esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 kd-TreeData Structure for Cell Subdivision
### Algorithm  
kd-tree is a binary space tree that partitions the space dimension-wise, and is a superset of the quad-tree and oct-tree. The kd-tree structure has a long tradition in computational geometry [36] in the context of solving range searching problems. kd-tree parallelization has been extensively investigated to increase construction speed [37; 38]. Specifically, given a set of spatial points, a kd-tree can store the points in an orderly manner in order to achieve quick range searching. In this work, the kd-tree is used to store the sub-cells instead of spatial points. A two-dimensional example is shown in Figure 3.  
Figure 2: Illustration of sub-cell coalescence when removing non-intersected cell grids. In a standard kd-tree, each level has \(k\) depths, i.e., \(k\)-times splitting (e.g., a 2D tree splits in the x and y directions successively, whereas a 3D tree splits in the x, y, and z directions). In the present work, extra flexibility is provided in the splitting procedure by enabling an arbitrary order of the splitting direction within each level. First, we explore all possible splitting directions at each depth, and choose the direction in which the splitting line/plane \(l\) does not intersect with the boundary. If the intersection cannot be avoided in any direction, a default splitting direction is chosen. Each split produces two new sub-cells. If any of the sub-cells is not intersected by the boundary, a corresponding leaf is created in the kd-tree. Otherwise, the split continues until the maximum level is reached. The pseudocode of the proposed algorithm is described in Algorithm 1. _Remarks_:  
1. After the kd-tree is constructed for a given cut element, a tree traversal algorithm, such as Depth First Search (DFS) or Breadth First Search (BFS), can be employed to extract all the leaves of the kd-tree and obtain the sub-cells stored therein. The tree traversal step is generally much faster than tree construction. 2. The intersection between the splitting line/plane and the boundary can be identified by checking the signed algebraic level sets [34; 35] between them, as discussed in Section 4. A line or plane is assumed to intersect the boundary if the bounding vertices of the line/plane have opposite signs. The algebraic level sets are a monotonic measure of distance to the NURBS boundary, enabling accurate judgment of the intersection. This intersection check does not introduce additional cost compared with a quad/oct-tree structure, as it is required in the latter as well. 3. In the included numerical examples, the cell is cut in the middle whenever an intersection is detected; this can be further enhanced by unequal splitting of the cells, albeit with the additional cost of determining an accurate intersection location. Figure 3: Illustration of kd-tree based sub-division. The maximum level illustrated here is three. Each level consists of two depths that represent different splitting directions; \(l_{i}\) (stored in nodes) and \(C_{i}\) (stored in leaves) denote a splitting line and a sub-cell, respectively.
# An Analysis of the Altitude Impact on Roots Compressor Operation for a Fuel Cell System
## 2 Materials and Methods  
In this section, the main aspects of the methodology followed during the simulations will be detailed. First, the fuel cell balance-of-plant model will be described, including the validation of the physical model used to simulate the stack response as a function of the cathode working pressure. Then, the characteristics and working map of the Roots compressor technology under investigation will be presented. Finally, the test matrix, including altitude variations, will be summarized.
# Spiking Neural P Systems for Basic Arithmetic Operations
## 3 Arithmetic Operation in Spiking Neural P Systems
### Binary Addition in SNP Systems  
The addition operation is the foundation of arithmetic operations. It involves adding two binary numbers with the same order while considering the possibility of a carry from the lower order. The basic idea of our designed binary addition SNPS is:  
1. By inputting the binary string of the addend from the lowest bit to the highest bit using the input neuron \(\sigma_{input}\), if the \(i\)-th bit (\(0\leq i\leq k-1\)) in the input string is 1, the neuron \(\sigma_{input}\) generates one spike; otherwise, it generates no spike. 2. After each bit of the augend is input, it is buffered in the system and waits for the input of the addend. When the highest bit of the augend is input, the addend is immediately input. 3. When the \(i\)-th bit (\(0\leq i\leq k-1\)) of the augend reaches the addition neuron \(\sigma_{Add}\), the \(i\)-th bit of the addend is taken out from the buffer and input to \(\sigma_{Add}\). The addition operation is performed by the rules in \(\sigma_{Add}\). Therefore, the spike neural p system \(\Pi_{\mathbf{BASNP}}\) for the k-bit binary number addition designed in this paper includes an input neuron, addition neuron, auxiliary neuron group, augend input auxiliary neuron group, added input auxiliary neuron group, and augend cache group of neurons. \(\Pi_{\mathbf{BASNP}}\) is defined as in Formula (3), and the membrane structure is shown in Figure 1.  
