esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Results
### Model Fitting
Water, a strongly polar solvent, is particularly adept at solubilizing hydrophilic phenolic compounds, including flavonoids and glycosides. Ethanol, although polar, exhibits some non-polar characteristics as well, enabling it to dissolve both hydrophilic and lipophilic phenolic compounds. The combined solubility properties of ethanol and water make their mixtures particularly efficient for the extraction of a wide spectrum of phenolic compounds from botanical sources, such as tomatoes and pumpkins. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**TPC** & \multicolumn{2}{c}{**1 Predictive Equations**} & **R2** & **R2 Adjusted** \\ \hline Tomato & \(-\)Y\({}^{-0.5}\) = \(-1.3419\) + 0.02943 ethanol + & & & \\  & 0.00969 time \(-\) 0.000317 ethanol \(\times\) & (4) & 98.51\% & 97.45\% \\  & ethanol \(-\) 0.000170 time \(\times\) time & & & \\  & 0.000107 ethanol \(\times\) time & & & \\  &  Y = \(7.47\) \(-\) 0.2195 ethanol + 0.1138 time + & & & \\ Pumpkin & 0.001166 ethanol \(\times\) ethanol \(-\) 0.002471 & (5) & 95.88\% & 92.94\% \\  & time \(\times\) time + 0.001463 ethanol \(\times\) time & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Quadratic models refer to polynomial predictive equations that are utilized to represent response surfaces of total phenolics (TPC) in tomato and pumpkin. The solubility of phenolic compounds in ethanol-water mixtures can be significantly enhanced through the manipulation of the ethanol-to-water ratio. Adjusting this ratio allows for the tuning of the solvent mixture's polarity, facilitating the selective extraction of distinct phenolic classes. Specifically, increased concentrations of ethanol preferentially extract more lipophilic phenolic compounds, whereas reduced concentrations are optimal for hydrophilic phenolics. This adaptability in solubility parameters renders ethanol-water mixtures highly effective for the extraction of phenolic compounds with diverse chemical characteristics.
## 4 Discussion
### Techniques for Measuring the Changes in the Residual Lower Limb
#### 4.1.5 Other Techniques (Contact Probes, Ultrasound, SXCT, and MRI)  
There is a low number of publications on contact probe, ultrasound, SXCT, and magnetic resonance imaging (MRI) techniques. In the contact probe technique, the residual limb volume is determined by measuring the position of the small contact probe that touches the surface of the residual limb. The position measurement of the contact probe is conducted using an instrument that is built up with a mechanical arm in which the stylus arm rotates around the residual limb [28]. Alternatively, this technique can be conducted using an electromagnetic sensor [34; 35]. For the ultrasound, SXCT, and MRI techniques, the residual limb volume is determined by constructing multiple 3D images that were captured. These techniques can construct both the internal and surface structures of the residual limb [4]. In the ultrasound technique, the image of the residual limb is captured by placing the residual limb inside a water-filled tank, and a non-contact ultrasound sensor moves around inside the tank. The captured image is used to construct the 3D image, and the residual limb volume can then be determined [42; 60]. There is only one study, conducted by [PERSON] et al. [24], that determined the residual limb volume using this ultrasound technique. Next, SXCT is the measurement technique that measures the residual limb while it is in the prosthetic socket [1], a technique which is like the bioimpedance technique. This technique has been also proven by [PERSON] et al. [29] as well as by [PERSON] et al. [37] to have less than 1.0% of volume errors. Other than that, there are only two publications that directly measured the residual limb volume using the MRI technique, namely [PERSON] et al. [41] and [PERSON] et al. [47], with one further study conducted by [PERSON] et al. [61] that did not directly involve the residual limb. In terms of the time taken to finish the scan process, the ultrasound technique takes 780 s (approx. 13 min), and the MRI technique takes 592 s (approx. 10 min), which are more time-consuming compared to the SXCT technique, which only takes 32 s [37; 58]. A technique with a long time of measuring will have a high potential of error due to subject movements.
