esa-sceva/satcom-chunk-collection huggingface dataset:
# Numerical and Experimental Analysis of Torsion Springs Using NURBS Curves
## 2 Torsion-Spring Design  
### NURBS Curve  
A range of research has been conducted on curve expression according to polynomial theory. Among the numerous curve-expression methods, NURBS is the most accurate technique used to express complex organic shapes in two and three dimensions [9; 10]. Due to its simple calculation method, NURBS is employed in a variety of industrial fields that require curved shapes. A NURBS curve can be expressed through a combination of parameters, including knot, control point, degree, and weight, in basis functions with a relatively simple calculation algorithm. In NURBS curves, the initial basis function can be expressed as in Equation (1).  
\[N(u)=\sum_{i=0}^{n}N_{i,p}(u), \tag{1}\]  
where \(N_{i,p}(u)\) is the B-spline basis function. The equation applied to the algorithm differs with the number and value of the knot vectors; Equation (1) may also be expressed as either Equation (2) or Equation (3). To define B-spline basis functions, we need one more parameter: the degree of these basis functions, \(p\). The i-th B-spline basis function of degree \(p\), written as \(N_{i,p}(u)\), is defined recursively as follows:  
\[N_{i,0}(u)=\left\{\begin{array}{rl}1&\text{if }u_{i}\leq u\leq u_{i+1}\\ 0&\text{Otherwise}\end{array}\right. \tag{2}\]  
\[N_{i,p}(u)=\frac{u-u_{i}}{u_{i+p}-u_{i}}N_{i,p-1(u)}+\frac{u_{i+p+1}-u}{u_{i+ p+1}-u_{i+1}}N_{i+1,p-1}(u), \tag{3}\]  
where \(i\) is the degree plus 1 (\(i=p+1\)), \(u_{i}\) is the knot, and \(u\) is the knot vector. The following basis function expresses the curve of a geometric shape as the degree (\(p\)) increases; however, as the function increases in complexity and decreases in accuracy, a suitable degree should be used according to the desired curve shape. The NURBS basis function can express the NURBS curve as a combination of the weight (\(w_{i}\)) and control point (\(P_{i}\)), as shown in Equation (4).  
\[C(u)=\sum_{i=0}^{n}\frac{N_{i,p}w_{i}}{\sum_{j=0}^{n}N_{j,n}w_{i}}P_{i}=\frac {\sum_{j=0}^{n}N_{i,p}w_{i}P_{i}}{\sum_{j=0}^{k}N_{i,p}w_{i}}, \tag{4}\]  
where \(P_{i}\) is the control point and \(w_{i}\) is the weight of control point. This equation can then be simplified into Equation (5).  
\[C(u)=\sum_{i=0}^{n}R_{i,p}(u)P_{i} \tag{5}\]The NURBS curve expressed by Equation (5) can be freely varied as the weight (\(w_{i}\)) increases and the control point (\(P_{i}\))shifts, demonstrating the relationship between the NURBS curve and these parameters.
## 2 Materials and Methods
### Antioxidant Activity
#### 2.6.2 ORAC Method  
The ORAC assay is based on the free radical reaction initiated by AAPH radicals. These react with a fluorescent substrate (fluorescein), giving rise to a non-fluorescent product. Therefore, the substrate concentration can be measured specifically, without interference and with high sensitivity. The reaction between AAPH and fluorescein is monitored by the decay of the fluorescent signal. The procedure according to [PERSON] et al. [27] was applied to performed the ORAC assay.  
