf{u})\), as \(r(s,(u^{-a},c^{a}))\) is independent of \(a\)'s actions.  
A key aspect of COMA is that it leverages a centralized critic to implement differential rewards, thus circumventing these issues. COMA learns a centralized critic \(Q(s,\mathbf{u})\), which estimates the \(Q\)-values of joint actions \(\mathbf{u}\) given a central state \(s\). For each agent \(a\), an advantage function can be computed by comparing the \(Q\)-value of the current action \(u^{a}\) with a counterfactual baseline that marginalizes out \(u^{a}\) while keeping the actions of other agents \(u^{-a}\) constant:  
\[A^{a}(s,\mathbf{u})=Q(s,\mathbf{u})-\sum_{u^{a}}\pi^{a}\big{(}u^{a}|\tau^{a} \big{)}Q\big{(}s,\big{(}\mathbf{u}^{-a}.u^{a}\big{)}\big{)} \tag{1}\]where \(A^{a}(s,u^{a})\) is a separate baseline for each agent, utilizing the centralized critic to infer counterfactuals where only the actions of agent \(a\) change. This inference is learned directly from the agent's experience, avoiding the need for additional simulations, reward models, or user-designed default actions.
# Fog Computing for Smart Cities' Big Data Management and Analytics: A Review
## 3 Service Delivery Models in Fog Computing
### Platform as a Service (PaaS)  
The platform as a service (PaaS) delivery model in fog computing is similar to the PaaS delivery model in cloud computing. It makes it easy to deploy customer created or acquired applications to federated fog nodes that form a cluster without incurring the cost and complexity of purchasing and managing the underlying fog infrastructure, which includes network, servers, operating systems, and storage hardware. The PasS service provider provides all the facilities, such as programming languages, libraries, and tools, necessary to support the full lifecycle of building and delivering applications and services. The PaaS customer has control over the deployed applications and configuration settings of the hosting environment. The PaaS solution of Hivecell [20] is an example of PaaS for edge and fog computing, allowing users to install rich distributed frameworks on a cluster of Hivecell devices very quickly with the click of a button. Hivecell's solution provides support for machine learning at the edge. It supports several distributed frameworks and machine learning solutions such as Kafka [21; 22], Kubernetes [23], and Tensorflow [24]. Each Hivecell device has a 256-core Compute Unified Device Architecture (CUDA) Graphical Processing Unit (GPU), which provides the necessary resources for training and testing models where needed.
## 2 Materials and Methods
### Investigation of the Nature of the Antimicrobial Compounds
#### 2.4.1 Synthesis of Organic Acids and Their Contribution to Antimicrobial Activity  
Organic Acids Concentration by HPLC  
The concentrations of lactic acid and acetic acid in the samples were quantified using the e2695 high-performance liquid chromatography (HPLC) system (Waters Alliance, Framingham, MA, USA), which was equipped with an Aminex Column HPX-87H 300 \(\times\) 7.8 mm (BIO RAD, Berkley, MI, USA) along with its precolumn Micro-Guard Cation H refill cartridges, 30 \(\times\) 4.6 m (BIO RAD). The run time was 30 min per sample with an injected volume of 10 \(\mu\)L. The mobile phase used was 0.005 M H\({}_{2}\)SO\({}_{4}\) at a flow rate of 0.6 mL per min. The retention times were 12.564 min for lactic acid and 14.783 min for acetic acid. Detection was carried out using the visible ultraviolet detector PDA 210 nm (2996) (Waters Alliance), following the internal standard method.  
In the case of phenylactic acid, its concentration was specifically determined using the method outlined by [PERSON] et al. [32]. The HPLC system employed remained consistent with the previously mentioned e2695 system (Waters Alliance), while the chromatographic column used was CORTECS C18 2.7 micron (100 \(\times\) 4.6 mm) (Waters Alliance). The retention time was 6.20-6.40 min.  
Two measurements of each acid concentration were performed on the same day.  
Antimicrobial Activity of the Cell-Free Supernatants at Different pHs  
To indicate whether the antimicrobial activity was attributable to the presence of organic acids, the pH of the CFS samples was acidified (pH 3.50) and neutralized (pH 7.00), being lower or higher than the pKa of the different expected acids, respectively (pA of lactic acid at 3.80; pKa of phenylacetic acid at 4.30; and pKa of acetic acid at 4.76). pH adjustments were achieved through the addition of 1 M NaOH or 1 M HCl [33; 34]. The antimicrobial activity of the pH-modified CFS against the indicator micro-organisms was determined by the agar well diffusion assay described above, using the untreated CFS as a reference.  