###### Abstract  
Subtropical forests have great potential as carbon sinks; however, the relationship between net ecosystem productivity (NEP) and climate change is still unclear. This study took Zhejiang Province, a subtropical region, as an example. Based on remote sensing classification data of forest resources, the integrated terrestrial ecosystem carbon cycle (InTEC) model was used to simulate the spatiotemporal dynamics of the forest NEP in Zhejiang Province during 1985-2015 and analyze its response to meteorological factors such as temperature, precipitation, relative humidity, and radiation. Three patterns emerged: (1) The optimized InTEC model can better simulate the forest NEP in Zhejiang Province, and the correlation coefficient between the simulated NEP and observed NEP was up to 0.75. (2) From 1985 to 2015, the increase in the total NEP was rapid, with an average annual growth rate of 1.52 Tg-C-yr\({}^{-1}\). During 1985-1988, the forests in Zhejiang Province were carbon sources. After 1988, the forests turned into carbon sinks and this continued to increase. During 2000-2015, more than 97% of the forests in Zhejiang Province were carbon sinks. The total NEP reached 32.02 Tg-C-yr\({}^{-1}\), and the annual mean NEP increased to 441.91 gC-m\({}^{-2}\)-yr\({}^{-1}\). The carbon sequestration capacity of forests in the east and southwest of Zhejiang Province is higher than that in the northeast of Zhejiang Province. (3) From 2000 to 2015, there was an extremely significant correlation between forest NEP and precipitation, with a correlation coefficient of 0.85. Simultaneously, the forest NEP showed a negative correlation with temperature and radiation, with a correlation coefficient of \(-0.56\) for both, and the forest NEP was slightly negatively correlated with relative humidity. The relative contribution rates of temperature, precipitation, relative humidity, and radiation data to NEP showed that the contribution of precipitation to NEP is the largest, reaching 61%, followed by temperature and radiation at 18% and 17%, respectively. The relative contribution rate of relative humidity is the smallest at only 4%. During the period of 1985-1999, due to significant man-made disturbances, the NEP had a weak correlation with temperature, precipitation, relative humidity, and radiation. The results of this study are important for addressing climate change and illustrating the response mechanism between subtropical forest NEP and climate change.  
subtropical forest; NEP; climate change; InTEC model; meteorological factors 2019, 10, 708; doi:10.3390/f10080708
## 4 Results and Discussion  
### Rheology  
The below rheological plots illustrate consistent viscoelastic transition temperature (TR) trends among the binders (see Figures 3 and 4). It is worth noting that at low temperatures, PB shows a higher phase angle value when compared with aged samples; this indicates that PB has lower rigidity. The TR for each of the studied aged binders increased with ageing, which implies an increase in hardness. The effect of ageing on pristine bitumen shifted the TR depending on the duration of ageing; for instance, the TR values of the most-aged binders, BRTFOT-225 and BPAV, increased by approximately 25 \({}^{\circ}\)C in comparison with the neat bitumen. The phase angle, tan \(\delta\), increased with temperature, signalling a reduction in material consistency, which means that the prevalent liquid-like character is inclined with temperature [41]. In order to have a clearer image of the bitumen TR range and the structural modifications, temperature-sweep experiments were plotted in terms of the elastic modulus \(G^{\prime}\). This experiment was conducted at a frequency of 1 Hz and at a constant heating rate (1 \({}^{\circ}\)C/min). The binder's elastic modulus was observed continuously during a temperature ramp.  
Figure 4 depicts the elastic modulus \(G^{\prime}(\omega)\) against temperature for all studied samples, in the temperature range 25 to 100 \({}^{\circ}\)C. In the temperature range 25-45 \({}^{\circ}\)C, the BRTFOT-75 and BRTFOT-150 binders had overlapped \(G^{\prime}(\omega)\) values, meaning their rigidity character is similar. At elevated temperatures, however, the aged binders showed higher \(G^{\prime}(\omega)\) values depending on their degree of ageing. For instance, PB had the lowest \(G^{\prime}(\omega)\) value in correlation with its tan \(\delta\) value. After 60 \({}^{\circ}\)C for virgin bitumen and after 70 \({}^{\circ}\)C for aged binders, nonlinearity tended to appear in the trends, indicating the starting point of the TR region. When the elastic modulus is no longer detected, the transition  
Figure 3: Temperature dependence (in the range 25 to 100 \({}^{\circ}\)C) of the loss tangent for pristine (PB) and aged bitumen samples (BRTFOT-75; BRTFOT-15; BRTFOT-225 and BPAV).  
process from viscoelastic to a liquid regime can be considered complete, and this proves that the liquid-like behavior increases with temperature.  
Interestingly, the viscoelastic responses of the PAV and RTFOT binders show similar rheological behavior. This analysis should prompt thinking that the two kinds of ageing processes (RTFOT 225 and PAV) could have similar effects on the structure and self-assembling properties of the binder.