In particular, in order to simplify the complex connections between neurons, the following conventions are used in the SNPS structure diagram in this paper:  
* Neuron-to-neuron connections are indicated by thin arrows, for example, the connection between \(\sigma_{aux1}\) and \(\sigma_{aux2}\) in Figure 1.
* Connections of neurons to groups of neurons are indicated by thick arrows. Specifically, if the front end of the thick arrow is a single neuron \(\sigma_{0}\), and the end is a neuron group \(\sigma_{\mathrm{x}}=\{\sigma_{1},\,\sigma_{2},\,\ldots,\,\sigma_{n}\}\), this means that each neuron \(\sigma_{i}\) (\(1\leq i\leq\mathrm{n}\)) in neuron \(\sigma_{0}\) is connected to neuron group \(\sigma_{\mathrm{x}}\); on the contrary, if the front end of the thick arrow is a neuron group \(\sigma_{\mathrm{x}}\), and the end is a single neuron \(\sigma_{0}\), this means that each neuron in the neuron group \(\sigma_{\mathrm{x}}\) has a connection to neuron \(\sigma_{0}\). * Group-to-neuron connections are indicated by thick arrows. If the front end of the thick arrow is a neuron group \(\sigma_{\mathrm{x}}=\{\sigma_{1},\,\sigma_{2},\,\ldots,\,\sigma_{n}\}\) and the end is a neuron group \(\sigma_{\mathrm{x^{\prime}}}=\{\sigma_{1^{\prime}},\,\sigma_{2^{\prime}},\,\ldots, \,\sigma_{n^{\prime}}\}\), then two neurons in the same order from the group \(\sigma_{\mathrm{x}}\) to the neuron group \(\sigma_{\mathrm{x^{\prime}}}\) are connected, that is, there is a connection from \(\sigma_{i}\) to \(\sigma_{i^{\prime}}\), \(1\leq i\leq\mathrm{n}\).
# Estimation of Seismically-Induced Crest Settlement of Earth Core Rockfill Dams
## 3 Validation of the Numerical Model  
The numerical model was validated against the centrifuge test measurements presented by [PERSON] et al. (2018). The centrifuge model and the corresponding numerical model are shown in Figure 3. The height and width of the ECRD were 5.2 m and 18.8 m, respectively. The model was significantly smaller than an earth core dam, but it was considered to be acceptable for validation purposes [PERSON] et al. (2018). The following pressure-dependent equations reported by [PERSON] et al. (2018) were applied to assign the shear wave velocities of the rockfill and core.  
\[V_{s}=109(\sigma_{c})^{0.24} \tag{5}\]  
\[V_{s}=41.8(\sigma_{c})^{0.39} \tag{6}\]  
where \(\sigma_{c}\) is the confining pressure (kPa) and \(V_{s}\) is the shear wave velocity (m/s). The equations were developed to match the resonant column test results of materials used in the centrifuge tests. Triaxial tests with specimens that were 50 mm diameter were also performed to measure the shear strengths. Table 2 lists the properties of the centrifuge model.  
