esa-sceva/satcom-chunk-collection huggingface dataset:
## 4 Discussion
### Numerical Simulation  
#### 4.1.1 Effect of Bone Curvature  
For curved bone models positioned parallel to the probe array (without bone tilt), the ST correction was sufficient and corrected the additional geometrical time shifts for curved bone interfaces compared to a flat bone plate. For the correction, it was assumed that ultrasound waves propagate in a straight direction, as described in ray theory [34].  
Figure 3: (**a**) Maximum projection B-mode image of human tibia bone at the central anteromedial region. The image was reconstructed and spatially compounded (by means of maximum projection) from measurements at all focus depths using conventional DAS beamforming. The range of interest (ROI) was manually selected (green lines). (**b**) Maximum projection B-mode image reconstructed from all focus depths with PAC (ST, ACF, CC). (**c**) Representative plots of \(\mathit{Ct.Th}^{MF}(x_{i})\) and \(\mathit{Ct.v_{11}}^{MF}(x_{i})\) without PAC and (**d**) with PAC. The dots indicate the estimations for each individual lateral scan position \(x_{i}\), and the straight lines are the estimations using a moving average filter. Means and standard deviations were determined from smoothed data. The number of individual scan positions contributing to the parameter estimations in (**c,d**) were 14 and 29, respectively.
# Three-Dimensional Assessment of Upper Limb Proprioception via a Wearable Exoskeleton
## 2 Materials and Methods
### Statistical Analysis  
Data normality was evaluated using the Shapiro-Wilk test, and sphericity condition for repeated measures analyses of variance (rANOVA) was assessed using the Mauchly test. The rANOVA test was used to examine the effects of the upper limb condition, the DoF, and the body's side on the dependent variables (Error Bias, and Matching Error). We considered three within-subject factors: (i) \"condition\" (2 levels: SJ and MJ), (ii) \"DoF\" (4 levels: AA\({}_{\text{Shoulder}}\), FE\({}_{\text{Shoulder}}\), FE\({}_{\text{Elbow}}\), and MJ), (iii) \"Side\" (2 levels: left and right) and their interaction. A post-hoc analysis was performed using the paired \(t\)-tests to evaluate the significant pairwise differences between each perturbation, DoF, and condition. All the tests have a statistical significance level set at 0.05, except for post-hoc analysis, where the significance level was reduced to 0.004 for Bonferroni corrections. Statistical analysis was conducted by using IBM SPSS Statistics 23.
## 5 Conclusions  
The decreasing availability of water for irrigation has become a growing worldwide concern, and advancements in technology are helping to address the challenge of improving irrigation water use efficiency. When it comes to producing high-quality tomatoes, both tomato yield and fruit quality parameters must be taken into consideration in irrigation management. In this study, the PlaSoMan smart system assessing both plant water status and soil moisture levels proved to be more effective, resulting in higher irrigation water use efficiency compared to the other two systems examined. Additionally, both the IriMan and PlaSoMan systems had lower blue water requirement values than FarMan, appearing as a more sustainable irrigation system. By utilizing PlaSoMan, farmers can save water, obtaining both environmental and economic benefits while producing high-quality crops valued by the processing industry, leading to higher prices.  
Conceptualization, G.G. and M.M.G.; methodology, G.G., M.M.G. and F.C.; validation, G.G. and M.M.G.; formal analysis, F.C. and A.G.; investigation, G.G., M.M.G. and F.C.; writing--original draft preparation, F.C. and A.G.; writing--review and editing, M.M.G., G.G. and F.C.; visualization, F.C. and A.G.; supervision, G.G. and M.M.G.; project administration, G.G. and M.M.G. All authors have read and agreed to the published version of the manuscript.  
This study was part of the \"Use of Innovative Systems Based on Wireless Sensor Networks in the Irrigation Scheduling of Processing Tomato\" Project (SIWIP--DM 15531/7818/2013), funded by the Italian Ministry of Agricultural, Food and Forestry Policies (MiPAAF).  