# Input Shaping Control of a Flexible Structure for Rest-to-Rest and Non-Rest-to-Rest Maneuvers
## Appendix C Trajectory Equations for Optimization  
The state equations related to \(\theta_{1}(t_{f}+\epsilon_{1}+\epsilon_{2}+\epsilon_{3})\), \(\dot{\theta}_{1}(t_{f}+\epsilon_{1}+\epsilon_{2}+\epsilon_{3})\), \(\theta_{2}(t_{f}+\epsilon_{1}+\epsilon_{2}+\epsilon_{3})\) and \(\dot{\theta}_{2}(t_{f}+\epsilon_{1}+\epsilon_{2}+\epsilon_{3})\) can be obtained using Equations (6)-(9) and using Table 2:  
\[\theta_{1}(t_{f}+\epsilon_{1}+\epsilon_{2}+\epsilon_{3}) =\theta_{1,0}^{\prime}=(2c_{3}^{4}\theta_{1,1}^{\prime}+2c_{3}^{4 }t_{0100}^{\prime}\theta_{1,1}^{\prime}-2b_{4}c_{1}u_{1}(1-A_{1}-A_{2}-A_{3}) +2c_{1}c_{3}^{2}\theta_{2,1}^{\prime}\] \[+2b_{4}c_{1}u_{1}(1-A_{1}-A_{2}-A_{3})\cos(c_{3}t_{0100}^{\prime} )-2c_{1}c_{3}\theta_{2,1}^{\prime}\sin(c_{3}t_{0100}^{\prime})+2c_{1}c_{3}^{2} t_{0100}^{\prime}\theta_{2,1}\] \[-2c_{1}c_{3}^{2}\theta_{2,1}^{\prime}\cos(c_{3}t_{0100}^{\prime} )+b_{2}c_{3}^{4}(t_{0100}^{\prime})^{2}u_{1}(1-A_{1}-A_{2}-A_{3})\] \[+b_{4}c_{1}c_{3}^{2}(t_{0100}^{\prime})^{2}u_{1}(1-A_{1}-A_{2}-A_{ 3}))/(2c_{3}^{4}) \tag{15}\] \[\dot{\theta}_{1}(t_{f}+\epsilon_{1}+\epsilon_{2}+\epsilon_{3}) =\theta_{1,0}^{\prime}=(c_{3}^{3}\dot{\theta}_{1,1}+c_{1}c_{3} \dot{\theta}_{2,1}^{\prime}+b_{4}c_{1}c_{3}t_{0100}^{\prime}u_{1}(1-A_{1}-A_{2 }-A_{3})\] \[+b_{2}c_{3}^{3}t_{0100}^{\prime}u_{1}(1-A_{1}-A_{2}-A_{3})-c_{1}c _{3}\dot{\theta}_{2,1}^{\prime}\cos(c_{3}t_{0100}^{\prime})+c_{1}c_{3}^{2} \theta_{2,1}^{\prime}\sin(c_{3}t_{0100}^{\prime})\] \[-b_{4}c_{1}u_{1}(1-A_{1}-A_{2}-A_{3})\sin(c_{3}t_{0100}^{\prime} ))/(c_{3}^{3})\] (16) \[\theta_{2}(t_{f}+\epsilon_{1}+\epsilon_{2}+\epsilon_{3}) =\theta_{2,0}^{\prime}=(c_{3}^{2}\theta_{2,1}^{\prime}\cos(c_{3}t_ {0100}^{\prime})+c_{3}\dot{\theta}_{2,1}\sin(c_{3}t_{0100}^{\prime})+b_{4}u_{1 }(1-A_{1}-A_{2}-A_{3})\] \[-b_{4}u_{1}(1-A_{1}-A_{2}-A_{3})\cos(c_{3}t_{0100}^{\prime}))/(c_{3 }^{2})\] (17) \[\dot{\theta}_{2}(t_{f}+\epsilon_{1}+\epsilon_{2}+\epsilon_{3}) =\theta_{2,0}^{\prime}=(c_{3}\dot{\theta}_{2,1}\cos(c_{3}t_{0100}^{ \prime})-c_{3}^{2}\theta_{2,1}^{\prime}\sin(c_{3}t_{0100}^{\prime})\] \[+b_{4}u_{1}(1-A_{1}-A_{2}-A_{3})\sin(c_{3}t_{0100}^{\prime}))/(c_{3 }) \tag{18}\]  
In Equations (A)-(A), \(\theta_{1,0}^{\prime}\), \(\dot{\theta}_{1,0}^{\prime}\), \(\theta_{2,0}^{\prime}\), and \(\dot{\theta}_{2,0}^{\prime}\) indicate angular values at V0 (see Figure 4 and Table 2). Likewise, \(\theta_{1,1}^{\prime}\), \(\dot{\theta}_{1,1}^{\prime}\), \(\theta_{2,1}^{\prime}\), and \(\dot{\theta}_{2,1}^{\prime}\) are the angular values at V1. Of course, these values are related to \(\theta_{1,11}^{\prime}\), \(\dot{\theta}_{1,11}^{\prime}\), \(\theta_{2,11}^{\prime}\), and \(\dot{\theta}_{2,11}^{\prime}\), i.e., the angular values at V11 or at the beginning (at \(t_{0}\)), which are known. The torque and time interval (or \"Segment Time\") values can be used by following Table 2.