If the halo disappeared when neutralizing the CFS, it suggested that the antimicrobial activity was attributed to the organic acids produced by the bacteria. In contrast, if no significant differences were observed (\(p>0.05\)), it indicated that the antimicrobial activity of the CFS remained consistent across different pH levels. This suggested that the antimicrobial activity primarily stemmed from the production of a compound other than organic acids [35].
## 3 Mode Analysis of Beat Wave Pattern
### Analysis of Propagation Characteristics of Leaky Wave  
When it comes to the leaky wave, it is unreasonable to neglect the fields in the corners. Some simplification is needed for obtaining the propagation constant because the consideration of the corner fields makes the number of unknowns larger than those of the equations. From Equation (13), we have  
\[k_{x3}^{2}+k_{y3}^{2}+\beta_{l}^{2}=k_{0}^{2}=\omega^{2}\mu_{0}\varepsilon_{0} \tag{18}\]  
where \(\beta_{l}\) is the longitudinal component of the propagation constant of the leaky wave. The fields grow exponentially as the distance from the center increases. In the corner regions, the fields grow in both \(x\) and \(y\) directions; however, in the third region in Figure 6, illustrated as \(\varepsilon_{3}\), the fields vary slowly in the \(y\) direction because the symmetry in angular direction is approximately satisfied when the distance from the center becomes larger than \(\lambda\). As a result, we have  
\[|k_{y3}|\ <<k_{0} \tag{19}\]  
In the third region, the component of the wave number in the y direction is negligible. Combining Equations (13), (17) and (18) for \(i=1\), the longitudinal wave number of the leaky mode can be solved neglecting the contributions of \(k_{y3}\) and \(k_{y1}\).  
The real parts of the longitudinal phase constants are solved and compared with the simulated results as shown in Table 2. The edge length a is set to be 14.4 mm. The obtained longitudinal phase constants are close to the wave numbers in vacuum at the frequencies in consideration. The relative error is \(\sim\)5%.  
The imaginary parts can hardly match the simulation results because (i) they cannot be accurately solved by Eigenmode Solver due to the limited calculation region [22] and (ii) the theoretical ones are also inaccurate due to the assumptions made in Section 3.3. The comparison between the simulated and calculated transverse field distributions is shown in Figure 8.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Frequency** & **Theoretical Value** & **Simulation Result** & **Relative Error** \\ **(GHz)** & **(rad/m)** & **(rad/m)** & **(\%)** \\ \hline
10 & 326.7 & 352.9 & \(-\)7.42 \\
10.2 & 338.6 & 363.0 & \(-\)6.71 \\
10.4 & 350.9 & 372.9 & \(-\)5.90 \\
10.6 & 360.8 & 382.7 & \(-\)5.74 \\
10.8 & 375.0 & 392.9 & \(-\)4.55 \\
11 & 387.0 & 403.2 & \(-\)4.00 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Theoretical and simulated real parts of longitudinal phase constants for guide mode.  
Figure 7: Field distribution of the lowest guided mode in cross-plane (**a**) field distribution from CST simulation (**b**) simulated and calculated field strengths along x axis.
# Theory of AdaDelSPGD Algorithm in Fiber Laser-Phased Array Multiplex Communication Systems
## 4 Conclusions  
In this paper, the AdaDelSPGD algorithm is proposed, which contains an adaptive gain adjustment coefficient to accelerate convergence. Firstly, the working principle of the phased array system based on the AdaDelSPGD algorithm is analyzed. The simulation results show that the AdaDelSPGD algorithm can significantly improve the convergence speed compared with the traditional SPGD algorithm.  
Based on the fiber laser-phased array communication system, the beam quality under different communication frequencies is analyzed. It is found that the quality of the beam is reduced by communication, and the higher the communication frequency, the lower the quality of beam. Secondly, by comparing the traditional SPGD algorithm and the AdaDelSPGD algorithm, it is proven that the AdaDelSPGD algorithm has a better effect. When three-channel 500 M communication is used, the contrast is improved by 25.9% and the main lobe energy concentration is improved by 15.9%. Finally, the optical power value and bit error rate are measured before and after the application of the AdaDelSPGD algorithm in different environments. The experimental results show that, after the algorithm is implemented, the optical power value is increased by more than 30%. When the communication distance is 20 m, the bit error rate of the system is reduced from 5.83 \(\times\) 10\({}^{-9}\) to 4.35 \(\times\) 10\({}^{-9}\) after phase locking by the AdaDelSPGD algorithm. When the communication distance is 3 km, the bit error rate of the system is reduced from 7.46 \(\times\) 10\({}^{-6}\) to 5.90 \(\times\) 10\({}^{-6}\) after phase locking by the AdaDelSPGD algorithm.  