Firstly, 1 L of 0.075 M sodium phosphate buffer at pH = 7 was prepared by mixing 4.04 g of sodium dihydrogen phosphate monohydrate and 8.14 g of disodium hydrogen phosphate dihydrate. Then 30 mL of 34.4 mg/g AAPH and 30 mL of 2.3 ug/g fluorescein solutions in previously prepared sodium phosphate buffer were prepared. The 2.3 ug/g fluorescein solution was prepared from 1000 ug/g stock solution of fluorescein in sodium phosphate buffer. The analysis was performed by mixing 800 uL of fluorescein with 100 uL of _Arctostaphylos uwa-ursi_ extract and 600 uL of AAPH and injecting them into an Alliance 2795 Separation Module (Waters, Milford, MA, USA) equipped with a 474 scanning fluorescence detector (\(\lambda_{\text{excitation}}\) = 491 nm and \(\lambda_{\text{emission}}\) = 515 nm). The system time running was set at 60 min, with 50 total injections/hour. The fluorescence intensity was measured every minute to obtain a fluorescein decay curve. The samples acquisition was performed at 40 \({}^{\circ}\)C without chromatographic column with water as the mobile phase and 0.5 mL/min flow. Injection volume was 20 uL. The concentration of extract has been determined experimentally by testing different dilutions of extract. Also blank was injected (800 uL of fluorescein + 100 uL of 80% methanol + 600 uL of AAPH). All samples were analyzed in triplicate. The results are expressed as Trolox equivalents. Trolox, used as a reference antioxidant, was dissolved in sodium phosphate buffer. The following concentrations of Trolox required for the calibration curve were prepared: 0, 50, 100, 150, 200, 250 ug/g.
Results showed that it is possible to reconstruct the target inside a head phantom of known shape with several unknown tissue layers [41]. This work investigates microwave head imaging further with the help a 3-D DBIM algorithm. This allows to test performance for more realistic scenarios, where weak target responses are captured by a limited number of antennas surrounding the head in a 3-D array. To this end, we have implemented an in-house GPU-based 3-D FDTD forward solver, which enables a computationally efficient 3-D implementation of our recently proposedDBIM-FISTA. By optimizing the FDTD code specifically for our application, we achieve a more computationally efficient implementation than previous work [3; 25] which used GPU-based platform Acceleware [42] to perform MWT reconstructions of numerical breast phantoms of varying tissue density. We also simplify the 3-D inversion further by considering a scalar Green's function, which assumes a single electric field component transmission by our linearly polarized antenna. We compare results from this approximation with the vectorial Green's function which considers all three electric field components inside the reconstruction domain. Importantly, our results show, for the first time in microwave head imaging, that the scalar 3-D approximation leads to almost identical results with the vectorial implementation. Our DBIM algorithm is also more efficient at each DBIM iteration, as the employed FISTA algorithm uses an accelerated momentum which leads to faster convergence than CG-type inverse solvers [43]. Moreover, as a shrinkage/thresholding algorithm, it helps to reduce the chance of getting stuck into local minima [44]. The algorithm is tested on different reconstruction scenarios with the MRI-based Zubal head phantom [45] and is validated with an experimental brain phantom. Beyond validating the algorithm, our study examines the benefits of imaging in 3-D by comparing with 2-D implementations for challenging target location and limited prior information of the head's structure. To this end, we use a cross-sectional axial slice from the 3-D brain model and compare reconstructed images for this slice using the 2-D and 3-D algorithm. The remainder of the paper is organized as follows: In Section 2, we review our recently proposed DBIM-FISTA algorithm [40] for reconstructing the spatial distribution of dielectric properties inside the region of interest. We also presents the algorithm's implementation in 3-D with our in-house, GPU-based FDTD forward solver. It also details the experimental head phantom and the different head models based on the Zubal head phantom used to test our algorithm. Reconstruction results for the numerical models and experimental phantom are presented in Section 3, followed by discussion in Section 4.
## 2 Materials and Methods  
### Test Sand  
The grain-size distribution curve of the test sand, obtained through the conventional sieve analysis test performed, is provided in Figure 1. The particle diameters corresponding to 10%, 30%, 50% and 60% finer were obtained as \(D_{10}\) = 0.19 mm, \(D_{30}\) = 0.245 mm, \(D_{50}\) = 0.265 mm and \(D_{60}\) = 0.275 mm. In view of these values, the uniformity (i.e., \(C_{\text{u}}=D_{60}/D_{10}\)) and curvature (i.e., \(C_{\text{c}}={D_{30}}^{2}/(D_{10}D_{60})\)) coefficients were calculated as 1.447 and 1.149, respectively; these values indicate that the test sand is _poorly graded_ (i.e., SP) based on the Unified Soil Classification System (USCS) [45].  
