esa-sceva/satcom-chunk-collection huggingface dataset:
# Effects and Mechanisms of Microbial Remediation of Heavy Metals in Soil: A Critical Review
## 4 Microbial Remediation of Heavy Metal-Contaminated Soil
### Comparison of Microbial Removal Ability  
#### 4.2.1 Microbial Remediation Potential  
Microbial remediation of heavy metal pollution of the soil has definite advantages including low cost and maintenance of the soil structure [19]. Numerous microbial species, including bacteria and fungi from _Bacillus_[54], _Pseudomonas_[34, 55], _Streptomyces_[56], _Aspergillus_[57, 58], _Rhizopus_[1] and _Penicillium_[23], have significant removal ability (Table 3). At present, we have found that a variety of bacteria can absorb soil heavy metals. Among them, _Escherichia coli_ K-12 can absorb the widest variety of metal ions; the outer membrane of this stain can absorb more than 30 different kinds of metal ions [16, 59]. _Rhizopus_ can absorb Zn, Cu, Cd, Pb, and other heavy metal ions [1], and _Thiobacillus_ can absorb heavy metal ions as well as inorganic ions, such as S, which combines with the metal ions to form a precipitate that can be separated from the soil [60].
# Simultaneous Coded Plane-Wave Imaging Using an Advanced Ultrasound Forward Model
## 2 Materials and Methods
### Discretization of the Model  
Let us assume that the signal \(y_{ji}(t)\) is sampled at frequency \(f_{s}\). Each entry \(y_{ji}[n]\) corresponds to the value of the respective continuous time signal at time \(t=t_{0}+n/f_{s}\), where \(t_{0}\) is the start time for reception and \(n=[1...N_{y}]\). The medium \(\Omega\) is partitioned into small cells of size \((\Delta x,\Delta z)\) that form an \(N_{z}\times N_{x}\) grid \(\mathbf{\Omega}\) (Figure 2b), where each entry \(\mathbf{\gamma}[m]\) represents the scattering coefficient at the \(\Omega\) grid cell defined by \(r=(x_{\Omega},z_{\Omega})\in\mathbf{\Omega}\) with:  
\[m=\left\lfloor\frac{x_{\Omega}}{N_{x}\Delta x}\right\rfloor N_{z}+\frac{z_{ \Omega}}{\Delta z} \tag{6}\]  
where \(\left\lfloor\,\right\rfloor\) is the floor function. Thus, the discretized TRF \(\mathbf{\gamma}\) is an \(N_{z}N_{x}\times 1\) vector that contains the scattering coefficients at each cell of the medium \(\mathbf{\Omega}\). From Equation (5), it is possible to write the discrete space-time expression of \(y_{ji}(t)\) as:  
\[\mathbf{y}_{ji}=\mathbf{e}+\sum_{i=1}^{N}\sum_{u=1}^{N}\mathbf{g}_{u_{j}v_{i}}, \tag{7}\]  
Figure 2: (**a**) Schematic representation of the ultrasound wave emitter \(j\), receiver \(i\), and the associated coordinate system. (**b**) Proposed discretization for the transducers and propagation medium \(\Omega\). The surfaces \(S_{j}\) and \(S_{i}\) are divided into \(N\) subdivisions.  
where \(\star\) is the discrete convolution, \(N\) is the number of subdivisions for each planar surface \(S_{j}\) and \(S_{i}\), and the bold entities are the discrete equivalents (vectors) of the corresponding continuous time/space signals.  