Conceptualization, H.Y., J.L. and L.G.; methodology, H.Y., J.C. and J.L.; software, J.C.; validation, H.Y. and J.C.; formal analysis, J.C.; investigation, H.Y., J.C. and J.L.; resources, J.L.; data curation, J.C., L.H. and M.C.; writing--review and editing, J.C. and D.C.; visualization, J.C., L.H. and M.C.; supervision, H.Y., J.L. and L.G.; project administration, H.Y., J.L. and L.G.; funding acquisition, H.Y. and J.L. All authors have read and agreed to the published version of the manuscript. This research received no external funding.  
The study did not require ethical approval. This study is not applicable to humans or animals.  
Not applicable.  
The authors declare no conflict of interest.
## 2 Methods
### Calculation Method of ICMV  
CMV is defined as the amplitude of first harmonic divided by the amplitude of the measured response acceleration at the fundamental frequency [31]:  
\[CMV=C\cdot\frac{A_{1}}{A_{0}} \tag{1}\]  
where \(C\) is a constant (\(C\) = 300), \(A_{0}\) is the vertical acceleration amplitude of the drum at the fundamental frequency, and \(A_{1}\) is the drum acceleration amplitude of first harmonic.  
CCV takes the first subharmonic (i.e., 0.5 \(\Omega\)) and higher-order harmonics into account [32]:  
\[CCV=\left[\frac{A(0.5\Omega)+A(1.5\Omega)+A(2.5\Omega)+A(3\Omega)}{A(2.5\Omega) +A(3\Omega)}\right]\times 100 \tag{2}\]  
where \(A(i\Omega)\) is the vertical acceleration amplitude of the drum at \(i\)-order harmonics.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \(w_{\text{opt}}\) & \(\gamma_{\text{d}}\) & **from** & **Natural** & **Liquid** & **Plasticity** & **C\({}_{\text{u}}\)** & **C\({}_{\text{c}}\)** & **CBR** & **Soil Type** \\
**Standard** & **Standard** & **Moisture** & **Content** & **Limit** & **Index** & **C\({}_{\text{u}}\)** & **C\({}_{\text{c}}\)** & **CBR** & **Soil Type** \\
**Proctor** & **Proctor** & **Proctor** & **Content** & **Limit** & **Index** & **C\({}_{\text{u}}\)** & **C\({}_{\text{c}}\)** & **CBR** & **Soil Type** \\ \hline
10.5\% & 1.88 g/cm\({}^{3}\) & 6–14\% & 34\% & 9.8\% & 21.58 & 0.54 & 8.2 & SM \\ \hline \end{tabular}
\end{table}
Table 2: Material Properties of Subgrade.  
Figure 4: The results of (**a**) standard Proctor test, (**b**) liquid-plastic limit test and (**c**) grain size analysis.  
By applying [PERSON]'s theoretical solution to a rigid cylinder on subgrades, the relationship among the contact force, drum displacement and vibration modulus (\(E_{\text{vib}}\)) can be determined as [7; 33; 34]:  
\[E_{vib}=\frac{1-\mu^{2}}{z_{d}}\cdot\frac{F_{s}}{L}\cdot\frac{2}{\pi}\left(1.8864 +\ln\frac{L}{b}\right) \tag{3}\]  
\[b=\sqrt{\frac{16}{\pi}\cdot\frac{R(1-v^{2})}{E_{vib}}\cdot\frac{F_{s}}{L}} \tag{4}\]  
\[F_{s}=m_{d}g+m_{0}e_{0}\Omega^{2}\cos(\Omega t)-m_{d}a \tag{5}\]  
where \(F_{s}\) is the contact force between the drum and soil, \(L\) is the drum length, \(b\) is the contact width, \(z_{\text{d}}\) is the drum displacement, \(\mu\) is the Poisson ratio, \(R\) is the radius of the drum, \(m_{\text{d}}\) is the weight of drum, \(m_{0}e_{0}\) is the eccentric moment of unbalanced mass, g is gravity acceleration, \(a\) is the acceleration of the drum, \(\Omega\) is the circular vibration frequency.