The numerical model was identical to the ECRD model described in the previous section, including the constitutive model, the damping formulation, and the lateral boundary conditions. The fixed condition was applied to the bottom boundary to simulate the rigid boundary of the centrifuge model, whereas the viscous dampers were used at the bottom boundary in the baseline ECRD model. Figure 4 compares the values measured by [PERSON] et al. (2018) and the computed _PGA_ profiles from the model defined by this study. The numerical analysis was shown to provide reliable estimates of the dam response. It was therefore concluded that the numerical model could be used to predict the settlement of ECRDs.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Layer** & **Unit Weight (kN/m3)** & **Friction Angle (o)** & **Cohesion (kPa)** & **Poisson’s Ratio** \\ \hline Rockfill & 21.09 & 40 & 2 & 0.30 \\ Core & 21 & 33 & 64 & 0.35 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Properties of the dam and foundation soil for the centrifuge model.
# Improved ECG Watermarking Technique Using Curvelet Transform
## 6 Experimental Results  
The demonstration of the presented work was assessed using parameters such as imperceptibility, data loss and the effect of ability to diagnose. Peak signal to noise ratio (PSNR), normalized correlation (NC), PRD and KL metrics were used to measure the imperceptibility and effect of ability to diagnose. Data loss can be estimated using MSE, bit error rate (BER) and SSIM [27]. In this, \(X_{c}\) was the host ECGimage and \(X_{w}\) was watermarked ECG, M \(\times\) N was the size of image M = no. of rows and N = number of columns.  
**A. Peak signal to noise ratio (PSNR):** The PSNR is usually expressed in terms of the logarithmic decibel scale. The following expression was used to calculate PSNR between two images.  
\[PSNR=20\log_{10}\left(\frac{\max(X_{\mathrm{c}})}{\sqrt{\frac{1}{\mathrm{M} \mathrm{N}}\sum_{\mathrm{i=1}}^{\mathrm{N}}\left[\mathrm{X_{\mathrm{c}}-X_{ \mathrm{w}}}\right]^{2}}}\right) \tag{11}\]
## 1 Introduction
### Unmanned Aerial Vehicles (UAV)  
UAVs or Unmanned Aerial Systems (UASs) are a relatively new technology in PA which has spread among agricultural users after 2000. Agricultural UAVs can carry several sensors, such as hyperspectral, multispectral (visible/near-infrared) or thermal cameras [38; 39]. Images acquired by UAVs require photogrammetry and mosaicization processes to merge multiple images acquired by the sensors. Similarly to airborne sensors, a specific calibration sensor is needed to correct the incident light during the acquisition time and obtain the correct reflectance value [40]. The spatial resolution of UAV-acquired images is primarily affected by the flight altitude. The higher the altitude, the lower the spatial resolution of the derived images. UAVs used for agricultural purposes are mainly ascribable to two main classes: fixed wings and multi-copters.  
Satellite, plane, and UAV-based VIs can be used to map in-field variability and drive variable rate management of the inputs. Nevertheless, the choice of the most appropriate sensors is not always an easy task, as it involves economic and agronomic constraints. Moreover, the actual prices of these different technologies sometimes do not include some costs (minimum order area, take-off, elaboration, etc.), leading to difficult and blinded choices for technicians and farm managers [41].  
In the current study, UAV-, plane- and satellite-acquired images were compared according to sensor quality, price, and profitability for variable rate nitrogen management. These sensors' varied data could be profitably used for several other applications (e.g., variable rate irrigation, stress and disease detection, yield estimation). However, variable rate nitrogen management was chosen as a standard technology because its use is validated by several scientific works involving remote sensors. This work analyzes the economic benefits provided by variable rate nitrogen application taking into account the price of  
Figure 1: Evolution of data volume per hectare provided by different constellations of satellites. Since the first civil satellite for earth observation was launched (Landsat 1), the amount of data provided per hectare has increased from 100 B to 100 MB (Pleiades-Neo).  
different remote sensing platforms to define the profitability of these technologies by estimating the final cost of images provided.