The discrete time convolution between \(\mathbf{e}\) and \(\mathbf{g}_{u_{i}v_{i}}\) in Equation (7) can be represented as a matrix product between \(\mathbf{E}\) and \(\mathbf{C}_{u_{i}v_{i}}\), where the \(N_{y}\times N_{y}\) Toeplitz matrix \(\mathbf{E}\) (constructed using \(\mathbf{e}\)) depends on the excitation signal and on the IR of the transducers, and the matrix \(\mathbf{C}_{u_{i}v_{i}}\) (of size \(N\times N\times N_{y}\times N_{x}N_{x}\)) is related to the forward/backward propagation of the wave inside the medium. Therefore, by applying Equation (A1) of Appendix A to Equation (7), we obtain:  
\[\begin{split}\mathbf{y}_{ji}=\mathbf{E}\Bigg{[}\sum\limits_{v=1 }^{N}\sum\limits_{u=1}^{N}\mathbf{C}_{u_{i}v_{i}}\Bigg{]}\boldsymbol{\gamma}= \mathbf{EC}_{ji}\boldsymbol{\gamma}=\boldsymbol{\Lambda}_{ji}\boldsymbol{ \gamma},\\ \text{with: }\begin{cases}\mathbf{C}_{ji}=\sum\limits_{v=1}^{N} \sum\limits_{u=1}^{N}\mathbf{C}_{u_{i}v_{i}},\\ \boldsymbol{\Lambda}_{ji}=\mathbf{EC}_{ji}.\end{cases}\end{split} \tag{8}\]  
In Equation (8), matrix \(\mathbf{E}\) depends on the excitation signal and the IR of the transducers. Matrix \(\mathbf{C}_{ji}\) depends solely on the geometry of \(j\), \(i\), and \(\Omega\). The kernel \(\boldsymbol{\Lambda}_{ji}\) gathers all the properties of \(\mathbf{E}\) and \(\mathbf{C}_{ji}\) inside one matrix.
# Mapping irrigated Areas Using Sentinel-1 Time Series in Catalonia, Spain
## 3 Methodology  
### Overview  
An overview of the methodology is presented in Figure 4. First, the average S1 SAR backscattering coefficients (\(\sigma^{\circ}\)) were calculated at both plot scale (SIGPAC plots) and grid scale (10 km \(\times\) 10 km). The mean signal at grid scale will be used to discriminate between rainfall and irrigation events. In general, we suppose that if the mean signal increases at the base of 10 km \(\times\) 10 km then a rainfall event had occurred. Next, the PCA and the WT were performed on the obtained S1 time series. Moreover, the PCA was applied on the temporal series of the NDVI established at plot scale using the S2 optical data. Finally, two classification approaches including the RF classifier and the CNN were investigated. In each approach, three scenarios have been tested. The first scenario is based on the use of SAR data only, the second scenario considers the use of optical data only, and the third scenario  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Data** & **Type** & **Satellite** & \begin{tabular}{c} **Spatial** \\ **Resolution** \\ \end{tabular} & \begin{tabular}{c} **Images** \\ **Number** \\ \end{tabular} & \begin{tabular}{c} **Frequency** \\ **Used** \\ \end{tabular} & \begin{tabular}{c} **Calibration** \\ **Performed** \\ \end{tabular} & \begin{tabular}{c} **Bands** \\ **Polarization** \\ \end{tabular} \\ \hline \multirow{4}{*}{\begin{tabular}{c} **Satellite** \\ **Images** \\ \end{tabular} } & \begin{tabular}{c} (Synthetic aperture \\ radar) SAR \\ \end{tabular} & Sentinel-1 & 10 m & 82 & 6 days & Geometric/Radiometric & VV, VH \\  & \begin{tabular}{c} **Optical** \\ \end{tabular} & Sentinel-2 & 10 m & 17 & \begin{tabular}{c} One \\ month \\ \end{tabular} & \
\begin{tabular}{c} Ortho-rectified \\ Reflectance \\ \end{tabular} &
\begin{tabular}{c} Near Infrared, \\ Red \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of the used remote sensing data.  
includes the combined use of both optical and SAR data. A detailed description of the methodology is further elaborated in the following sub-sections.