Figure 1: Grain-size distribution curve of the test sand.  
Other physical attributes of the test sand included a specific gravity of \(G_{\rm s}\) = 2.65 (measured as per ASTM D854 [45]), along with maximum and minimum void ratios (measured as per ASTM D4253 [46] and ASTM D4254 [47]) of \(e_{\rm max}\) = 1.07 and \(e_{\rm min}\) = 0.76, respectively. In view of the \(e_{\rm max}\) and \(e_{\rm min}\) values, the test sand can be characterized as having relatively poor compactability. It should be mentioned that the mineralogical composition of the examined sand was dominated primarily by _silica_, along with traces of 2.3% _magnesium silicate_ and 1.2% _ferric oxide_.
# Object-Based Time-Constrained Dynamic Time Warping Classification of Crops Using Sentinel-2
## 4 Discussion
### Segmentation of SITS  
Segmentation of satellite images is one of the main challenges of an OBIA approach [71]. A very good indicator of the spatial match between delineated agricultural fields and reference objects is represented by the low value of the US metric (i.e., 0.04 for TA1 and 0.02 for TA2). The US is considered the most important indicator of the segmentation accuracy [55; 72] since it is difficult to re-process and classify correctly the initially under-segmented objects [73]. OS value was higher for TA2 since the circle-pivot irrigation parcels had mainly two sizes, of 50 or 200 ha, the bigger ones being over-segmented. As expected, the Sentinel-2 time series provided satisfactory agricultural field delineation capabilities especially in regions with smaller fields [73].  
The two test areas presented a high complexity of cropping cycles and, therefore, changes in the geometry of parcels throughout the entire time frame analyzed. Incorporation of multi-temporal images in the segmentation procedure allowed the delineation of homogeneous objects through time. We used all cloud free 10 m spatial resolution bands in the segmentation process. Other solutions may require either a knowledge-driven selection of images or a statistical selection (e.g., principal component analysis). Furthermore, combining multiresolution segmentation with superpixels can help in reducing the resources and time needed for the segmentation process [74].
# Joint Pedestrian and Body Part Detection via Semantic Relationship Learning
## 3 Our Approach
### Body Part Indexed Feature (BPIF)  
The aim of BPIF is two-fold: (i) encode the semantic relationship between individual body parts (i.e., head, head-shoulder, upper body, and whole body), and (ii) highlight the features for each body part. As shown in Figure 2, BPIF is composed of two components. One component combines the features from all the body parts and forms a joint feature map, which is inspired by the modified shape indexed features [24] used for face landmark regression. The second component is the per body part features at a more detailed scale. We provide the details of how to compute BPIF in Algorithm 1, and we also give an example of this process in Figure 3. The entire BPIF is followed by two convolutional layers for feature dimensionality reduction.  
```
0:\(F,R_{1},R_{2},R_{3},R_{4},N_{s}\) \(F\) is the image features using a backbone \(R_{1},R_{2},R_{3}\) and \(R_{4}\) are the sets of different body parts' bounding boxes of the BiC results \(N_{s}\) is the BPIF scale hyper-parameter Output:\(O_{1},O_{2},O_{3},O_{4}\) \(O_{1},O_{2},O_{3}\) and \(O_{4}\) are the BPIF, which be used to regress the corresponding bounding boxes in the refinement module function G_BPIF(\(F,R_{1},R_{2},R_{3},R_{4},N_{s}\)) \(R^{\prime}_{i}=\text{RoI Align}(F,R_{i},N_{s}/2)\) where \(i=1,2,3,4\) and \(R_{i}\in[512,N_{s}/2,N_{s}/2]\) \(f_{all}=\begin{bmatrix}R^{\prime}_{1}&R^{\prime}_{2}\\ R^{\prime}_{3}&R^{\prime}_{4}\end{bmatrix}\) where \(f_{all}\in[512,N_{s},N_{s}]\) \(R_{i}=\text{RoI Align}(F,R_{i},N_{s})\) where \(i=1,2,3,4\) and \(R_{i}\in[512,N_{s},N_{s}]\) \(O_{i}=\text{concat}(F_{all},R_{i})\) where \(i=1,2,3,4\) and \(O_{i}\in[1024,N_{s},N_{s}]\) return\(O_{1},O_{2},O_{3},O_{4}\) endfunction
```  
**Algorithm 1** Compute BPIF  
It is worth noting that unlike HeadNet [21] the Body-in-Context (BiC) and Refinement modules in our model do not share parameters. Our considerations are as follows. The cascaded object  
Figure 3: An example of how to compute BPIF features based on the preliminary detection of the pedestrian and body parts.  