# Axial Compression Behavior of Steel Angle-Corrugated Steel Plate-Confined Concrete Columns
## 6 Summary
#### 5.1.3 ACI 318-14  
Similar to Eurocode 4-2004, ACI 318-14 also does not consider the confinement of core concrete, whose compressive strength is even reduced by 15%. The calculation method is shown in Equation (20).  
\[N_{\rm u-ACI}=0.85f^{\prime}_{\rm c}A_{\rm c}+f_{\rm y2}A_{\rm s2} \tag{20}\]  
The mean value of \(N_{\rm u-FEM}/N_{\rm u-Gal}\) is 1.374, and the standard deviation is 0.078. The calculated results have strong dispersion. In Eurocode 4-2004 and ACI 318-14, the confinement  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Specimen**} & \multicolumn{2}{c}{**GB50936-2014**} & \multicolumn{2}{c}{**Eurocode 4-2004**} & \multicolumn{2}{c}{**ACI 318-14**} & \multicolumn{2}{c}{**DBJ/T13-51-2010**} & \multicolumn{2}{c}{**AIJ-2001**} \\ \cline{2-11}  & \(N_{\rm u-Gal}\) & \(N_{\rm u-FEM}/N_{\rm u-Gal}\) & \(N_{\rm u-FEM}/N_{\rm u-Gal}\) & \(N_{\rm u-EM}/N_{\rm u-Gal}\) & \(N_{\rm u-EM}/N_{\rm u-Gal}\) & \(N_{\rm u-EM}/N_{\rm u-Gal}\) & \(N_{\rm u-EM}/N_{\rm u-Gal}\) & \(N_{\rm u-EM}/N_{\rm u-Gal}\) \\ \hline SA-CS-15 & 3206.1 & 0.842 & 2250.1 & 1.200 & 1945.9 & 1.387 & 3210.0 & 0.841 & 1915.1 & 1.410 \\ SA-CS-16 & 3210.8 & 0.860 & 2305.9 & 1.197 & 2003.7 & 1.378 & 3222.6 & 0.857 & 1904.0 & 1.450 \\ SA-CS-17 & 3111.3 & 0.787 & 2126.2 & 1.152 & 1829.9 & 1.338 & 3122.5 & 0.784 & 1870.6 & 1.309 \\ SA-CS-18 & 3216.2 & 0.810 & 2204.7 & 1.182 & 1896.6 & 1.374 & 3212.1 & 0.811 & 1937.4 & 1.345 \\ SA-CS-19 & 3235.4 & 0.811 & 2217.8 & 1.183 & 1907.8 & 1.375 & 3227.0 & 0.813 & 1948.5 & 1.347 \\ SA-CS-20 & 3253.2 & 0.812 & 2230.9 & 1.184 & 1918.9 & 1.377 & 3242.0 & 0.815 & 1959.6 & 1.348 \\ SA-CS-21 & 3272.2 & 0.812 & 2244.0 & 1.184 & 1930.0 & 1.377 & 3256.9 & 0.816 & 1970.7 & 1.348 \\ SA-CS-22 & 3287.6 & 0.813 & 2257.1 & 1.184 & 1941.1 & 1.377 & 3271.8 & 0.817 & 1981.8 & 1.349 \\ SA-CS-23 & 3377.4 & 0.796 & 2222.5 & 1.158 & 1996.7 & 1.346 & 3346.5 & 0.803 & 2037.4 & 1.319 \\ SA-CS-230 & 2627.2 & 0.871 & 1866.3 & 1.267 & 1557.9 & 1.469 & 2649.0 & 0.864 & 1598.5 & 1.432 \\ SA-CS-280 & 3645.2 & 0.858 & 2585.8 & 1.222 & 2197.3 & 1.423 & 3631.3 & 0.861 & 2237.9 & 1.398 \\ SA-CS-330 & 4820.7 & 0.884 & 3450.7 & 1.235 & 2955.6 & 1.442 & 4773.0 & 0.893 & 2996.2 & 1.422 \\ Mean value & 0.806 & & 1.183 & 1.374 & & 0.808 & & 1.345 \\ Standard deviation & 0.038 & & 0.068 & & 0.078 & & 0.037 & & 0.064 \\ \hline \hline \end{tabular}
\end{table}
Table 4: _Cont._effect on the core concrete is ignored, and the bearing capacity is the simple superposition of the concrete and steel angle. It is undoubtable that the calculation results are smaller than the actual results.