## 3 Results and Discussion
### Effect of Varying Upsetting Ratios and Punch's Pitch Angle on Flange-Forming Force
\begin{tabular}{c c c c} \hline \hline
**Case No.** & **\(H0\)/D0** & **S0/D0** & \(\alpha\) \\ \hline
2 & 1 & 2 & 2 \\ \hline
3 & 1 & 3 & 3 \\ \hline
4 & 1 & 4 & 4 \\ \hline
5 & 2 & 1 & 2 \\ \hline
6 & 2 & 2 & 3 \\ \hline
7 & 2 & 3 & 4 \\ \hline
8 & 2 & 4 & 1 \\ \hline
9 & 3 & 1 & 3 \\ \hline
10 & 3 & 2 & 4 \\ \hline
11 & 3 & 3 & 1 \\ \hline
12 & 3 & 4 & 2 \\ \hline
13 & 4 & 1 & 4 \\ \hline
14 & 4 & 2 & 1 \\ \hline
15 & 4 & 3 & 2 \\ \hline
16 & 4 & 4 & 3 \\ \hline \hline \end{tabular}  \end  
To assess factor influence (Table 9), the sum of squares is calculated using Equations (7)-(9). This forms the basis for comparing mean-centered variation (Equation (10)), leading to percentage factor influence determination (Equation (11)):  
\[T=\sum_{i=1}^{n}Y_{i} \tag{7}\]  
\[CF=\frac{T^{2}}{n} \tag{8}\]  
\[S_{j}=\sum_{i=1}^{n_{ji}}\frac{j_{i}^{2}}{n_{ji}}-CF \tag{9}\]  
\[S_{T}=\sum_{j=1}^{n}S_{j} \tag{10}\]  
\[P_{j}=\frac{S_{j}}{S_{T}} \tag{11}\]  
where \(Y_{i}\) is the measurement at test condition \(i\); \(n\) is total trials; \(n_{ji}\) is factor \(j\)'s trial number at level \(i\); and \(ji\) is factor \(j\)'s sum at level \(i\). The analysis of the factors' influence reveals that the most significant factor affecting the flange-forming force is \(S0/D0\), accounting for 65% of the variation. \(H0/D0\) follows with 21.1% influence, while \(\alpha\) has a comparatively smaller impact at 13.9%. Therefore, achieving the minimum flange-forming force requires setting the parameters at \(H0/D0=1\), \(S0/D0=0.2\), and \(\alpha=5^{\circ}\). These optimized parameters are then utilized for simulation and experimental verification. The simulation and experimental results using the optimized parameter set are presented in Figure 7a, showing a simulated flange-forming force of 10.6 tons and experimental verification of 10.2 tons, as displayed in Figure 7b. Consequently, the simulated flange-forming force results exhibit high accuracy when compared with the experimental results, with a deviation of only 3.92% according to expression (2). Figure 6: Influence levels of parameters \(H0/D0\), \(S0/D0\), and \(\alpha\) on the flange-forming force.
## 1 Introduction  
The effective management of large flows of various information cannot be organized without the use of computer information and analytical systems (IAS). In scientific and technical applications, IASs are of particular value, providing deep analytical processing of the results of previous studies and the possibility of planning new experiments [1; 2; 3].  
Currently, the National Nuclear Center (RSE NNC RK) conducts a large number of scientific works [4; 5; 6; 7; 8; 9; 10; 11]. It should be noted that for more than 30 years, the RSE NNC RK has been conducting the work to justify the safety of atomic energy at the unique experimental test benches \"ANGARA\" and \"VCG-135\" [12; 13; 14; 15; 16; 17]. During this time, a large amount of experimental information has been accumulated on the processes occurring during the development of postulated severe accidents at nuclear reactors. The knowledge gained when studying these processes makes it possible to reasonably solve the problems of choosing the principles of operation of passive safety systems of nuclear power reactors and the formation of technical requirements for the designs of these systems. Experimental test benches of the RSE NNC RK enable the conducting of physical modeling of processes typical for the final stage of an accident in water-cooled reactors caused by an imbalance between an energy release in nuclear fuel and heat removal (accidents of the LOCA, ULOF type). At the same time, the main attention during research is paid to studying the processes of interaction between the melt of materials of the reactor core (corium) with:  
- Coolant (water);  
- Concrete (melt trap, concrete load-bearing structures);  
- Candidate materials for the protection of a trap;Material (steel) of a reactor pressure vessel.  
The information obtained during the experiments, for the most part, is heterogeneous, however, it has a number of common features that make it possible to link the results of individual experiments and their series into a single whole. Using the methods of qualitative and quantitative analysis aimed at summarizing the results of individual experiments, all the information received was processed in order to bring it to a single format.  
The purpose of creating an IAS was to provide access to both individual and generalized research data, as well as to a validated mathematical apparatus designed to process experimental data and carry out predictive calculations. At the same time, the main tasks to be solved are to increase the speed of processing and the reliability of the analysis of experimental data and, ultimately, the convenience of planning future experiments.  