detection [33] often shares parameters, but the paper in [16] shows that while iterative bounding box regression is a post-processing procedure used to improve bounding boxes accuracies, cascaded regression is a resampling procedure that changes the distribution of hypotheses to be processed by the different stages. Further, different from normal cascaded object detection, BiC and Refinement modules in our model have different objectives and inputs. While BiC module uses the RoI features per proposal to jointly regress the pedestrian and body part bounding boxes, the refinement module takes the BPIF features to refine the locations of the initial bounding box detections by BiC.
## 5 Hamiltonian Formulation of the Space Dimension Dynamics  
Here, we will apply the general framework of Hamiltonian mechanics to the equations of renormdynamics. By this method we made good motivation for an explicit form of \(D(x)\): we use a simple example of Hamiltonian mechanics and show how to use it to find the dimension \(D\) of space as a function of distance \(x\). Let us consider the simplest Hamiltonian dynamics  
\[\dot{x}_{1}=\{x_{1},H\},\quad\dot{x}_{2}=\{x_{2},H\} \tag{18}\]  
for dynamical variables (phase space) \((x_{1},x_{2})\), Hamiltonian \(H\)  
\[H=\frac{p^{2}}{2m}+V(x)=\frac{x_{1}^{2}}{2m}+V(x_{2}) \tag{19}\]  
and Poisson structure  
\[\{A,B\}=f_{mn}\frac{\partial A}{\partial x_{n}}\frac{\partial B}{\partial x_{ m}}=f_{12}\left(\frac{\partial A}{\partial x_{1}}\frac{\partial B}{\partial x _{2}}-\frac{\partial A}{\partial x_{2}}\frac{\partial B}{\partial x_{1}} \right). \tag{20}\]  
Instead of solving the system of motion equations, having one integral of motion-Hamiltonian, we may find \(x_{1}\) from the Hamiltonian, insert it in the motion equation for \(x_{2}\) and solve it. Similarly, we consider our coupling constant dynamics. The variables \(x,D\) and \(\alpha\) are nonnegative, so it is natural to introduce, free from this restriction, variables: \(t=\ln x\), \(x_{1}=\ln\alpha_{s}\) and \(x_{2}=\ln D\). Then from (15) we obtain the following Hamiltonian and motion equations  
\[H(x_{1},x_{2},t)=x_{1}-V(x_{2},t)=E\Rightarrow x_{1}=V(x_{2},t)+E,\] \[\dot{x}_{1}=f_{12}\frac{\partial V}{\partial x_{2}},\] \[\dot{x}_{2}=-f_{12},\;V(x_{2},t)=\ln\left(\frac{\pi^{(D-2)/2}}{2 \Gamma(D/2)}(D-2)\frac{k-x^{2}}{x^{3-D}}\right)-E. \tag{21}\]  
We may also take \(x_{1}=\alpha_{s}=\alpha,\;E=0\), then  
\[x_{1}=V(x_{2},t)=(k-x^{2})x^{D-3}=(k-x^{2})x^{\exp(x_{2})-3}=(k- e^{2t})e^{t(e^{-t}-3)},\] \[\dot{x}_{1}=\frac{\partial V}{\partial x_{2}}=(k-x^{2})x^{e^{2}-3 }\ln xe^{x_{2}}=(k-e^{2t})te^{t(e^{-t}-3)}e^{-t},\;f_{12}=1,\] \[\dot{\alpha}=\beta=te^{-t}\alpha=\beta_{1}\alpha,\;\beta_{1}=\ln \frac{\alpha e^{3t}}{k-e^{2t}}\] \[\dot{x}_{2}=-1\Rightarrow x_{2}=-t+\ln c,\;D=c/x,\;c=1, \tag{22}\]Let us return to the general expression (16)  
\[H=\frac{p^{2}}{2m}+V(x)=\frac{x_{1}^{2}}{2m}+V(x_{2}) \tag{19}\]0 \[H=\frac{p^{2}}{2m}+V(x)=\frac{x_{1}^{2}}{2m}+V(x_{2}) \tag{19}\]1  
where for simplicity we set the integration constant \(c=1\) and defined \(D(x)=1/x\). Note that \(x>0\) and \(\alpha_{s}\geq 0\) when \(x<\min(1/2,\sqrt{k})=1/2\) or \(x>\max(1/2,\sqrt{k})=\sqrt{k}=0.72\) while \(\alpha_{s}<0\) for \(1/2<x<0.72\), cf. \[H=\frac{p^{2}}{2m}+V(x)=\frac{x_{1}^{2}}{2m}+V(x_{2}) \tag{19}\]2  