## 3 Results and Discussion
### Isolation and Identification of the Active Substances in the A. xylocarpa Leaf Extracts  
Partitioning showed that the ethyl acetate fraction had higher inhibitory activity than the aqueous fraction (Figure 2). At 300 mg DW equivalent extract/mL, the ethyl acetate fraction inhibited the seedling length of _L. sativum_ by 1.9-2.1 times greater than that of the aqueous fraction. Therefore, the growth inhibitory substances in the ethyl acetate fraction were separated through a series of bioassay-guided fractionations. The most active fraction was then purified using HPLC, and two active substances were found. The molecular formula of substance 1 was determined as C\({}_{8}\)H\({}_{8}\)O\({}_{4}\) using HRESIMs at m/z 167.03 [M\(-\)H] \(-\) (calcd. for C\({}_{8}\)H\({}_{7}\)O\({}_{4}\), 167.03). The \({}^{1}\)H NMR spectrum (400 MHz, CD\({}_{3}\)OD) of the substance showed \(\rm{\delta_{H}}\) 3.89 (3H, s), 7.56 (1H, d, \(J\) = 1.7), 7.55 (1H, dd, \(J\) = 8.7, 1.7), and 6.84 (1H, d, \(J\) = 8.7). The substance was identified as 4-hydroxy-3-methoxy benzoic acid (vanillic acid). Substance 2 was determined as C\({}_{10}\)H\({}_{10}\)O\({}_{4}\) using HRESIMs at m/z 193.05 [M\(-\)H] \(-\) (calcd. for C\({}_{10}\)H\({}_{9}\)O\({}_{4}\), 193.05). The \({}^{1}\)H NMR spectrum (400 MHz, CD\({}_{3}\)OD) of the substance showed \(\rm{\delta_{H}}\) 3.90 (3H, s), 7.60 (1H, d, \(J\) = 15.9), 6.31 (1H, d, \(J\) = 15.9), 7.18 (1H, d, \(J\) = 1.9), 7.06 (1H, dd, \(J\) = 8.1, 1.9), and 6.81 (1H, d, \(J\) = 8.1). The substance was identified as 4-hydroxy-3-methoxy cinnamic acid (_trans_-ferulic acid).  
Vanillic acid and _trans_-ferulic acid are phenolic compounds, biosynthesized from phenylalanine via the shikimic acid pathway in plants. Vanillic acid is a hydroxybenzoic acid derivative found in several natural sources [55; 56; 57]. This compound has been reported to have multiple activities, including anti-inflammatory, antimicrobial, anticancer, and antioxidant [58; 59]. On the other hand, _trans_-ferulic acid, a hydroxycinnamic acid derivative, is present in many edible plants [60; 61]. Many studies have found that _trans_-ferulic acid  
Figure 2: The effect of the aqueous and ethyl acetate fractions on the (**A**) shoot and (**B**) root length of _Lpidium sativum_ exposed to four concentrations. Means \(\pm\) SE with six replicates (10 seeds/replicates). The different letters on each column indicate significant differences ([PERSON]’s HSD, \(p<0.05\)).  
possesses different beneficial biological activities, including antioxidants [62; 63]. To our best knowledge, _A. xylocarpa_ leaves are a source of vanmillic acid and _trans_ -ferulic acid with phytotoxic effects.
## 3 Current Measurement Techniques
### Snow Property Determination Techniques
#### 3.2.1 _In-Situ_ Snow Stations  
There are numerous point snow height measurement devices on the market, with a wide range of prices and corresponding accuracies (highest accuracy is achieved using a laser. This has a quoted accuracy of \(\pm\)1 cm [36]. SLF are currently undertaking long-term tests to confirm this accuracy over snow). As they are point based and short-range, these devices are capable of measuring snow height continuously during a snowstorm (the laser snow height sensor is less effective in snow storms) and can be easily connected for remote data access. Note that the structure required to hold the instrument can sometimes have an influence on its measurement.  