The novelty of this research is the creation of an IAS for scientific research, in particular, the research processes of a severe accident with melting of a nuclear reactor core and retention of the melt in the reactor pressure vessel. It is also worth noting that the preservation of scientific data will ensure their continuity for the next generation and open up the possibility of assessing changes in the properties of materials over time.
## 4 Experiments and Results
### Experimental Results
#### 4.3.3 Fine-Tuning Results  
Figure 11 shows the loss changes of Deformer during fine-tuning. The orange line (pre-trained) demonstrates a rapid decline in loss during fine-tuning, indicating a high level of learning efficiency. The blue line (without pre-training) exhibits a slower loss decrease. At 20,000 steps, the fine-tuning process based on pre-training demonstrated a significant performance advantage compared to that without pre-training.  
To assess the classification efficacy of Deformer across different music genres, the confusion matrix depicted in Figure 12 is provided. The confusion matrix presents true-positive, true-negative, false-positive, and false-negative results, providing a clear classification performance evaluation. The fact that the predicted results are clearly distributed along the diagonal of the confusion matrix indicates that most of the predictions are correct. It can be seen that Deformer exhibited exceptional performance in the \"classical\" and \"pop\" categories, achieving impeccable accuracy with zero misclassifications within these genres. This outcome highlights its acute understanding of the unique attributes associated with these music genres. However, it exhibited inaccuracies within the \"rock\" and \"blues\" genres. Specifically, a few samples falling under the \"rock\" category were incorrectly classified as \"blues\" and \"metal\". Likewise, a subset of \"blues\" samples was inaccurately classified as \"jazz\" and \"metal\". These misclassifications suggested potential limitations of Deformer, particularly when differentiating between genres having nuanced or overlapping traits. Analyzing the confusion matrix is vital as it paves the way for prospective refinements and emphasizes the need to improve the discriminatory capabilities of the model when classifying music belonging to closely related genres such as \"rock\" and \"blues\".  
Table 3 presents the accuracy, precision, recall, and F1 scores for the proposed pre-trained Deformer, Deformer without pre-training used for the ablation experiment, and ResNet-BiGRU and S3T as two baseline models. To complete the comparison, two additional results [25; 26] are given, which demonstrated high accuracy in audio music genre classification. The pre-trained Deformer reached a classification accuracy of 84.5%, which is 3.4% higher than that of ResNet-BiGRU (81%), 3.3% higher than that of S3T (81.1%), 0.6% higher than that of M2D [25] (83.9%), and 4.8% higher than that of the Jukebox model pre-trained with CALM (79.7%) [26]. The pre-trained Deformer significantly outperformed its non-pre-trained counterpart in terms of accuracy, precision, recall, and F1 score, with the latter only achieving an accuracy and recall of 0.37, a precision of 0.3334, and an F1 score of 0.3464. This comparison highlights the importance of pre-training in enhancing the performance of Deformer for music classification. It is worth noting that all data presented in Table 3 were obtained through testing on the GTZAN dataset.  
Figure 11: Cross entropy loss in fine-tuning of Deformer and ablation experiment.
## 5 Numerical Results
### BER in Several Classes of NLOS Channels  
In the second simulation, we first assess the performance of CP/CS-SC-FDE compared with CP-SC-FDE in the Rayleigh fading channel. The simulation parameters are shown in Table 1. The value of \(E_{b}/N_{0}\) is from 0 to 18 dB. The simulation result is shown in Figure 9. As a reference, the curve of ideal synchronization is also shown. Ideal synchronization means that although PwMP is not the FAP, the synchronization offset caused by NLOS will be manually eliminated. This is equivalent to an accurate search for FAP. Since the FAP searching algorithms in [28; 33; 34; 35] cannot search the FAP accurately, the BER performance of these algorithms must not be as good as that of ideal synchronization. The optimal performance can be achieved under ideal synchronization, so the performance of CP-SC-FDE and CP/CS-SC-FDE systems is investigated and compared with the curve of ideal synchronization in this simulation. According to the above theoretical analysis, CP/CS-SC-FDE can still achieve the same performance as ideal synchronization without eliminating TO. As seen in Figure 9, when the channel is a Rayleigh channel, due to the LISI caused by TO, the BER is poor in the CP-SC-FDE system. On the contrary, in the CP/CS-SC-FDE system, since LISI is eliminated, the BER result is similar to that under ideal synchronization.  