Not applicable.  
The data used and/or analyzed during the current study will be available from the authors upon reasonable request.  
The authors declare no conflict of interest.
## 2 Materials and Methods
### Single Unit Transfer Matrix  
For the continuous layer of Figure 1a, the transfer matrix takes the form [60]:  
\[\mathbf{M}_{c}=\left[\begin{array}{cc}\cos\phi&\frac{1}{Q}\sin\phi\\ -Q\sin\phi&\cos\phi\end{array}\right], \tag{5}\]  
where \(\phi=kd\) is the phase increment, \(d\) the layer thickness and \(Q=k\mu\).  
The transfer matrix for the discrete system given in Figure 1b is [41]:  
\[\mathbf{M}_{d}=\left[\begin{array}{cc}\frac{\gamma-m\omega^{2}}{\gamma}& \frac{2\gamma-m\omega^{2}}{\gamma^{2}}\\ -m\omega^{2}&\frac{\gamma-m\omega^{2}}{\gamma}\end{array}\right]. \tag{6}\]  
As a consequence of the symplectic structure of the problem, energy conservation implies that the transfer matrices are unimodular; such a property holds also for more complex elastic systems. Therefore, the evaluation of only the first invariant of \(\mathbf{M}\), i.e., the trace, will be sufficient to determine the dispersion properties.
## 2 Basic Principles of RNS Arithmetic
### Arithmetic Operations in RNS  
Due to the carry-free nature of RNS arithmetic, addition, subtraction, and multiplication can be executed in parallel, independently for each modulus, following the rule below:  
\[A\circ B=(\alpha_{1},\alpha_{2},\ldots,\alpha_{k})\circ(\beta_{1},\beta_{2}, \ldots,\beta_{k})=\]  
\[=\Big{(}\big{|}\alpha_{1}\circ\beta_{1}\big{|}_{m_{1}},\big{|}\alpha_{2}\circ \beta_{2}\big{|}_{m_{2}},\ldots,\big{|}\alpha_{k}\circ\beta_{k}\big{|}_{m_{k}} \Big{)},\]  
where \(\circ\in\{+,-,\times\}\) denotes modular arithmetic operations, with \(\alpha_{i}=\big{|}A\big{|}_{m_{i}}\) and \(\beta_{i}=\big{|}B\big{|}_{m_{i}}\) for \(i=1,2,\ldots,k\).
# Efficient Estimation of Generative Models Using Tukey Depth
## 5 Synthetic Experiments
### Experiment  
We started by generating 30 synthetic datasets of size \(n=100\) and size \(n=250\) from \(P(x|\theta)\) with \(\theta=0.3\). The left panel of Figures 1 and 2 shows an example of such a dataset for \(n=100\) and \(n=250\), respectively. The middle and right panels show the halfspaces and resulting TDC as the inner border of all the halfspaces for \(\alpha=0.05\) and \(0.1\), respectively. Since \(\theta=0.3\), on average 30% and 70% of the samples were generated from \(f(x)\) and \(g(x)\), respectively. Since most of the samples are generated from \(g(x)\), the data are slightly spread in the upper right part according to the property of \(g(x)\), as shown in Figure 4.  
For each of the synthetic datasets, we used the ABC rejection algorithm to estimate the posterior probabilities in Equation (10). As discussed above, the quality of the approximation to the true posterior distribution depends on the statistics used in the ABC algorithm. Therefore, we compared the following four sets of statistics.  
1. TDC with \(\alpha=0.05\)
2. TDC with \(\alpha=0.4\)
3. Multiple TDCs for \(\alpha=0.05,\,0.1,\,0.2\) and \(0.4\)
4. Common statistics (mean and covariance matrix)  
For each simulation of the ABC rejection algorithm (Algorithms 1 and 2), a total of \(N=10^{5}\) iterations were run, and the 1% of the \(\widehat{\theta}\) samples with the smallest distance, \(\rho\), were accepted and added to \(\widehat{\theta}\) (code line 5 in Algorithm 1 and code line 6 in Algorithm 2). All experiments, including the generation of the synthetic datasets, were repeated five times to remove any noticeable Monte Carlo error in the results. In all experiments, \(n_{u}=10\) directional vectors were used, but new vectors were generated for each independent run to ensure that the results did not depend on any specific choices of directional vectors.  