We may exclude the negative interval \((1/2,0.72)\) by using different mass scales \(\mu\): \(r\mu_{1}=1/2\), \(r\mu_{2}=0.72\), \(\mu_{2}/\mu_{1}=1.44\). Alternatively, we may close the negative interval by taking \(\sqrt{k}=1/2\Rightarrow\alpha_{s}=3/16=0.1875\) in the last formula of (23), c.f.
# Phase Reversal Method for Damage Imaging in Composite Laminates Based on Data Fusion
## 3 Results
### Numerical Analysis Results
The arrival-time comparison of the damage scattering signals received by the sensors at the symmetrical positions at four linear measurement points is shown in Figure 5. The damage scattering signals first arrived at the positive direction of the \(x\)-axis and \(y\)-axis, so it could be concluded that the damage was located in the first quadrant of the coordinate system with the center of the plate as an origin. Since the damage was located in the first quadrant, the signals of forward points on the \(x\)-axis and \(y\)-axis were selected for phase reversal damage detection. The phase corresponding to the frequencies in the frequency band near the center frequency of the damage scattering signal on the \(x\)-axis is shown in Figure 6. The phase was obtained by the Fourier transform, and the frequency interval was 5 kHz. As shown in Figure 6, the phase difference between the scattered signals obtained by different sensors was different. According to the PRM, the scattered damage signals can be reconstructed, and the similarity of the reconstructed signals can be used as a damage-imaging index. As shown in Figure 7, the imaging matrices of measurement points on the \(x\)-axis and \(y\)-axis can be obtained respectively by Equations (7) and (8). The imaging results in Figure 7 show the geometric characteristics of the phase-reversal method. Specifically, the imaging result obtained by the linear receiving arrays in the same direction formed a hyperbola, which passed through the damage. By applying the proposed data-fusion method, the imaging matrices were obtained by Equation (9), and they were overlapping, but the corresponding curves met at the damage position. According to Equation (9), the imaging matrices shown in Figure 7 were superimposed and fused, and the imaging curves obtained from measuring points in different directions will intersect at the damage area. At this time, multiplying the superimposed imaging matrices can eliminate the phase artifacts, noise artifacts, and distortion caused by the change of the external environment and the dependence of wave velocity and wavelength on frequency. As shown in Figure 8, the imaging results were obtained by the combined addition and multiplication method of the correlation coefficient based on data fusion. The actual damage location coordinates were (50 mm, 70 mm), and the damage location coordinates by PRM and CAMM were (51 mm, 70 mm). Figure 6: Phase spectrum of the damage scattering signal on the \(x\)-axis. Figure 8: Damage-imaging result obtained by numerical analysis. Figure 7: (**a**) Imaging result on the \(x\)-axis. (**b**) Imaging result on the \(y\)-axis.