Figure 8: The channel estimation output in CP/CS-SC-FDE.  
Figure 7: The channel estimation output in CP-SC-FDE.  
Then, we assess the performance of CP/CS-SC-FDE compared with CP-SC-FDE in the COST207-BU channel with 12 non-zero taps and TDL-C channel with 24 non-zero taps, respectively. The COST207-BU channel represents the bad urban scenario from the COST 207 channel model standard [41]. The TDL-C channel represents the bad NLOS scenario from the 3 GPP channel model standard [42]. The COST207-BU channel and TDL-C channel are NLOS channels, where the PwMP is not the FAP. The simulation parameters are shown in Table 1. The value of \(E_{b}/N_{0}\) is from 0 to 33 dB. The simulation result is shown in Figure 10. The BER curves of ideal synchronization in COST207-BU and TDL-C channels are also shown as a reference. As seen in Figure 10, the BER is poor in the CP-SC-FDE system. On the contrary, in the CP/CS-SC-FDE system, the BER result is similar to that under ideal synchronization.
## 4 Design of the PV Voltage Dynamics
### Parameters Design  
The PV voltage behavior is designed considering real and equal poles \((s-P)^{2}\) for the closed-loop transfer function (58). The magnitude \(P\) of the poles is given in (59), which requires the value of \(k_{i}\) given in (60) to ensure that both poles are real and equal.  
\[P=\frac{k_{p}}{2\cdot C_{pv}} \tag{59}\]  
\[k_{i}=\frac{k_{p}^{2}}{4\cdot C_{pv}} \tag{60}\]  
Figure 10: Complete control structure.  
The largest deviation in the PV voltage (58) occurs when the voltage reference \(v_{r}\) exhibits step changes, which is the most common waveform of the P&O reference. Equation (61) formalizes such a step change in the Laplace domain, where \(\Delta v_{po}\) is the perturbation magnitude imposed on the P&O algorithm.  
\[v_{r}=\frac{\Delta v_{po}}{s} \tag{61}\]  
Then, replacing the previous \(v_{r}\) waveform into the transfer function (58), considering the \(k_{i}\) value given in (60), and applying the inverse Laplace transformation, leads to the following time-domain waveform of \(v_{pv}\):  
\[v_{pv}=\Delta v_{po}\cdot\left[1+(P\cdot t-1)\cdot e^{-P\cdot t}\right] \tag{62}\]  
The P&O algorithm design requires two parameters [27]: the first one is the perturbation magnitude \(\Delta v_{po}\), already used to obtain expression (62); the second one is the perturbation period \(T_{a}\), which defines the interval between perturbations. [PERSON] et al. demonstrated in [27; 28] that a stable operation of the P&O requires a \(T_{a}\) longer than the settling time \(t_{s}\) of the PV voltage (i.e., \(t_{s}<T_{a}\)). Moreover, [PERSON] also demonstrated that such a settling time changes with the irradiance value imposed by the environmental conditions. Therefore, the voltage controller must be designed to ensure such a stability requirement.  
The settling time is calculated when the PV voltage enters an acceptable band \([1-\epsilon,1+\epsilon]\%\) around the final value, where the most commonly adopted band is \(\epsilon=2\%\). Then, the settling time is calculated when \(v_{pv}=\Delta v_{po}\cdot(1+\epsilon)\), which is solved using expression (62) as given in (63), where \(W(\cdot)\) is the Lambert-W function.  