## 2 Formulation in Banach Space
After substituting into (8), we obtain  
\[\det\mathbf{V}=\det[\mathbf{I}_{m}-\Psi(G)]\
eq 0. \tag{5}\]5  
and hence  
\[\det\mathbf{V}=\det[\mathbf{I}_{m}-\Psi(G)]\
eq 0. \tag{5}\]6  
which is Equation (6), i.e., the solution of the problem (3). **3. Direct Computational Method (DCM)**  
In this Section, we consider the ideal case where the kernel \(K(x,t)\) in (1) is a separable function, i.e., has the special form  
\[\det\mathbf{V}=\det[\mathbf{I}_{m}-\Psi(G)]\
eq 0. \tag{5}\]7  
where the functions \(g_{j}(x)\), \(h_{j}(x)\), \(j=1,2,...,m\), are continuous on \([a,b]\) and preferably, but not necessarily, linearly independent sets. Substituting (9) into (1), we obtain  
\[\det\mathbf{V}=\det[\mathbf{I}_{m}-\Psi(G)]\
eq 0. \tag{5}\]8  
Define the row vector of functions  
\[G=\lambda\big{(} \begin{array}{ccc}g_{1}&g_{2}&\ldots&g_{m}\end{array} \big{)},\quad g_{j}=g_{j}(x)\in C[a,b],\quad j=1,2,\ldots,m, \tag{11}\]  
and the column vector of linear bounded functionals  
\[\Psi(u)=\left( \begin{array}{c}\Psi_{1}(u)\\ \Psi_{2}(u)\\ \vdots\\ \Psi_{m}(u)\end{array} \right),\quad\Psi_{j}(u)=\int_{a}^{b}h_{j}(t)u(t)dt,\quad j =1,2,\ldots,m. \tag{12}\]  
By means of (11) and (12) and after setting \(u=u(x)\) and \(f=f(x)\), Equation (10) may be put in the vector form  
\[u-G\Psi(u)=f\quad x\in[a,b]. \tag{13}\]  
Further, by taking \(X=C[a,b]\) and defining the operator \(T:X\to X\) by \(Tu=u-G\Psi(u)\), Equation (13) may be cast in the operator form (3), namely  
\[Tu=u-G\Psi(u)=f. \tag{14}\]  
Provided condition (5) is fulfilled, the unique solution of (14) follows from Theorem 1, and specifically from Formula (6). If the functions \(g_{j}(x)\), \(h_{j}(x)\), \(j=1,2,\ldots,m\), and \(f(x)\) are such that the evaluation of \(\Psi(G)\) and \(\Psi(f)\) can be performed by analytic means, i.e., without the use of numerical tricks, and then the solution of (14) is the exact closed-form solution of the integral Equation (1). **4. Degenerate Kernel Methods (DKM)**  
If the kernel \(K(x,t)\) in (1) is not separable, then we can consider approximating it in a way that makes it separable. There are several mathematical means to accomplish this [7]. We discuss here two such common methods for general continuous kernels.
## 2 Optimization  
Neural network training is an optimization problem with non-convex objective function \(J\): the minimization problem \(\min_{\theta}\int(\theta;\mathcal{D}_{\text{train}})\). During the training process, model parameters \(\theta\) are iteratively updated in order to reduce the cost \(J\) on the training data \(\mathcal{D}_{\text{train}}\). In subsequent sections, we use bold symbols such as \(\theta\) for vector quantities and regular ones for scalars. The most commonly used stopping criterion for the iterative training process is the predefined number of passes through all available training data, i.e., epochs. One epoch often consists of multiple iterations.  
There are various optimization algorithms used for training neural networks, which differ in the way they update network parameters. We describe the most commonly used optimization algorithms in the subsections below. Up to date, there is no clear answer nor consensus on which optimization algorithm is _universally_ the best. Two metrics often used to evaluate efficiency of an optimization algorithm are:* **Speed of convergence**: The time needed for algorithm to reach the optimal value
* **Generalization**: The model performance on new data  
The optimization of deep neural networks comes with many challenges. One of them is a highly non-convex objective function \(J\) with numerous suboptimal local minima and saddle points. Other challenges include high-dimensionality of search space (deep models often have to learn millions of parameters) and choice of appropriate values for hyperparameters of the model. We overview classical and adaptive optimization algorithms commonly used to optimize neural networks' cost in the following subsections. Summary of update rules of overviewed optimization algorithms can be found in the Appendix A.