# Anomaly Detection of Remote Sensing Images Based on the Channel Attention Mechanism and LRX
## 3 Hyperspectral Anomaly Detection Based on the Channel Attention Mechanism and LRX
### Channel Attention Network  
The channel attention network is shown in the left part of Figure 1. The channel attention matrix, denoted as \(M_{c}\), can be obtained from the channel attention network. The process of the channel attention network is shown as follows.  
First, the input image with dimensions \((H,W,D)\) is fed into the channel attention network, where \(H\) and \(W\) denote the spatial dimensions, and \(D\) represents the number of channels. Second, the global average pooling (AvgPool) and global maximum pooling (MaxPool) operations are applied to the input image along the spatial dimensions with the size of \(H\times W\). These pooling operations aggregate information across the entire spatial extent, resulting in two matrices, both with a size of \(1\times 1\times D\), namely \(M_{a}\) and \(M_{m}\). AvgPool calculates the average value for each channel, providing a measure of the average activation within each channel, while MaxPool identifies the maximum value for each channel, indicating the most salient activation within each channel. Third, The matrices \(M_{a}\) and \(M_{m}\) obtained from global pooling operations are fed into a fully connected network to extract important features \(F_{a}\) and \(F_{m}\), respectively. Fourth, the extracted feature vectors, \(F_{a}\) and \(F_{m}\), are combined by element-wise summation, resulting in a single combined feature vector. Finally, the combined feature vector is then passed through a sigmoid activation function, which allowing the model to assign weights or importance coefficients to different channels. The output of the sigmoid activation function represents the weight coefficients associated with each channel. These coefficients are used to generate the channel attention matrix, denoted as \(M_{c}\), with dimensions \(1\times 1\times D\). Therefore, the channel attention matrix captures the relative importance of each channel in the input data. By incorporating the channel attention matrix into the proposed network, the model can effectively emphasize relevant channels and suppress irrelevant ones during the feature extraction process, which helps to enhance the discriminative power of the network and improve hyperspectral anomaly detection performance. The channel attention matrix \(M_{c}\) can be calculated by Equation (5).  
\[M_{c}=Sigmoid(Dense(AvgPool(F))+Dense(Maxpool(F))), \tag{5}\]  
Figure 1: Network structure of the proposed hyperspectral anomaly detection algorithm based on the channel attention mechanism and LRX.
# Biofilm Lifestyle in Recurrent Urinary Tract Infections
## 6 Strategies for Eradication of Biofilms
### Antimicrobial Peptides (AMPs) and Antimicrobial Lipids (AMLs)  
Antimicrobial peptides (AMPs) are small proteins that play a defensive role as a member of innate immune response in many organisms. AMPs were suggested as promising anti-biofilm agents because of their ability to disrupt cell membranes by inducing membrane depolarization and perforation, which increases membrane permeability, enabling better penetration of antimicrobials and biofilm inhibitory agents [204; 205; 206]. The structure and shape of AMPs are critical to assure electrostatic interactions to interrupt cell membrane and biofilm [207]. Antimicrobial Lipids (AMLs) are known as single-chain lipid amphiphiles, including fatty acids and monoglycerides [208]. The AMLs also manipulate membrane permeability via destruction of the electron transport chain and by targeting the bacterial signal transduction systems, leading to loss of membrane selectivity, increasedperforation and eventually, cell lysis [208; 209]. The antimicrobial applications of AMPs and AMLs have been repeatedly examined against several bacteria [210; 211; 212].  
An intracellular signal molecule \"alarmone\" is produced in stressed bacteria in response to drastic conditions. In harsh conditions, stringent factors convert uncharged tRNA to alarmones. The archetypical alarmone 5\({}^{\prime}\)-diphosphate 3\({}^{\prime}\)-diphosphate guanosine (ppGpp) which binds to RNA polymerase changes the preference of promoter, and hence changes the transcription rates [213; 214; 215]. It was documented that the stringent response could regulate the biofilm formation in _E. coli_ and _S. mutans_, suggesting that degrading alarmone signal could lead to inhibition of biofilm formation [215; 216; 217; 218]. Other peptides, like the synthetic cationic peptide LL-37, and D-enantiomeric peptides DJK-5 and DJK-6, were also reported for their anti-biofilm activities [169; 219].