\[t_{s}=\frac{1-W\big{(}-\epsilon\cdot e^{1}\big{)}}{P} \tag{63}\]  
Substituting the value of \(P\), given in (59), into the previous expression enables to calculate the \(k_{p}\) value required to impose the desired settling time \(t_{s}\):  
\[k_{p}=2\cdot C_{pv}\cdot\frac{1-W\big{(}-\epsilon\cdot e^{1}\big{)}}{t_{s}} \tag{64}\]
# Kernel Density Estimation on the Siegel Space with an Application to Radar Processing +
## 2 The Siegel Space
### The Siegel Disk  
The Siegel disk \(\mathcal{D}_{n}\) is the set of complex matrices \(\left\{Z|I-Z^{*}Z\geq 0\right\}\), where \(\geq\) stands for the Loewner order (see [24] for details on the Loewner order). Recall that for \(A\) and \(B\) two Hermitian matrices, \(A\geq B\) with respect to the Loewner order means that \(A-B\) is positive definite. The transformation  
\[Z\in\mathcal{H}_{n}\mapsto(Z-iI)(Z+iI)^{-1}\in\mathcal{D}_{n}\]  
is an isometry between the Siegel upper half space and the Siegel disk. Let \(C=\begin{pmatrix}I&-iI\\ I&iI\end{pmatrix}\). The application \(g\in Sp(n,\mathbb{R})\mapsto CgC^{-1}\) identifies the set of isometries of \(\mathcal{H}_{n}\) and of \(\mathcal{D}_{n}\). Thus, it can be shown that a matrix \(g=\begin{pmatrix}A&B\\ \overline{A}&\overline{B}\end{pmatrix}\in Sp(n,\mathbb{C})\) acts isometrically on \(\mathcal{D}_{n}\) by  
\[g.Z=(AZ+B)(\overline{A}Z+\overline{B})^{-1},\]where \(\overline{A}\) stands for the conjugate of \(A\). The point \(iI\) in \(\mathcal{H}_{n}\) is identified with the null matrix noted 0 in \(\mathcal{D}_{n}\). Let \(Z\in\mathcal{D}_{n}\). There exists \(P\) a diagonal matrix with decreasing positive real entries and \(U\) a unitary matrix such that \(Z=UPU^{t}\). Let \(\tau_{1}\geq...\geq\tau_{n}\) be such that  
\[P=\begin{pmatrix}th(\tau_{1})&&&\\ &\ddots&\\ &&&th(\tau_{n})\end{pmatrix}.\]  
Let  
\[A_{0}=\begin{pmatrix}ch(\tau_{1})&&&\\ &\ddots&\\ &&ch(\tau_{n})\end{pmatrix},\,B_{0}=\begin{pmatrix}sh(\tau_{1})&&&\\ &\ddots&\\ &&&sh(\tau_{n})\end{pmatrix}\]  
and  
\[g_{Z}=\begin{pmatrix}U&0\\ 0&\overline{U}\end{pmatrix}\cdot\begin{pmatrix}A_{0}&B_{0}\\ A_{0}&B_{0}\end{pmatrix}.\]  
It can be shown that  
\[g_{Z}\in Sp(n,\mathbb{C})\text{ and }g_{Z}.0=Z. \tag{3}\]  
We provide now a correspondence between the elements of \(\mathcal{D}_{n}\) and the elements of \(\mathfrak{p}\) defined in Equation (1). Let  
\[H_{Z}=\begin{pmatrix}\tau_{1}&&&&\\ &\ddots&&\\ &&\tau_{n}&&\\ &&&-\tau_{1}&&\\ &&&\ddots&\\ &&&&-\tau_{n}\end{pmatrix}\in\mathfrak{a}, \tag{4}\]  
and  
\[a_{Z}=\begin{pmatrix}e^{\tau_{1}}&&&\\ &\ddots&&\\ &&e^{\tau_{n}}&&\\ &&&e^{-\tau_{1}}&&\\ &&&\ddots&\\ &&&e^{-\tau_{n}}\end{pmatrix}\in A=exp(\mathfrak{a}).\]  
It can be shown that there exists \(k\in K\) such that  
\[Cexp(Ad_{k}(H_{Z}))C^{-1}.0=Z,\]  
or equivalently  
\[Cka_{Z}kC^{-1}.0=Z.\]  
Recall that Equation (2) gives \(Ad_{k}(H)\in\mathfrak{p}\) and \(kak\in exp(\mathfrak{p})\). The distance between \(Z\) and \(0\) in \(\mathcal{D}_{n}\) is given by  
\[d(0,Z)=\left(2\sum\tau_{i}^{2}\right)^{1/2} \tag{5}\]  
(see p. 292 in [20] ).