# Intelligent Reflecting Surface-Assisted Wireless Communication Using RNNs: Comprehensive Insights
###### Abstract  
By adjusting the propagation environment using reconfigurable reflecting elements, intelligent reflecting surfaces (IRSs) have become potential techniques used to improve the efficiency of wireless communication networks. In IRS-assisted communication systems, accurate channel estimation is crucial for optimizing signal transmission and achieving high spectral efficiency. As mobile data traffic continues to surge and the demand for high-capacity and low-latency wireless connectivity grows, IRSs are becoming pivotal technologies in the development of next-generation communication networks. IRSs offer the potential to revolutionize wireless propagation environments, improving network capacity and coverage, particularly in high-frequency wave scenarios where traditional signals encounter obstacles. Amidst this evolving landscape, machine learning (ML) emerges as a powerful tool to harness the full potential of IRS-assisted communication systems, particularly given the escalating computational complexity associated with deploying and operating IRSs in dynamic environments. This paper presents an overview of preliminary results for IRS-assisted communication using recurrent neural networks (RNNs). We first implement single- and double-layer LSTM, BiLSTM, and GRU techniques for an IRS-based communication system. In the next phase, we explore a hybrid approach, combining different RNN techniques, including LSTM-BiLSTM, LSTM-GRU, and BiLSTM-GRU, as well as their reverse configurations. These RNN algorithms were evaluated with respect to bit error rate (BER) and symbol error rate (SER) for IRS-enhanced communication. According to the experimental results, the BiLSTM double-layer model and the BiLSTM-GRU combination demonstrated the highest BER and SER accuracy compared to other approaches.  
intelligent reflecting surface; machine learning; recurrent neural network +
Footnote †: journal: _Mathematics_  
1226  
Hotelligent reflecting surface; machine learning; recurrent neural network 1226
## 2 The Idea of the Proposed Method  
The data received for processing are typical BGS, i.e., a set of scattering spectra obtained for each point of the optical sensor. These data can be easily visualized as an image (Figure 2), in which the abscissa axis is the distance, the ordinate axis is the frequency, and the color information characterizes the radiation intensity. Given that the original frequency resolution is relatively low, the method entails upsampling, which involves the generation of new pixels. In the simplest case, the color of these pixels is determined by a linear approximation based on neighboring pixels.  
To calculate the BFS of spectrum \(i\), a certain set \(P\) is selected, consisting of \(N\) consecutive spectra that will be involved in digital signal processing. This choice is made based on the computing resources and the tasks facing the researcher. How to determine the optimal value of \(N\) will be shown in the subsequent parts of this paper. It is worth noting that the set \(P\) does not contain a spectrum with the number \(i\).  
Next, the cross-correlation function (CCF) of spectrum \(i\) and spectrum \(i+1\), the first of the spectra of set \(P\), is calculated. The maximum of this function determines the shift of the  
Figure 2: The principle of the proposed method.  
spectra relative to each other, at which their maximum overlap will occur. All values of spectrum number \(i+1\) are shifted by the value \(d\):  
\[d_{i+1}=Max\_j\sum_{-N}^{N}S_{i+1;j}S_{i;j-n}\, \tag{3}\]  
\[S_{i+1;j}=S_{i+1;j+d_{i+1}}, \tag{4}\]  
where \(n\) is the argument of the CCF, \(Max\_j\) is the function returning the coordinate \(j\) of the maximum value of the CCF. If the spectrum with index \(i+m\) does not fall into the set \(P\) because the end of the fiber line has been reached, then it is replaced by the spectrum with index \(N-m\), where \(m\) is an integer value. Thus, the coordinates of the BGS maxima with numbers \(i\) and \(i+1\) (or \(N-m\)) become almost equal. An exact match is not achieved due to the error of the correlation method, which takes its own value for each of the spectra of set \(P\) and can even change the sign. Thereafter, all shifted BGS are normalized and added up, and the BFS value is calculated from the resulting spectrum using the LCF method.  
An algorithm was developed and subsequently applied to both the simulated data and the experimental data (Figure 3) to assess the efficacy of the proposed approach.  
At the outset of the calculations, two independent processing branches are established. The first of these incorporates data processing. The traditional BFS extraction method, LCF, is employed to derive the BFS 1 set. The second branch commences with resampling and continues processing according to the aforementioned algorithm (Figure 3). At the conclusion of each branch, the precision and accuracy parameters are analyzed, and the results are ultimately compared.