The performance for a set of summary statistics in the ABC algorithm to approximate the true posterior probabilities was measured by the average mean absolute errors (AMAEs)  
\[\text{AMAE}=\frac{1}{30\cdot 5}\sum_{i=1}^{30}\sum_{k=1}^{5}|\widehat{P}_{j,i,k }-P_{j,i}|, \tag{12}\]  
where the sums go over the 30 datasets and five Monte Carlo repetitions. \(P_{j,i}\) and \(\widehat{P}_{j,i,k}\) refer to the true posterior probability and its \(k\)-th Monte Carlo estimate, respectively.  
The computations were run using the EasyABC package in R [43]. More specifically we used EasyABC to run the rejection algorithm.
# Generalized Sketches for Streaming Sets
## 4 Preliminaries
### Oph  
OPH [17] can be viewed as a sampling method, which samples (at most) \(k\) distinct elements from each set of interest without replacement and then estimates the Jaccard similarity of two sets based on their sampled elements. Compared with the well-known sketch method MinHash [16], which is used to estimate set Jaccard similarity, OPH reduces the time complexity of processing each element in set \(N_{u}\) from \(O(k)\) to \(O(1)\). In detail, to build a sketch of set \(N_{u}\subseteq W\), OPH [17] uses a single permutation function \(\pi(\cdot):W\to W\) to process each element in a set \(N_{u}\). Specifically, it evenly divides \(W=\{1,\ldots,p\}\) into \(k\) bins: \(W_{j}=\left\{\left\lfloor\frac{p(j-1)}{k}+1\right\rfloor,\ldots,\left\lfloor \frac{p^{j}}{k}\right\rfloor\right\}\), \(1\leq j\leq k\). The OPH sketch of set \(N_{u}\) is a vector \(\vec{x}_{u}=(x_{u,1},\ldots,x_{u,k})^{\mathsf{T}}\), where each element \(x_{u,j}\), \(1\leq j\leq k\), is computed as  
\[x_{u,j}=\left\{\begin{array}{ll}\min_{w\in N_{u}\wedge\pi(w)\in W_{j}}\pi( w),&\exists w\in N_{u},\pi(w)\in W_{j}\\ \emptyset,&\text{otherwise}.\end{array}\right.\]  
Given that at least one of \(x_{u,j}\) and \(x_{v,j}\) does not equal \(\emptyset\), [PERSON] et al.[17] observed that \(x_{u,j}=x_{v,j}\) occurs with probability \(J_{u,v}\), and proposed estimating \(J_{u,v}\) based on this observation. Let \(\mathbf{1}(\mathbb{P})\) be the indicator function that equals one when the predicate \(\mathbb{P}\) is true, andzero otherwise. Formally, OPH estimates the Jaccard similarity \(J_{u,v}\) of two sets \(N_{u}\) and \(N_{v}\) based on their OPH sketches \(\vec{x}_{u}\) and \(\vec{x}_{v}\) as  
\[\hat{J}_{u,v}=\frac{\sum_{i=1}^{k}\mathbf{1}(x_{u,i}=x_{v,i}\wedge x_{u,i}\
eq \emptyset\wedge x_{v,i}\
eq\emptyset)}{\sum_{i=1}^{k}\mathbf{1}(x_{u,i}\
eq \emptyset\lor x_{v,i}\
eq\emptyset)}.\]  
As shown in Algorithm 1, one can apply the above OPH algorithm online to stream \(\Gamma\) and compute the OPH sketch of each user's interest set \(N_{u}\), \(u\in U\).  