In [31], eight methods of SWE and HNW measurement/calculation are compared (Snow Pillow, Snow Power, Parsivel, Rainingauge, SNOWPACK, COSMO-7, SIMPLE-SWE/HNW, and a randomapplication of new snow). The outcome of this comparison is that a RMSE of \(<\)60 mm or 8% in the measurement of SWE is good, as is an absolute accuracy of \(<\)5 mm in HNW.
## 3 Enhanced Interpolation Approach
### Optimizing FFT Operations  
With the help of the time-frequency decoupling, the FFT algorithm could be readily introduced to accelerate the summation of trigonometric items in the simulation. Based on Equations (24) and (34), Equation (13) could be reformulated as  
\[x_{j}(t)=\text{Re}\Bigg{\{}2\sqrt{\Delta\omega}\sum_{k=1}^{j}\sum_{q=1}^{N_{ \Phi}}a_{q}^{jj}(t)\sum_{l=1}^{N}\Phi_{q}^{jj}(\omega_{l})\beta_{jk}(\omega_{l} )e^{i[\theta_{jk}(\omega_{l})-\phi_{kl}]}e^{-i\omega_{l}t}\Bigg{\}} \tag{35}\]  
It can be seen that the FFT could be used to calculate the summation with respect to \(l\) in Equation (35) for each \(j\), \(k\) and \(q\). To generate an \(n\)-variate ground motion sample, a total of \(n(n+1)N_{\Phi}/2\) FFT operations was required.  
In order to further optimize the FFT operations, Equation (35) could be recast by exchanging the summation order, i.e.,  
\[x_{j}(t)=\text{Re}\Bigg{\{}2\sqrt{\Delta\omega}\sum_{q=1}^{N_{\Phi}}a_{q}^{jj}( t)\sum_{l=1}^{N}\Phi_{q}^{jj}(\omega_{l})e^{-i\omega_{l}t}\sum_{k=1}^{j}\beta_{ jk}(\omega_{l})e^{i[\theta_{jk}(\omega_{l})-\phi_{kl}]}\Bigg{\}} \tag{36}\]  
In this moment, the FFT would be used for the summation with respect to \(l\) only for each \(j\) and \(q\). Thus, the number of FFT operations was reduced to \(nN_{\Phi}\). Details about the usage of FFT in Equation (36) are given in Appendix A.
# Human-Like Walking with Heel Off and Toe Support for Biped Robot
## 2 Methods
### The Bipedal Robotic Gait  
When the contact point between the foot and ground changes during walking, the biped robot translates into the next walking phase that has quite different dynamical characteristics, resulting in many difficulties to the control of the biped robot. This paper is focused on the realization of the so-called \"heel off and toe support\" on a biped robot. Therefore, the bipedal robotic gait is simplified from the human walking pattern to some extent. First, the double support phase is assumed to be instantaneous. Second, when the swing foot strikes the ground, the sole is parallel to the ground. The desired robotic walking motion can then be regarded as including three phases: a heel support phase, a toe support phase, and an instantaneous double support phase (or impact phase). Figure 3 shows the bipedal robotic walking pattern with state transition events. Each phase is introduced as follows.  
1. Heel support phase (HSP). This phase starts when the toe of the swing leg lifts off the ground. The whole foot of the stance leg is assumed to remain flat and motionless on the ground without slipping. At the same time, the swing leg swings in the forward direction. In this phase, the biped robot is fully actuated because it has the same numbers of degrees of freedom (DOF) and actuators.
2. Toe support phase (TSP). This phase starts when the heel of the stance leg lifts off the ground. In this phase, the stance foot rotates around its toe, which is virtually pivoted to the ground, and the swing leg continues to swing forward. The biped robot is under-actuated because there is no actuation between the stance foot and the ground.
3. Impact Phase (IP). Leg roles exchange takes place in this phase. After the swing foot strikes the ground, the swing leg becomes the new stance leg, while the original stance leg rises from the ground and becomes the swing leg.  
Figure 2: The seven-link biped robot model with associated geometric and inertial properties. The corresponding links on each leg are geometrically and inertially identical.