```
input :stream \(\Gamma\), \(k\). output :\((x_{u,1},\ldots,x_{u,k})\), \(u\in U\). foreach user \(u\) in set \(U\)do for\(i=1,\ldots,k\)do \(x_{u,i}\leftarrow\emptyset\);  end foreach\(e=(u,w)\) in \(\Gamma\)do \(i_{w}\leftarrow\left\lfloor\frac{\pi(w)}{k}\right\rfloor+1\); if\(x_{u,i_{w}}==\emptyset\)then \(x_{u,i_{w}}\leftarrow\pi(w)\);  end if else \(x_{u,i_{w}}\leftarrow\min(x_{u,i_{w}},\pi(w))\);  end if  end foreach
```  
**Algorithm 1**Online update procedure of OPH [17].
## 2 Equivalent Range Model for GEO-LEO BiSAR  
### Imaging Geometry and Signal Model  
The GEO-LEO BiSAR system uses geosynchronous SAR as the illuminator, which can provide wide beam coverage on the Earth's surface. The LEO receiver can choose an interested target scene within the illuminated area and exploit various imaging modes for different observation purposes, e.g., sliding-spotlight and terrain observation by progressive scans (TOPS).  
In Figure 1, the imaging geometry of GEO-LEO BiSAR in reference target local coordinate system (RTLC) [6] is illustrated. The potential imaging area is supposed to be illuminated by the GEO-SAR. The LEO receiver travels from \(A\) to \(C\) in orbital trajectory along the y-axis and works in sliding-spotlight mode. \(P\) is an arbitrary target located in the imaging scene. \(R_{T0}\) and \(R_{R0}\) are the instantaneous slant ranges from \(P\) to the transmitter and the receiver at beam center crossing time, respectively. \(\theta_{\mathrm{s}}\) is the squint angle of the LEO receiver at the beam center crossing time.  
Assuming the signal transmitted by the GEO-SAR is a linear frequency modulation pulse, the received signal after demodulation is then given by  
\[S_{r}(t,\tau) =\omega_{r}\bigg{(}\tau-\frac{R_{bi}(t)}{c}\bigg{)}\omega_{a} \bigg{(}\frac{t-t_{0}}{T_{a}}\bigg{)}\] \[\times\exp\bigg{[}j\pi k_{r}\bigg{(}\tau-\frac{R_{bi}(t)}{c} \bigg{)}^{2}-j2\pi f_{0}\frac{R_{bi}(t)}{c}\bigg{]} \tag{1}\]  
where \(t\) and \(\tau\) represent the slow time and fast time variables, respectively. \(\omega_{r}\) and \(\omega_{a}\) are the range and azimuth envelopes, respectively. \(f_{0}\) denotes the carrier frequency and \(c\) is the speed of light. \(T_{a}\) represents the synthetic aperture time and \(k_{r}\) is the range chirp rate. \(t_{0}\) is the beam center crossing time of an arbitrary target \(P\). \(R_{bi}(t)\) is the bistatic range history, which will be analyzed in the next subsection in detail.
# Context-Aware Bidirectional Neural Model for Sindhi Named Entity Recognition
## 6 Conclusions  
In this paper, we propose the CaBiLSTM neural architecture for Sindhi named entity recognition and obtains excellent results in the entity extraction task. Based on the BiLSTM-Attention-CRF, we introduce task-specific contextual representation learning in the form of joint character-level and word-level representations. In addition, we exploit the neural baseline models, the impact of dropout, the context window size, and the pretrained representations, including SdGloVe and SdfasText. Our proposed CaBiLSTM model obtain new state-of-the-art performance by yielding the excellent F1-score of 91.25% on the SiNER dataset without relying on external language-specific resources, such as dictionaries or gazetteers. In the future, we intend to exploit the CaBiLSTM model on the other NER datasets. Moreover, our proposed model can be applied to sequence tagging tasks, such as part-of-speech tagging.  
Conceptualization, W.A.; Formal analysis, J.K., R.K. and Y.R.; Funding acquisition, Z.X.; Methodology, W.A. and Z.X.; Project administration, Z.X.; Supervision, Z.X.; Validation, J.K. and R.K.; Visualization, Y.R.; Writing--original draft, W.A.; Writing--review & editing, J.K. and Y.R. All authors have read and agreed to the published version of the manuscript.  
This work was funded by the National Key R&D Program of China (No.2018 YFB1005100 & No. 2018 YFB1005104).  
Figure 5: Label-wise F1-score of the CaBiLSTM model on the test set.  
\begin{table}
\begin{tabular}{l l c c c} \hline \hline
**Paper** & **Model** & **Precision\%** & **Recall\%** & **F1-Score\%** \\ \hline \hline \multirow{2}{*}{Existing work [21]} & BiLSTM-CRF (GloVe) & 84.40 & 84.93 & 84.67 \\  & BiLSTM-CRF (fastText) & 90.83 & 87.54 & 89.16 \\ \hline \multirow{3}{*}{Our work} & CaBiLSTM (SdGloVe) & 88.37 & 89.25 & 88.79 \\  & CaBiLSTM (SdfasText) & **90.27** & **90.64** & **90.11** \\ \cline{1-1}  & CaBiLSTM (CRL) & **90.43** & **91.76** & **91.25** \\ \hline \hline \end{tabular}
\end{table}
Table 8: The comparison of our proposed CaBiLSTM model with the previous works on SiNER dataset using SdGloVe and SdfasText representations. Bold font denotes the best results.
# Along-Track Multistatic Synthetic Aperture Radar Formations of Miniatellites
## 4 Control of Sensor Position  
### Relation between Formation Distance, PRF, and System Performance  
Equation (2) provides the conditions for optimal spacing of output samples in a formation, according to a given value of PRF. In case of not uniform output sampling, a degradation of performance is expected as explained in [6; 7; 8]. In the limit conditions, some output samples coincide, and the corresponding rows of the design matrix \(\mathbf{H}\) are linearly dependent. In this case, the inversion is not possible unless such rows are discarded, reducing this way the reconstruction capability of the formation to the case \(R<N\).  
In SAR design, it is common to select PRF within definite intervals to avoid the returning echoes to collide with nadir returns or with transmitting pulses [19]. The interval of existence of valid PRFs is then a function of the acquisition geometry, in particular of the incidence angles. Once the geometry of acquisition and the swath width is chosen, only some intervals of PRF values are possible. Ideal formation distance must be set according to Equation (2) and such constraint.  
In a realistic context, however, the sensor distance cannot be controlled with infinite precision. More commonly, sensors are uniformly set (i.e., nominally in ideal positions, for a given PRF) but, for a uncontrolled extent, \(\delta x\) that is often modeled as a zero-mean random variable Gaussian distributed with standard deviation of few meters:  
\[dx_{i}=i\cdot dx+\delta x. \tag{23}\]  
From Equation (2), it is easy to infer that the minimum distance between a good sensor separation and the next bad separation is as little as \(N/(N-1)\cdot 2v/(N\cdot PRF)\). For a practical system with a PRF under 1000 Hz and \(N=5\), this distance amounts to about 3.5 m. It means that the physical separation existing between a good phase center positioning of two consecutive sensors and the closest bad positioning is of the same order of the antenna length. The sensor position in orbit should be controlled within a small fraction of such value, let us say better than 0.3 m. Currently, such a tight control of the sensors position is hardly reachable. Moreover, due to the chaotic behavior of satellites along the orbit, the goal positions, even if reached, could not be guaranteed for a long time, unless the frequent maneuver is adopted, with consequent decreasing of the life span of the mission.  
Of course, due to the duality of sensor position and PRF, it is possible to mitigate the degradation due to the loss of the control of sensor position by tuning the PRF.
# A Novel Approach for the Estimation of Doubly Spread Acoustic Channels Based on Wavelet Transform
## 3 WT-Based Sparse Channel Estimation
### Cwt  
As mentioned before, WT is an effective measurable tool to analyze non-stationary signal, and the instantaneous frequency of HFM varies with time. Therefore, WT is a preferable choice for the time-frequency analysis of HFM signal. The CWT of the received signal \(r(t)\) can be expressed below:  
\[W_{r}(a_{W},b)=\frac{1}{\sqrt{a_{W}}}\int_{-\infty}^{+\infty}r(t)\psi^{*}( \frac{t-b}{a_{W}})dt \tag{9}\]  
where \(\psi(t)\) is the basis function that called mother wavelet [20], and \(a_{W}\) and \(b\) are the time scale and time shift, respectively.  
Selection of proper mother wavelet is very important for effectively time-frequency analysis. There are different types of mother wavelet, such as Haar, Daubachies, Sine and Gaussian. In addition, they all satisfy the following admissible condition [21]:  
\[C_{\psi}=\int_{R}\frac{|\hat{\psi}(w)|^{2}}{|w|}dw<\infty \tag{10}\]  
where \(\hat{\psi}(w)\) is the Fourier transform of \(\psi(t)\).  
It is easy to verify that a signal with finite length in both time domain and frequency domain will satisfy (10), [PERSON], [PERSON] et al. [22] points out that the WT efficiency will increase if characteristic of mother wavelet is closer to the input signal. So we consider to employ the transmitted HFM signal as mother wavelet, and since the transmitted signal has limited samples, thus it's length is limited and can satisfy (10).
## 2 Materials and Methods
### Data Analysis  
#### 2.4.1 Spectral Data Extraction  
A square region of 100 \(\times\) 100 pixels around the center of each file in the calibrated image was taken as the region of interest (ROI), where the WHC traits had been measured. All spectral data of each pixel contained in the ROI were extracted and averaged into one mean spectrum, which stood for the file. After all filets finished this procedure, a spectral matrix of 90 samples \(\times\) 198 bands was constructed. The identification of ROIs and extraction of spectral data from the ROIs were carried out using ENVI 4.8 (Exelis Visual Information Solutions, Boulder, CO, USA).
## 4 Results and Discussion
### Effect of Product Flow Rate and Cycle Times on Oxygen Production Performance of CP-\(\pi\) RFA  
The oxygen product flow rate will affect the oxygen purity and recovery. Figure 13 shows the changes in oxygen product purity with the cycle times and the oxygen product flow rate for the CP-\(\pi\) RFA. The oxygen product purity increases from 66% to 98.6% significantly after the eighth cycle, and since then enters the stable cycle process. The oxygen product purity decreases from 98.6% to 78.5%. Under the same conditions, increasing the product flow rate requires increasing the feed airflow, which will further increase the airflow speed and the mass transfer movement in the adsorber. In addition, due to the constant mass transfer coefficient of the adsorbent, the higher product flow rate prolongs the mass transfer area and reduces the oxygen purity.  
Figure 12: Comparison of axial O\({}_{2}\) purity profiles at the end of the 4 steps in the cycle steady state for the CP-\(\pi\) RFA:(**a**) Pr, (**b**) Ad, (**c**) Cb, (**d**) Pu.  
The oxygen product flow rate has an important influence on the oxygen production performance. By lowering the oxygen product purity, it will generate more oxygen which can decrease operational costs, reduce the equipment size, and save the initial investment. For instance, oxygen product purity of 80% can meet a lot of industrial requirements.  
Compared with the traditional ones, the RFA is convenient for large-scale, has low pressure resistance, and saves energy. The concentration of PSA oxygen production can reach 95% [39]. Generally, the product concentration is adjusted according to user needs. In many cases, the oxygen concentration is set to 90%. Different types of molecular sieves have different productivity. Industrial oxygen molecular sieves are designed to be 80-100 m\({}^{3}\)/h through the conversion of vacuum swing adsorption (VSA), and oxygen productivity of PSA is lower than VSA [40].